Allan built a doghouse and he wanted the house to have an area of 24 square feet. He also wanted the width to be 2/3 the length. What are the dimensions of the doghouse?

Answer:

triangular prism

Step-by-step explanation:

triangular prism is a prism in the shape of a triangle at 2 opposing faces

Answer:

that is a triangular prism

Answer:

2 hours 30 minutes = goal

Saturday = 1 hour 10 minutes

Sunday = 1 hour 15minutes

Total = 2 hours 25 minutes

No he will not meet his goal. He will be short 5 minutes of practice.

Explanatiory:

if I’m wrong, I’m sorry. If I’m right, mark me brainlest!

Answer:

ill see im on the yest rn

Step-by-step explanation:

The height of the building is approximately 1,984.44 feet.

To find the height of the building, we can use trigonometry. Let's assume the height of the building is represented by 'h' in feet.

From the given information, we know that the angle of elevation to the top of the building is 14° and the distance from the base of the building to the point of observation is 1.5 miles.

We need to convert the distance from miles to feet because the height of the building is in feet. Since 1 mile is equal to 5,280 feet, the distance from the base of the building to the observer is 1.5 * 5280 = 7,920 feet.

Now, we can set up the trigonometric relationship:

tan(angle of elevation) = height / distance

tan(14°) = h / 7,920

To solve for 'h', we can multiply both sides of the equation by 7,920:

h = 7,920 * tan(14°)

Calculating this using a calculator, we find:

h ≈ 1,984.44 feet

Therefore, the height of the building is approximately 1,984.44 feet.

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The answer is approximately 45.82%, which is closest to 41.2% which is calculated using the binomial distribution formula.

To solve this problem, we can use the binomial distribution formula, which is:

\(P(X ≤ k) = Σ^n_i=0 (n choose i) p^i (1-p)^(n-i)\)

Where:

X= number of senior adults who wear glasses for driving

k= maximum number of senior adults who wear glasses for driving that we're interested in (in this case, 16)

total number of senior adults in the group (in this case, 20)

p =probability that a senior adult wears glasses for driving (in this case, 0.81)

We want to find P(X ≤ 16), which represents the probability that no more than 16 senior adults wear glasses for driving.

Using the formula above, we get:

\(P(X ≤ 16) = Σ^20_i=0 (20 choose i) 0.81^i (1-0.81)^(20-i)\)

Calculating this sum exactly can be quite tedious, but we can use a normal approximation to get an estimate.

Utilizing the mean (np = 20*0.81 = 16.2) and the standard deviation (sqrt(np(1-p)) = 1.94) of the binomial dissemination, able to surmise the likelihood utilizing the ordinary dissemination as taken after:

P(X ≤ 16) ≈ P(Z ≤ (16 - 16.2)/1.94) 

Where Z =standard normal random variable.

Using a standard normal distribution table or a calculator, we can find that:

P(Z ≤ (16 - 16.2)/1.94) ≈ P(Z ≤ -0.103)

≈ 0.4582

hence, the answer is approximately 45.82%, which is closest to 41.2%.

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2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.

Step 1: Calculate the mean of the data set

The given data set is: 22, 28, 30, 28, 35, 30, 28

The mean is calculated by adding up all the numbers and dividing by the total number of values:

Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)

Step 2: Calculate the absolute deviations

The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:

|22 - 28.71| = 6.71

|28 - 28.71| = 0.71

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

|35 - 28.71| = 6.29

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

Step 3: Calculate the MAD

The MAD is the mean of the absolute deviations:

MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)

Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.

Difference = 31 - 28.71 = 2.29

Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

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Answer:

\(N + Q = 32\) and \(.05N + .25Q = 3.00\)

Step-by-step explanation:

Given that there is a collection of nickels and quarters.

Let N be the number of coins of nickels and

Q be the number of coins of quarters.

It is given that total number of coins are 32.

Number of coins of nickels + Number of coins of quarters = 32

\(\therefore \bold{N+Q=32}\) is the first equation.

Now, we know that value of a one quarter coin is 25 cents or \(\$\frac{25}{100} = \$0.25\)

and value of a one nickel coin = 5 cents = $0.05

Total value of all nickel coins = Number of nickel coins \(\times\) value of one nickel coin = \(.05N\)

Similarly,

Total value of all quarter coins = Number of quarter coins \(\times\) value of one quarter coin = \(.25Q\)

Total value of coins is 3 dollars.

\(\therefore \bold{.05N + .25Q = 3.00}\) is the second equation.

So, the answer is:

\(N + Q = 32\) and \(.05N + .25Q = 3.00\)

The determinant of the given 3 × 3 matrix [12.2, 13.3, 9; 1, -4, -17; 21.4, -15, 0] is -2835.4.

To evaluate the determinant of a 3 × 3 matrix, we can use the formula:

det(A) = a(ei - fh) - b(di - fg) + c(dh - eg),

where a, b, and c represent the elements of the first row, and d, e, and f represent the elements of the second row.

In this case, the matrix is:

[12.2, 13.3, 9;

1, -4, -17;

21.4, -15, 0].

Using the formula, we can calculate the determinant as follows:

det(A) = 12.2((-4)(0) - (-15)(-17)) - 13.3((1)(0) - (21.4)(-17)) + 9((1)(-15) - (21.4)(-4)).

Simplifying the expression, we get:

det(A) = 12.2(255) - 13.3(363.8) + 9(-59.4).

Evaluating the expression, we find that:

det(A) = -2835.4.

Therefore, the determinant of the given matrix is -2835.4.

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We should use minimum of 8 classes.

To calculate the minimum number of classes, we will use the rule of thumb given by Sturges, which states that the number of classes in a histogram should be selected using the following formula:

\(\[\large k=1+\log _{2}n\]\)

Where k represents the number of classes and n is the total number of observations.

Using this formula, we can calculate the minimum number of classes as follows:

\(\[\large k=1+\log _{2}n\]\)

Substituting the values given in the problem statement, we get:

\(\[\large k=1+\log _{2}(69)\]\)

Using logarithm rules, we can simplify this expression as:

\(\[\large k=1+\frac{\ln 69}{\ln 2}\]\)

Evaluating this expression using a calculator, we get:

\(\[\large k\approx 7.8\]\)

Since the number of classes must be a whole number, we should round up to the next integer to get the minimum number of classes.  

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Answer:

-10

Step-by-step explanation:

-8 + n/2 = -13

n/2 = -13 + 8

n/2 = -5

n = -5 * 2

n = -10

Hope it helps!

Answer:

\(5pqr-2qr+pq-pr\)

Step-by-step explanation: It seems as though something is missing from this question... Perhaps the values of the variables (P, Q, R)?

If not, I was able to get this answer by combining like terms. Without numbers, that is as far as you can go!

Hope this helps!

Answer:

Rate of interest (R) = 6.5 % per year

Step-by-step explanation:

Given:

Amount borrow(P) = $2300

Amount (A) = $2748.50

Number of month(T) = 36 month = 3 year

Find:

Rate of interest (R)

Computation:

Simple interest (I) = Amount (A) - Amount borrow(p)

Simple interest (I) = $2748.50 - $2300

Simple interest (I) = $448.50

Simple interest (I) = PRT

$448.50 = ($2300)(R)(3)

0.065 = R

Rate of interest (R) = 6.5 % per year

The rate of interest that should be charged is 6.5%.

Given that,

Based on the above information, the calculation is as follows:

Simple interest = Amount - Amount borrow

= $2748.50 - $2300

= $448.50

Now  

Simple interest  = PRT

$448.50 = ($2300)(R)(3)

0.065 = R

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The value of one share today is $18.39.

Annual growth rate for two years is 20% i.e. g = 20% Dividend growth decreases to 8% for the next two years i.e. g1 = 8% and it is 4% thereafter i.e. g2 = 4%Current dividend = $2.

Required rate of return = 15%To calculate the value of one share, we need to use the Gordon Growth Model.D1 = D0 (1+g) Where,D0 = Current dividendg = Annual growth rateD1 = Dividend after one yearD1 = 2(1+20%) = $2.4 (Dividend growth rate of 20%).

For the next year, i.e., year 2, the dividend growth rate will be 20%.D2 = D1 (1+g)D2 = 2.4(1+20%) = $2.88Using the Gordon Growth Model,V0 = (D1) / (k-g)Where,k = Required rate of returng = Growth rateV0 = (2.88) / (15%-20%) = -$57.60

This value is not acceptable, since it is negative. This happened because the growth rate is greater than the required rate of return.

This means the growth rate is unsustainable.In order to solve this issue, we need to use the dividend growth model, where different growth rates can be used for different time periods.

Gordon Growth Model is used to calculate the intrinsic value of a stock based on a future series of dividends that grow at a constant rate.

The value of a share today is calculated based on the future dividends, so it is important to project the future dividends and discount them back to the present value.

So, we will use the dividend growth model for three years and then apply Gordon Growth Model.Value of Dividend at the end of Year 3,D3 = D2 (1+g2)D3 = 2.88 (1+4%) = $2.9984 (8% for two years and 4% for 3rd year).

Value of Dividend at the end of Year 2,D2 = D1 (1+g1)D2 = 2.4 (1+8%) = $2.592 (20% for two years)Value of Dividend at the end of Year 1,D1 = D0 (1+g)D1 = 2 (1+20%) = $2.4 (20% for first year).

Now we can apply the Gordon Growth Model,V3 = D4 / (k-g2)V3 = 2.9984 / (15%-4%) = $26.88Now we need to discount it to the present value,V0 = V3 / (1+k)^nWhere,n = number of yearsV0 = 26.88 / (1+15%)^3V0 = $18.39Hence, the value of one share today is $18.39.

Therefore, the correct option is b) $18.39.

In this question, we are required to calculate the value of one share today with given data.

To calculate the value of one share, we need to use the Gordon Growth Model, which is used to calculate the intrinsic value of a stock based on a future series of dividends that grow at a constant rate.

The annual growth rate for two years is 20% i.e. g = 20%. Dividend growth decreases to 8% for the next two years i.e. g1 = 8% and it is 4% thereafter i.e. g2 = 4%. The current dividend is $2 and the required rate of return is 15%.We first calculated the dividend for year 1, which is $2.4. Using this, we calculated the dividend for year 2, which is $2.88. But, the value of share calculated using the Gordon Growth Model was negative.

This happened because the growth rate was greater than the required rate of return. This means the growth rate was unsustainable.
To solve this, we used the dividend growth model, where different growth rates can be used for different time periods. Using this model, we calculated the value of dividend at the end of year 3, year 2, and year 1.

The value of dividend at the end of year 3 was $2.9984.Using this value, we applied the Gordon Growth Model to calculate the intrinsic value of a share, which is $26.88.

To calculate the present value of this share, we discounted it to the present value using the formula V0 = V3 / (1+k)^n, where n is the number of years.

On substituting the values, we got the value of one share today, which is $18.39. Hence, the correct option is b) $18.39.

Hence, the value of one share today is $18.39.

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Answer:

$16200

Step-by-step explanation:

24 times 350=8400

8400+7000+800

Answer:

x=-7 y=-2x²-4x-5

Step-by-step explanation:

the first one is: The value of 1 in carmen's number is 3 times the value the value of the 1 in michelles's number

and the second is:

The width of the enlarged photo is 12 inches

The length of the original photo = 10 inches

The width of the original photo = 8 inches

The length of the enlarged photo = 15 inches

The width of the enlarged photo = x

Then the proportion of the length and width of the original and enlarged photo will be

10 / 8 = 15 / x

Cross multiply the terms

10x = 15 × 8

Multiply the terms in the equation
10x = 120

Divide both side of the equation by 10

10x / 10 = 120 / 10

x = 120 / 10

Divide the terms

x = 12 inches

Hence, the width of the enlarged photo is 12 inches

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The points are K(0, 6), L(-8, 0), J(9, 4).

Given that is a coordinate plane with Points K, L, J we need to determine the location of the points,

So,

You require the point's coordinates, which are made up of an x-coordinate (horizontal) and a y-coordinate (vertical), in order to label it on a coordinate plane.

So, Point K is at 6 units upwards from the origin so the point (0, 6) the x-intercept is zero.

Point L is 8 units vertically left side so the point is (-8, 0) here the y-intercept is zero.

Point J is 9 units vertically right side and 4 units upwards so the point is (9, 4).

Hence the points are K(0, 6), L(-8, 0), J(9, 4).

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Answer: 112

Step-by-step explanation:

88 x 88 = 7744

7744 x 99 = 766656

766656 x 104 = 79732224

79732224 x 378= 30138780672

Well you get the idea

The standard matrix for the linear transformation can be obtained by applying the transformation to the standard basis vectors. Additionally, an explicit formula for the transformation can be derived by observing the pattern in how the transformation operates on the basis vectors.

To determine the determinant of the linear transformation, we need to compute the determinant of its standard matrix. The standard matrix is obtained by applying the transformation to the standard basis vectors [1, 0] and [0, 1], and arranging the resulting vectors as columns. Let's denote the resulting vectors as [a, b] and [c, d]. The standard matrix for the transformation is then [[a, c], [b, d]]. The determinant of this matrix, denoted as det(A), provides the determinant of the linear transformation.

To find the explicit formula for the linear transformation, we examine how it operates on the basis vectors [1, 0] and [0, 1]. By applying the transformation, we obtain [a, b] and [c, d] respectively. From this pattern, we can deduce the formula for the transformation as T(x, y) = [ax + by, cx + dy], where a, b, c, and d are the entries of the standard matrix.

In summary, the determinant of the linear transformation is given by det(A), where A is the standard matrix. The standard matrix is obtained by applying the transformation to the standard basis vectors, and the explicit formula for the transformation is T(x, y) = [ax + by, cx + dy].

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Answer:

The length is 15.71 feet.

Step-by-step explanation:

The head coach trainer claims that the percentage of football injuries occurring during practices is too high for his conference.

To test the claim, we can use a hypothesis test. The null hypothesis (H₀) would state that the percentage of football injuries occurring during practice is not significantly different from the reported national percentage of 57.6%. The alternative hypothesis (H₁) would state that the percentage is indeed different from 57.6%.

Using the given sample data, we can calculate the sample proportion of injuries occurring during practice as 17/36 = 0.4722. To determine if this proportion significantly differs from 57.6%, we can perform a hypothesis test using the z-test for proportions.

After obtaining the z-score, we can interpret it by comparing it to the critical value. If the z-score falls in the critical region (beyond the critical value), we reject the null hypothesis and conclude that there is evidence to support the claim made by the head coach trainer.

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Answer:

9

Step-by-step explanation:

you have to plug in the numbers and solve it, so it would go as follows:

-(-3^2)- 2(-5)(2) - /2/

-9 + 20 - 2 =

9

i hope this helps

The reflection of angle K across the line y = 2 results in angle K' with the same measure of 83 degrees.

When an angle is reflected across a line, its measure remains the same. The reflection only changes the position of the angle, not its size.

In this case, we have angle K with a measure of 83 degrees, and it is reflected across the line y = 2 to obtain angle K'.

To determine the measure of angle K', we need to understand how the reflection affects the position of the angle.

The line y = 2 represents a horizontal line at the y-coordinate of 2. When angle K is reflected across this line, it will be flipped over the line while maintaining its measure.

Since the line of reflection is horizontal, the measure of angle K' will be the same as angle K.

Therefore, the measure of angle K' is also 83 degrees.

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Answer:

\(m\angle 1 = 40^\circ\)

Step-by-step explanation:

First, notice that the two lines are parallel as indicated by the arrow.

Therefore, by the Alternate Interior Angles Theorem:

\(\angle 1\cong \angle 2\)

So:

\(m\angle 1 = m\angle 2\)

Substitute:

\((2x+20)=(3x+10)\)

Solve for x. Subtract 2x from both sides:

\(20=x+10\)

And subtract 10 from both sides:

\(x=10\)

We know that:

\(m\angle 1 = 2x+20\)

Substitute. Hence:

\(m\angle 1 =2(10)+20=40^\circ\)

The general solution of the system is: x = x (free parameter), y = (7/2)x, and z = -(3/2)x. This represents the set of all solutions to the system of equations.

To find the general solution of the system represented by the augmented matrix, we can perform row operations to bring the matrix to its reduced row-echelon form (RREF). The RREF will reveal the solution of the system.

Let's work through the row operations step by step:

Row 2 = Row 2 - 2 × Row 1

Row 3 = Row 3 - 4 × Row 1

The new augmented matrix after the first row operation:

[ 2 -7 3 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Next, divide Row 1 by 2:

Row 1 = Row 1 / 2

The updated augmented matrix:

[ 1 -7/2 3/2 0 ]

[ 0 0 0 0 ]

[ 0 0 0 0 ]

Now, we can see that the second and third rows consist of all zeros. This indicates that the system has infinitely many solutions.

To express the general solution, we can assign a parameter to one of the variables (let's choose x):

x = Free parameter

Then, we can express the other variables in terms of x:

y = (7/2)x

z = - (3/2)x

Therefore, the general solution of the system is:

x = x (free parameter)

y = (7/2)x

z = -(3/2)x

This represents the set of all solutions to the system of equations. By assigning different values to the parameter x, we can obtain infinitely many solutions.

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There are a total of 2,598,960 ways to deal 5 cards to each of the five players in a game of poker.

To calculate the number of ways to deal the cards, we can use the concept of combinations. In this case, we need to determine the number of combinations of 5 cards from a deck of 52 cards.

The number of combinations can be calculated using the formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen.

In this scenario, there are 52 cards in the deck, and each player is dealt 5 cards. So, we need to calculate C(52, 5) for each player. Since there are five players, we multiply the result by 5.

Therefore, the total number of ways to deal 5 cards to each of the five players is C(52, 5) = (52! / (5! * (52 - 5)!)) = 2,598,960.Hence, there are 2,598,960 ways to deal the cards in a game of poker when each of the five players is dealt 5 cards from a 52-card deck.

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Answer:

9890

Step-by-step explanation:

khkyuyukrfqz

Answer:

1st one is yes

2nd no

3rd no

Step-by-step explanation: