why is h=root3*a/2
(equilateral triangle)

Answer:

Step-by-step explanation:

Option 1 total:

Option 2 total:

The difference:

As we see the option 1 is cheaper by $851.70

Correct answer choice is the last one

A linear regression model of the form Y = β0 + β1X + ε can be written as:

Yi = β0 + β1Xi + ei .

A linear regression model of the form Y = β0 + β1X + ε can be written as:

Yi = β0 + β1Xi + ei

Where ei is the residual for observation i. The plot of ei against Xi is known as a residual plot. The purpose of a residual plot is to check for non-linearity, unequal error variances, and outliers.

In this case, it appears that there is non-linearity present in the data. There appears to be a curved pattern in the residuals, suggesting that a linear regression model may not be the best approach to analyzing the relationship between Y and X. A transformation of the data, such as taking a logarithm of the variables, could potentially alleviate the non-linearity in the data.  This could potentially improve the fit of the linear regression model.

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Answer:

108$

Step-by-step explanation:

The graph of the function f is concave up on the interval: (-1.341, -0.240) and (0.964, 1.5). Option b is correct.

On which intervals is the graph of the function f concave up?

To determine the intervals where the graph of f is concave up, we need to analyze the second derivative of f. Let's analyze the options:

a. (-1.5, -1.341) and (-0.240, 0.964)

b. (-1.341, -0.240) and (0.964, 1.5)

c. (-0.714, 0.333) and (1.381, 1.5)

d. (-1.5, -0.714) and (0.333, 1.381)

To find the concavity of f, we need to calculate the second derivative, f''(x). Since we are not given the second derivative, we cannot directly analyze the concavity.

Therefore, we need to calculate f''(x) by taking the derivative of f'(x):

f'(x) = (x² + 1)sin(3x - 1)

Taking the derivative of f'(x) gives:

f''(x) = 2xsin(3x - 1) + (x² + 1)(3cos(3x - 1))

By analyzing the intervals given in the options and evaluating the sign of f''(x) within each interval, we can determine the intervals where the graph of f is concave up. Calculating f''(x) and evaluating its sign within each interval will provide the solution.

Therefore, the answer is that the graph of f is concave up on the interval (-1.341, -0.240) and (0.964, 1.5).

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Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.

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Answer:C

Step-by-step explanation:45

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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Answer:

-6(y+3)

Step-by-step explanation:

Answer:

VW = 8

Step-by-step explanation:

Because this trapezoids are similar

PS : TW = PQ : TU = QR : UV = RS : VW

We can take for example this equation

QR : UV = RS : VW

6 : 4 = 12 : VW

6*VW = 4*12

VW = 4*12/6 = 8

Answer:  x = 8

Step-by-step explanation:

From all the other dimensions given, you can see that the small trapezoid's sides are each 2/3 of the large trapezoid.

6= 2/3(9) . 4= 2/3(6) .12= 2/3(18) .  so take 2/3(12) = 8

Step-by-step explanation:

given points are,

A = -4 , -8

B = 11 , 5

2) we know,

distance = √(x_2 - x_1)² + (y_2 - y_1)²

according to the formula we got,

→ √(11 - (-4))² + (5 - (-8)²

→ √(15)² + (11)²

→ √25 + 121

→ √146

→ 12.08 ans.

3) Midpoint = (x_1 + x_2 /2 ) + (y_1 + y_2 /2 )

according to the formula

→ (-4) + 11 /2) , ((-8) + (5)/2)

→ 7/2 , -3/2

→ 3.5 , -1.5

therefore, Midpoints of the given line segment is ( 3.5, -1.5)

4) point in the 3/10 the way from A to B

→ 12.08/10

→ 1.208

now, 1.208 × 3

→ 3.624

therefore, point away from A to B is 3.62

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

Step-by-step explanation:

A( -4 , -8)  ; B( 11 , 5)

\(a) AB = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{2})^{2}}\\\\=\sqrt{(11-[-4])^{2}+(5-[-8])^{2}}\\\\=\sqrt{(11+4)^{2}+(5+8)^{2}}}\\\\=\sqrt{15^{2}+13^{2}}\\\\\=\sqrt{225+169}\\\\=\sqrt{394}\\\\\)

b)

\(Midpoint(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2})\\=(\dfrac{-4+11}{2},\dfrac{-8+5}{2})\\\\\)

\(=(\dfrac{7}{2},\dfrac{-3}{2})\)

= (3.5 , - 1.5)

c) m : n = 3 : 7

\(\left ( \dfrac{mx_{2}+nx_{1}}{m+n} , \dfrac{my_{2}+ny_{1}}{m+n} \right )\\\\= \left ( \dfrac{11*3+(-4)*7}{3+7}, \dfrac{5*3+(-8)*7}{3+7} \right )\\\\= \left ( \dfrac{33-21}{10},\dfrac{15-56}{10} \right )\\\\=\left ( \dfrac{12}{10},\dfrac{-41}{10} \ right )\)

Answer:

3, 1, -1, -3

-15

Step-by-step explanation:

The nth term is 5 - 2n.

Put n as 1, 2, 3, 4, and 10.

5 - 2(1)

5 - 2 = 3

5 - 2(2)

5 - 4 = 1

5 - 2(3)

5 - 6 = -1

5 - 2(4)

5 - 8 = -3

5 - 2(10)

5 - 20 = -15

The first four terms are 3, 1, -1, -3.

The 10th term is -15.

Answer:

The first four terms using the formula

5 - 2n is

First term

5 - 2(1) = 5 - 2 = 3

Second term

5 - 2(2) = 5 - 4 = 1

Third term

5 - 2(3) = 5 - 6 = - 1

Fourth term

5 - 2(4) = 5 - 8 = - 3

The first four terms are 3, 1 , - 1 , -3

The 10th term is

5 - 2(10) = 5 - 20 = - 15

Hope this helps you

Since the 1980s, the percentage of Americans who are members of a workplace union has declined significantly.

According to data from the Bureau of Labor Statistics, the union membership rate in the United States has experienced a substantial decrease over the past few decades. In the 1980s, the union membership rate was around 20% of the total workforce. However, as of the most recent available data, which is from 2020, the union membership rate stands at approximately 10.8%.

This indicates a decline of about 9.2 percentage points since the 1980s. The reasons for this decline include various factors such as changes in labor laws, economic shifts, and shifts in industries and employment patterns.

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The probability that the sample of 40 automotive services will have a mean service time greater than 136 minutes is approximately 3.36%.

a. To compute the standard error of the mean, we can use the formula:

Standard Error of the Mean = Standard Deviation / √(Sample Size)

Given that the standard deviation is 26 minutes and the sample size is 40, we can calculate the standard error as follows:

Standard Error of the Mean = 26 / √(40) ≈ 4.12 minutes

b. To find the probability that the sample mean service time will be greater than 136 minutes, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.

The formula to calculate the z-score is:

z = (x - μ) / (σ / √n)

Where:

x = sample mean (136 minutes)

μ = population mean (130 minutes)

σ = standard deviation (26 minutes)

n = sample size (40)

Plugging in the values, we get:

z = (136 - 130) / (26 / √40) ≈ 1.83

Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 1.83. The probability of a z-score greater than 1.83 corresponds to the area under the curve to the right of 1.83.

Using a standard normal distribution table, the probability is approximately 0.0336 or 3.36%.

Therefore, the probability that the sample of 40 automotive services will have a mean service time greater than 136 minutes is approximately 3.36%.

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If completion times for a certain marathon race was 3 hours with a standard deviation of 0.5 hours , then At least 75% of the completion times are between 2 hours and 4 hours , the correct answer is (a) .

The Chebyshev's inequality, for any data set and any value k greater than 1, at least 1 - 1/k² of the data values lie within k standard deviations of the mean.

In this case, we can use Chebyshev's inequality with k=2 ,

Using k=2, we have ,

⇒ At least 1 - 1/k² = 1 - 1/2² = 1 - 1/4 = 0.75 = 75% ,

So , at least 75% of the completion time lies between, (μ ± 2σ) ,

Substituting the values of mean (μ) = 3 and σ = 0.5 ,

We get ;

⇒ 3 ± 2×0.5

⇒  3 ± 1

⇒ (2,4)

So, At least 75% of the completion time are between 2 hours and 4 hours

Therefore, the correct answer is (a) At least 75% of the completion times are between 2 hours and 4 hours.

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The given question is incomplete , the complete question is

The completion times for a certain marathon race was 3 hours with a standard deviation of 0.5 hours.

What can you determine about these data by using Chebyshev's Inequality with k=2?

(a) At least 75% of the completion times are between 2 hours and 4 hours

(b) At least 88.9% of the completion times are between 2 hours and 4 hours

(c) At most 88.9% of the completion times are between 2 hours and 4 hours

(d) No more than 75% of the completion times are between 2 hours and 4 hours.

The weight of each box that Lucy is shipping is 11.5 pounds.

To find the weight of each box, we need to subtract the weight of the envelope from the total weight and then divide by the number of boxes. Here's how to do it step by step:
1. Start with the total weight: 65 pounds
2. Subtract the weight of the envelope:

65 pounds - 7.5 pounds = 57.5 pounds
3. Divide by the number of boxes:

57.5 pounds / 5 boxes = 11.5 pounds per box

So the weight of each box is 11.5 pounds.

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Answer:

-4

Step-by-step explanation:

the required slope can be calculated using the formula:

\(s=\frac{Y_C-Y_D}{X_C-X_D}=\frac{5-1}{2-3}=-4.\)

Answer:

It is 1 cent cheaper  to pay 5.46 for 7 apples.

Step-by-step explanation:

Find the unit rate:

5.46 /7 = 0.78

This is the cost for 1 apple

3.95/5 = 0.79

This is the cost for 1 apple

Answer:

5 apples for 3.95 is the better deal

Step-by-step explanation:

If you divide 7 by 5.46 you should get roughly 1.28, so $1.28 per apple

and if you divide 5 by 3.95 you should get roughly 1.26, meaning $1.26 per apple. You can verify this by multiplying 1.26 by 5 and 1.28 by 7

The norm of u is 276.46 and the distance between u and v is 259.98 in M22 with the standard inner product.

To find the norm ||u|| of the vector u=[39 276] in M22 with the standard inner product, we use the formula:

||u|| = sqrt(<u,u>)

where <u,u> is the dot product of u with itself.

<u,u> = (39 * 39) + (276 * 276) = 76461

Therefore, ||u|| = sqrt(76461) = 276.46 (rounded to two decimal places).

To find the distance d(u,v) between vectors u=[39 276] and v=[-64 19] in M22 with the standard inner product, we use the formula:

d(u,v) = sqrt(<u-v,u-v>)

where <u-v,u-v> is the dot product of the difference between u and v with itself.

<u-v,u-v> = (39 - (-64))^2 + (276 - 19)^2 = 12769 + 54756 = 67525

Therefore, d(u,v) = sqrt(67525) = 259.98 (rounded to two decimal places).

Therefore, the norm of u is 276.46 and the distance between u and v is 259.98 in M22 with the standard inner product.

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tan (α + π/6) = [(-7/√15) + (√3/3)]/[1 - (-7/√15)*(√3/3)]= - 7(√3) - 5 / 4(√15) - 21

Given the conditions cot(α)=− 4/7 ,

cos(α)<0,

tan(α+ π/6 )

tan(α+ π/6)

Let's find sin α first.

sin α = cos α * cot α= -7/4cos α(From given data cot α= -4/7)

Therefore, sin² α = 1 - cos² α= 1 - (cos α)²

(1)Using (1)sin² α + (cos α)² = 1cos² α + (cos α)² = 1cos² α = 1 - (7/4)²= -15/16

Now, as given cos α < 0

Therefore, cos α = - √15/4=- (√15)/4

Now, tan(α+ π/6)can be written as: tan(α+ π/6) = (tan α + tan (π/6))/[1 - tan α * tan (π/6)]...

(2)tan α = sin α/cos α= - 7/(√15)

Therefore, tan (α + π/6) = [(-7/√15) + (√3/3)]/[1 - (-7/√15)*(√3/3)]= - 7(√3) - 5 / 4(√15) - 21

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If m ∈ ℤ, prove that a^m ⋆ a^n = a^(m+n) for all n ∈ ℤ^+.

To prove this statement, we can use mathematical induction.

Base Case (m = 1):

a^1 ⋆ a^n = a ⋆ a^n = a^(1+n) = a^(1+n) is true.

Inductive Step:

Assume that the statement holds for some arbitrary m = k. That is, a^k ⋆ a^n = a^(k+n) for all n ∈ ℤ^+.

We want to show that the statement also holds for m = k + 1:

a^(k+1) ⋆ a^n = (a^k ⋆ a) ⋆ a^n (using associativity of the group operation)

= (a^k ⋆ a^n) ⋆ a (using the inductive hypothesis)

= a^(k+n) ⋆ a (using the inductive hypothesis)

= a^(k+n+1) (using the property of exponentiation)

Thus, the statement holds for m = k + 1.

By mathematical induction, we conclude that a^m ⋆ a^n = a^(m+n) for all m, n ∈ ℤ^+.

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Answer:

817

Step-by-step explanation:

Answer:

20/27

Step-by-step explanation:

Answer:

x = 16

4x = 64

Step-by-step explanation:

The sum of the exterior angles of any polygon is 360°

Add the given angles and solve for x

93 + 46+ 3x + 62 + 4x +47 = 360

7x + 248 = 360

7x = 360 –248

x = 16

4(16) = 64

Answer:

Step-by-step explanation:

3x(5x+8y)=15x^2+24xy

4x(3x^2+5x-7)=12x^3+20x^2-28x

(3x+4y)(2x-7y)=6x^2+8xy-21xy-28y^2=6x^2-13xy-28y^2

(2-3a)(2a^2-3a+7)=4a^2-6a+14-6a^3+9a^2-21a=-6a^3+13a^2-27a+14

Given a ferris wheel has a diameter of 225 feet and a passenger gets in a car and travels 38 feet when the wheel stops to let more passengers on, we need to find the angle of rotation to the nearest degree.

We will solve the problem by using the formula of the length of the arc of a sector which is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle of rotation. First, we need to find the radius of the ferris wheel which is half of its diameter. Therefore, radius, r = 225 / 2 = 112.5 feet. The length of the arc covered by the passenger is 38 feet, so we can substitute the values of L and r in the formula of the length of the arc of a sector to get 38 = 112.5θ. Therefore, the angle of rotation, θ = 38 / 112.5 = 0.34 radians.To convert radians to degrees, we use the formula θ (in degrees) = θ (in radians) × 180° / π. Substituting the value of θ in degrees, we get θ (in degrees) = 0.34 × 180° / π = 19.47° ≈ 19°.Therefore, the angle of rotation of the ferris wheel to the nearest degree is 19 degrees. We can conclude that the angle of rotation is much smaller than a quarter of a complete circle which is 90 degrees. This is expected as the length of the arc covered by the passenger is much smaller than the circumference of the ferris wheel which is about 706.86 feet. Hence, the passenger travels only a small fraction of the circle which corresponds to a small angle of rotation of the ferris wheel.

The angle of rotation of the ferris wheel to the nearest degree is 19 degrees.

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Answer:

75m

Step-by-step explanation:

They are similar triangles: they have two corresponding angles: in a triangle with an angle of 90°, the other two will be of 45°.

Now that we know they are similar, we can calculate the ratio of the sides, by doing 10/2=5

We want to know the side AT, so we can do that by multiplying DC for 5:

DC = 15 × 5 = 75m

You can also check this by applying Pythagoras' Theorem:

DB =

\( \sqrt{15^{2} + 2^{2} } \)

Which equals 15.1 m

The hypotenuse of the other triangle is 15.1 × 5 = 75.5 m

Finally, we can apply for the last time the Pythagoras' Theorem to find AT:

\( \sqrt{75.5^{2} - 10 {}^{2} } \)

Which equals 74.8 = 75 m

Answer:

16.75 meters

Step-by-step explanation:

This problem is a plug in problem.

H = 0.20x + 12.75

we plug in 20 for x which gives us

(0.20 * 20) + 12.75

which equals

4 + 12.75

giving us

16.75 meters

Answer:

16.75 meters

Step-by-step explanation:

First of all, in this x=20

let's plug it in

y=0.20×20+12.75

y=4+12.75

y=16.75