1. Yes, this is a binomial distribution.
2. n = 200, p = 0.25.
3. The mean of X is 50. This means that we can expect to get 50 cherry flavored Starburst candies on average.
4. The standard deviation of X is 7.07. This means that the number of cherry flavored candies is likely to be close to the mean of 50, but it could vary by up to 7.07 in either direction.
5. The probability of getting exactly 60 cherry flavored Starburst is 0.108.
6. The probability of getting at most 60 cherry flavored Starburst is 0.619.
A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies since there are 4 flavors. The probability that each Starburst is cherry flavor is 0.25. Since we are buying one bag of Starburst, the number of cherry flavored candies in the bag can be represented by a binomial distribution with n = 200 and p = 0.25. This means that the mean of X (the number of cherry flavored candies) is 50. The standard deviation of X is 7.07, which means that the number of cherry flavored candies is likely to be close to the mean of 50, but could vary by up to 7.07 in either direction. The probability of getting exactly 60 cherry flavored Starburst is 0.108, and the probability of getting at most 60 cherry flavored Starburst is 0.619.
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On a given day, the price of a gallon of milk had a mean price of $2.03 with a standard deviation of $0.07. A particular food store sold milk for $1.96/gallon. Interpret the Z-score for this gas station. A) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores. B) The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores. C) The milk price of this food store falls 7 standard deviations above the mean milk price of all food stores. D) The milk price of this food store falls 7 standard deviations below the mean milk price of all food stores.
Three standard deviations contain a portion of the data equal to 88.9%.
That is 3 times $0.11 = $0.33Range is $3.95 ± $.33.What is Chebyshev's theorem?The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality. The likelihood of an occurrence deviating significantly from its predicted value is calculated using Chebyshev's theorem. Contents table: Formula of the Chebyshev theorem. Only data sets with a bell-shaped relative frequency histogram can use the approximate Empirical Rule. It calculates the percentage of measurements that are one, two, or three standard deviations off the mean. All potential data sets can be used to prove Chebyshev's Theorem.According to Chebyshev's theorem, you can use the equation to roughly estimate the fraction of the data that lies within k standard deviations of the mean given a normal distribution.
Portion of data[tex]$=\left(1-1 / k^2\right)$[/tex]
The answer is, per Chebyshev's theorem, the range of of prices in which [tex]$88.9 \%$[/tex] of data lies is [tex]$[\$ 3.62, \$ 4.28]$[/tex].
The equation for Chebyshev's theorem is:
Portion of data [tex]$=\left(1-1 / k^2\right)$[/tex]
Where:
- k is the number of standard deviations a value is from the mean.
In this case the portion of data interest is [tex]$88.9 \%$[/tex]
Solve the equation for k
[tex]& 0.889=\left(1-1 / k^2\right. \\[/tex]
[tex]& -0.111=-1 / k^2 \\[/tex]
[tex]& k^2=1 / 0.111 \\[/tex]
[tex]& k^2=9.0 \\[/tex]
[tex]& k=3.0[/tex]
Three standard deviations contain a portion of the data equal to[tex]$88.9 \%$[/tex].
That is 3 times [tex]$\$ 0.11=\$ 0.33$[/tex]
Range is [tex]$\$ 3.95 \pm \$ .33$[/tex].
The complete question is,
Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.95 with a standard deviation of $0.11. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside.
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Among all positive numbers a, b whose sum is 8 , find those for which the product of the two numbers and their difference is largest.
The value of 1st number is 4 + 4/√3 and value of 2nd number is 4 - 4/√3
let the 2 number be a,b
given a+b=8 -- (i)
let the difference of the number is x
so let a-b =x
a-b = x ---(ii)
adding equation (i) and equation (ii) we get
2a = 8 +x
=> a = (8+x)/2
so a = 4+x/2
subtract (ii) from (i) we get:
2b = 8-x
=> b = (8-x)/2
so b = 4-x/2
now the product of both number and their difference is given as a*b*x
=> (4+x/2)*(4-x/2) *x
=> (16 - x²/4)*x
=> 16x - x³/4
let the above value be A
so A = 16x - x³/4
in order to find maximum value of A we have to made dA/dx = 0
=> d(16x - x³/4)dx
=> 16 - 3x²/4
so 16 - 3x²/4 =0
=> 3x²/4 = 16
=> 3x² = 64
=> x² = 64/3
so x = 8/√3
now we got value of x
so a = 4+ x/2
=> 4 + 8/2√3
=> 4 + 4/√3
so value of a = 4 + 4/√3
value of b = 4 - 4/√3
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List the sample space for rolling a fair eight-sided die.
A. S = {1}
B. S = {8}
C. S = {1, 2, 3, 4, 5, 6}
D. S = {1, 2, 3, 4, 5, 6, 7, 8}
The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.
Given an eight-sided die,
to find the sample space,
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.
when eight sides die is tossed there will be 8 sample spaces that are,
1, 2, 3, 4, 5, 6, 7, 8,
so S = {1, 2, 3, 4, 5, 6, 7, 8}
Hence option D is correct.
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A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upwards to form an open box. If the volume of the box is 1716in ^3, what were the original dimensions of the piece of metal
The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.
Let us suppose the width of the rectangular metal = w.
Then the length of the rectangular metal is = 20 + w
Given that squares of 4in are cut from the four corners, then the new width and length will be:
width = w - 8
length = 20 + w - 8
The height of the rectangular metal when the flaps are folded are 4 in.
The volume of the rectangular prism is:
V = (l)(w)(h)
Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:
1716 = (w - 8)(20 + w - 8)(4)
1716 = 80w + 4w^2 - 32w - 640 - 32w + 256
1716 = 4w^2 + 16 w - 384
4w^2 + 16w -384 - 1716 = 0
4w^2 + 16w - 2100 = 0
w^2 + 4w - 525 = 0
w^2 + 25w - 21w - 525 = 0
w(w + 25) - 21 (w + 25) = 0
(w - 21) (w + 25) = 0
w = 21
w = -25
The dimensions of the box cannot be negative hence, the width is 21.
length = 20 + 21
length = 41
The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.
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18[1/2log(x+y)-1/9log(x-y)]
Write the expression as a single logarithm
In order to get another number, a number must be raised to a certain power, which is known as a logarithm.
What is a logarithm in simple terms?Binary logarithms, which have a base of 2, natural logarithms, which have a base of e 2.71828, and common logarithms with a base of 10 are the four most popular varieties of logarithms.Exponent or power, known as a logarithm, to which a base must be raised in order to produce a certain number.If bx = n, then the expression for x is written as x = logb n, where x is the logarithm of n to the base b.For instance, since 23 = 8 and 8 has a base of 2, the logarithm of 8 in base 3 is 3, or 3 = log2.In order to get another number, a number must be raised to a certain power, which is known as a logarithm (see Section 3 of this Math Review for more about exponents).calculation is attached below :
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review the following credit terms and identify the one that states that the buyer will receive a 3% discount if the payment is made within 15 days. otherwise, full payment is expected within 45 days of the invoice date. multiple choice question. 3/10, n/45 3/15,45 3/15, n/45 3/45, n/15
The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.
This term can be expressed as a formula and calculation as follows:
Discount = 3% of Invoice Total
Payment due within 15 days = Invoice Total - Discount
Payment due within 45 days = Invoice Total
For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).
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What is the domain ?
The domain of the given set of functions is (Alex, Alesia, Bob, Yolanda, Maria , Elvis)
What is Domain ?The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A-> B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.
The domain of the given set of functions is (Alex, Alesia, Bob, Yolanda, Maria , Elvis)
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what is the slope through the line of (2, 6) and (8, 4)
Answer:
-1/2
Step-by-step explanation:
first u would label ur x and ys 2,6 would be x1, y1 then u would put 8,4 would be x2 and y2 . You would put 4-6 as y2 - y1 and 8-2 as x2 - x1 to get -2 divided by 4 to get your -1/2
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 250 minutes was $70 while in February, the total cost for 275 minutes was $72. The constant charge for each minute used is: 00.1 0.09 0.08
$50 is the constant charge used for each minute.
We must put up two variables in order to fix this issue. In this instance
F = constant Fee
R = rate used per minute.
So the cost for the month of January is calculated like this:
F+250R= 70
And the cost for February is calculated like this:
F+275R= 72
So no we have a system of equations we can solve simultaneously. This can be solved using different methods, elimination, substitution, graphically, or by using matrices. I will solve this by substitution.
So let's solve the first equation for R:
[tex]R = \frac{70-F}{250}[/tex]
And let's substitute this first equation into the second equation:
[tex]F+275(\frac{70-F}{250})= 72[/tex]
And now we can solve this for F:
[tex]F+275(\frac{70-F}{250})= 72\\F+11(\frac{70-F}{10})= 72\\F+(\frac{770-11F}{10})= 72.....eq(1)\\[/tex]
We can multiply both sides by 10 so we get:
[tex]10*F+10(\frac{770-11F}{10})= 10*72\\\\10F+770-11F= 720\\\\770-720 = 11F - 10F\\50 = F[/tex]
Therefore, $50 is the constant charge used for each minute.
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3x^2+6x=-3
what is this
Answer:
x=-1
Step-by-step explanation:
3x^2+6x=-3
factor:
3x(x+2)=-3
Here, its obvious what x has to be: -1, just solve to confirm:
(3*-1)(-1+2)=-3
(-3)(1)=-3
-3=-3
Hope this helps.
A shoe store recorded the number of customers who made a purchase out of a sample of 100 customers who entered the store each day. The boxplot shown summarizes the recorded data for one year. Based on the boxplot, which of the following statements is true?
A. The range of the number of customers making a purchase is greater than 32.
B. The interquartile range of the number of customers making a purchase is 25.
C. The number of days that had at least 26 customers making a purchase is greater than the number of days that had at most 11 customers making a purchase
D. The number of days that had from 11 to 26 customers making a purchase is equal to the number of days that had at most 14 customers making a purchase.
E.The difference between the median and the lower quartile for the customers making a purchase is less than 2.
Less than 2 units separate the median from the lower quartile for customers making purchases. The correct option is E.
Quartile deviation: The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q-1. The median or second quartile is also referred to as Q-2. Third quartile: Also referred to as the higher quartile or Q-3.
Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q-3) and lower quartile (Q-1) can be used to depict quartile deviation as the letters Q-D. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.
The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.
Therefore, the correct answer is option E.
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Someone is having a wedding, and they need champagne bottles. The bottles are 25.4 oz, the glasses are 6 oz a person, and there are going to be 80 guests. How many champagne bottles are going to be needed to serve all the guests?
Find the values of x and the measure of each angle labeled in the figure.
(2x) degrees
(3x + 5) degrees
The angles for the triangle are 42°, 68° and 70° and x=21.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
As sum of all angles of a triangle is 180°
2x+3x+5+4x-14=180
x=21
hence,
The angles for the triangle are 42°, 68° and 70° and x=21.
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Right question:-
Angles in the question are 2x°,(3x+5)° and (4x-14)° of a triangle.
song of myself is written by?
Answer:
“Song of myself ” is written by Walt Whitman in 1855
hope it helps<3Answer:
The Song of Myself is written by Walt Whitman in 1855
Step-by-step explanation:
Brick San Antonio playing a game of counters Rick has some counters Selma has twice as many counters as Rick Tony has six counters Leston Selma in total they have 54 counters the number of count as Rick has: the number of count as Tony has = 1: P work out the value of paid
If Brick San Antonio playing a game of counters Rick has some counters Selma. the number of count as Tony has = 1: P work out the value of paid is 1.5.
How to find the number of count?Let x represent the number of counter brick
Let 2x counter represent Selma
Let 2x -6 counter represent Tony
Hence,
x+2x+2x -6 =54
5x -6 =54
5x =60
x =60/5
x =12
So Brick has 12
Tony has 2×12 -6
= 24 -6
=18
Thus
12:18 = 1: 18/12
=1:1.5
Hence,
P =1.5
Therefore the number of count as Tony has = 1: P work out the value of paid is 1.5.
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here is the score data for the ultra-marathon race. assume distribution to be normal. women: 1674, 1622, 1637, 1838, 1964, 1836, 1728, 1913, 1885, 1932; men: 1852, 2403, 2383, 2336, 2597, 2581, 2169, 2120. calculate a 95% two-sided confidence interval on the mean for women and men separately. assume distribution to be normal.
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.
What is mean?In mathematics, particularly in statistics, there are various types of means. Each mean serves to summarise a certain set of data, frequently in order to better comprehend the overall significance of a specific data set.A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe this central tendency statistic.It is calculated by merely dividing the total number of values in a data collection by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.Given data :
calculate a 95% two-sided confidence interval on the mean for women and men separately :
A) The confidence interval for women: [1711.70] <u< [1894.10]
Women = [tex]\frac{1674+ 1622 + 1637 + 1838 + 1964 + 1836 + 1728 +1913 + 1885 + 1932}{10}[/tex] = 1802.9
B) B) The confidence interval for men: [2096.50] <u< [2513.80]
Men = [tex]\frac{1852 + 2403 + 2383 + 2336 + 2597 + 2581 + 2169 + 2120}{8}[/tex] = 2305.125
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allie is completing a long division problem that may or may not have a remainder. In each box drag the apropreite digit to show the correct way to divide
The required correct way of division has been shown, as per the long division.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The questions seem to be incomplete, so we assume the number 729 that Allie divides it by the number 9.
According to the question,
Long division,
9 ] 729 [8 1
- 72
---------------
0 9
- 9
---------------
0
Thus, the required correct way of division has been shown, as per the long division.
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I need help with this. Please take your time and don't give wrong answers.
Answer:
transformed function, g (x) =1/7x+5
Step-by-step explanation:
Is |x|=-6 equivalent to x=6 or x=-6
Answer: x=6
Step-by-step explanation: The absolute value | x | of a real number is a positive value of x even if the value of x had a sign(negative sign, etc.).
Which students ran faster than Amy?
Students that ran faster than Amy are Chris and Ethan.
Speed is the ratio between distance and time. The formula for speed
v = d ÷ t
d = distances (miles)t = time (hours)v = velocity (mph)Amy's speed
d = 2 milest = 36 minutes = 36/60 hours = 0.6 hoursv = d ÷ tBrian's speed
From the time versus distance graph from 0 miles to 2 miles it can be seen that the time required is 40 minutes.d = 2 milest = 40 min = 40/60 h = 2/3 hv = d ÷ tChris's speed
The equation y = 3/42 xEthan's speed
From the table, we can use any data.Pick data #2d = 3 milest = 33 min = 33/60 h = 11/20 hv = d ÷ tLearn more about speed here: https://brainly.com/question/24872445
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Write the equation as a single logarithm and show your steps 3log4x-2log4y
The equation as a single logarithm is log(4x)^3)/(4y)^2
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]
Log with base e = 2.71828... is written as
[tex]\ln(x)[/tex]
Log with base 10 is written as
[tex]\log(x)[/tex]
Given;
Equation=3log4x-2log4y
=log(4x)^3-log(4y)^2
=log(4x)^3)/(4y)^2
Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2
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The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom. Here are the results:
A Venn Diagram has 2 overlapping groups: Bride, 17 and Groom, 20. The overlapping area shared by both Bride and Groom is 42. The area not included by any group is identified as 1. In this sample, are the events "bride" and "groom" mutually exclusive?
In this sample, the events "bride" and "groom" are not mutually exclusive.
In logic and probability theory, mutually exclusive events are events that do not take place at the same time. This means that any such two or more events are not going to happen together but will take place at different times. For example - when a die is rolled, we might get any of the six numbers but they don't appear at the same time together.
In the given problem we see that the randomly selected person can either be the groom's friend or the bride's friend or they can be a friend of both of them. This means that both events can take place together at the same time. And, hence, these are not mutually exclusive events.
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In a right triangle, the lengths of the legs are a and b. find the hypothenus if
B) a=1, b=1
C) a=5, b=6
B) In a right triangle where a=1 and b=1, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 1^2 + 1^2 = 1+1 =2, so c = √2
C) In a right triangle where a=5 and b=6, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 5^2 + 6^2 = 25+36 =61, so c = √61
assume a multiple-choice question on an online quiz has 6 answer choices in it, which are shown in random order to each student. in how many ways can this question be displayed? enter the answer as an integer.
6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.
6! = 720
6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
So the answer is 720 ways.
There are 720 ways in which a multiple-choice question on an online quiz with six answer choices can be displayed. This is calculated by multiplying all the integers from 1 to 6, which is referred to as 6 factorial, or 6!. 6! is calculated by multiplying 6 x 5 x 4 x 3 x 2 x 1, which equals 720. This means that there are 720 possible combinations of answer order that can be shown to each student when they take the quiz. With such a wide variety of possible answers, students can focus on the content of the question rather than on the order of the answers, which can help to reduce bias and ensure the validity of the quiz.
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Here is a sketch of y=x²+bx+c
The curve intersects
the x-axis at (2, 0) and point P
Work out the x-coordinate of the turning point
the y-axis at (0, -14)
of the graph.
You must show your working.
The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14) of the graph x is 9/2.
What is the x-coordinate?The turning point's x-coordinate will be "9/2."
The answer to the query is
y = [tex]x^{2}[/tex] + bx + c
curving goes by.
(2 , 0)
and,
(0 , 14)
Putting (0, 14) results in
→ 14 = 0 + 0 + c
c = 14
then,
→ y = [tex]x^{2}[/tex] + bx + 14.
Putting in (2, 0) gives us
→0 = 4 + 2b + 14
-2b = 18
b = - 18 /2
= -9
then,
→ y = [tex]x^{2}[/tex] - 9x + 14.
the discovery of
→ dy / dx = 0
dy/dx = 2x - 9
turning point
→ dy / dx = 0
2x - 9 = 0
x = 9/2.
The curve intersects
The x-axis at (2, 0) and point P work out the x-coordinate of the turning point the y-axis at (0, -14) of the graph x is 9/2.
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In parallelogram ABCD, AC = 14 and BD = 2x+4. What value of x makes this parallelogram a rectangle?
4
10
2
5
The value of x makes that makes the parallelogram a rectangle is D. 5
How to calculate the parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. The interior opposite angles of it are equal. Additionally, the angles on the same side of the transversal are complementary to one another or add up to 180 degrees.
This will be:
2x + 4 = 14
Collect the like terms
2x = 14 - 4.
2x = 10
Divide
x = 10 / 2
x = 5
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convert the line integral to an ordinary respect to the parameter and evalluate it c isthehelix (7cost, 7sint, t) 0
The Ordinary integral of the Line integral [tex]\int _c {(y-z)} \, ds[/tex] where C is the helix ⟨7cos t, 7sin t, t⟩ is [tex]\int\limits^0 _{-2\pi} \sqrt{50}{(7sin\ t -t)} \, dt[/tex] and its value in the range -2π ≤ t ≤ 0 is 10√2 π²
We have x = 7cos t, y = sin t and z = t.
We also need ds =[tex]\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2} +(\frac{dy}{dt})^{2} }dt[/tex]
ds = [tex]\sqrt{(-7sin\ t)^{2} +(7cost\ t)^{2} +(1)^{2} }dt[/tex]
= [tex]\sqrt{49sin^{2}t +49cos^{2}t+1 }dt[/tex]
= [tex]\sqrt{49(sin^{2}t +cos^{2}t)+1 }dt[/tex]
ds = [tex]\sqrt{50}dt[/tex]
Now, [tex]\int _c {(y-z)} \, ds[/tex] = [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]
Evaluating the integral [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]
[tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex] = [tex]\sqrt{50}\ {[-7cos\ t -\frac{t^{2} }{2} ]}\limits^0 _{-2\pi}[/tex]
= [tex]\sqrt{50}\ {[-7+7+2\pi ^{2}]}[/tex]
= [tex]10\sqrt{2}\pi ^{2}}[/tex]
The question is incomplete, the complete question is
" Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.[tex]\int _c {(y-z)} \, ds[/tex] ; C is the helix ⟨7cos t, 7sin t, t⟩, for -2π ≤ t ≤ 0 "
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. a) In ∆PQR, perimeter=24cm, p+q=18 cm and q+r=14 cm, find the area of ∆PQR.
The area of ∆PQR is 42 [tex]cm^{2}[/tex]
We can use Heron's Formula to find the area of a triangle when we have the length of its three sides. Heron's Formula states that the area of a triangle with sides p, q, and r is:
Heron's Formula :
Area =[tex]\sqrt(s(s-p)(s-q)(s-r))[/tex]
where s is the semi-perimeter of the triangle (half of the perimeter).
In this case, we know that the perimeter of the triangle is 24 cm and p+q = 18 cm, and q+r = 14 cm. We can use these equations to find the length of the third side, r.
p+q+r = 24 cm
r = 24 - (p+q) = 24 - 18 = 6 cm
Now we can use this information to find the semi-perimeter of the triangle:
s = (24 cm) / 2 = 12 cm
Now we can substitute the values of p, q, r, and s into Heron's formula to find the area of the triangle:
Area = √(12 x (12-18) x (12-14) x (12-6))
Area = √(12 x (-6) x (-2) x 6)
Area = √(12 x (-12) x (-12))
Area = √(12 x 144)
Area = √(1728) = 42 [tex]cm^{2}[/tex]
Therefore, the area of ∆PQR is 42[tex]cm^{2}[/tex]
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Consider a linear model for the progression of a contagious virus through a population, described by: Si+1=S; - ali, li+1=1; +al; - B1, Ri+1 = R; + 1;In this model S; describes the number of people that have never been infected, I; describes the number of people who are currently infected, and R; describes the number for people that have recovered from infection, with i representing time counted in days. a is a parameter that describes the infectivity of the virus, and B is a parameter that describes how long it takes to recover from an infection. (a) Write a matrix expression Tit1 = A7; for this model, with a = 0.10 and B = 0.05
The matrix expression for this model is given by
T=
[ 1-a, a, 0; 0, 1-B, B; 0, 0, 1]
When a = 0.10 and B = 0.05, the matrix expression becomes:
T=
[ 0.90, 0.10, 0; 0, 0.95, 0.05; 0, 0, 1]
This matrix expression describes the transition probabilities of the virus over time. Specifically, it describes the probability of a person who has never been infected (S) becoming infected (I) in the next day (a = 0.10), the probability of a person who is infected (I) in the current day in the next day (B = 0.05), and the probability of a person who has recovered (R) staying recovered in the next day (1). Thus, this matrix expression models the progression of a contagious virus through a population over time.
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Help me please asap!!!!!thank you!
The cosecant of angle U is csc(U) = 1 / sin(U) = √55 / 4
How to find the cosecant of angle U?To find the cosecant of angle U in triangle UTV, we need to find the sine of angle U. To do this, we can use the sides of the triangle that are opposite and adjacent to angle U. In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]VT^2 + UT^2 = UV^2[/tex]
4^2 + (√39)^2 = UV^2
16 + 39 = UV^2
55 = UV^2
UV = √55
So, the length of the hypotenuse is √55. To find the sine of angle U, we can use the ratio of the opposite side (UT) to the hypotenuse:
sin(U) = UT / UV = 4 / √55
The cosecant of angle U is then:
csc(U) = 1 / sin(U) = √55 / 4.
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