find an equation of the plane through the point (-5, -1, 3) and perpendicular to the vector (-5, 4, 2). do this problem in the standard way or webwork may not recognize a correct answer.

i got you, buddy!

To rewrite the equation in standard form, we need to complete the square for both x and y terms.

Starting with the x terms: x^2 + 4x + y^2 - 10y = 7 (x^2 + 4x) + y^2 - 10y = 7 (x^2 + 4x + 4) + y^2 - 10y = 7 + 4 (adding and subtracting 4 to complete the square for x) (x + 2)^2 + y^2 - 10y = 11

Now completing the square for y terms: (x + 2)^2 + y^2 - 10y = 11 (x + 2)^2 + (y^2 - 10y + 25) = 11 + 25 (adding and subtracting 25 to complete the square for y) (x + 2)^2 + (y - 5)^2 = 36

Therefore, the equation in standard form is: (x + 2)^2 + (y - 5)^2 = 36

The least number of units that should be produced in order for the average total cost per unit to be $11 or less is 200.

The average total cost per unit is the total cost divided by the number of units produced. Let's denote the total cost as C and the number of units as x. Then the average total cost per unit is:

ATC = C/x

The total cost is the sum of the initial cost and the cost per unit of the product times the number of units produced:

C = 800 + 7x

Substituting this expression for C into the formula for ATC, we get:

ATC = (800 + 7x)/x

We want to find the least number of units, x, that should be produced in order for the average total cost per unit to be $11 or less. This can be written as an inequality:

ATC ≤ 11

(800 + 7x)/x ≤ 11

Multiplying both sides by x, we get:

800 + 7x ≤ 11x

4x ≤ 800

x ≤ 200

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The fraction of days the man does not wear a hat is 0.

To solve this problem, let's analyze the possible scenarios:

The man chooses a drawer with hats in the morning and returns the hat to the same drawer in the evening.

The man chooses a drawer with hats in the morning and returns the hat to the other drawer in the evening.

The man chooses an empty drawer in the morning and does not wear a hat.

Let's calculate the probabilities for each scenario:

Probability of choosing a drawer with hats in the morning: There are two drawers, so the probability is 2/2 = 1.

Probability of returning the hat to the same drawer in the evening: There is a 1/2 chance of choosing the same drawer, so the probability is 1/2.

Probability of choosing a drawer with hats in the morning: 2/2 = 1.

Probability of returning the hat to the other drawer in the evening: There is a 1/2 chance of choosing the other drawer, so the probability is 1/2.

Probability of choosing an empty drawer in the morning: There is a 0/2 chance of choosing a drawer with hats, so the probability is 0.

Now, let's calculate the fraction of days the man does not wear a hat:

Fraction of days without a hat = (Probability of scenario 3) = 0.

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Regression equation are calculations used to predict a person's to score on one variable when that person's score on another variable is already known. So, option(C) is right one.

Statistical study is used to collect and analyze data and is useful in census. The collected data is used to interpret economic activities. Statistics can be qualitative or quantitative in nature. The regression analysis is used to determine the line of best fit for the dependent variable and independent variables. The equation form of regression line is written as, Y= a + bX, where

It is an analysis to measure the relationship between a dependent variable and two or more. independent variables. So the correct choice is the regression equation.

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Complete question:

____ ____ are calculations used to predict a person's to score on one variable when that person's score on another variable is already known.

A. Pearson product-moment correlation coefficient

B. Coefficient of determination

C. Regression analysis

D. Point-biserial correlation coefficient

Answer:

84

Step-by-step explanation:

A= Bh

Base is 12

Height is 7

= 84

Answer:

84

Step-by-step explanation:

The numerator and denominator is D. 3 and 116.

In fractions, the numerator and denominator are the two constituent parts. They comprise fractions, in other words. A fraction's top digit is always referred to as the numerator. It displays the quantity of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.

For an ANOVA procedure with k groups (in this case, k=4), the degrees of freedom for the numerator and denominator of the F-statistic are given by:

- Numerator degrees of freedom: k-1

- Denominator degrees of freedom: n-k, where n is the total sample size (in this case, n=4*30=120)

Therefore, for the given ANOVA procedure with four samples of 30 observations each, the numerator and denominator degrees of freedom for the critical value of F are:

- Numerator degrees of freedom: 4-1 = 3

- Denominator degrees of freedom: 120-4 = 116

So the answer is D. 3 and 116.

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Answer:

10x^2 - 40x = 10x(x - 40)

H.A. y = 1/2

V.A. x = 0, x = 40

Answer:

Step-by-step explanation:

3 -2

The a survey of 1,150 people for choose their favorite laundry detergent from brands. If percent value of people who choose brand A is 3, then the number of people who chose A as their favorite brand are 30 , 35 , 40.

We have a survey results of total 1150 people. That is sample size = 1150

The survey is based on their favorite laundry detergent from brands A, B, and C. The percent of people who chose A as their favorite brand = x %

If x = 3, we have to determine the number of people who chose A as their favorite brand. So, we use percentage formula, for each option and see for which number of people percent is equals to 3. Now, percent formula is [tex] \frac{value}{total \: value}×100%.[/tex]

a) [tex] (\frac{20}{1150 }) 100 \% = 1.73 \%[/tex] ≈ 2%

b) [tex] (\frac{25}{1150 }) 100 \% = 2.17 \%[/tex] ≈ 2%

c) [tex] (\frac{30}{1150 }) 100 \% = 2.60\%[/tex] ≈ 3 %

d) [tex] (\frac{35}{1150 }) 100 \% = 3.04\%[/tex]≈ 3 %

e)[tex] (\frac{40}{1150 }) 100\% = 3.48 \%[/tex] ≈ 3%

f)[tex] (\frac{45}{1150 }) 100 \% = 3.91 \%[/tex]≈ 4%

g)[tex] (\frac{50}{1150 }) 100 \% =4.35 \%[/tex] ≈ 4%

Hence, all such numbers are 30 , 35 , 40.

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Complete question:

A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand? Indicate all such numbers.

a)20

b) 25

c)30

d) 35

e) 40

f) 45

g) 50

If x percent of people chose A as their favorite brand, then the number of people who chose A can be found by multiplying x percent by the total number of people surveyed:

number of people who chose A = (x/100) * 1150

Since x is rounded to the nearest integer and equals 3, we have:

number of people who chose A = (3/100) * 1150 = 34.5, which is closest to 35.

If x percent chose brand A as their favorite and x is rounded to the nearest integer, it means that x lies between x-0.5 and x+0.5. In other words, x-0.5 <= actual percentage of people who chose A <= x+0.5.

From the given information, we know that x rounded to the nearest integer is 3. Therefore, we have:

2.5 <= x <= 3.5

Since x represents the percentage of people who chose brand A, we can find the number of people who chose A as their favorite by multiplying x with the total number of people surveyed (1150). Therefore, the number of people who chose brand A lies between:

2.5% of 1150 <= number of people who chose A <= 3.5% of 1150

28.75 <= number of people who chose A <= 40.25

Since the number of people who chose A must be a whole number, the only possible value for the number of people who chose is 29.

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Answer: We can simplify the left side of the equation as follows:

7×10^0 - 3×10^-1 = (7/1)×10^0 - (3/10)×10^0 = (7-0.3)×10^0 = 6.7×10^0

Substituting this into the given equation, we get:

6.7×10^0 = k×10^0

Dividing both sides by 10^0, we get:

k = 6.7

Therefore, the value of k that satisfies the given equation is 6.7.

Using the following pattern and inductive reasoning, predicted answer to 9 x 7,654,321 - 1 is 73,888,889.

The pattern:

When you subtract 1 from a number that ends with a sequence of n consecutive digits (all equal to d), the result is a number that ends with the same n digits followed by ([tex]10^{n}[/tex] - 1) -d.

For example:

If you subtract 1 from a number that ends with three 7's, the result is a number that ends with three 6's, i.e., (777-1=776).

If you subtract 1 from a number that ends with four 2's, the result is a number that ends with four 1's, i.e., (2222-1=2221).

Applying this pattern to 9 x 7,654,321 - 1:

The number ends with one 9, so n=1 and d=9.

Therefore, the result will end with one 8 (one less than 9), followed by ([tex]10^{1}[/tex] - 1) - 9 = 0, i.e., it will end with 8.

So, the predicted answer is 73,888,889.

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Part A) the p-value is 0.0025.

Part B) the positive critical value is:zα/2 = |1.645| = 1.645 (rounded to three decimal places).

what is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Part A) For a left-tailed test with a test statistic of z = -2.816, the p-value can be calculated using a standard normal distribution table or a calculator. The p-value is the area to the left of the test statistic in the standard normal distribution.

Using a standard normal distribution table, the area to the left of z = -2.816 is 0.0025. Therefore, the p-value is 0.0025.

Alternatively, using a calculator such as the TI-84, the p-value can be found by entering the command "normalcdf(-9999,-2.816)" which gives a result of 0.0025, accurate to 4 decimal places.

Therefore, the p-value is 0.0025.

Part B) For a two-tailed test at a significance level of α = 0.10, the critical values can be found using a standard normal distribution table or a calculator. The critical values are the z-scores that leave α/2 in each tail.

Using a standard normal distribution table, the critical value for α/2 = 0.05

Therefore, the positive critical value is:zα/2 = |1.645| = 1.645 (rounded to three decimal places)

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If a force of 18 lb is required to hold a spring stretched 2 inches, the work done in stretching the spring from its natural length to 4 inches beyond is 72 lb*in.

To find the work done in stretching the spring from its natural length to 4 inches beyond, we need to first find the spring constant k.

Using Hooke's law, we know that F = kx, where F is the force applied, x is the displacement from the natural length, and k is the spring constant.

So, when the spring is stretched 2 inches beyond its natural length, we have:

18 lb = k * 2 in

Solving for k:

k = 9 lb/in

Now, to find the work done in stretching the spring from its natural length to 4 inches beyond, we use the equation for work:

W = (1/2)kx²

Where x is the displacement from the natural length, which in this case is 4 - 0 = 4 inches.

W = (1/2) * 9 lb/in * (4 in)²

W = 72 lb*in

So, the work done in stretching the spring from its natural length to 4 inches beyond is 72 lb*in.

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The ordered pair of one of the zeros for the following function is (x +8)

We have that the function is a quadratic function written as;

f(x)=x2+7x−8

Using the factorization method of solving quadratic functions;

Multiply the coefficient of  x squared by the constant in the expression, we have;

1(-8) = -8

Now, find the pair factors of the product that sum up to give 7, we have;

8x and -x

Substitute the values

x² + 8x - x - 8

group in pairs

(x² + 8x) - (x - 8)

factorize

x(x + 8) - 1(x + 8)

Then, we have;

x = 1

x = -8

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Answer:

B. no, the survey represented both groups in the population of students

Step-by-step explanation:

It says, "surveyed all students"

The absolute maximum value of f(x,y) subject to the constraint [tex]x^2 + y^2 = 49[/tex] is 30√2, which occurs at the point (5√2/2, 3√2/2), and the absolute minimum value is -30√2, which occurs at the point (-5√2/2, -3√2/2).

Lagrange Multiplier is a  method used to find the extreme values of a function subject to one or more constraints. The method involves introducing a new variable, called a Lagrange multiplier, for each constraint in the problem.

We can use the method of Lagrange multipliers to find the absolute extrema of the function f(x,y) = 5x + 9y subject to the constraint [tex]x^2 + y^2 = 49.[/tex] We start by defining the Lagrangian function L(x,y,λ) as:
L(x,y,λ) = f(x,y) - λg(x,y)

where g(x,y) = [tex]x^2 + y^2 - 49[/tex] is the constraint function and λ is the Lagrange multiplier.
Taking partial derivatives of L with respect to x, y, and λ, we get:
∂L/∂x = 5 - 2λx = 0

∂L/∂y = 9 - 2λy = 0

∂L/∂λ = x² + y² - 49 = 0

∂L/∂λ [tex]= x^2 + y^2 - 49 = 0[/tex]

Solving these equations simultaneously, we get:
x = ±5√2/2, y = ±3√2/2, λ = 5/7
These are the critical points of f(x,y) subject to the constraint [tex]x^2 + y^2 = 49.[/tex]
To determine which of these critical points are absolute maxima and minima, we need to evaluate the function f(x,y) at these points and compare the values. We have:
f(5√2/2, 3√2/2) = 5(5√2/2) + 9(3√2/2) = 30√2

f(-5√2/2, -3√2/2) = 5(-5√2/2) + 9(-3√2/2) = -30√2

So, the absolute maximum value of f(x,y) subject to the constraint [tex]x^2 + y^2 = 49[/tex] is 30√2, which occurs at the point (5√2/2, 3√2/2), and the absolute minimum value is -30√2, which occurs at the point (-5√2/2, -3√2/2).

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If gender and handedness were independent, it would mean that the proportion of left-handed individuals would be the same for both men and women, and that knowing someone's gender would not provide any information about their handedness.

Gender and handedness are associated because women are more likely to be left-handed than men. D

The fact that women are about six times as likely to be left-handed as men suggests that there is a relationship between gender and handedness, and that knowing someone's gender can provide some predictive power for their handedness.

To conclude that gender and handedness are associated.

The proportion of left-handed people would be the same for both men and women if gender and handedness were independent, and knowing someone's gender would not reveal anything about their handedness.

Given that women are more likely to be left-handed than males, gender and handedness go hand in hand.

Given that women are almost six times more likely to be left-handed than males, there may be a correlation between gender and handedness, and one's gender may be able to predict someone's handedness.

to draw the conclusion that handedness and gender are related.

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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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Answer:

2 specials are made possible

Step-by-step explanation:

2 of each category

Answer:

The answer is 6

Step-by-step explanation:

The answer is the total number of drinks,sandwiches and desserts

T(s)=2+2+2=6

The researcher interested in analyzing the frequency of some combination of possible responses to multiple categorical variables should construct a contingency table.

A contingency table is a two-way table that displays the frequency of observations or counts for two or more categorical variables. The table is constructed by tabulating the counts or percentages of the variables in rows and columns. The contingency table can be used to identify relationships between variables and can be helpful in analyzing data and developing hypotheses.

In a contingency table, the frequency of observations is summarized in rows and columns, as well as in the margins. The marginal totals represent the total counts or percentages for each variable, and they are typically displayed at the bottom or the right side of the table.

The marginal totals provide an overview of the overall distribution of the variables and can be helpful in identifying patterns or trends. A researcher interested in analyzing multiple categorical variables may need to construct a multiple contingency table. This type of table displays the frequency of observations for more than two categorical variables.

The table is constructed by tabulating the counts or percentages of the variables in rows and columns, as well as in the margins. In summary, a researcher interested in analyzing the frequency of some combination of possible responses to multiple categorical variables should construct a contingency table.

The contingency table summarizes the frequency of observations in rows, columns, and margins, providing a comprehensive overview of the distribution of the variables. The table can be helpful in identifying relationships between variables and developing hypotheses.

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If the equation of the line that contains diagonal MT is y = -2x + 3, the equation of the line that contains diagonal AH is y = -2x + 3.

In a rhombus, the diagonals intersect at a 90-degree angle and bisect each other. Therefore, if the point of intersection of the diagonals is known, we can find the equations of the diagonals by using the midpoint formula and the slope formula.

To find the equation of the diagonal that contains point A, we first need to find the coordinates of point A. Since the diagonals bisect each other, point A is the midpoint of diagonal MT. We can use the midpoint formula to find the coordinates of point A:

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

x = (4 + x₂)/2 and y = (-5 + y₂)/2

Multiplying both sides by 2, we have:

2x = 4 + x₂ and 2y = -5 + y₂

Simplifying, we have:

x₂ = 2x - 4 and y₂ = 2y + 5

Now, we can use the slope formula to find the slope of the diagonal AH. Since diagonal MT has a slope of -2, we know that the product of the slopes of the diagonals of a rhombus is -1. Therefore, the slope of diagonal AH is:

m = 1/2 = -1/m'

where m' is the slope of the line that contains diagonal AH.

Solving for m', we have:

m' = -2

Now we have the slope and a point on the diagonal AH (point A). We can use the point-slope form of the equation of a line to find the equation of diagonal AH:

y - (-5) = -2(x - 4)

y + 5 = -2x + 8

y = -2x + 3

In conclusion, we can find the equation of the diagonal that contains point A in a rhombus by using the midpoint formula and the slope formula. Since the diagonals of a rhombus bisect each other and are perpendicular, we can use this information to find the equation of the second diagonal once we know the equation of the first diagonal.

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The area of window is 14.56 sq ft. The contractor should pay $101.92 to replace the window.

a) To find the area of the window, we need to use the formula for the area of a trapezoid, which is:

Area = (1/2) * (sum of parallel sides) * (height)

In this case, the sum of the parallel sides is 4 + 5 = 9 feet, and we know that one of the other sides is 3 feet. To find the height, we need to use the Pythagorean theorem:

[tex](Height)^{2}[/tex] = [tex](5-4.5)^{2}[/tex] +[tex]3^{2}[/tex]

[tex](Height)^{2}[/tex] = 0.25 + 9

[tex](Height)^{2}[/tex] = 9.25

Height ≈ 3.04 feet

So the area of the trapezoidal window is:

Area = (1/2) * (4 + 5) * 3.04

Area ≈ 14.56 square feet

b) To find the cost of replacing the window, we need to multiply the area of the window by the cost per square foot of the glass. In this case, the cost is $7 per square foot. So the cost of replacing the window is:

Cost = Area * Cost per square foot

Cost = 14.56 * 7

Cost ≈ $101.92

Therefore, the contractor should expect to pay about $101.92 to replace the window with glass that costs $7 per square foot.

Correct Question :

A contractor is replacing a trapezoidal window on the front of a house with measurements as length of parallel side be 4ft and 5 ft and the length of one of the two other side is 3 ft.

a) find the area of the window. ft

b) if the glass for the window costs $7 per square foot, about how much should the contractor expect to pay to replace the window?

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Answer:

the boxplot tells us that the median height of males in the data set is approximately 174.7 cm. The middle 50% of the males in the data set have heights between approximately 153 cm (25th percentile) and 194 cm (75th percentile). There are no outliers in the data set.

Step-by-step explanation:

The boxplot provides a visual representation of the distribution of the heights of males in the data set. The box represents the middle 50% of the data, with the bottom of the box indicating the 25th percentile and the top indicating the 75th percentile. The line within the box represents the median height, which is the middle value of the data set. The whiskers represent the range of the data, with the bottom whisker extending from the bottom of the box to the smallest observation within 1.5 times the interquartile range (IQR) below the bottom of the box, and the top whisker extending from the top of the box to the largest observation within 1.5 times the IQR above the top of the box. Any outliers beyond the whiskers are indicated as individual points.

The probability distribution of random variable x is

a) 1.78 is the anticipated value of x;

b) The variance of x is 0.6484.

(a) The expected value of x can be found using the formula:

[tex]E(x) = Σ[x * f(x)][/tex]

where x's potential values are all added up.

Using the given probability distribution, we have:

[tex]E(x) = (0 * 0.27) + (1 * 0.35) + (2 * 0.05) + (3 * 0.25) + (4 * 0.08)[/tex]

[tex]E(x) = 1.78[/tex]

As a result, 1.78 is the expected value of x.

(b) The variance of x can be found using the formula:

[tex]Var(x) = E(x^2) - [E(x)]^2[/tex]

where E(x) represents the anticipated value of x and E(x2) represents the expected value of x2.

To find E(x^2), we can use the formula:

[tex]E(x^2) = Σ[x^2 * f(x)][/tex]

Using the given probability distribution, we have:

[tex]E(x^2) = (0^2 * 0.27) + (1^2 * 0.35) + (2^2 * 0.05) + (3^2 * 0.25) + (4^2 * 0.08)[/tex]

[tex]E(x^2) = 3.33[/tex]

Consequently, the variation of x is:

[tex]Var(x) = E(x^2) - [E(x)]^2[/tex]

[tex]var(x) = 3.33 - (1.78)^2[/tex]

[tex]var(x) = 0.6484[/tex] (rounded to four decimal places)

x's variance is 0.6484

As a result, x's variance is 0.6484.

1.78 is the anticipated value of x

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Answer:

x - matinee tickets

y - evening tickets

x≥0

y≥0

5x+8y≤40

the probability of choosing exactly 5 red marbles when 12 marbles are chosen at random is approximately 0.028.

This is a hypergeometric probability problem .

The total number of ways to choose 12 marbles from 27 is:

${{27}\choose{12}} = \frac{27!}{12!15!} = 10,!626,!766$

The number of ways to choose 5 red marbles and 7 blue marbles is:

$ {{15}\choose{5}}\cdot{{12}\choose{7}} = \frac{15!}{5!10!}\cdot\frac{12!}{7!5!} = 300,!450$

So the probability of choosing exactly 5 red marbles is:

$P(\text{5 red}) = \frac{300,!450}{10,!626,!766} \approx 0.028$

what is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event.

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In the given equation, find sales = 0.22 + 1.8 (degrees over 32 Fahrenheit), the "y-intercept" is the value of "find sales" when the "degrees over 32 Fahrenheit" is equal to 0.

To find the y-intercept, substitute 0 for "degrees over 32 Fahrenheit":

Find sales = 0.22 + 1.8(0)
Find sales = 0.22

So, the y-intercept is 0.22.

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

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The trend in the boiling points of the molecules shown is primarily determined by their intermolecular forces. As the intermolecular forces between molecules increase, so does the boiling point.
Based on the information given, we need to identify statements that explain the trend in boiling points of molecules with similar or identical molecular weight. When considering boiling point trends, key factors to take into account are molecular size, polarity, and intermolecular forces.

In conclusion, Molecules with stronger intermolecular forces, such as hydrogen bonding or dipole-dipole interactions, typically have higher boiling points. Additionally, molecules with larger surface areas or more polar bonds may exhibit higher boiling points due to increased interactions between the molecules.

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The dimensions of the rectangular sticker with perimeter of 20 centimeters and area of 21 square centimeters are either 3 cm by 7 cm or 7 cm by 3 cm.

To find the dimensions of the rectangular sticker, we need to use the given information about its perimeter and area. Let's start by using the formula for perimeter of a rectangle:

Perimeter = 2(length + width)

We know that the perimeter of the sticker is 20 centimeters, so we can write:

20 = 2(length + width)

Simplifying this equation, we get:

length + width = 10

Now let's use the formula for area of a rectangle:

Area = length x width

We know that the area of the sticker is 21 square centimeters, so we can write:

21 = length x width

We now have two equations with two variables (length and width). We can use substitution to solve for one of the variables. Let's solve for width in terms of length using the perimeter equation:

width = 10 - length

Now we can substitute this expression for width into the area equation:

21 = length x (10 - length)

Expanding the right side, we get:

21 = 10 length - length^2

Rearranging and simplifying, we get a quadratic equation:

length^2 - 10 length + 21 = 0

We can solve this quadratic equation using factoring or the quadratic formula. Factoring gives us:

(length - 3)(length - 7) = 0

So the possible values for length are 3 and 7. If we plug these values into the width equation, we get:

width = 10 - length

For length = 3, width = 7
For length = 7, width = 3

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The test statistic value is -2.03.

What is the mean and standard deviation?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It displays the degree of variance from the mean (average). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

We can use a one-sample t-test to test whether the mean endurance time of the tires is significantly different from the claimed value of 40000 km. The test statistic is given by:

[tex]t = (x - \mu) / (s / \sqrt{(n)})[/tex]

where x is the sample mean (39750 km), μ is the claimed mean (40000 km), s is the sample standard deviation (387 km), and n is the sample size (25).

Substituting the values, we get:

[tex]t = (39750 - 40000) / (387 / \sqrt{25})[/tex]

t = -250 / (387/5)

t = -2.03

Therefore, the test statistic value is -2.03.

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