In 2003, a school population was 1389. By 2008 the population had grown to 1654

87 is the test score is 1.2 standard deviations above the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.

We need to find the test score is 1.2 standard deviations above the mean

1.2 standard deviations is 1.2×15 =18

So 105-18=87

87 is the score that is 1.2 standard deviations from the mean.

Hence, 87 is the test score is 1.2 standard deviations above the mean.

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The largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

Let [tex]$a_1, a_2, \ldots, a_k$[/tex] be the [tex]$k$[/tex] consecutive positive integers, such that [tex]$a_1 + a_2 + \ldots + a_k = 3^{11}$[/tex]. The average of these [tex]$k$[/tex] numbers is [tex]$\frac{a_1 + a_k}{2} = \frac{3^{11}}{k}$[/tex], which is an integer if and only if [tex]$k$[/tex] divides [tex]$3^{11}$[/tex].

The largest divisor of  [tex]$3^{11}$[/tex] is  [tex]$3^{11}$[/tex] itself, so the largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

However, [tex]$k$[/tex] must also be an integer greater than 0, so the largest possible value of [tex]$k$[/tex] for which [tex]$3^{11}$[/tex] is expressible as the sum of [tex]$k$[/tex] consecutive positive integers is [tex]$3^{11} - 1 = 177147$[/tex].

This problem is about finding the largest number of consecutive positive integers whose sum is equal to a given number. In this case, the given number is [tex]$3^{11}$[/tex].

By using the formula for the sum of consecutive integers, the average of the numbers is calculated, and the requirement for this average to be an integer is used to find the largest possible value of [tex]$k$[/tex], which represents the number of consecutive positive integers. The solution shows that the largest possible value of [tex]$k$[/tex] is [tex]$177147$[/tex].

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Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.

Here,

Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:

H + I = 100 (since a total of 100 cups were sold)

We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:

3.50H

And the total revenue from iced coffee drinks is:

2.00I

To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:

3.50H - 2.00I

We want this expression to equal zero, so we can set it equal to zero and solve for H:

3.50H - 2.00I = 0

3.50H = 2.00I

H = (2/3.50)I

H ≈ 0.57I

Since H + I = 100, we can substitute 0.57I for H in the equation:

0.57I + I = 100

1.57I = 100

I ≈ 63.7

Rounding to the nearest whole number, we get:

I = 64

Therefore, H = 100 - I = 36

So the difference in revenue between the hot and iced coffee drinks sold yesterday is:

3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56

The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

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The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero

A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.

What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"

Answer:

1/24

Explanation:

1                                                    1        8

-    ÷    8       This translates to:   -   ÷    -

3                                                   3        1

1                1

-         =     -

3x8          24

Hope this helps!

Answer:

1 to 7.99 miles

Step-by-step explanation:

According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.

Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.

The equation for the table is r = -3s + 15,

when s = 0, r = 15 and when s = 9, r = -12

the formula for Δr in terms of Δs is Δr = -3Δs.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given value of r is varying at a constant rate with respect to s,

given table for r and s

s(independent quantity)            r(dependent quantity)

1                                                           12

3                                                           6

9                                                           ?

12                                                          -21

since both quantities vary at a constant rate so it is the condition of a linear equation,

y = mx + c

where m is the slope or the rate of change,

let s₁ = 1, s₂ = 3 and r₁ =  12, r₂ = 6

coordinates for graphs (1, 12) and (3, 6)

the equation is a form of s and r is

r = ms + c (because s is independent and r is dependent)

A: formula for Δr in terms of Δs is

Δr = mΔs

m = Δr/Δs = (6 - 12)/(3 - 1)

m = -3

Δr = -3Δs

the equation will be,

r = -3s + c

when s = 1 r = 12

12  = -3(1) + c

c = 15

the formula for r in terms of s  is,

r = -6s + 15

B: the value of r when s = 0

r = -3(0) + 15

r = 15

and when s = 9

r = -3(9) + 15

r = -12

C: true and false;

i.  The graph that represents s in terms of r is linear: True

ii.  r is proportional to s: False, no r is not proportional to s because the relation between r and s has a constant

iii. Δr is proportional to Δs: True because the relation is Δr = -3Δs.

iv. The graph of r in terms of s is a straight line that passes through the origin (0, 0): False, because when s = 0 r = 15, so the graph does not pass from the origin.

Hence equation for r and s is: r = -3s + 15

when s = 9, r = -12 and when s = 0, r = 15

and Δr = -3Δs.

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The ordered pair (4, 1) is not a solution to the system,

- x + y = - 3 and x + 3y = 6.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, A system of linear equations - x + y = - 3 and x + 3y = 6.

An ordered pair must satisfy both equations simultaneously.

For, - x + y = - 3

- 4 + 1 = - 3.

- 3 = - 3 (satisfied).

For, x + 3y = 6.

4 + 3(1) = 6.

4 + 3 = 6.

But, 7 ≠ 6.

Therefore, the ordered pair is not a solution.

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The area of the lawn in the Wilson family's back yard is 4400 square feet.

The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.

Let us assume that A₁ be the area of the reactangular plot.

Using the formula for the area of rectangle,

A₁ = 100 × 80

A₁ = 8000 sq. ft.

The family planted a garden with a length and width of 60 feet.

This means, the shape of the garden must be square.

Using the formula for the area of square,

A₂ = 60 × 60

A₂ = 3600 sq. ft.

The family planted a lawn in the remaining area of the back yard, as shown.

Let us assume that A represents the area of the lawn in the Wilson family's back yard.

A = A₁ - A₂

A = 8000 - 3600

A = 4400 sq. ft.

Therefore, the required area is: 4400 sq.ft.

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Respuesta:

x = 47

Explicación paso a paso:

Necesitamos resolver x en este problema.

[tex]x+4x=235[/tex]

Combinar los términos x juntos
[tex]5x=235[/tex]

Divide 5 en ambos lados

[tex]x=47[/tex]

Nuestra respuesta es 47

Answer: x = 4

Step-by-step explanation:

Translating the problem into mathematical terms:

Let's call the number x. Then the problem can be written as:

5 * (2x - 3) - (x + 8) = 13

Expanding the left side of the equation:

5 * 2x - 5 * 3 - x - 8 = 13

Simplifying the left side of the equation:

10x - 23 - x - 8 = 13

Combining like terms:

9x - 31 = 13

Adding 31 to both sides of the equation:

9x = 44

Dividing both sides of the equation by 9:

x = 4.88888...

Since x has to be a whole number, we round down to the nearest whole number:

x = 4

Therefore, the number that satisfies the equation is 4.

Answer:

To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.

2.85 lbs ÷ 0.19 lbs/cat = 15 cats

Therefore, Carly can feed 15 cats.

The perimeter of the figure is given by the sum of the perimeter of rectangle and a semicircle P = 20.28

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the figure be represented as P

Let the width of the rectangle W = 4

So , the radius of the circle = 4 / 2 = 2

Now , the length of the rectangle = 5

And , the perimeter of the figure = 5 + 5 + 4 + ( perimeter of semicircle )

where the perimeter of semicircle = πr

On simplifying , we get

The perimeter of the figure P = 14 + 2π

The perimeter of the figure P = 14 + 6.28

The perimeter of the figure P = 20.28

Hence , the perimeter of the figure is 20.28

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Answer:

$9.20 per toy or $9.20/1

Step-by-step explanation:

$46/5 hours=9.2

Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK

Step-by-step explanation:

If the car’s average tire pressure is on target, the probability that the TPMS will trigger a warning is 0.0000.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Given:

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 31 psi (pounds per square inch.)

Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Target pressure = 31 psi

So, 26% of 31,

31 x 0.26 = 8.06

TPMS warns at below (31 - 8.06) = 22.94

Let X be tire pressure.

µ = 31, σ = 2

P(X < 22.94)

= P(x-µ / σ < (22.94 - 31) / 2)

= P(Z < -4.03)

= 0.0000 {from the z-score table}

Hence, the probability is zero.

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Answer: The range rule of thumb is used to estimate the standard deviation by taking the range of the data and dividing it by 4:

s = (max - min) / 4

In this case, the range is 191.1 cm - 150.0 cm = 41.1 cm.

s = 41.1 cm / 4 = 10.275 cm

This estimate of the standard deviation is 10.275 cm, which is close to the actual standard deviation of 10.84 cm. Since the difference between the two is less than 1.4 cm, we can say that the estimate is accurate.

In this type of puzzle, "knight" means that the speaker is telling the truth, and "knave" means that the speaker is lying.

Let's start by analyzing the first two statements:

U says: None of us is a knight.

V says: At least three of us are knights.

If U is a knight, then his statement is false, meaning that at least one of the six is a knight, which contradicts V's statement that at least three of them are knights. Therefore, U must be a knave.

Next, let's look at the statement of W:

W says: At most three of us are knights.

If W is a knight, then his statement is true, meaning that there are three or fewer knights among the six. Since U is a knave, this would mean that at most two of the remaining five are knights, which contradicts V's statement that at least three of them are knights. Therefore, W must be a knave.

Continuing in this way:

X says: Exactly five of us are knights.

If X is a knight, then his statement is false, meaning that exactly five of them are not knights. But since U is a knave, this means that U is a knight, which is a contradiction. Therefore, X must be a knave.

Y says: Exactly two of us are knights.

If Y is a knight, then his statement is true, meaning that exactly two of them are knights. Since U is a knave, this means that exactly two of the remaining five are knights, which means that W, X, Y, Z are knaves. This is consistent with all of the statements so far, so Y must be a knight.

Z says: Exactly one of us is a knight.

If Z is a knight, then his statement is true, meaning that exactly one of them is a knight. Since Y is a knight, this means that Y is the only knight, and U, V, W, X, Z are all knaves. This is consistent with all of the statements so far, so Z must be a knight.

Therefore, the knights are Y and Z, and the knaves are U, V, W, X.

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Answer:

Step-by-step explanation:

Let, width = x

length = x+4

perimeter, 2(x+4+x) = 40

4x+8 = 40

4x = 32

x = 8

so, (x+4) = 8+4 = 12

so, the area would be,

= 12 * 8 = 96 in²

The given assertion states that the length of BD in its simplest radical version is 7/√2.

A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.

Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:

AC² = AD * DC = 7 * 5 = 35

When we square the two edges, we obtain:

AC = √35

Now, we can use the fact that BD is an altitude to write:

BD = (AC * AD) / hypotenuse

where hypotenuse is the length of BC.

Using the Pythagorean Theorem, we can find the length of BC:

BC² = AC² + AB²

Since triangle ABC is a right triangle, we have AB = BC, so we can write:

BC² = AC² + BC²

Simplifying, we get:

BC² / AC² = 2

When we square the two edges, we obtain:

BC / AC = √2

Multiplying both sides by AC, we get:

BC = AC * √2 = √35 * √2 = √70

Now, we can substitute the values of AC, AD, and BC into the formula for BD:

BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2

Therefore, the length of BD in simplest radical form is 7 / √2.

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The distance between X and B is 67.5 feet for the given triangle.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

As per the given figure, we have two similar triangles, as below:

ΔXAB and ΔXCD are similar,

So AB/CD = BX/DX

45/63 = BX/(BX+BD)

45/63 = BX/(BX+27)

45(BX+27) = 63BX

63BX - 45BX = 1215

18BX = 1215

BX = 67.5

Thus, the distance between X and B is 67.5 feet.

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The exact values of two trigonometric functions are listed below:

- 2√2 / 3 and ± √6 / 3

In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.

Since sin(π/3-a) if cos(a)=-0.6 and π < a < 3π/2

Then, by the fundamental formula:

cos α = - √(1 - sin² α)

cos α = - √[1 - (1 / 3)²]

cos α = - √(8 / 9)

cos α = - 2√2 / 3

sin (π/3-a):

sin (π/3-a) = ± √[(1 - cos a) / 2]

sin (π/3-a) = ± √[[1 - (0.6)] / 2]

sin (π/3-a) = ± √6 / 3

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Answer:

Form W-2 is completed by an employer and contains important information that you need to complete your tax return. It reports your total wages for the year and the amount of federal, state, and other taxes withheld from your paycheck.

Form 1040 is used by U.S. taxpayers to file an annual income tax return.

Head of household offers wider tax brackets, a bigger standard deduction and faster eligibility for other write-offs.

Step-by-step explanation:

Answer:

86.4 ft^2

Step-by-step explanation:

Answer: 4/3

Step-by-step explanation:

Look at the points (0,-4) (3,0)

Formula: y2-y1/x2-x1

Substitute: 0-(-4)/3-0 = 4/3

Please make me brainliest, I would also add you as friend if you make me brainliest!

Let's consider what the question asks for:

--> slope of line

The slope of the line is calculated by:

  [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  --> where:

      [tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]

Let's find our points

  [tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]

Let's plug these points into our equation:

 [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]

Answer: 4/3

Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.

Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.

Step-by-step explanation:

In each case, the response variable, the explanatory variables, and the probability distribution is specified.

Before answering this question, let's us understand the Generalized linear models

Generalized linear models (GLMs) are used to model a response variable that has a non-normal distribution by linking the mean of the response variable to a linear combination of explanatory variables through a link function.

The Identification of cases are given below:

a) Response variable: number of trips per week to the supermarket for a household

Explanatory variables: number of people in the household, household income, distance to the supermarket

Probability distribution: Poisson

Justification: The response variable "number of trips per week" is count data and can be modeled using a Poisson distribution.

Linear component: log(μ) = β0 + β1 * number of people in the household + β2 * household income + β3 * distance to the supermarket

b) Response variable: person's weight

Explanatory variables: age, sex, height, mean daily food intake, mean daily energy expenditure

Probability distribution: Gaussian (Normal)

Justification: The response variable "person's weight" is continuous and approximately normally distributed.

Linear component: μ = β0 + β1 * age + β2 * sex + β3 * height + β4 * mean daily food intake + β5 * mean daily energy expenditure

c) Response variable: proportion of mice infected after exposure to bacteria

Explanatory variables: exposure level

Probability distribution: Binomial

Justification: The response variable "proportion of mice infected" is binary (yes/no) and can be modeled using a binomial distribution.

Linear component: logit(p) = log(p/(1-p)) = β0 + β1 * exposure level

The linear component represents the relationship between the mean of the response variable and the explanatory variables.

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____ The given question is incomplete, the complete question is given below:-

The following associations can be described by generalized linear models. For each one, identify the response variable and the explanatory variables, select a probability distribution for the response (justifying your choice) and write down the linear component.

a. The association between the number of trips per week to the supermarket for a household and the number of people in the household, the household income and the distance to the supermarket.

b. The effect of age, sex, height, mean daily food intake and mean daily energy expenditure on a person’s weight.

c. The proportions of laboratory mice that became infected after exposure to bacteria when five different exposure levels are used and 20 mice are exposed at each level.

The number of pea is 6. By using formulas of mean, median and mode.

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. It is frequently referred to as the "average" and is the most widely used measure of central tendency.

Taking pea counts into account,

A pod of peas contains 4, 5, 6, 7 or 8 peas.

Number of pods: 2, 10, 18, 6, and 14

The mode is the number that corresponds to the highest frequency.

The frequency of each number in the list is 1.

Mode is not possible with the information provided.

The middle value, after sorting the numbers in ascending or descending order, is the median if all of the numbers are odd.

The median of the given numbers is.

Replace the values in the formula to get the mean value.

Mean = 4+5+6+7+8/5 = 30/5 = 6

Consequently, based on the quantity of peas provided, the values of the following measure are as follows:

It is impossible to use Peas in a Pod mode.

The median number of peas in a pod is 6.

the typical quantity of peas is 6.

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Answer:

(3, -7)

Step-by-step explanation:

If you choose 3 as one of your x-coordinates, you simply need to solve for y to get -7 as your y-coordinate:

[tex]3x+y=2\\3(3)+y=2\\9+y=2\\y=-7[/tex]