each piece of candy in a store costs a whole number of cents. casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or n pieces of purple candy. a piece of purple candy costs 20 cents. what is the smallest possible value of n?(2019 amc 12b

Answers

Answer 1

To find the smallest possible value of n, we need to consider the cost of each candy option. We know that each piece of candy costs a whole number of cents,

which means that the cost of 12 pieces of red candy, 14 pieces of green candy, and 15 pieces of blue candy must be multiples of 12, 14, and 15 cents, respectively. Let's consider the cost of 12 pieces of red candy. Since the cost must be a multiple of 12 cents, the total cost of 12 pieces of red candy must be 12x cents, where x is some whole number.

Similarly, the total cost of 14 pieces of green candy must be 14y cents, and the total cost of 15 pieces of blue candy must be 15z cents, where y and z are whole numbers. Now let's consider the cost of n pieces of purple candy. We know that each piece costs 20 cents, so the total cost of n pieces of purple candy is 20n cents.



We also know that Casper has exactly enough money to buy any of these options. This means that the total cost of the candy he chooses must be less than or equal to the amount of money he has. Let M be the amount of money Casper has. Then we have: 12x + 14y + 15z ≤ M, 20n ≤ M.



We want to find the smallest possible value of n, so we should start by finding the largest possible value of x, y, and z that still satisfies the inequality above. To do this, we can use the fact that the greatest common divisor of 12, 14, and 15 is 1. This means that any number that is a multiple of 12, 14, and 15 must be a multiple of their least common multiple, which is 12 x 14 x 15 = 2520.


So we can write: 12x + 14y + 15z = k(2520), where k is some whole number. This equation tells us that the cost of any combination of red, green, and blue candy that Casper chooses must be a multiple of 2520 cents. Now we can substitute this equation into the first inequality above: k(2520) ≤ M.



Dividing both sides by 2520, we get: k ≤ M/2520
So the largest possible value of k that still satisfies the inequality is ⌊M/2520⌋, where ⌊⌋ denotes the floor function. Now we can use this to find the smallest possible value of n. We know that the total cost of n pieces of purple candy must be less than or equal to M,

so we can write: 20n ≤ M - k(2520), Substituting the largest possible value of k that we found above, we get: 20n ≤ M - ⌊M/2520⌋(2520), To find the smallest possible value of n, we want to maximize the right-hand side of this inequality. This happens when the floor function evaluates to its smallest possible value,

which is ⌊M/2520⌋ - 1. So we can write: 20n ≤ M - (⌊M/2520⌋ - 1)(2520), Simplifying, we get: 20n ≤ M - 2520⌊M/2520⌋ + 2520, 20n ≤ M - 2520(⌊M/2520⌋ - 1), Since n is a whole number, the smallest possible value of n that satisfies this inequality is: n = ⌊(M - 2520(⌊M/2520⌋ - 1))/20⌋ + 1.



This formula gives us the smallest possible value of n that allows Casper to buy a whole number of purple candies with the money he has.

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Related Questions

Find the area under the standard normal curve to the right of z=0. 69. Round your answer to four decimal places, if necessary. Answer1 Point- Tables- Keypad- Keyboard ShortcutsIf you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key.

Answer Normal Table −[infinity] to −z

Answers

The area under the standard normal curve to the right of z = 0.69 is approximately 0.2451.

How to calculate the value

Using a standard normal table:

Locate the row for 0.6 in the left-hand column of the table and the column for 0.09 along the top row of the table.

The intersection of the row and column gives the area to the left of z = 0.69, which is 0.7549.

Subtract this area from 1 to find the area to the right of z = 0.69:

area to the right of z = 0.69 = 1 - 0.7549 = 0.2451

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For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

f (x) = StartFraction 2 x Superscript m Baseline Over x + a EndFraction
a = –1, m = 0
a = 1, m = 0
a = –1, m = 1
a = 1, m = 1

Answers

For a = 1 and m = 1 does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1.

To find the values of a and m that give the function f(x) a horizontal asymptote at y = 2 and a vertical asymptote at x = 1, we need to analyze the behavior of the function as x approaches 1 and as x goes to infinity.

When x approaches 1 from the left and right sides, the denominator of f(x) approaches 0, so there is a vertical asymptote at x = 1. To have a vertical asymptote at x = 1, the numerator of f(x) cannot approach 0 as x approaches 1, so m must be greater than or equal to 1.

When x goes to infinity or negative infinity, the function f(x) approaches 2, which means there is a horizontal asymptote at y = 2. To have a horizontal asymptote at y = 2, the degree of the numerator must be equal to or less than the degree of the denominator. The degree of the numerator is m, and the degree of the denominator is 1.

So, the values of a and m that give f(x) a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 are:

a = 1, m = 1

Substituting a = 1 and m = 1 into f(x), we get:

f(x) = 2x/(x+1)

which has a vertical asymptote at x = 1 and a horizontal asymptote at y = 2.

Therefore, the answer is a = 1, m = 1. The other values of a and m do not give a vertical asymptote at x = 1 and/or a horizontal asymptote at y = 2.

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Answer:

CCCCCCCC

Step-by-step explanation:

Edg 2023

I have no idea what this is​

Answers

So, I haven’t done this type of thing in awhile, but it looks like reflection to me. Because it’s reflecting over the x axis. I’m sorry if this doesn’t help

In a small town, households recycle on average 30% of their waste. The new recycling committee wants to increase this proportion and study the relationship between recycling and income. They select 25 households from the two wealthier neighborhoods and estimate a 92% confidence interval for the true proportion of recycling. What is the error term of this interval?. 1605 2. 00 points out of 3. 00 P Flag question 2. The same recycling committee also focuses on poor neighborhoods. How many households do they need to sample to get a 95% confidence interval, with an error of +/-0. 09? 100 3. Finally, the same recycling committee wants to know the probability of 12 random households recycling more than 45% of their waste. This probability is: 1292

Answers

A) the error term is 0.16039
B) number of households required to get a 95% confidence interval, with an error of ± 0.09 is 21.
C) The probability of 12 random households recycling more than 45% of their waste is approximately 0.045 or 4.5%.

Here are the steps to arrive at the above

Error term = z√(p(1-p)/n)

Error term = 1.75 √(0.30(1-0.30)/25)
= 0.16039

Thus, the error term is 0.16039

2 ) to find the ample size required to estimate the proportion of recycling in poor neighborhoods with an error of +/-0.09 and a 95% confidence level,

n = (z² * p * (1-p)) / E²

n = (1.96² * 0.5 * (1-0.5)) / 0.09²

= 21


So the number of households required to get a 95% confidence interval, with an error of ± 0.09 is 21.

3)  To calculate the probability of 12 random households recycling more than 45% of their waste,

P(X > 12) = 1 - P(X <= 12)

P(X > 12) = 1 - P(X <= 12)

= 1 - 0.955

= 0.045


So the the probability of 12 random households recycling more than 45% of their waste is 0.045.

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Full Question:

In a small town, households recycle on average 30% of their waste. The new recycling committee wants to increase this proportion and study the relationship between recycling and income. They select 25 households from the two wealthier neighborhoods and estimate a 92% confidence interval for the true proportion of recycling. What is the error term of this interval?

The same recycling committee also focuses on poor neighborhoods. How many households do they need to sample to get a 95% confidence interval, with an error of +/-0. 09?

Finally, the same recycling committee wants to know the probability of 12 random households recycling more than 45% of their waste. This probability is: ?

A circle with center is shown in the figure below.
S
T
W
R
U
V
(a) Name a radius:

(b) Name a diameter:
(c) Name a chord:
(d) If the length of is units,
what is the length of ?

Answers

The names of the radius , chord and diameter of a circle are as follow,

Radius of the circle are PQ, PM , And PR.

Diameter of the circle is QM

Chord of the circle is ON.

Length of QM in the circle = 4units.

In the attached figure of the circle,

Center of the circle is P.

radius of the circle is a distance from the center of the circle to its circumference.

Radius = PQ, PM , And PR.

Diameter of the circle passing through center P is QM.

Chord of the circle representing a line segment having endpoints on the circumference of the circle.

Chords are ON and MQ.

Diameter is the longest chord.

length of PR is 2 units,

PR is radius

QM is diameter

QM = 2(PR)

length of QM = 2(2)

                      = 4 units.

Therefore, for the given circle we have,

Radius are PQ, PM , And PR.

Diameter is QM

Chord is ON.

Length of QM = 4units.

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The above question is incomplete, the complete question is:

A circle with center P is shown in the figure below.

(a) Name a diameter:

(b) Name a radius:

(c) Name a chord:

(d) If the length of PR is 2 units, what is the length of QM

Attached figure.

Please help me with this question!!!!!

Answers

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Suppose pigs (P) can be fed corn-based feed (C) or soybean-based feed (S) such that the production function is P = 2C + 5S. If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, what is expansion path?

a. C =5S/2

b. The horizontal axis

c. The vertical axis

d. S =2C/5

Answers

If the price of corn feed is $4 and corn feed is on the horizontal axis, and the price of soybean feed is $5 and soybean feed lies on the vertical axis, then the expansion path is C =5S/2 (option a).

To find the expansion path, we need to find the optimal combination of inputs that will maximize pig production while keeping the cost of production at a minimum. This can be achieved by calculating the ratio of the prices of the two inputs, which is given by:

Price ratio = Price of soybean-based feed/Price of corn-based feed

Price ratio = 5/2

Now, we can use this price ratio to find the optimal combination of inputs that will minimize the cost of production while maximizing pig production. This can be done by solving for the quantity of soybean-based feed used in terms of the quantity of corn-based feed used:

S = (5/2)C

This equation represents the expansion path, which shows the optimal combination of inputs that will minimize the cost of production while maximizing pig production. We can prove this by substituting the value of S into the production function:

P = 8C + 25((5/4)C)

P = 8C + 31.25C

P = 39.25C

Hence the correct option is (a)

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Molly placed $220.00 in a savings account. This savings account earns 4.2% interest per year. She did not add or take out any money from this account. How much money did she earn in interest at the end of six years? PLSSSSSSSSSSSS HURRY ASAP IN CLASS NOW

Answers

Answer:

Molly earned $55.44 in interest at the end of six years.

Step-by-step explanation:

To calculate the interest earned by Molly's savings account, we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the initial amount of money deposited ($220.00)

Rate is the annual interest rate (4.2% or 0.042 as a decimal)

Time is the number of years the money is invested (6 years)

Plugging in the values, we get:

Interest = $220.00 x 0.042 x 6

Interest = $55.44

Therefore, Molly earned $55.44 in interest at the end of six years.

A submarine is currently at -15 feet and then dives 32 more feet down , what is the submarine depth after the dive

Answers

The submarine depth after the dive is determined as 17 feet.

What is the current depth of the submarine?

The current depth of the submarine is calculated as follows;

If the submarine is currently at a depth of -15 feet and then dives an additional 32 feet down, the new depth can be calculated by adding the two depths.

-15 feet + 32 feet = 17 feet

Therefore, the submarine is at a depth of 17 feet after the dive.

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ow many incongruent primitive roots does 13 have? find a set of this many incongruent primitive roots modulo 13.

Answers

There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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Macy makes a fruit punch by mixing green apple juice and carrot juice.
For every 2
cups of carrot juice, she uses 4
cups of green apple juice.

Answers

The unit rate of the juice is 0.5 carrot juice per green apple juice

Calculating the unit rates of the juice

From the question, we have the following parameters that can be used in our computation:

For every 2 cups of carrot juice,She uses 4 cups of green apple juice.

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

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What is the domain and range of the following relation? Is it a function?{(1, -2), (-2. 0), (-1, 2), (1, 3)}

Answers

The given relation is a set of four ordered pairs {(1, -2), (-2, 0), (-1, 2), (1, 3)}. The first element of each pair represents the input or domain value, and the second element represents the output or range value.

The domain of the relation is the set of all first elements of the ordered pairs, which is {1, -2, -1}. Notice that there are two ordered pairs with input value 1 and one ordered pair with input value -2 and -1. Therefore, we can simplify the domain as {-2, -1, 1}.

The range of the relation is the set of all second elements of the ordered pairs, which is {-2, 0, 2, 3}.

To check whether the relation is a function or not, we need to ensure that each input value (i.e., element of the domain) is associated with a unique output value (i.e., element of the range). In other words, there should not be more than one ordered pair with the same first element.

In this case, the input value 1 is associated with two different output values (-2 and 3), which violates the definition of a function. Therefore, the relation is not a function.

To make it a function, we can either remove one of the ordered pairs with input value 1 or change one of the output values associated with input value 1.

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Is it true that If A is a 3×3 matrix, then det5A = 5detA.

Answers

Yes, it is true that if A is a 3×3 matrix and K is a scalar, then det(KA) = [tex]K^3[/tex] det(A).

To see why this is true, let's use the definition of the determinant of a matrix. For a 3×3 matrix A with entries[tex]ka_{11}, ka_{12}, ka_{13}, ka_{21}, ka_{22}, ka_{23}, ka_{31}, ka_{32}, ka_{33}[/tex], the determinant det(A) is given by:

[tex]det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)[/tex]

Now consider the matrix KA, where K is a scalar. The entries of KA are simply the entries of A multiplied by K. In other words, the entries of KA are:

[tex]ka_{11}, ka_{12}, ka_{13}, ka_{21}, ka_{22}, ka_{23}, ka_{31}, ka_{32}, ka_{33}[/tex]

Using the same formula as above, we can calculate the determinant of KA:

[tex]det(KA) = (K a_{11})(K a_{22})(K a_{33}) - (K a_{11})(K a_{23})(K a_{32}) - (K a_{12})(K a_{21})(K a_{33})+ (K a_{12})(K a_{23})(K a_{31}) + (K a_{13})(K a_{21})(K a_{32}) - (K a_{13})(K a_{22})(K a_{31)[/tex]

Substituting in the entries of KA, we get:

[tex]det(KA) = (K a_{11})(K a_{22})(K a_{33}) - (K a_{11})(K a_{23})(K a_{32}) - (K a_{12})(K a_{21})(K a_{33})+ (K a_{12})(K a_{23})(K a_{31}) + (K a_{13})(K a_{21})(K a_{32}) - (K a_{13})(K a_{22})(K a_{31)[/tex]

Simplifying this expression, we get:

[tex]det(KA) = K^3 (a_{11} a_{22}a_{33} - a_{11}a_{23}a_{32} - a_{12}a_{21}a_{33} + a_{12}a_{23}a_{31} + a_{13}a_{21}a_{32} - a_{13}a_{22}a_{31})[/tex]

But this is just the same as[tex]K^3[/tex] times the determinant of A! Therefore, we have shown that det(KA) =[tex]K^3[/tex]det(A) for any 3×3 matrix A and scalar K.

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Question

Is it true that If A is a 3×3 matrix, then det (KA) = K^3 * det(A)

Complete this questions with answers from parts A to C and I will give u brainlist.

Answers

The lowest angle of elevation at which the astronomer can observe the star is 20.8°

We know that the angle of elevation is nothing but the angle between the horizontal line of sight and the straight line to a given object.

In this scenario, let us ssume that θ be an angle of elevation.

Since an astronomer is in the middle of the field,the 100 value is split in half.

The field is surrounded by the trees 20 m tall and the tripod holding the telescpoe 1 m above the ground.

This means that the vertical distance is 19 m and the horizontal distance is 50 m.

Consider the tangent of angle θ

tan(θ) = opposite side of angle θ / adjacent side of angle θ

tan(θ) = 19/50

tan(θ) = 0.38

θ = arctan(0.38)

θ = 20.8°

This is the angle of elevation.

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IS ABC = DEF IF SO , NAME THE CONGRUENCE POSTULATE THAT APPLIES .

Answers

The congruence postulate that applies is C. Congruent - SSS

What are congruent triangles?

When the properties (i.e length of sides and/or internal angles) of two or more triangles are equal, then it can be said that they are congruent. This congruent relations can be expressed using either of the following postulates: Angle-Side-Side, Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Side-Side-Side (SSS) etc.

Considering the given triangles ABC and DEF, it is was given that:

AB ≅ DE

BC ≅ EF

CA ≅ FD

Therefore, it can be concluded that the two triangles are congruent by Side-Side-Side (SSS) relations. So that the required congruence postulate that applies is C. Congruent - SSS

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schools in a certain state receive funding based on the number of students who attend the school. to determine the number of students who attend a school, one school day is selected at random and the number of students in attendance that day is counted and used for funding purposes. the daily number of absences at high school a in the state is approximately normally distributed with mean of 120 students and standard deviation of 10.5 students. (a) if more than 140 students are absent on the day the attendance count is taken for funding purposes, the school will lose some of its state funding in the subsequent year. approximately what is the probability that high school a will lose some state funding?

Answers

The probability that high school A will lose some state funding is approximately 0.0287 or 2.87%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.

We can use the normal distribution to approximate the probability that high school A will lose some state funding. Let X be the number of absent students on the selected school day. We know that X follows a normal distribution with mean µ = 120 and standard deviation σ = 10.5.

We need to find the probability that X is greater than 140. To do this, we standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - µ) / σ = (140 - 120) / 10.5 = 1.90

We can now use a standard normal distribution table or calculator to find the probability that a standard normal variable is greater than 1.90. The result is approximately 0.0287.

Therefore, the probability that high school A will lose some state funding is approximately 0.0287 or 2.87%.

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A jar contains 5 red discs, 10 blue discs and m green discs. A disc is selected at random and replaced. This process is performed four times. a) Write down the probability that the first disc selected is red. b) Let X be the number of red discs selected. Find the smallest value of m for which Var(X)<0.6.

Answers

For a jar contains 5 red discs, 10 blue discs and m green discs,

a) The probability that the first disc selected is red is equals to

[tex]\frac{5}{15 + m}.[/tex]

b) The smallest value of m for which Var(X)< 0.6 is equals to 13.

We have a jar contains different colour discs. Number of red discs = 5

Number of green discs = m

Number of blue discs = 10

Total number of discs = 5 + 10 + m

= 15 + m

The process is performed four times, so, possible value n = 4. We have to determine the probability that the first disc selected is red.

a) Probability is defined as the ratio of favourable outcomes to the total possible outcomes. So, the probability that the first disc selected is red,[tex] P(red) = \frac{ 5}{(15 + m)}[/tex]

(b) The variance is calculated as

[tex]σ_{X²} = Var (X)[/tex]

[tex]= ∑_i (x_i − μ)² p(x_i) \\ [/tex]

= np(1 - p)

= [tex] 4(\frac{5}{15 + m})×(1- \frac{5}{15 + m}) < 0.6[/tex]

[tex] \frac{20( 10 - m)}{(15 + m)²} < 0.6[/tex]

=> 200 - 20m < 0.6( 15 + m)²

=> 200 - 20m < 9.0 + 0.6 m² + 18

=> 0.6m² + 20m - 200 + 27 > 0

=> 0.6m² + 20m - 173 > 0

=> m > 12.2075, so, m = 13

Hence, the smallest value of m for which Var(X)<0.6 is 13.

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Identify the segment bisector of QR. Then find QR. *

Answers

The segment bisector of QR is Ml.

The length of QR is equal to 32 units.

How to determine the midpoint of a line segment?

In Mathematics, the midpoint of a line segment with two end points can be determined or calculated by adding each end point on a line segment together and then divide by two (2).

Since Ml is the midpoint and segment bisector of line segment QR, we have the following:

Line segment QM = Line segment MR

2x + 6 = 5x - 9

5x - 2x = 9 + 6

3x = 15

x = 15/3

x = 5.

Now, we can determine line segment QR as follows:

QM = 2x + 6 = 2(5) + 6 = 16 units.

MR = 5x - 9 = 5(5) - 9 = 16 units.

QR = QM + MR

QR = 16 + 16

QR = 32 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

the length of a swimming pool is 7m longer than its width. the total area of the swimming pool is 120m^2. Find the length and width of the swimming pool

Answers

Answer:  Hence, the length of swimming pool is 52 m and its breadth if 25 m.  

Step-by-step explanation:

The perimeter of rectangular swimming pool is 154 m and its length is 2 meter more than twice its breadth.

how many respondents to a poll are needed, at a minimum, for its results to be accepted as adequately representative of a much larger population?

Answers

The number of respondents needed in a poll to adequately represent a larger population depends on several factors, such as the size of the population, the level of confidence desired, and the margin of error tolerated.

The general rule of thumb is that a sample size of at least 400 respondents is needed to provide a representative sample for a population of 100,000 or less. However, for larger populations, a sample size of at least 1,000 respondents may be required.

It is also important to note that a larger sample size does not always guarantee more accurate results. Other factors such as the sampling method, the wording of the questions, and the response rate can also impact the accuracy of poll results. Therefore, it is essential to carefully design and conduct polls to ensure their results are adequately representative of the larger population.

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This trapezoid represents the base of a right prism that has a surface area of 1280 square feet. The sum of the lengths of the legs of the trapezoid is 52 feet. What is the height of the prism?

Answers

Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

The mean weight of a breed of yearling cattle is 1150 pounds. Suppose that weights of all such animals can be described by a normal model with a standard deviation of 54 pounds

A) a steer weighing 1000 pounds is ___ standard deviations below the mean

B) which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?

Answers

A) A steer weighing 1000 pounds is 2.78 standard deviations below the mean.

B) A z-score of 1.85 is closer to the mean than a z-score of -2.78, we can conclude that a steer weighing 1000 pounds is more unusual than one weighing 1250 pounds.

A) To find how many standard deviations below the mean a steer weighing 1000 pounds is, we need to use the formula for standard score (or z-score):

z = (x - μ) / σ

where x is the weight of the steer, μ is the mean weight, and σ is the standard deviation. Substituting the values we have:

z = (1000 - 1150) / 54

z = -2.78

B) To determine which is more unusual, we need to compare the z-scores for a steer weighing 1000 pounds and one weighing 1250 pounds. Using the same formula as before:

For a steer weighing 1000 pounds:

z1 = (1000 - 1150) / 54

z1 = -2.78

For a steer weighing 1250 pounds:

z2 = (1250 - 1150) / 54

z2 = 1.85

A positive z-score means the weight is above the mean, while a negative z-score means the weight is below the mean. Therefore, a steer weighing 1250 pounds is 1.85 standard deviations above the mean, while a steer weighing 1000 pounds is 2.78 standard deviations below the mean.

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another chool is also cosidering changing thier pizza vendor. the school selects seperate random samples of 50 freshman, 50 sophiomres, 50 jjuniors, and 50 seniors. each student tries

Answers

If another school is considering changing their pizza vendor, they may also select separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors to gather feedback from the students. By doing so, they can obtain a representative sample of the entire student population and ensure that each grade level is equally represented.

This will provide valuable insight into the preferences and opinions of the students, allowing the school to make an informed decision on which pizza vendor to choose. It is important to consider the feedback of all students in the decision-making process to ensure that the majority of the student body is satisfied with the food options provided by the school.

Step 1: Select random samples of students from each grade level.
Step 2: Provide the new pizza to each student in the samples.
Step 3: Ask the students to evaluate the pizza based on taste and quality.
Step 4: Collect the feedback from all 200 students.
Step 5: Analyze the data to determine if the majority of students prefer the new pizza vendor.

Based on the analysis, the school can make an informed decision about whether to change their pizza vendor or not.

another school is also cosidering changing thier pizza vendor. the school selects seperate random samples of 50 freshman, 50 sophiomres, 50 jjuniors, and 50 seniors. each student tries

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the inevitable difference between the mean of a sample and the mean of a population based on chance alone is a) sampling error. b) confidence interval. c) random sample. d) probability.

Answers

The inevitable difference between the mean of a sample and the mean of a population based on chance alone is known as sampling error.

Sampling error is a result of the random nature of sampling from a population, meaning that any given sample is unlikely to perfectly represent the entire population. This is where probability comes into play, as the likelihood of obtaining a certain sample is dependent on the probability of each member of the population being selected.

Therefore, in order to minimize sampling error, researchers often use random sampling techniques to ensure that each member of the population has an equal probability of being selected for the sample.

The inevitable difference between the mean of a sample and the mean of a population based on chance alone is a) sampling error. This occurs because a random sample may not perfectly represent the entire population, leading to slight variations in the mean.

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7. I could sum help on this ASAP

Answers

The side lengths for this problem are given as follows:

[tex]d = 7\sqrt{3}[/tex][tex]b = \frac{5\sqrt{2}}{2}[/tex]

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.

For segment d, we have that it is opposite to the angle of 60º, while 7 is the adjacent segment, hence:

tan(60º) = d/7

[tex]\sqrt{3} = \frac{d}{7}[/tex]

[tex]d = 7\sqrt{3}[/tex]

For segment b, it is opposite/adjacent (does not matter as sin(45º) = cos(45º)) to an angle of 45º, while the hypotenuse is of 5 units, hence:

sin(45º) = b/5

[tex]b = 5 \times \frac{\sqrt{2}}{2}[/tex]

[tex]b = \frac{5\sqrt{2}}{2}[/tex]

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find the standard deviation. the top nine scores on the organic chemistry midterm are as follows. 80, 30, 34, 32, 55, 27, 38, 41, 84

Answers

Answer:

Approximately 20.33 (rounded to two decimal places)

Step-by-step explanation:

To find the standard deviation, we will first find the mean (average) of the scores, then find the variance, and finally take the square root of the variance to get the standard deviation.

Calculate the mean:

(80 + 30 + 34 + 32 + 55 + 27 + 38 + 41 + 84) / 9 = 421 / 9 = 46.78 (rounded to two decimal places)

Calculate the variance:

a. Find the difference between each score and the mean, and then square the differences (rounded to two decimal places).

(80 - 46.78)^2 = 1103.57

(30 - 46.78)^2 = 281.57

(34 - 46.78)^2 = 163.33

(32 - 46.78)^2 = 218.45

(55 - 46.78)^2 = 67.57

(27 - 46.78)^2 = 391.25

(38 - 46.78)^2 = 77.09

(41 - 46.78)^2 = 33.41

(84 - 46.78)^2 = 1385.33

b. Find the sum of the squared differences.

1103.57 + 281.57 + 163.33 + 218.45 + 67.57 + 391.25 + 77.09 + 33.41 + 1385.33 = 3721.57

c. Divide the sum of the squared differences by the number of scores (n = 9).

3721.57 / 9 = 413.51 (rounded to two decimal places)

Calculate the standard deviation:

Take the square root of the variance.

√413.51 = 20.33 (rounded to two decimal places)

The standard deviation of the scores is approximately 20.33 (rounded to two decimal places).

A survey question asked of unmarried men was, "What is the most important feature you consider when deciding to date somebody?". The results were found to depend on whether the interviewer was male or female. This is an example of

Answers

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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PLS HELP WUICKLY ILL GIVE BRAINLYIST!!!

Answers

The length from least to greatest is √3, √5, π, 2√3.

We have the lengths as π, √3, 2√3, √5.

Now, writing the decimals for each

π= 3.14

√3 = 1.732

2√3 = 3.464

√5= 2.23

So, arranging the length from least to greatest is √3, √5, π, 2√3.

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Barbara built a woodshed. She

made the base of the woodshed in

the shape of the drawing. What is

the area of the base of Barbara's

woodshed? Include the unit.


12 ft

6 ft

11 ft

7 ft

Answers

The area of the base of Barbara's woodshed is 72 square feet.

To find the area of the base of Barbara's woodshed, we need to know the shape of the base. In this case, the base is in the shape of a rectangle. A rectangle is a four-sided figure with opposite sides parallel and equal in length.

To calculate the area of a rectangle, we need to multiply its length by its width. In this case, the length of the rectangle is 12 feet, and its width is 6 feet. So, the area of the base of the woodshed is:

Area = Length x Width

Area = 12 ft x 6 ft

Area = 72 square feet

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Complete Question:

Barbara built a woodshed. She made the base of the woodshed in the shape of the drawing. What is the area of the base of Barbara's woodshed? Include the unit. When the dimensions are given as 12 ft,6 ft, 11 ft and 7 ft.

True or False?

When rainfall increases, the water level in the lake goes up. Rainfall is the independent variable in this situation. (4 points)

True
False
2.
(07.07)
Alexander can earn money for the cans he recycles. Which of the following statements describes the variables in this situation correctly? (4 points)

The number of cans recycled is the independent variable because it affects the amount of money earned.
The number of cans recycled is the dependent variable because it affects the amount of money earned.
The amount of money earned is the independent variable because it affects the number of cans recycled.
The amount of money earned is the dependent variable because it affects the number of cans recycled.
3.
(07.07)
Calvin's plane is flying at a speed of 600 miles per hour. If y represents the distance the plane has traveled and z represents the time it has spent traveling, which of the following equations shows the relationship between y and z? (4 points)

y = 600 + z
z = 600 + y
z = 600y
y = 600z
4.
(07.07)
It costs $1.58 to buy a bag of popcorn. Which of the following equations shows the amount of money needed, z, to buy n bags of popcorn? (4 points)

z = 1.58 + n
n = 1.58 + z
z = 1.58n
n = 1.58z
5.
(07.07)
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f).

Elapsed Time
(seconds) Distance Traveled
(feet)
1 6.2
2 12.4
3 18.6
4 24.8

Which of the following equations represents the relationship between the distance traveled and the elapsed time? (4 points)

f = 6.2 + n
n = 6.2 + f
f = 6.2n
n = 6.2f

Answers

It is a true statement that when rainfall increases, the water level in the lake goes up. The rainfall is the independent variable in the situation.

Is rainfall the independent variable?

The answer is yes because independent variable is the one that is manipulated or changed in an experiment. The dependent variable is the one that is observed or measured.

In this situation, rainfall is independent variable because it is what is being manipulated or changed. The water level in the lake is the dependent variable because it is what is being observed or measured.

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