. . Roulette: In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, 3, 4, .., 36. The odd-numbered slots are Red, and even-numbered slots are black. The numbers are green. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. What is the probability that the metal ball does not land on green? (leave the answer as a simplified fraction like 4/5)

There are either approximately 1.8 million or 102 million ways to select a committee of 10 senate members with the same number of Ds and Rs, depending on the method used.

We will use the concept of combinations to find the number of ways to select a committee of 10 Senate members with the same number of Democrats (Ds) and Republicans (Rs).

1. Determine the number of Democrats and Republicans to select: Since the committee must have the same number of Ds and Rs, we need to select 5 Democrats and 5 Republicans.

2. Calculate the combinations: Use the combination formula, which is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items, and k is the number of items to select.

3. Apply the formula for Democrats: Assuming there are D Democrats, the number of ways to select 5 Democrats would be C(D, 5) = D! / (5! * (D-5)!).

4. Apply the formula for Republicans: Assuming there are R Republicans, the number of ways to select 5 Republicans would be C(R, 5) = R! / (5! * (R-5)!).

5. Calculate the total ways: Multiply the number of ways for both Democrats and Republicans to get the total ways of forming the committee: Total ways = C(D, 5) * C(R, 5).
To select a committee of 10 with an equal number of Ds and Rs, we need to choose 5 Ds and 5 Rs. We can do this in the following ways:
- Choose 5 Ds from the 25 available, and then choose 5 Rs from the remaining 20. This can be done in (25 choose 5) * (20 choose 5) ways, which is approximately 1.8 million ways.
- Alternatively, we can choose 10 senators from the 50 available, and then assign 5 to be Ds and 5 to be Rs. The number of ways to do this is (50 choose 10) * (10 choose 5), which is approximately 102 million ways.

So, the number of ways to select a committee of 10 Senate members with the same number of Democrats and Republicans is given by the product of the combinations C(D, 5) and C(R, 5).

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The number of years that the glory days of the cowboy period lasted was about 2 decades.

The glory days of the cowboy times is typically deemed as the span between the conclusion of the Civil War in 1865 to around the dawn of the1900s. During these years, cowboys played an indispensable role in boosting and improving the American West peculiarly in the cattle industry.

With bravery and courage, they would drive a herd of cattle across wide expanses frequently grappling with harsh conditions and situations of peril. The genesis of industrialization phased out the cowboy era with train networks expediting the transportation of both bovine species and freight with efficiency.

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Answer: $8.40

Step-by-step explanation: Fairly simple, 2/4=1/2, so half of sixteen is eight and then you add the .40, which you should get 8.40 dollars

The statement is true, under certain conditions.

If fx(a, b) and fy(a, b) both exist and are continuous at (a, b), then f is differentiable at (a, b). In other words, if the partial derivatives of f with respect to x and y both exist and are continuous at (a, b), then f is differentiable at (a, b).

The differentiability of f at (a, b) means that there exists a linear transformation T such that:

f(a + h, b + k) = f(a, b) + fx(a, b)h + fy(a, b)k + ε(h, k)

where ε(h, k) is a function that goes to zero faster than (h, k) as (h, k) goes to (0, 0). In other words, ε(h, k) satisfies:

lim(h,k)→(0,0) ε(h, k) / ||(h, k)|| = 0

The linear transformation T is given by:

T(h, k) = fx(a, b)h + fy(a, b)k

In this sense, the partial derivatives of f measure the sensitivity of the function to changes in the x and y directions at (a, b), respectively. If both partial derivatives exist and are continuous, then f is well-behaved enough to be approximated by a linear function at (a, b), which is the definition of differentiability.

However, if one or both of the partial derivatives are not continuous at (a, b), then f may still be continuous at (a, b), but it will not be differentiable at (a, b).

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Answer: &1,552.50

Step-by-step explanation: Step 1: Multiply Shaquana and Briana deposits of $230 times both interest rates.
Step 2: Shaquana dollar amount adds up to $1006.25. Brianna’s dollar amount adds up to $1,092.50.
Step 3: Multiply both totals times 18yrs.
Step 4: Subtract 18,112.50 from 19,665 and you find that Brianna will have $1552.50 more than Shaquana.

Brianna would have $290 more in her account than Shaquana after 18 years.

The final amount in Shaquana's account is:

[tex]A=230e^0^.^0^4^3^7^5^\times^1^8[/tex]

[tex]A=230e^0^.^7^8^7^5[/tex]

A=230×1.082

= $249

For Brianna, we have:

P = $230

r = 4.75% / 12 = 0.0039583333

t = 18 × 12 = 216 months

So, the final amount in Brianna's account is:

A = $230×(1 + 0.0039583333)²¹⁶

A=230(1.00395)²¹⁶

A=230×2.34

A=538.2

Therefore, the difference in the final amounts is:

$538.2 - $249= $289.2

So, Brianna would have $290 more in her account than Shaquana after 18 years.

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If the probability that a tire has an expected life of at least 30000 miles is 0.85, then the probability that a tire will have a life of less than 30000 miles is 0.15.

Using this information, we can find the probability that among 20 tires, a certain number will have a life of less than 30000 miles. This can be done using a binomial distribution, where the probability of success (a tire having a life of at least 30000 miles) is p = 0.85 and the number of trials is n = 20.

The probability of having k tires with a life of less than 30000 miles is given by the formula:

[tex]P(k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where (n choose k) represents the number of ways to choose k items out of n, and is calculated by the formula:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can find the probabilities of having 0, 1, 2, ..., 20 tires with a life of less than 30000 miles.

For example, the probability of having exactly 3 tires with a life of less than 30000 miles is:

P(3) = (20 choose 3) * 0.85^17 * 0.15^3

= 1140 * 0.085 * 0.003375

= 0.02736

Similarly, we can find the probabilities of having any other number of tires with a life of less than 30000 miles.

Note that the sum of all these probabilities is equal to 1, since one of these outcomes must occur.

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To prove that DE is parallel to FB, we can use the property that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

We can see triangles AED and CFB with DE and FB as their respective midsegments. Then, we can show that these triangles are similar and that their corresponding sides are proportional. This will imply that DE and FB are parallel.

Proof:

ABCD is a parallelogram, E is the midpoint of AB and F is the midpoint of DC.

Given

Construct triangles AED and CFB with DE and FB as their midsegments, respectively.

Definition of midsegment

AE = ED and CF = FB

Given that E and F are midpoints

AD = BC

Opposite sides of a parallelogram are congruent

∠AED = ∠DCF

Opposite angles of a parallelogram are congruent

∠ADE = ∠CDB

Alternate interior angles formed by parallel lines and a transversal

Triangles ADE and CFB are similar

By angle-angle similarity (AA)

AD/CF = DE/FB

Corresponding sides of similar triangles are proportional

Substituting AD = BC and simplifying, we get:

BC/CF = DE/FB

Since CF = FB (given), we have:

BC/FB = DE/FB

Therefore, BC = DE

Since the corresponding sides of similar triangles are proportional, we can equate BC/CF and DE/FB to get this result.

Hence, DE is parallel to FB

If a line segment joining the midpoints of two sides of a triangle is parallel to the third side, then it is half its length.

Therefore, DE is parallel to FB, as required.

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The trigonometric identity cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x

A trigonometric identity is a mathematical expression that contains trigonometric ratios.

To prove that : cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = sin²x + 1 ​, we proceed as follows

We need to show that Left hand side L.H.S = right hand side R.H.S

Now

So, substituting the values of the variables into the equation, we have that

L.H.S = Cos²(180 - x) + 2CosxCos(90 + x)tan(360 - x) = (-Cosx)² + 2Cosx(-sinx)(-tanx)

= (Cosx)² + 2Cosxsinxtanx

Now tanx = sinx/cosx,

So, substituting the values of the variables into the equation, we have that

(Cosx)² + 2Cosxsinxtanx = (cosx)² + 2cosxsinxsinx/cosx

= cos²x + 2sin²x

= cos²x + sin²x + sin²x

Now the trigonometric identity cos²x + sin²x = 1.

So, we have that

cos²x + sin²x + sin²x = 1 + sin²x = R.H.S

So, cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x

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We can be 95% confident that the true average insulin-binding capacity of the group receiving the low dose is between(0.306 and  1.054). units higher than the group receiving the high dose.

To calculate the 95% confidence interval for the difference in the true average insulin-binding capacity between the two groups of diabetic rats, we will use the t-distribution formula for independent samples.

First, we need to calculate the pooled variance (Sp^2) and the standard error (SE) of the difference:

Sp^2 = [(n1 - 1) * s1^2 + (n2 - 1) * s2^2] / (n1 + n2 - 2)
Sp^2 = [(8 - 1) * 0.51^2 + (13 - 1) * 0.35^2] / (8 + 13 - 2)
Sp^2 ≈ 0.2149

Sp = sqrt(Sp^2) ≈ 0.4635

SE = sqrt[(Sp^2 / n1) + (Sp^2 / n2)]
SE ≈ sqrt[(0.2149 / 8) + (0.2149 / 13)] ≈ 0.1787

Next, we need the t-value for a 95% confidence interval with n1 + n2 - 2 degrees of freedom. For 19 degrees of freedom, the t-value is approximately 2.093.

Now, we can calculate the confidence interval:

CI = (x1 - x2) ± t * SE
CI = (1.98 - 1.30) ± 2.093 * 0.1787
CI = 0.68 ± 0.374

Therefore, the 95% confidence interval for the difference in the true average insulin-binding capacity between the two samples is approximately (0.306, 1.054).

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The solution of the equation is determined as;

1. p = 0 or - 6.

2. x = -7 twice

3. k = -7 or 4

4. r = 1 or 8

5. m = -3/2 or -5.

6. m = 4/3 or -8

The expression can be factorized as follows;

1. p² = -6p

p(p + 6) = 0

p = 0 or p + 6 = 0

p = 0 or - 6

2. x² = -49 - 14x, factorize as follows;

put the both constant and variables on one side;

x² + 14x + 49 = 0

(x + 7)(x + 7) = 0

x = -7 twice

3. k² - 28 = -3k, factorize as follows;

k² + 3k - 28 = 0

k² + 7k - 4k - 28 = 0

(k + 7)(k - 4) = 0

k = -7 or 4

4. r² = 9r - 8, factorize as follows;

r² - 9r + 8 = 0

r² -r - 8r = 0

(r - 1)(r - 8) = 0

r = 1 or 8

5. 2m² + 13m + 15 = 0, factorize as follows;

2m² + 3m + 10m + 15 = 0

(2m + 3)(m + 5) = 0

2m = -3 or m = -5

m = -3/2 or -5

6. 3m² + 20m - 32 = 0, factorize as follows;

3m² - 4m + 24 m - 32

(3m - 4)(m + 8) = 0

3m = 4 or m = -8

m = 4/3 or -8

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To solve this problem, we'll need to use vector addition and trigonometry. Let's start by defining our variables:

Let v be the velocity of the plane relative to the air.
Let w be the velocity of the wind.
Let s be the speed of the plane relative to the ground.
Let θ be the angle between the plane's heading and the true north.

(a) We know that the plane's speed relative to the ground is s, and its speed relative to the air is v. We can use vector addition to find the velocity of the plane relative to the ground in terms of v and w:

s = ||v + w||

where ||v + w|| represents the magnitude (or speed) of the vector v + w. We can also use trigonometry to find the angle between the plane's heading and the true north:

θ = se - tan^-1(w/v)

where tan^-1 is the inverse tangent function.

From here, we can use some basic trigonometry to solve for v in terms of s and θ:

v = s*cos(θ)

and w in terms of v and s:

w = (v + s*cos(θ))/tan(θ)

(b) To find the true velocity of the plane in terms of v and w, we need to subtract the velocity of the wind from the velocity of the plane relative to the air:

v_true = v - w

(c) To find the velocity of the wind in terms of v and w, we can rearrange the equation for w:

w = (v + s*cos(θ))/tan(θ)

to solve for w:

w = (v/tan(θ)) + s*cos(θ)/tan(θ)

Then, we can substitute v_true for v to get:

w = (v_true/tan(θ)) + s*cos(θ)/tan(θ)

Finally, we can round the speed of the wind to the nearest whole number:

speed of the wind ≈ ||w|| ≈ ||(v_true/tan(θ)) + s*cos(θ)/tan(θ)||

Note that we don't have actual values for s, θ, v, or w, so we can't compute an actual answer. However, this is the general method you would use to solve the problem.
To represent the terms you provided.

(a) The velocity of the plane relative to the air is Vp_a = (Vp_t - Vw) with a bearing of θ.

(b) The true velocity of the plane is Vp_t = (Vp_a + Vw) with a bearing of φ.

(c) The velocity of the wind is Vw = (Vp_t - Vp_a) with a bearing of (φ - θ). To find the speed of the wind, calculate the magnitude of Vw and round to the nearest whole number.

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Sarah, Tony, and Megan are helping their parents plan the layout of the backyard, the correct expression would be: 2[tex]x^2[/tex] + 12x + 25. The correct option is A.

We must add the areas of the patio, pool, and fire pit in order to obtain the expression that denotes the entire backyard.

The patio's area is as follows given that it is 5 feet long and as wide as the fire pit:

Patio space is calculated as follows: 5 * 5 (5 feet by 5 feet)

The fire pit has dimensions of 6 feet by 2x feet. Therefore, the area of the fire pit is:

Fire pit area = width * length = 6 * (2x) = 12x square feet

Now, we can add the areas together to get the expression for the total backyard area:

Total backyard area = Patio area + Pool area + Fire pit area

Since the dimensions of the pool are not provided, we cannot include it in the expression. Therefore, the correct expression would be:

2[tex]x^2[/tex] + 12x + 25

Thus, the correct option is a.

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The linear pattern between Shops and Crimes is established through the visible increasing trend formed by data points within the scatterplot.

This is further reinforced by the noteworthy clustering of evidence along the least squares line, implying an undeniable relationship exists between the number of coffee shops and cases of reported property crime in these counties.

Moreover, the correlation coefficient, at 0.94, strongly accentuates the strong positive link that has been deduced between both external and internal variables. .

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The graph of Chloe's temperature of the day is plotted

Given data ,

To graph Chloe's data, we can use a line graph with time (in hours) on the x-axis and temperature (in degrees Fahrenheit) on the y-axis. Here is the graph:

The graph has five line segments:

From 6 a.m. to 8 a.m., the temperature rises from 54°F to 58°F. This is a line with a slope of 2/2 = 1, passing through the points (6, 54) and (8, 58).

From 8 a.m. to 12 p.m., the temperature rises from 58°F to 70°F. This is a line with a slope of 3/4, passing through the points (8, 58) and (12, 70).

From 12 p.m. to 2 p.m., the temperature stays at 70°F. This is a horizontal line passing through the point (12, 70).

From 2 p.m. to 4 p.m., the temperature drops from 70°F to 68°F. This is a line with a slope of -1/2, passing through the points (2, 70) and (4, 68).

From 4 p.m. to 12 a.m., the temperature drops from 68°F to 63°F. This is a line with a slope of -5/8, passing through the points (4, 68) and (12, 63).

Hence , the graph is plotted

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The percentage of the females in grade 11 and 12 is 60%. Option C

A number can be expressed as a fraction of 100 using a percentage. The letter "%" stands for it. To find a percentage, divide the value under consideration by all possible values, then multiply the result by 100.

Females in grade 11 can be obtained from;

Number of students in grade 11 = 27 + 50

Percentage of female students = 50/27 + 50 * 100/1

= 65%

Females in grade 12;

Number of students in grade 12= 37 + 61

Percentage of female students in grade 12 = 61/37 + 61 * 100

= 62%

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The statement is false.

In fact, the correct statement is the opposite: if the linear transformation T(x) = Ax is one-to-one, then the columns of A form a linearly independent set.

To see why, suppose that T(x) = Ax is one-to-one, which means that for any two distinct vectors x1 and x2, we have T(x1) = Ax1 and T(x2) = Ax2, and Ax1 ≠ Ax2. This implies that x1 ≠ x2, since if x1 = x2, then we would have Ax1 = Ax2, which contradicts the assumption that Ax1 ≠ Ax2.

Now suppose that the columns of A are linearly dependent, which means that there exist scalars c1, c2, ..., cn, not all zero, such that c1a1 + c2a2 + ... + cnan = 0, where a1, a2, ..., an are the columns of A. Then we can rewrite this equation as A(c1e1 + c2e2 + ... + cnen) = 0, where e1, e2, ..., en are the standard basis vectors. Since not all of the ci's are zero, there exists a non-zero vector c = (c1, c2, ..., cn) such that Ac = 0. But this means that T(c) = Ac = 0, which contradicts the assumption that T(x) is one-to-one, since c ≠ 0 but T(c) = 0. Therefore, the columns of A must be linearly independent if T(x) = Ax is one-to-one.

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Answer:

[tex]7 \times 5 \times 9 = 315[/tex]

The volume of this rectangular prism is 315 cubic units.

The amount more that the Penders budgeted for transportation than they spent on transportation is $ 3.30.

Looking at the Budget presented by the Penders, we see that they budgeted for Gasoline and Parking to the tune of :

= 85 + 70

= $ 155

The Penders however spent a different amount on transport to the tune of :

= 101. 70 + 50

= $151. 70

This then means that they spent less than they budgeted for transport and the difference was :

= 155 - 151. 70

= $ 3.30

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The dimensions of the actual painting are 32 inches by 40 inches.

option B.

The dimensions of the actual painting is calculated as follows;

scale factor = actual size/scaled size

4/1 = actual size/scaled size

Cross-multiply;

actual size = 4 x scale size

The actual sizes of 8 inches by 10 inches is calculated;

actual sizes = 4 x 8 inches, and 4 x 10 inches

actual sizes = 32 inches by 40 inches

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This value represents the greatest distance between the particle and the origin during the time interval [0, 3].

To find the greatest distance between the particle and the origin during the time interval [0, 3], we need to find the position function of the particle, differentiate it to find the velocity function and analyze the critical points.

Let x(t) be the position function of the particle. Unfortunately, you haven't provided the specific position function, so I will use a generic one: x(t) = at^3 + bt^2 + ct + d. You'll need to substitute your given function here.

Step 1: Find the velocity function by differentiating the position function with respect to time:
v(t) = dx(t)/dt = 3at^2 + 2bt + c

Step 2: Find the critical points by setting the velocity function equal to zero and solving for t:
0 = 3at^2 + 2bt + c      
   
Step 3: Analyze the critical points and endpoints of the given interval [0, 3] by plugging them into the position function x(t):
x(0), x(t1), x(t2), and x(3) (where t1 and t2 are the critical points found in step 2)

Step 4: Determine which of these values corresponds to the greatest distance from the origin. Remember that distance is always positive, so take the absolute value of the positions if necessary.

The answer will be the largest absolute value among the positions x(0), x(t1), x(t2), and x(3). This value represents the greatest distance between the particle and the origin during the time interval [0, 3].

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The surface area of the rectangle is 216 square feet.

In the given rectangle length is 6 ft, width is 2 ft and height is 12 ft

Surface face area = 2(lb+bh+hl)

l is length , b is breadth and h is height

Surface area = 2(6×2 + 2×12 + 12×6)

=2(12+24+72)

=2(108)

= 216 square feet

Hence, the surface area of the rectangle is 216 square feet.

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Answer:

i think the answer will be a horizontal line

The area of the parallelogram in the middle of the shape would be 6 units ²

The area of a parallelogram can be found by the formula :
= Base x Height

We can find the base of the parallelogram in the middle of the shape to be :

= Base of Parallelogram 1 - Base of Parallogram 2

= 5 - 3

= 2

The height would be:

= Height of Parallelogram 2 - Height of Parallogram 1

= 6 - 3

= 3

The area of the parallelogram is:

= 2 x 3

= 6 units ²

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A) True.

Verification is the process of determining whether a computational model accurately represents the real-world system it is intended to simulate.

Verification is an important step in the process of developing and evaluating computational models. The goal of verification is to determine whether a model is accurately representing the real-world system it is intended to simulate. This is important because if a model is not accurate, it can lead to incorrect predictions and decisions.

Verification involves comparing the output of a computational model with experimental data collected from the real system. This comparison can take many forms, depending on the type of model and the nature of the experimental data. In some cases, the comparison may involve a direct quantitative comparison between the model output and the experimental data. In other cases, the comparison may be more qualitative, involving an assessment of whether the model output captures the key features of the experimental data.

The process of verification can be iterative, involving multiple rounds of model refinement and comparison with experimental data. This is particularly important for complex systems, where small errors or uncertainties in the model can have significant impacts on the accuracy of the predictions.

Overall, verification is an important step in the process of model development and evaluation, helping to ensure that computational models are accurate and reliable tools for predicting real-world behavior.

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Given bakery can offer 27 distinct types of breakfasts.

The number of pastries available must be multiplied by the number of beverages available in order to determine how many distinct breakfast options are available at the bakery.

The overall amount of varied breakfast options is nine pastries and three beverage selections.

3 drinks plus 9 pastries equal 27 distinct breakfast options.

As a result, the bakery offers 27 distinct breakfast options.

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The standard error of the proportion decreases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population proportion.

To calculate the standard error of the proportion, we can use the formula:
SE = √(p(1-p)/n)
Where:
SE = standard error
p = proportion of the population
n = sample size
For each sample size, we can plug in the values and calculate the standard error:
A. For a sample size of 30:
SE = √(0.39(1-0.39)/30) = 0.088
B. For a sample size of 60:
SE = √(0.39(1-0.39)/60) = 0.062
C. For a sample size of 90:
SE = √(0.39(1-0.39)/90) = 0.051

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The inverse of the given function include the following: B. f-¹(x) = (x³ + 4)/7.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = ∛(7x - 4)

x = ∛(7y - 4)

x³ = 7y - 4

7y = x³ + 4

y' = f-¹(x) = (x³ + 4)/7

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Answer:

21.7 in^2

Step-by-step explanation:

A = 6a^2 =6 · 1.9^2 = 21.66in²

Round: 21.7 in^2

The answer is that about 443 students at Fair Oaks High would be willing to pay $5.00 to see a play at their school.

If 85% of 5,000 high school students are willing to pay $5.00 to see a play at their school, then the number of students who would be willing to pay $5.00 is:

85% of 5,000 = 0.85 x 5,000 = 4,250

So, out of the 5,000 high school students surveyed, 4,250 would be willing to pay $5.00 to see a play.

To find the number of students at Fair Oaks High who would be willing to pay $5.00, we need to know what proportion of the 5,000 students surveyed are from Fair Oaks High.

If we assume that the proportion of students from Fair Oaks High is the same as the proportion of students surveyed, then we can calculate the number of students from Fair Oaks High who would be willing to pay $5.00 as follows:

Number of students at Fair Oaks High = (Proportion of students from Fair Oaks High) x (Number of students willing to pay $5.00)

Assuming that Fair Oaks High has 520 students out of a total of 5,000 students surveyed, then the proportion of students from Fair Oaks High is:

520/5,000 = 0.104

So, the number of students from Fair Oaks High who would be willing to pay $5.00 is:

0.104 x 4,250 = 442.5

Therefore, the answer is that about 443 students at Fair Oaks High would be willing to pay $5.00 to see a play at their school.

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Answer:

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

Step-by-step explanation:

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