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The total cost of the plywood Mr. Richardson needs for the doghouse is $80. The correct option is D.

To calculate the total cost of the plywood, we first need to find the total surface area of the rectangular prism-shaped doghouse, subtract the surface area of the opening, and then multiply it by the cost per square foot. Let's assume the dimensions of the doghouse are length (l), width (w), and height (h), and the opening's dimensions are length (l1) and height (h1).

Calculation steps:
1. Surface area of the doghouse: 2lw + 2lh + 2wh
2. Surface area of the opening: l1h1
3. Subtract the opening's area: (2lw + 2lh + 2wh) - l1h1
4. Multiply by the cost per square foot: [ (2lw + 2lh + 2wh) - l1h1 ] * $2

Plug in the given dimensions for the doghouse and the opening to calculate the total cost, which comes out to be $80 (Option D).

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Answer: 1

Step-by-step explanation: the lowest number they divide into evenly is 1

Answer:

3

Step-by-step explanation:

b=3 and its the same question on other side except the expression is in multiplication parenthesis.

Jaya's age is 2828, which is the middle age of the three siblings

What is an integer?

An integer is an whole number without decimal or fractional part, which means 1,2,3 are integers since they not in decimals or fractions.

Note the word consecutive means the ages of the three siblings are one after the other.

Let us assume the youngest sibling's age is X

Next sibling's age is X+1

The last sibling's age is X+2

sum of their ages=X+X+1+X+2

sum of their ages=3X+3

sum of their ages=8484

8484=3X+3

8484-3=3X

X=(8484-3)/3

X=age of the youngest sibling=2827

the age of the next sibling=2828

age of the last sibling=2829

The middle age is 2828(i.e2827+2828+2829)/3))

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Answer:

Jaya's age is 28.

Step-by-step explanation:

26+28+30=84

Hope this helps!

Please mark as brainliest if correct!

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The quadratic function graphed is defined as follows:

g(x) = -4(x - 1)² + 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The coordinates of the vertex in this problem are given as follows:

(1,3).

Hence:

g(x) = a(x - 1)² +  3.

When x = 2, g(x) = -1, hence the leading coefficient a is obtained as follows:

-1 = a + 3

a = -4.

Hence the function is:

g(x) = -4(x - 1)² + 3.

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Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

none of the provided approximations for the probabilities are accurate.To determine which statement is true, we need to calculate the probabilities of selecting each color marker.

Total number of markers = 20 green + 44 orange + 30 blue = 94 markers.

P(blue) = Number of blue markers / Total number of markers = 30 / 94 ≈ 0.319.

P(green) = Number of green markers / Total number of markers = 20 / 94 ≈ 0.213.

P(orange) = Number of orange markers / Total number of markers = 44 / 94 ≈ 0.468.

Based on the calculations, none of the given statements are true. The actual probabilities are approximately:

P(blue) ≈ 0.319,
P(green) ≈ 0.213,
P(orange) ≈ 0.468.

Therefore, none of the provided approximations for the probabilities are accurate.

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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The value of x is 1/3

Equations are expressions separated by an equal sign

Given the following equation

21x = 7

We are to find the value of x. Divide both sides by 21

21x/21 = 7/21

x = 7/21

x = 1/3

Hence the value of x is 1/3

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Answer:

57.6

Step-by-step explanation:

since 80 is x. you plug in 80 into x

0.47(80)+20

37.6+20

57.6

Answer:

57.6 dont really no how to explain it

Answer:

f = 5

g = -3

Step-by-step explanation:

11f + 14g = 13        Q1

11f + 10g = 25       Q2

Q1 - Q2  =

4g = -12

g = -3

put it back in the equation

11f + 10g = 25

11f + 10 (-3) = 25

11f + -30 = 25

11f = 55

f = 5

Answer:

f = 5 , g = - 3

Step-by-step explanation:

11f + 14g = 13 → (1)

11f + 10g = 25 → (2)

subtract (2) from (1) term by term to eliminate f

(11f - 11f) + (14g - 10g) = 13 - 25

0 + 4g = - 12

4g = - 12 ( divide both sides by 4 )

g = - 3

substitute g = - 3 into either of the 2 equations and solve for f

substituting into (1)

11f + 14(- 3) = 13

11f - 42 = 13 ( add 42 to both sides )

11f = 55 ( divide both sides by 11 )

f = 5

solution is f = 5 , g = - 3

Answer:

ned more info

Step-by-step explanation:

The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We are told that Matthew wants to estimate the mean height of students attending his college.

Now, let us say the total number of students in his college is x.

If he decides to select 100 students randomly to record their height, it means this 100 student is a sample out of the total number of students which is x that is the population.

In conclusion, we can say that the population of this research by Matthew is the total number of students that attend the college.

Hence, The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.

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The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

The equation can be simplified as follows:

7y + 8 = 9 + 3y + 2y

We have to combine like terms

Hence,

7y + 8  = 9 + 3y + 2y

7y + 8 = 9 + 5y

subtract 5y from both sides

7y - 5y + 8 = 9 + 5y - 5y

2y + 8 = 9

Let's subtract 8 from both sides

2y + 8 - 8 = 9 - 8

2y = 1

Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1

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Answer:

10/12

Step-by-step explanation:

We dont need to change the denominator, so we can just add 7 + 3 which is 10, so the answer is 10/12

Have a good day!

Answer:

-1/2f I think

Step-by-step explanation:

distribute the -1/2

use differentiation rules

calculate all together

then simplify

Hope this helps

If the company spends $8.25 on parts and $11.80 on labor, then the change in cost is -$6.

We need to use differentials to approximate the change in cost for the manufacturing of a calculator,

given M(x, y) = 20x² + 15y² - 10xy + 40, where x is the cost of parts and y is the cost of labor.

The current cost is $8 on parts and $12 on labor, and the new cost will be $8.25 on parts and $11.80 on labor.

First, compute the partial derivatives with respect to x and y.
dM/dx = 40x - 10y
dM/dy = 30y - 10x

Evaluate the partial derivatives at the current costs (x = 8, y = 12).
dM/dx(8, 12) = 40(8) - 10(12) = 320 - 120 = 200
dM/dy(8, 12) = 30(12) - 10(8) = 360 - 80 = 280

Find the change in x and y.
Δx = 8.25 - 8 = 0.25
Δy = 11.80 - 12 = -0.20

Use differentials to approximate the change in cost.
ΔM ≈ (dM/dx)(Δx) + (dM/dy)(Δy)
ΔM ≈ (200)(0.25) + (280)(-0.20) = 50 - 56 = -6

Approximately, the change in cost is -$6 if the company spends $8.25 on parts and $11.80 on labor.

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we determine if g(x) has a maximum and minimum on the set S, providing a proof or disproof. In part (c), we find the global maxima and minima of g(x) on S, if they exist. Finally, in part (d), we argue informally whether the sufficient conditions for maxima are satisfied by considering the properties of g(x).

We are given the set S = [-10, 10] and need to answer various questions related to the function g(x) defined on S. In part (a), we define the function g(x) with different expressions for x in different intervals, and then plot the function and analyze its continuity on S.

In part (b), we determine if g(x) has a maximum and minimum on the set S, providing a proof or disproof. In part (c), we find the global maxima and minima of g(x) on S, if they exist. Finally, in part (d), we argue informally whether the sufficient conditions for maxima are satisfied by considering the properties of g(x).

(a) The function g(x) is defined differently for two intervals within S. We plot the function on a graph and analyze its continuity. By evaluating the limits from the left and right at the point t, we can determine if g(x) is continuous at t and therefore continuous on the entire set S.

(b) To determine if g(x) has a maximum and minimum on S, we need to analyze the behavior of the function within the interval [-10, 10]. We consider the critical points and endpoints of S and examine whether g(x) attains its maximum and minimum values at any of these points.

(c) By examining the critical points and endpoints of S, we can find the global maxima and minima of g(x) if they exist. This involves evaluating the function g(x) at these points and comparing the values to determine the maximum and minimum values within the set S.

(d) To argue informally whether the sufficient conditions for maxima are satisfied, we consider properties such as differentiability, the sign of the derivative, and the behavior of the function near critical points. By analyzing these factors, we can determine if g(x) satisfies the conditions for having maxima within the set S.

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Answer:

Half of 21 in a radius is 10.5.

Answer:

21/2=10.5

Step-by-step explanation:

21/2

Answer: 532

Step-by-step explanation:

14% of 3800 is 532

In infinite series is that if the term of the series are not approaching to 0 then the series cannot possible to converging.Limit does not gives you information whether series will converge or diverge.

A series is said to be converge if it converges to a value as the terms of series tends to infinity. A series is said to diverge if it does not converge to a value but keeps on either increasing or decreasing as the terms of series tends to infinity.

By using the limit comparison test.

By divergent test

By absolutely convergent test

Divergence tests provide certain conditions for divergent series while convergence tests provide certain conditions for convergent series.

Now \(\lim_{n \to \infty} a_n\)\(\neq\)0

Then series divergent.

\(\lim_{n \to \infty} a_n\) =0

Then series may converge or diverge.

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Answer:

the answer is 579.768

Step-by-step explanation:

but I don't know if that's the correct answer

The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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9514 1404 393

Answer:

  168

Step-by-step explanation:

Below are shown the 7 different kinds of arrangements that can be made. Each of these can be permuted into 24 different arrangements by assigning colors in a different order than the one used here:

  {1, 2, 3, 4} ⇒ {green, blue, red, yellow}

Then the total number of possible correct colorings is 7·24 = 168.

__

These colorings were found using a computer program that identified all 168 viable colorings, then eliminated permutations. It started by identifying ways to color 2 rows, then adding rows based on that.

_____

You'll notice that the last on the attached list most closely matches the one in the problem statement.

Answer:

x=(2,-5.3)

Step-by-step explanation:

Hope this helps

The surface area is increasing at the rate of (60 x + 150) cm² per second.

Let the side of the cube be x cm.

s = x cm

Surface area of the cube will be:

S = 6 x² cm²

Now, we are given that, the side of the cube is expanding 5 cm per second.

So, the side of the cube after 1 second will be:

s' = x + 5 cm

Surface area will be:

S' = 6 (x + 5)² cm²

S' = (6x² + 150 + 60 x) cm²

Change in the surface area is:

ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²

ΔS = (60 x + 150) cm²

Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.

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Answer:

D (-3, 1)

Step-by-step explanation:

Answer: B 0.50

Step-by-step explanation:The probability P(number greater than 4) is (b) 0.50

How to determine the probability P(number greater than 4).

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

A fair, eight-sided number cube

This means that

Sample size = 8

Numbers greater than 4 = 4

The probability

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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