Simplify the expression using the given values

Answer:

\(15-4\sqrt{15}\)

Step-by-step explanation:

\(\sqrt{5}\left(3\sqrt{5}-4\sqrt{3}\right)\\\\\mathrm{Apply\:the\:distributive\:law}:\\\quad \:a\left(b-c\right)=ab-ac\\\\a=\sqrt{5},\\\:b=3\sqrt{5},\:c=4\sqrt{3}\\\\=\sqrt{5}\times\:3\sqrt{5}-\sqrt{5}\times\:4\sqrt{3}\\\\=3\sqrt{5}\sqrt{5}-4\sqrt{5}\sqrt{3}\\\\Simplify\:\:\:3\sqrt{5}\sqrt{5}-4\sqrt{5}\sqrt{3} \: :15-4\sqrt{15}\\\\=15-4\sqrt{15}\)

The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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Answer:

walk = 9/30 -  bike = 3/30 - car = 6/30 - bus = 12/30

Step-by-step explanation:

Answer:

A 573308928

B. 124176266400000000000000000

The unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.

To find the unit cost of each movie pack, we need to divide the total cost by the number of passes in each pack.

The unit cost for Cinema A's twelve-pack can be calculated as follows:

unit cost for Cinema A = $66 / 12 passes = $5.50 per pass

The unit cost for Cinema B's five-pack can be calculated as follows:

unit cost for Cinema B = $29 / 5 passes = $5.80 per pass

So, the unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.

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Answer:

18/2 : 9

Step-by-step explanation:

Answer:

A) y=-4x+20

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-4(x-3)

y=-4x+12+8

y=-4x+20

The value of the range of the exponential function f(x) = 2ˣ + 25 is,

⇒ (25, ∞ )

We have to given that;

the exponential function is,

⇒ f(x) = 2ˣ + 25

Now, We can formulate;

The range of the function is,

⇒ y ∈ (25, +∞)

Hence, The value of the range of the exponential function f(x) = 2ˣ + 25 is,

⇒ (25, ∞ )

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Answer:

jk

Step-by-step explanation:

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Answer:

sin X = cos Y

Step-by-step explanation:

sin X = opp / hyp = 3/5

Cos y = adj / hyp = 3/5

sin X = cos Y

Answer: She can spend $5.50 on snacks for each child.

Step-by-step explanation:

First break everything down:

Total Cost: $33

Number of child : 6

Second do 33÷6= $5.50

Given expression:

             A  = \(\frac{1}{2}(b_{1} + b_{2} )\)

Solve for b₁;

  Solution:

This is a subject of the formula problem.

  Given expression:

               A  = \(\frac{1}{2}(b_{1} + b_{2} )\)

First, multiply both sides by 2;

          2 x A  = 2 x \(\frac{1}{2}(b_{1} + b_{2} )\)  

              2A  = b₁  + b₂

Then subtract b₂ from both sides;

           2A - b₂ = b₁ + b₂ - b₂

                 b₁ = 2A - b₂

The solution is   b₁ = 2A - b₂

To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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Answer:

63

Step-by-step explanation:

This is a cyclic quadrilateral, meaning that its opposite angles are supplementary. So, x=180-117=63.

Given:

Radius of flower garden is 17yd.

Radius of outer edge is 20 yd.

Required:

To find the number of bags.

Explanation:

The are of the garden is

The area of the outer ring is,

The path area= overall area- garden area

Find the number of bag of sand required

Final Answer:

174 bags required.

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Answer:

15,18,21

Step-by-step explanation:

Answer:

15 18 21

Step-by-step explanation:

its skskskskskksksskskkssksksksk

Answer:

24 ;] ;] ;]

Step-by-step explanation:

from spongebob

Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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Answer:

DC

Step-by-step explanation:

DC

It’s opposite the smallest angle.

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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Answer: 77 degrees

mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.

Answer:

527 sq. ft

Step-by-step explanation:

multiply the length and width measurements of the room to get the whole area

Answer:

A = 527 ft^2

Step-by-step explanation:

We want to find the area

A = l*w

A = 17 ft * 31 ft

A = 527 ft^2

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

\({ \tt{u(t) = 8t - 14}} \\ { \tt{s(t) = {t}^{2} - 16}} \\ \\ { \tt{s[u(t)] = {(8t - 14)}^{2} - 16}} \\ { \tt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: s[u(t)]= (64 {t}^{2} - 224t + 196) - 16 }} \\ { \tt{ \: \: \: \: \: s[u(t)] = {64t}^{2} - 224t + 180}}\)

So;

\({ \tt{s[u(3)] = 64 {(3)}^{2} - (224 \times 3) + 180}} \\ = { \tt{576 - 672 + 180}} \\ = { \tt{84}}\)

The required real-world problem is below that can be solved using the equation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

A construction company is building a new housing development and wants to know how many houses they need to build to reach a certain profit margin. They know that each house costs $9 to build and they want to sell each house for $21.

If they build x number of houses, the equation to calculate their profit is:

21x - (4x + 9) = profit.

To reach a certain profit margin, the company can set that equation equal to a specific value and solve for x.

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Answer:

The correct option is C

Step-by-step explanation:

ANOVA is the correct option because it can be used to carry out comparison of average of more than  two groups