Pythagorean Theorem: Sylvie is making book ends for her shelf. She needs to make 2 identical book ends and she wants to cover the edges in felt so they don’t scratch. Sylvie knows the vase will be 8 inches long and the height will be 12 inches. How much felt does she need to cover all 3 sides of both book ends?

Answer:

answer: D

Step-by-step explanation:

Three cylinders and one cone of the same height and diameter.

Here, the volume of a cylinder is [tex]\pi r^{2} h[/tex]

So, the same of 3 cylinders is [tex]3\pi r^{2} h[/tex]

The same as a cone is [tex]\frac{\pi r^{2}h}{3}[/tex]

here  [tex]3\pi r^{2} h[/tex] > [tex]\frac{\pi r^{2}h}{3}[/tex]

so D is not possible

The solution for "m" for the equation is 8.3.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression

5m + 2 - 3.9m = 2.1(m — 3)

5m + 2 -3.9m = 2.1m - 3(2.1)

1.1m + 2 = 2.1m - 6.3

compare variables on one side and constant other,

2  + 6.3 = 2.1m - 1.1m

8.3 = m

Hence the value of m is 8.3.

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The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.

What is margin of error?

The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.

Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.

Here,

Number of samples, N=2000

Probability of responding correctly,

=1092/2000

=0.546

Z-score at 90% confidence level,

=1.645

Margin of Error ME,

=z*√(p*(1-p)/N)

=1.645*√(0.546*(1-0.546)/2000)

=1.645*√(0.546*0.454)/2000

=1.645*√(0.248/2000)

=1.645*√0.000124

=1.645*0.011

=0.0180

With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.

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The square matrix can be formed using this system of equations option second is correct.

Matrix:

A matrix is ​​a rectangular array of numbers, variables, symbols, or expressions defined for operations such as subtraction, addition, and multiplication. The size of a matrix (called matrix order) is determined by the number of rows and columns in the matrix. The order of a matrix with 6 rows and 4 columns is expressed as 6×4 and read as 6×4.

We have three linear equations:

3x - 2y = -2

7x + 3y = 26

-x  -11y = 46

To solve the above equations we can use the matrix concept:

The matrix will be:

[tex]\left[\begin{array}{ccc}3&-2&-2\\7&3&26\\-1&-11&-46\end{array}\right][/tex]

The above matrix is a square matrix.

Square Matrix:

A square matrix is ​​a matrix that has the same number of rows and columns. Its order is of the form n x n. The product of these rows and columns also gives the number of elements in a square matrix, so the number of elements in it is always a perfect square.

Thus, the square matrix can be formed using this system of equations option second is correct.

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The values of variables in the kite is - x = 35°, y = 12.5°. The angles measures of the kite are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.

What is a kite?

A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry. Another name for kites is deltoids.

The given angles of the kite are -

∠a = (3x+5)°

∠b = y°

∠c = (2y-20)°

∠d = (4x-30)°

According to the properties of kite -

The two angles are equal where the unequal sides meet.

So, ∠a = ∠d

(3x+5)° = (4x-30)°

3x - 4x = -30 - 5

-x = -35

x = 35°

Substituting to find the value of ∠a -

∠a = (3x+5)°

∠a = [3(35)+5]°

∠a = (105+5)°

∠a = 110°

Substituting to find the value of ∠d -

∠d = (4x-30)°

∠d = [4(35)-30]°

∠d = (140-30)°

∠d = 110°

According to the properties of the kite ∠ADC = 90°.

So, ∠c = 90°/2 as line BD is a bisector.

(2y-20)° = 90°/2

2(2y-20)° = 90°

(4y - 40)° = 90°

4y = 90° - 40°

4y = 50°

y = 12.5°

Substituting to find the value of ∠b -

∠b = y°

∠b = 12.5°

Substituting to find the value of ∠c -

∠c = (2y-20)°

∠c = [2(12.5)-20]°

∠c = (25-20)°

∠c = 5°

Therefore, the value of angles are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.

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Answer:

▪ 20% of 15 ml

(20/100) × 15 ml = 3% pure milk fat

The probability that the first girl is the first to flip a head is; 1/2.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that if the number of toss required is odd as in one attempt represent odd number , we have following sequence of events

H, TTH, TTTTH.....

The required probability P will be as;

P = 1/2 + (1/2)³ + (1/2)⁵..........

As she flipped it in first go the probability is 1/2.

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a. The linear equation is -75x+700 which represents the situation.

b. The slope represents the rate of change in the amount owed.

c. The y-intercept represents the amount that Jeremy borrowed from his dad.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. The general form is y=ax+b, where a is the slope and b is the y-intercept.

a. We know that general form of an equation is y=ax+b.

So, after substituting (0,700) and (8, 100) into y=ax+b, we get,

700= 0+b

b=700

100=8a+700

a=-75

Hence, the linear equation is -75x+700 which represents the situation.

b. The slope represents the rate of change in the amount owed.

c. The y-intercept represents the amount that Jeremy borrowed from his dad.

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The limit of f(x) as x approaches 3 does not exist, as the lateral limits are different.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

On the graph of a function, the limit of f(x) as x approaches a value of a is defined considering it's lateral limits, that is:

If the lateral limits are different, then the limit does not exist.

To the left of x = 3, the line ends at point (3,1), hence the lateral limit to the left of x = 3 is given as follows:

1.

To the right of x = 3, the line begins at point (3,3), hence the lateral limit to the right of x = 3 is given as follows:

3.

As the lateral limits as x approaches 3 are different, the limit of f(x) as x approaches x does not exist.

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The percentage by mass of water contained in the original sample is 24.8%.

Percentage:

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",[1] although the abbreviations "pct.", "pct" and sometimes "pc" is also used.[2] A percentage is a dimensionless number (pure number); it has no unit of measurement.

To find the percent by mass of water in the original sample, we need to find the mass of the water that was lost upon heating. We can do this by subtracting the constant mass (6.20 g) from the initial mass (8.24 g).

mass of water = 8.24 g - 6.20 g = 2.04 g

To find the percentage, we divide the mass of water by the initial mass and multiply by 100:

percent by mass of water = (2.04 g / 8.24 g) x 100 = 24.8%

So the percentage by mass of water contained in the original sample is 24.8%.

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The length of one side of the frame is 5.7 inches.

A square is a quadrilateral with 4 sides equal to each other. Opposite sides of a square is parallel to each other.

The picture frame is a square. Therefore, all it's sides are equal to each other.

Hence, using Pythagoras's theorem, the side length of the square can be found as follows:

c² = a² + b²

where

Therefore,

x² + x² = 8²

2x² = 64

divide both sides by 2

x² = 64  /2

x = √32

x = 5.65685424949

x = 5.7 inches

Therefore,

length of side frame = 5.7 inches

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The cost of 250 kg of coal is 500 dollars.

One tonne of coal cost $2000. The cost of 250kg of the same coal can be found as follows:

Let's convert the mass of the coal in kilograms to tonnes.

Hence,

1 kilogram = 0.001 tonnes

250 kilogram = ?

cross multiply

mass of the coal in tonnes = 0.001 × 250

mass of the coal in tonnes = 0.25 tonnes

Hence,

1 tonne = 2000 dollars

0.25 tones = ?

cross multiply

mass of 250 kg of coal = 0.25 × 2000

Therefore,

mass of 250 kg of coal = 500 dollars

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There are a few ways to tell if a dataset contains outliers, one of which is by using summary statistics.

Outliers are data points that fall far outside of the main body of a dataset. They can have a significant impact on the overall summary statistics of a dataset, such as the mean and standard deviation.

Given the summary statistics below for the size of a sample of automobile engines:

Mean: 2.5

Median: 2.5

Mode: 2.5

Standard deviation: 0.5

We can tell that there are no outliers in the data set because the mean, median, and mode are all equal. This indicates that the values in the dataset are tightly clustered around a central value, which is a good indication that there are no outliers. Additionally, the standard deviation is relatively small, which also suggests that the values in the dataset are not spread out very much, again indicating that there are no outliers.

Another approach is using the interquartile range (IQR). This can be calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3) of a dataset. Values that fall outside of the range of 1.5*IQR below the first quartile (Q1) or above the 3rd quartile (Q3) are considered outliers.

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Answer:

1 penguin = $26.97

Step-by-step explanation:

188.88/7=

26.971429 which approximately equals 26.97

Answer:

the value of f(8) is 31

Step-by-step explanation:

To find the value of f(x) = 3x + 7 for x = 8, we need to substitute 8 in for x in the equation and perform the arithmetic.

f(x) = 3x + 7

f(8) = 3(8) + 7

f(8) = 24 + 7

f(8) = 31

[tex]f(x)=3x+7[/tex] x = 8

Substitute 8 with x:

[tex]f(8)=3(8)+7[/tex]

[tex]f(8)=24+7[/tex]

[tex]\fbox{f(8) = 31}[/tex]

The solution for the system of equations:

2x + 3y = 0

-4x - y = 30

is y = 7 and x = -10.5

Here we want to solve the following system of equations:

2x + 3y = 0

-4x - y = 30

By combining the equations.

If we add two times the first equation and the second equation, we will get:

2*(2x + 3y) + (-4x - y) = 0 + 30

We can simplify that to get:

4x + 6y - 4x - y =  30

5y = 30

Now we can solve that for y.

y = 30/5

y = 7

Now to find the value of x, we can replace y by 7 in one of the equations of the system.

2x + 3*7 = 0

2x = -21

x = -21/2

x = -10.5

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The expression that is equivalent to -4x³ -12x³ + 9x² will be -16x³ + 9x²

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to -4x³ -12x³ + 9x² will be:

= -4x³ -12x³ + 9x²

= -16x³ + 9x²

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Answer:

D. 88.47 in3

Step-by-step explanation:

The volume of a single coin would be the volume of a cylinder with a radius of 1.4 inches and a height of 0.0625 inches. The formula for the volume of a cylinder is V = πr^2h. So, V = 3.14 * (1.4^2) * 0.0625 = 0.38 in^3

Since there are 230 coins, the total volume of the coins would be 230* 0.38 = 87.40 in^3

So, the answer would be 87.40, which is closest to D. 88.47 in3

Answer: D: 88.47 in³​

Step-by-step explanation:

So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h

Take 1.4 and times it by itself

1.4 x 1.4 = 1.96

Now multiply 1.96 by 0.0625

1.96 x 0.0625 = 0.1225

And times 0.1225 by pi, or in this case, 3.14

0.1225 x 3.14 = 0.38465

Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.

0.38465 x 230 = 88.4695 in³

Now round it to the nearest hundredth: 88.47 in³

That is your answer.

Also I took the same test and I picked 88.47 inches cubed and got it right.

Proof:

Have a good day :)))

The probability distribution of X is given as follows:

A probability is defined as the division of the number of desired outcomes by the number of total outcomes.

A probability distribution gives the probability of all the possible outcomes in the context of a problem.

There are two outcomes for this problem, listed as follows:

Only one of the 1000 combinations are a winning combination, hence the probability distribution of X is given as follows:

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Answer:

1st number = 5.5

2nd number = -1.25

Step-by-step explanation:

1)  7x + 6y = 31     (multiply entire equation by 3) → 21x + 18y = 93

2)  3x - 10y + 29  (multiply entire equation by 7) →  21x - 70y = 203

3)    21x + 18y = 93

4)  -(21x - 70y = 203)    now subtract equation (4) from equation (3) to make the x terms drop out

0 + 88y = -110

y = -110/88 = -1.25   now plug this into equation (1) and solve for x

7x + 6(-1.25) = 31

7x = 38.5

x = 38.5/7 = 5.5

The Standard form of polynomial [tex]8x^2y^-\frac{3x^2y}{2} +4x^4-7xy^3[/tex] will be.[tex]-7xy^3+8x^2y^2-\frac{3x^2y}{2}+4x^3[/tex], Option D is right choice.

We have the polynomial.  [tex]8x^2y^-\frac{3x^2y}{2} +4x^4-7xy^3[/tex]

then change it to standard form,

We are aware that in standard form the power of variables should be listed in decreasing order, in this example we have two variables first is x and second is y.

First write, highest degree term of y which has degree 3, next write second term of y which has degree 2 and write third term of y which has degree 1 and last one writes the term which is independent of y.

thus, we write in standard form with respect to y.

hence our required polynomial is. [tex]-7xy^3+8x^2y^2-\frac{3x^2y}{2}+4x^3[/tex].

option D is right choice.

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Answer: 99.6 min

Step-by-step explanation:

(a) Mean of given sample = 75

(b) Mean (60, 80) = 70

(c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

The given sample is (60, 70, 80, 90)

(a) Mean of sample = (60+70+80+90)/4 = 300/4 = 75

(b) Mean of any 2 of scores

let's take (60,80)

mean(60,80) = (60+80)/2 = 70

(c) All possible samples of size 2 are

(60,70), mean(60,70) = 65

(60,80), mean(60,80) = 70

(60,90), mean(60,90) = 75

(70,80), mean(70,80) = 75

(70,90), mean(70,90) = 80

(80,90), mean(80,90) = 85

Therefore, for the given sample (a) Mean of the sample = 75, (b) Mean (60, 80) = 70, (c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.

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The complete question is:

How did the Chapter 6 test go? Today, we will be taking a sample from a population. We will use the average from the sample to estimate the average for the population. Let's start with a very simple example. My 5th period is very small. There were only 4 students who took the chapter 6 test. Their scores were: 60, 70, 80, and 90. Answer the following questions:

(a) Find the mean of the sample

(b) Take a sample of any 2 of the scores. Find the mean of your sample.

(c) Figure out all of the possible samples of size two. Calculate a sample mean for each sample of 2.

Answer:

Step-by-step explanation:

Yes, there is an end behavior for a square root function. The end behavior of a square root function is determined by the sign of the leading coefficient of the equation. For example, if the leading coefficient is positive, then the end behavior will be asymptotic to the positive x-axis as x increases, and asymptotic to the negative x-axis as x decreases. Conversely, if the leading coefficient is negative, then the end behavior will be asymptotic to the negative x-axis as x increases, and asymptotic to the positive x-axis as x decreases.

Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.

If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.

So finally 1000 mg = 1 g

Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

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Answer:

(x – 3)2 = 49 can be written as (x – 3) = ± √49.

To solve for x, we can square root both sides:

x -3 = ±7

Now we can add 3 to both sides:

x = 3 ±7

So the values of x are:

x = 3 + 7 = 10

x = 3 - 7 = -4

Hence the values of x are -4 and 10.

Step-by-step explanation:

Answer: Did you mean (x - 3)² = 49? If so, the answers are -4 and 10

Step-by-step explanation: This equation is a simple quadratic. We can square root both sides to get:

x - 3 = -7

OR

x - 3 = 7

(Remember 49 has a positive square root and a negative square root)

Now simple rearranging will yield our two answers: 10 and -4.

Answer:

To find out how many minutes Susanna paid for, we need to convert the fraction of an hour to minutes.

There are 60 minutes in an hour. So, to find out how many minutes 3/5 of an hour is, we can multiply 3/5 by 60:

3/5 * 60 = 36

Therefore, Susanna paid for 36 minutes of parking.

Answer:

36 minutes

Step-by-step explanation:

We need to convert hours to minutes and then multiply by a fraction.

1 hour = 60 minutes

3/5 of 60 minutes

3/5 * 60

180/5

36 minutes