Translation
AABC is translated 4 units to the right and 5 units down. Answer the questions to
find the coordinates of A after the translation.
1. Give the rule for translating a point 4 units right and 5 units down. (2 points)
(x,y) → (x
y
)

(a) The distribution of X is X ~ N(151, 24)

(b) The probability that the average price is between $152 and $155 is 0.950

(c) The quartile for the average textbook price for this sample size is $167.2

(d) The assumption of normal distribution is necessary

Given that

Mean = 151

Standard deviation = 24

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(151, 24)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (152 - 151)/24 and z = (155 - 151)/24

Evaluate

z = 0.042 and z = 0.167

So, we have

P = P(0.042 < z < 0.167)

Evaluate

P = 0.95044

Approximate

P = 0.950

This is calculated as

Q₃ = Mean + 0.675 * Standard deviation

So, we have

Q₃ = 151 + 0.675 * 24

Evaluate

Q₃ = 167.2

Hence, the quartile for the average textbook price for this sample size is $167.2

Yes, the assumption is necessary

This is because

The distribution has a sample size greater than 25 as required by the central limit theorem

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After considering the given data we conclude that Jada's conclusion is not correct because she only tested two values of x for each function and concluded that a will always be greater than b for larger x values.

So , this is not true in general. In order to  see why, let's provide a specified comparison between the two functions for a general value of x by forming an algebraic expression
a(x) = 2(2) = 4
b(x) = 4x² + 2x
We clearly  see that b(x) grows much faster than a(x) as x gets larger. In fact, for any value of x greater than 1/2, b(x) will be greater than a(x).
Then, Jada's conclusion is not correct in general.
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Answer: 98 deg

Step-by-step explanation:

angles 3 and 4 are supplementary; this means their sum is 180 degrees.

so simply put, 180 - angle 3 = angle 4

180 - 82 = 98

The value of angle ABC in the equilateral triangle formed by points D, E, and C, given angle EAB is 80°, is 50°.

Let's solve the problem step by step:

In an equilateral triangle, all three angles are equal. Let's denote the measure of angle ABC as x.

Since the triangle is equilateral, angle BAC is also equal to x.

The sum of angles in a triangle is

=180°

Therefore, we can write the equation:

= x + 80 + x = 180.

Simplifying the equation, we have:

= 2x + 80 = 180.

Subtracting 80 from both sides:

= 2x = 100.

Dividing both sides by 2:

=x = 50.

Thus, angle ABC measures 50°.

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The complete question is:

The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 80°, then what is the value of angle ABC? Give your answer in degrees (°).

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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Answer:

The area is 44

Step-by-step explanation:

If you add the numbers that across from each other you would get 12+12+2+2+8+8= 44

The surface area of the cylinder is 603.19 square meters

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

Radius, r = 8 meters

Height, h = 4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 8 * (8 + 4)

Evaluate

Surface area = 603.19

Hence, the surface area is 603.19 square meters

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The required standard error of the mean is 2.4 units.

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 36 units and the sample size is 225. Therefore, the standard error of the mean is:

SE = σ / √n = 36 / √225
     = 36 / 15 = 2.4 units

Therefore, the standard error of the mean is 2.4 units.

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The required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

The distance traveled by Zeek is:

84,240,000,000,000 miles away / 2.5 = 33,696,000,000,000 miles away

We can write this in scientific notation as:

3.3696 × 10¹³ miles

Thus, the required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

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Answer:

96π

Step-by-step explanation:

the shape is made up of a cylinder and a cone.

Volume of cylinder = π r ² h

= π (3)² (9)

= 81π.

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) (5) π (3)²

= 15π

volume of composite solid = 81π + 15π = 96π

About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

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The value of x using Tangent - Secant theorem is: 16

The tangent-secant theorem states that when a tangent and secant possess a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.

We are given:

internal part of the secant = (x + 9),

external part of the secant = 9,

tangent = 15,

According  to Tangent-secant Theorem:

(x + 9) * 9 = 15²

9x + 81 = 225

9x = 144

x = 144/9

x = 16

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3.6 years will have passed when 115 grams of thorium 234 is left.

(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:

[tex]A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams[/tex]

Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.

(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:

[tex]A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years[/tex]

Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.

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The value of sin(θ - φ) = sin(A - B) in simplest form is sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

Use the trigonometric identity sin(α - β) = sin α cos β - cos α sin β to find sin(θ - φ), where θ = A and φ = B.

First, find cos A and sin B using the given information:

Since sin A = 53/45, use the Pythagorean identity cos² A + sin² A = 1 to find cos A:

cos² A + (53/45)² = 1

cos² A = 1 - (53/45)²

cos A = ± √(1 - (53/45)²)

Since A is a positive acute angle, take the positive square root:

cos A = √(1 - (53/45)²)

Similarly, since cos B = 29/20, use the Pythagorean identity cos² B + sin² B = 1 to find sin B:

sin² B = 1 - cos² B

sin B = ± √(1 - cos² B)

Since B is a positive acute angle, take the positive square root:

sin B = √(1 - (29/20)²)

Use the identity sin(α - β) = sin α cos β - cos α sin β to find sin(A - B):

sin(A - B) = sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

Simplifying this expression:

sin(A - B) = (53/60) - √(2561)/900

Finally, use the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ to find sin(θ - φ) = sin(A - B):

sin(A - B) = sin θ cos φ - cos θ sin φ

= sin A cos B - cos A sin B

= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)

= (53/60) - √(2561)/900

Therefore, the value of sin(θ - φ) = sin(A - B) in simplest form is:

sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800

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The actual bridge deck measures 4,320 square feet in size.

First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.

The scaled length of the bridge deck is 36 inches, so the actual length is:

36 inches x 60 = 2,160 inches

The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:

24/5 inches x 60 = 288 inches

To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:

Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet

Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet

Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet

Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.

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Answer:

[tex]h(x) = 2 {x}^{2} + 5x - 3[/tex]

[tex]h(x) = (2x - 1)(x + 3)[/tex]

-The component functions must both be linear.

-The component functions must have y-intercepts with different signs.

The total area that needs to be covered which is indicated by the shaded area would be =220ft²

To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;

Area of rectangule =2( length×width)

where ;

length = 22ft

width = 5ft

area = 2× 22×5

= 220ft²

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The derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

The given function is  f(x)=(3x²−4x+1)⁴

We have to find the derivative of the function

By using chain rule we find the derivative

f'(x)=4(3x²−4x+1)³ d/dx(3x²−4x+1)

=4(3x²−4x+1)³ (6x-4)

Hence, the derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)

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The monthly cost for 56 minutes of calls is given as follows:

$18.05.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

For 38 minutes of call, the price increases by $4.94, hence the slope of the linear function, representing the cost per minute, is given as follows:

m = 4.94/38

m = 0.13.

56 minutes is 30 minutes less than 86 minutes, hence the cost is given as follows:

C(56) = 21.95 - 30 x 0.13

C(56) = $18.05.

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The piecewise linear equation is y = -0.556x - 2.444, -8 ≤ x ≤ 1, y = 1.333x - 4.333, 1 < x ≤ 4 and y = -0.667x - 3.667 4 < x ≤ 10

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

X: -8, 1, 4, 10

Y: 2, -3, 1, -3

In the interval [-8, 1], we have

X: -8, 1

Y: 2, -3

A linear equation is represented as

y = mx + c

Using the points, we have

-8m + c = 2

m + c = -3

So, we have

m = -0.556

c = -2.444

So, we have

-0.556x - 2.444, -8 ≤ x ≤ 1

In the interval (1, 4], we have

X: 1, 4

Y: -3, 1

Using the points, we have

m + c = -3

4m + c = 1

So, we have

m = 1.333

c = -4.333

So, we have

1.333x - 4.333, 1 < x ≤ 4

In the interval (4, 10], we have

X: 4  10

Y: 1   -3

Using the points, we have

4m + c = 1

10m + c = -3

So, we have

m = -0.667

c = 3.667

So, we have

-0.667x - 3.667 4 < x ≤ 10

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12.1 Alternative Hypothesis, 12.2 The level of significance will typically be set at α = 0.05 (5%), 12.3 In terms of tails, we will perform a two-tailed test. 12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test,

To test if there is a significant difference between the survey results and the director's claim, we will perform a hypothesis test using a one-sample proportion test.

12.1 Alternative Hypothesis: The alternative hypothesis would be that the proportion of the workforce supporting the new shift pattern is not equal to 90%. We can express this as H1: p ≠ 0.9.

12.2 The level of significance for testing the difference between the director's claim and the survey results will typically be set at α = 0.05 (5%).

12.3 In terms of tails, we will perform a two-tailed test. This is because we are testing if the proportion is significantly different from the claimed value (90%), which could be either higher or lower.

12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test, we divide α equally between the two tails. So, the rejection region will be split into two parts, one in the left tail and one in the right tail.

12.5 The rejection region is determined by the critical values. In this case, the critical values will be based on the standard normal distribution and the significance level α. The values that indicate the rejection region are the critical values of the standard normal distribution associated with α/2 (in each tail) based on the sample size.

12.6 Let's calculate the test statistic. The sample proportion in favor of the new shift pattern is 85/100 = 0.85. The expected proportion under the null hypothesis is 0.9. The standard error can be calculated using the formula: SE = sqrt(p * (1-p) / n), where p is the expected proportion and n is the sample size. Plugging in the values, we have SE = sqrt(0.9 * 0.1 / 100) ≈ 0.03. The test statistic can be calculated as (sample proportion - expected proportion) / SE, which gives (0.85 - 0.9) / 0.03 ≈ -1.67.

12.7 Referring to the rejection region and the test statistic, if the test statistic falls within the rejection region (i.e., if it is beyond the critical values), we will reject the null hypothesis. If the test statistic is not in the rejection region, we will fail to reject the null hypothesis.

12.8 Based on the calculated test statistic of -1.67 and the critical values associated with α/2, we would compare the test statistic with the critical values to determine if it falls within the rejection region. If it does, we would reject the null hypothesis and conclude that there is a significant difference between the survey results and the director's claim.

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Answer:

60 and 40

Step-by-step explanation:

a) To find the number of people who like both tea and coffee, we can use the formula:

Number of people who like both = Number of people who like tea + Number of people who like coffee - Number of people who like only teaPlugging in the given values, we get:

Number of people who like both = 50 + 30 - 20 = 60Therefore, there are 60 people who like both tea and coffee.

b) To find the number of people who like either of the drinks, we can add the number of people who like tea only, the number of people who like coffee only, and the number of people who like both tea and coffee. Mathematically,

Number of people who like either drink = Number of people who like tea only + Number of people who like coffee only + Number of people who like both tea and coffeePlugging in the given values, we get:

Number of people who like either drink = 20 + (30-60) + 50 = 40Therefore, there are 40 people who like either tea or coffee (or both).

Answer:

D

Step-by-step explanation:

Answer:

LN and NK

Step-by-step explanation:

A perpendicular bisector of a line segment divides the line segment into 2 equal halves.

Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.

The two equal halves are segment LN and segment NK.

Therefore, segment LN is congruent to segment NK.

The total cash due at signing is $3800.

Option A is the correct answer.

We have,

The total cash due at signing is the sum of the down payment, security deposit, acquisition fee, and the first month's lease payment.

So,

Down payment = $2500

Security deposit = $375

Acquisition fee = $500

First month's lease payment = $425

The total cash due at signing is:

= $2500 + $375 + $500 + $425

= $3800

Thus,

The total cash due at signing is $3800.

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A hot dog costs 2.25 we get it by solving the equation

Let's denote the cost of one hot dog by x.

Then we can set up two equations:

5x + 6y = 18.39

x + 2y = 4.63

where y is the cost of one bag of chips.

We want to solve for x.

Let us isolate variable y in the second equation

y = 4.63 - x/2

Substitute the y equation in the equation (1)

[tex]$5x + 6\left(\frac{4.63 - x}{2}\right) = 18.39$[/tex]

Simplifying this equation gives:

5x + 13.89 - 3x = 18.39

2x = 4.5

x = 2.25

Hence, a hot dog costs 2.25.

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The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄

There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.

Now, we are given the fraction as an improper fraction in the form of 2³₄.

Rewriting as a whole number and a fraction gives:

2 + ³/₄

Breaking down the whole number into a fraction is done as:

1 + 1 + ³/₄

= ⁴/₄ + ⁴/₄ + ³/₄

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Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

If Keenan earns 1 mile for every $8 he spends, then he would need to spend 8 times as much money to earn the same number of miles as he did before.

In other words, he would need to spend $8 to earn 1 mile instead of $1 to earn 1 mile under the old program.

To calculate the new amount of money Keenan needs to spend to earn the miles for his trip, we would need to multiply the old amount by 8.

For example, if under the old program, Keenan needed to spend $10,000 to earn 25,000 miles for his trip, under the new program he would need to spend:

$10,000 x 8 = $80,000

So under the new program, Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.

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