can someone work out this number:
A rectangular field measures 616m by 456m.
Fencing posts are placed along its sides at equal distances. What will be the distance between the posts if they are placed as far as possible? How many posts are required?​

Time taken to reach the population size to reach 37,500 is 195 minutes.

Given that, a bacterial culture initially starts with 2,500 bacteria.

The population size of the bacterial culture doubles every 15 minutes, so in x minutes, the population size should double x/15 times. We can write this as an equation:

2,500 × 2^(x/15) = 37,500

[tex]2500\times2^\frac{x}{15} =37500[/tex]

Now, we can take the logarithm of both sides to solve for x:

[tex]log_22500\times2^\frac{x}{15} =log_237500[/tex]

x/15 = 13

So x = 195 minutes.

Therefore, time taken to reach the population size to reach 37,500 is 195 minutes.

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Answer:

5

Step-by-step explanation:

5y - 21 = 19 - 3y

Add 3y on both sides

5y + 3y - 21 = 19

8y - 21 = 19

Add 21 on both sides

8y = 19 + 21

8y = 40

Divide 8 on both sides

y = 40/8

y = 5

Answer:

y=5

Step-by-step explanation:

5y - 21 = 19 - 3y

+21. +21

5y=40-3y

+3y +3y

8y=40

divide 40 by 8

40/8=5

R is reflexive and circular if and only if it is an equivalence relation.

Reflexivity and circularity of R:

To prove that R is reflexive, we need to show that for every element an in the set, aRa holds. Reflexivity ensures that every element is related to itself.

To prove that R is circular, we need to demonstrate that if aRb and bRc, then cRa holds. Circular property implies that if two elements are related in one direction, they are also related in the reverse direction.

Equivalence relation:

An equivalence relation must satisfy three properties: reflexivity, symmetry, and transitivity. We have already established reflexivity in Step 1.

To show symmetry, we need to prove that if aRb, then bRa holds. However, this property is not given in the original statement of circularity.

Since R is reflexive and circular, it is an equivalence relation. However, the circular property alone is not sufficient to guarantee symmetry and transitivity, which are necessary for equivalence relations.

Therefore, R being both reflexive and circular is the condition for it to be an equivalence relation.

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Rounding up to the nearest whole number, you would need to survey approximately 753 randomly selected air passengers to be 90% confident that the sample percentage is within 3.5 percentage points of the true population percentage.

To determine the sample size needed for estimating a population percentage with a specified margin of error and confidence level, we can use the formula for sample size calculation for proportions. The formula is:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the required sample size,

Z is the Z-score corresponding to the desired confidence level (for a 90% confidence level, Z ≈ 1.645),

p is the estimated population proportion (since we don't have an estimate, we can use 0.5 for maximum sample size),

E is the desired margin of error (in decimal form).

In this case, the desired margin of error is 3.5 percentage points, which is 0.035 in decimal form.

Plugging in the values, we have:

n = (1.645^2 * 0.5 * (1-0.5)) / 0.035^2

Calculating this expression gives us:

n ≈ 752.93

Rounding up to the nearest whole number, you would need to survey approximately 753 randomly selected air passengers to be 90% confident that the sample percentage is within 3.5 percentage points of the true population percentage.

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Answer: 42,120

Step-by-step explanation:

Area is calculated by multiplying the length of a shape by its width-

In order to construct a right triangle with a given hypotenuse and acute angle, draw a straight line segment that represents the given hypotenuse.

Mark one endpoint of the hypotenuse as point A.

From point A, construct a perpendicular line to the hypotenuse. This perpendicular line will represent one of the legs of the right triangle.

Use a protractor to measure the given acute angle from the perpendicular line you just drew.

From the point where the acute angle intersects the perpendicular line, draw another line segment that extends away from the hypotenuse. This line segment will represent the other leg of the right triangle.

The intersection point of the two legs will be the third vertex of the right triangle.

Make sure to measure and construct accurately to ensure the triangle is a right triangle with the desired properties.

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The statement regarding regression which is true is (c) independent variables are known as predictors. The joint probability of selecting Dish A and enjoying it is 0.462. The wrong about the regression model is that (d) the analyst included all four dummy variables in the model.

In regression analysis, the independent variables (also known as predictors or input variables) are used to predict or explain the dependent variable (also known as the outcome or response variable). The independent variables are typically numerical or categorical variables that are believed to have a relationship with the dependent variable.

The probability of selecting Dish A and enjoying it is given as follows:

Probability of choosing Dish A = 0.71

Probability of enjoying Dish A = 0.65

Probability of selecting Dish B = 0.29

Probability of enjoying Dish B = 0.19

The joint probability of selecting Dish A and enjoying it is:

0.71 * 0.65 = 0.4615 (rounded to 4 decimal places)

Hence, the answer is 0.462. (rounded to 3 decimal places)

The analyst wants to analyze the impact of class standing on the GPA of students in the Gies College of Business. The analyst creates a regression model for the prediction: Ĝ = bo + b1(Freshman) + b2(Sophomore) + b3(Junior) + b (Senior).

The regression model is incorrect since the analyst included all four dummy variables in the model.

Hence, the correct option is (d) The analyst included all four dummy variables in the model.

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By using the fundamental theorem of calculus, the derivative of the given function h(x) = ∫[tex]e^{x-1}[/tex] ln(t) dt is obtained as [tex]e^{x-1}[/tex] (ln(t) + 1/t).

To find the derivative of the function h(x) = ∫[tex]e^{x-1}[/tex] ln(t) dt using Part 1 of the Fundamental Theorem of Calculus, we first need to rewrite the integral in terms of x.

Let's define a new variable u = [tex]e^{x-1}[/tex] ln(t).

Then, we have du/dx = d([tex]e^{x-1}[/tex] ln(t))/dx.

Now, we can rewrite the integral as ∫ du/dx dx = ∫ du.

Since du/dx = d([tex]e^{x-1}[/tex] ln(t))/dx, we can differentiate the expression ex-1 lnt with respect to x to find du/dx.

Applying the chain rule, we have:

du/dx = d([tex]e^{x-1}[/tex] ln(t))/dx = d([tex]e^{x-1}[/tex])/dx × ln(t) + [tex]e^{x-1}[/tex] × d(lnt)/dx.

The derivative of ex-1 with respect to x is simply ([tex]e^{x-1}[/tex])' = [tex]e^{x-1}[/tex], and the derivative of ln(t) with respect to x is (ln(t))' = 1/t.

Substituting these derivatives back into the equation, we have:

du/dx = [tex]e^{x-1}[/tex] × ln(t) + [tex]e^{x-1}[/tex] × (1/t).

Now, we can simplify the expression:

du/dx = [tex]e^{x-1}[/tex] (ln(t) + 1/t).

Finally, we can rewrite the integral with the simplified expression:

∫ du = ∫ [tex]e^{x-1}[/tex] (ln(t) + 1/t) dx.

Thus, the derivative of h(x) = ∫[tex]e^{x-1}[/tex] ln(t) dt is [tex]e^{x-1}[/tex] (ln(t) + 1/t).

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The Triangle Inequality Theorem, if CE + DE > CD, then Dora is the fastest from the church. Conversely, if CD + DE > CE, then Diego is the fastest.

To determine which student is the fastest between Diego and Dora,  more information about their locations and the distances involved.

The Triangle Inequality Theorem states that in a triangle, the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side.

Assuming that Diego, Dora, and the church form a triangle, compare the distances between each student and the church to determine who is the fastest.

The distances between Diego and the church, Dora and the church, and Diego and Dora are as follows:

Distance between Diego and the church: d1

Distance between Dora and the church: d2

Distance between Diego and Dora: d3

According to the Triangle Inequality Theorem, for any triangle, the sum of the lengths of any two sides is greater than or equal to the length of the remaining side.

d1 + d2 ≥ d3

d1 + d3 ≥ d2

d2 + d3 ≥ d1

The student who is closest to the church is the fastest, the inequalities to determine which student that is.

The first inequality: d1 + d2 ≥ d3. If Diego is closer to the church (d1 < d2), then we can rewrite the inequality as d1 + d2 ≥ d1 + d3, which simplifies to d2 ≥ d3. This means that if Diego is closer to the church, he would be the fastest.

If Dora is closer to the church (d2 < d1), then the inequality becomes d1 + d2 ≥ d2 + d3, simplifying to d1 ≥ d3. if Dora is closer the fastest.

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The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

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Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

Answer:

[tex]s^2Y(s)+38Y(s)=g(s)[/tex]

Step-by-step explanation:

Given the second order differential equation with initial condition.

[tex]y''+36y=g(t); \ y(0)=0, \ y'(0)=0, \ and \ y''(0)=1[/tex]

Take the Laplace transform of each side of the equation.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Laplace Transforms of DE's:}}\\\\L\{y''\}=s^2Y(s)-sy(0)-y'(0)\\\\\ L\{y'\}=sY(s)-y(0) \\\\ L\{y\}=Y(s)\end{array}\right}[/tex]

Taking the Laplace transform of the DE.

[tex]y''+36y=g(t); \ y(0)=0, \ y'(0)=0, \ and \ y''(0)=1\\\\\Longrightarrow L\{y''\}+38L\{y\}=L\{g(t)\}\\\\\Longrightarrow s^2Y(s)-s(0)-0+38Y(s)=g(s)\\\\\Longrightarrow \boxed{\boxed{s^2Y(s)+38Y(s)=g(s)}}[/tex]

Thus, the Laplace transform has been applied.

The number of days for which temperature recording was made is 35 days

We take the sum of the height of each bar in the chart given .

Here, we have:

Total number of days = 11 + 2 + 6 + 4 + 6 + 6

Total number of days = 35 days

Therefore, the number of days for which temperature was recorded is 35 days .

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The equation for a in terms of t, where a direct variation with t and a = 68 when t = 20, is a = 3.4t.

In a direct variation, two variables are related by a constant ratio. In this case, the variable a varies directly with t.

We can write the equation as a = kt, where k represents the constant of variation. To find the value of k, we can use the given information that a = 68 when t = 20.

Plugging these values into the equation, we have 68 = k * 20. Solving for k, we divide both sides by 20, which gives k = 68/20 = 3.4.

The equation for a in terms of t is a = 3.4t. This means that for any given value of t, we can find the corresponding value of a by multiplying t by 3.4.

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The sampling distribution is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n1 and n2 are large: (A) TRUE

The central limit theorem states that as sample sizes increase, the distribution of the sample means approaches a normal distribution regardless of the shape of the population distribution, as long as the samples are randomly selected and independent.

Therefore, if the populations from which the samples are drawn are normal, the sampling distribution of the means will also be normal.

However, even if the populations are nonnormal, the sampling distribution will still be approximately normal if the sample sizes are large enough.

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The probability that someone would not prefer dogs is 0.345.

The probability that someone would not prefer dogs is determined using the formula below:

Probability = {(cat alone) + (neither car nor dog)}/total number of people

those who prefer cats alone (cat alone) = 100

those who prefer neither cats nor dogs (neither car nor dog) = 17

total number of people = 87 + 52 + 100 + 17

total number of people = 256

Probability = 117 / 256 = 0.345

Therefore, the probability that someone would not prefer dogs is 0.345.

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a) The value of S4 = -5/8 and S₅ = -19/40

b) The interval estimate for the value of the series has an error of | S₄ - L | = |-5/8 - L|, which measures how close our estimate is to the actual value of L.

Now, let's consider the convergent alternating series ∑ (n = 1 to ∞) (-1)ⁿ/n! = L. Here, n! denotes the factorial function, which means n! = n(n-1)(n-2)...321. This series has a finite sum L, which we want to estimate. To do this, we can look at the nth partial sum of the series, denoted by Sn, which is the sum of the first n terms of the series.

To compute Sn, we simply add up the first n terms of the series. For example, when n = 4, we have:

S4 = (-1)¹/¹! + (-1)²/²! + (-1)³/³! + (-1)⁴/⁴! = -1 + 1/2 - 1/6 + 1/24 = -5/8

Similarly, we can compute the (n+1)th partial sum, denoted by Sₙ₊₁, which is the sum of the first (n+1) terms of the series. For example, when n = 4, we have:

S₅ = (-1)¹/¹! + (-1)²/²! + (-1)³/³! + (-1)⁴/⁴! + (-1)⁵/⁵! = -1 + 1/2 - 1/6 + 1/24 - 1/120 = -19/40

Now, to find bounds on the sum of the series, we can use the fact that the series is alternating and convergent. In particular, we know that the sum of the series is between two consecutive partial sums, i.e.,

Sₙ ≤ L ≤ Sₙ₊₁

This means that if we want to estimate the value of L, we can simply compute Sₙ and Sₙ₊₁ and use them to find an interval that contains L. For example, when n = 4, we have:

S4 = -5/8 and S₅ = -19/40

Therefore, we have:

-19/40 ≤ L ≤ -5/8

This interval estimate for the value of the series has an error of | S₄ - L | = |-5/8 - L|, which measures how close our estimate is to the actual value of L.

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Complete Question:

Consider the convergent alternating series  ∑ (n = 1 to ∞) (-1)ⁿ/n!  = L.

Let Sn be the nth partial sum of this series. Compute Sₙ and Sₙ₊₁ and n=1 use these values to find bounds on the sum of the series.

If n = 4, then Sₙ =----- and Sₙ₊₁ = ---

This interval estimate for the value of the series has error | Sₙ - L|

log a 343 is approximately equal to 2.535 using the given approximations of loga7≈0.845 and loga5≈0.699.

To evaluate log a343, we can use the property of logarithms that states log a (x^n) = n log a (x). We know that 343 is equal to 7^3, so we can write log a 343 as 3 log a 7. Using the approximation loga7≈0.845, we can substitute that value in for log a 7:

log a 343 = 3 log a 7
≈ 3(0.845)
≈ 2.535

Therefore, log a 343 is approximately equal to 2.535 using the given approximations of loga7≈0.845 and loga5≈0.699.

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The slope of the line passing through (4, 4) and (0, -2) is 1.5

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

The slope of a straight line is the ratio of its rise to its run. It is given by:

Slope = Rise / Run

Hence, for the line shown passing through (4, 4) and (0, -2):

Slope = (-2 - 4) / (0 - 4) = 1.5

The slope of the line is 1.5

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Using the given information, the volume of the rectangular prism is 6,048 cubic units.

A rectangular prism is a three-dimensional geometric shape that has six rectangular faces, each with an identical size and form.

To compute the volume of a rectangular prism, multiply the length (L), width (W), and height (H).  

In this case, we are given:

L = 18

W = 21

H = 16

Volume = L × W × H

= 18 × 21 × 16

= 6,048 cubic units

Therefore, the volume of the rectangular prism is 6,048 cubic units.

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A regular hex decagon's measure of one internal angle is 7.5 degrees more than a regular dodecagon's measure of one interior angle.

We must ascertain the measure of each individual angle in each polygon in order to compare the differences in one inside angle between a regular hex decagon and a regular dodecagon.

The following formula can be used to determine the size of each interior angle in a regular polygon with n sides:

Interior Angle = (n - 2) x 180 / n

Regular hex decagon:

Interior Angle = (16 - 2) * 180 / 16

= 14 * 180 / 16

= 2520 / 16

= 157.5 degrees

Regular dodecagon:

Interior Angle = (12 - 2) * 180 / 12

= 10 * 180 / 12

= 1800 / 12

= 150 degrees

Difference = Measure of hexadecagon angle - Measure of dodecagon angle

= 157.5 degrees - 150 degrees

= 7.5 degrees

Therefore, the measure of one interior angle of a regular hex decagon is 7.5 degrees greater than the measure of one interior angle of a regular dodecagon.

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Using the formula of probability, the probability of the card either being r or s is 2/3

The probability that the card drawn at random will either be marked r or s can be calculated by dividing the total number of cards by the number of possible outcomes.

Assuming the possible outcomes are r and s;

Number of possible outcomes = 2

Total amount in the event = 3

The probability of selecting either r or s will be;

Probability = Number of favorable outcomes / Total number of possible outcomes;

p = 2/3

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The probability that the selected marble will be blue is 5//12

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

Marbles = 600

Red to blue marbles = 7 to 5

This means that

Red : blue = 7 : 5

The probability that the marble will be blue is calculated as

P = Blue/Blue + Red

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

P = 5/(5 + 7)

Evaluate the sum

P = 5/12

Hence, the probability that the marble will be blue is 5//12

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In this random graph, we expect to find approximately 14 unordered cycles of length three.

In an undirected random graph of eight vertices, where the probability of an edge existing between any pair of vertices is 1/2, we can calculate the expected number of unordered cycles of length three.

To determine the expected number, we need to analyze the probability of forming a cycle of length three through any three vertices.

To form a cycle of length three, we must select three distinct vertices. The probability of selecting a particular vertex is 1, and the probability of not selecting it is (1 - 1/2) = 1/2. Hence, the probability of selecting three distinct vertices is (1)(1/2)(1/2) = 1/4.

Since we have eight vertices, the number of ways to choose three distinct vertices is given by the combination formula C(8, 3) = 8! / (3! * (8 - 3)!) = 56.

Therefore, the expected number of unordered cycles of length three is the product of the probability and the number of ways to choose the vertices: (1/4) * 56 = 14.

Therefore, in this random graph, we expect to find approximately 14 unordered cycles of length three.

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The interquartile range of a data-set is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

The quartiles of a data-set are given as follows:

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Answer:

700

Step-by-step explanation:

4(175)=700

The number that best represents the model given above would be = 75%. That is option B.

To determine the number that best represents the given model, the number of boxes that are shaded and not shaded is taken note of.

The number of boxes that are shaded = 75

The number of boxes that are not shaded = 15

The total number of boxes = 100 boxes.

Therefore the model can be said to contain 75% of shades boxes.

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Farzana makes 38.3 pounds of egg salad each week for her sandwich shop.

Farzana makes 5 pounds of egg salad each day from Monday to Saturday, totaling 6 days. On Sunday, she makes 8.3 pounds of egg salad. To calculate the total amount of egg salad Farzana makes in a week, we need to add up the amounts from each day.

From Monday to Saturday, she makes a total of 5 pounds * 6 days = 30 pounds of egg salad.

On Sunday, she makes 8.3 pounds of egg salad.

To find the total amount for the week, we add the amounts from Monday to Saturday to the amount from Sunday:

30 pounds + 8.3 pounds = 38.3 pounds

Therefore, Farzana makes 38.3 pounds of egg salad each week for her sandwich shop.

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A can be factored as [tex]A = PDP^{(-1)}[/tex]

The columns of matrix P are n linearly independent eigenvectors.

D is a diagonal matrix whose diagonal entries are the eigenvalues corresponding to the eigenvectors in P.

To show that if matrix A has n linearly independent eigenvectors, then so does its transpose [tex]A^T[/tex], we can use the following argument:

Let [tex]v_1, v_2, ..., v_n[/tex] be n linearly independent eigenvectors of A corresponding to eigenvalues [tex]λ_1, λ_2, ..., λ_n,[/tex] respectively. Then, by definition, we have:

[tex]A v_1 = λ_1 v_1 \\ A v_2 = λ_2 v_2 \\ A v_n = λ_n v_n[/tex]

Taking the transpose of both sides of these equations, we get:

[tex](A v_1)^T = (λ_1 v_1)^T \\ v_1^T A^T = λ_1 v_1^T[/tex]

Similarly,

[tex]v_2^T A^T = λ_2 v_2^T\\ v_n^T A^T = λ_n v_n^T[/tex]

Now, let's examine the equations

[tex]v_1^T A^T = λ_1 v_1^T \: and \: v_2^T A^T = λ_2 v_2^T[/tex]

. If we subtract [tex]λ_1[/tex] times the first equation from [tex]λ_2[/tex] times the second equation, we get:

[tex]v_2^T A^T - λ_2 v_1^T A^T = λ_2 v_2^T - λ_1 λ_2 v_1^T \\ (v_2^T - λ_1 v_1^T) A^T = (λ_2 - λ_1 λ_2) v_2^T[/tex]

Notice that [tex]v_2^T - λ_1 v_1^T[/tex] is a non-zero vector because [tex]v_1 \: and \: v_2[/tex] are linearly independent. Therefore, for the equation above to hold [tex]A^T[/tex]

must have an eigenvector corresponding to the eigenvalue [tex](λ_2 - λ_1 λ_2)[/tex]

By repeating this process for all pairs of eigenvectors [tex](v_i, v_j)[/tex] and eigenvalues [tex](λ_i, λ_j)[/tex], we can see that [tex]A^T[/tex] has at least n linearly independent eigenvectors corresponding to its eigenvalues.

Now, based on the Diagonalization Theorem, if A has n linearly independent eigenvectors, it can be factored as:

[tex]A = PDP^{(-1)}[/tex] Where P is a matrix whose columns are the n linearly independent eigenvectors of A, and D is a diagonal matrix whose diagonal entries are the corresponding eigenvalues.

Therefore, we can complete the statements as follows:

A can be factored as [tex]A = PDP^{(-1)}[/tex]

The columns of matrix P are n linearly independent eigenvectors.

D is a diagonal matrix whose diagonal entries are the eigenvalues corresponding to the eigenvectors in P.

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The option which is not a reasonable value for the true mean SAT score of graduating high school seniors is 496.6.

Given that,

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors.

The study found that the mean SAT score was 524 with a margin or error of 20.

We have to find the reasonable value for the true mean SAT score of graduating high school seniors

We have,

Mean SAT score = 524

Margin of error = 20

True mean SAT score will be in the range of 524 ± 20.

The range is (544, 504).

The value which does not fall in the range is 496.6.

Hence the correct option is a.

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Answer:

Step-by-step explanation:

You want the price per ounce and the best deal, given 6-, 10-, and 16-ounce bricks cost $3.59, $4.79, and $7.89.

The unit price is found by dividing the price by the number of units. Here, our unit is 1 ounce, so we divide each price by the number of ounces to find the price per ounce. The calculator display attached shows the result to 4 decimal places. Here, we round to 2 dp.

The lowest price per ounce is obtained with the 10 oz brick.

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