What is the standard form of the line that passes through the points (-4, 6) and (0, -7)?
Ax+4y= -7
B
4x+y=-7
13x + 4y = -28
D-4x+y=-28
30960995

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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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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A bag of chips costs $0.95, a bottle of Water Costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

Let x be the cost of a bag of chips in dollars.

Since a bottle of water costs twice as much as a bag of chips, a bottle of water costs 2x dollars.

A gallon of milk costs $1.90 more than a bottle of water, so a gallon of milk costs 2x + $1.90 dollars.

Using the given information, we can set up the following equation to represent the total cost:

3(2x + $1.90) + 5(2x) + 8x = $28.50

Simplifying the equation, we get:

6x + $5.70 + 10x + 8x = $28.50

24x + $5.70 = $28.50

Subtracting $5.70 from both sides, we get:

24x = $22.80

Dividing both sides by 24, we get:

x = $0.95

Therefore, a bag of chips costs $0.95, a bottle of water costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.

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Answer:

-2x^2 - 2x + 5

Step-by-step explanation:

Combine like terms (same variable and degree) to simplify

3x^2-5x^2+5x-7x+3+2

-2x^2-2x+5

Answer:

Combining like terms, we get:

-2x² - 2x + 6

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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Please upload an image or give a question.

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:

A = 36π units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here r = 6 , then

A = π × 6² = 36π units²

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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1. The area of the fort is 27 square feet.

2. No, Carlos was not correct

3.  The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

1. The area of the fort can be calculated by multiplying the length and width of the rectangle. In this case, the length is 6 feet and the width is 4.5 feet. Therefore, the area can be calculated as:

Area = Length × Width

= 6 feet × 4.5 feet

= 27 square feet

So, the area of the fort is 27 square feet.

2. No, Carlos was not correct. The actual area of the fort is 27 square feet, not 13.5 square feet as he determined.

3. Carlos made a mistake in his calculation. Instead of multiplying the length and width together, he likely mistakenly multiplied them as if he was finding the perimeter or added them together. The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

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The sum of their ages if the son’s age is X is 3X.

We are given that;

x=A father is twice as old as his son

Now,

If the son’s age is X,

Then the father’s age = 2X.

The sum of their ages

= X + 2X

= 3X.

Therefore, by algebra the answer will be 3X.

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Answer:

The answer to this question is vertical angles

Step-by-step explanation:

angle 5 and 8

 Those are vertical angles formed by two crossing lines and they are equal

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 (°).

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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(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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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 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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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 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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The value of given expression is 57.

We are given that;

|—15u| + |3v| + 3

u=3, v = 3

Now,

To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:

|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57

Therefore, by the given expression the answer will be 57.

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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 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 average response time for the ambulance company is 13 minutes, with 95% of response times falling between 10 and 16 minutes.

The response times for a specific ambulance company follow a normal distribution with a mean of 13 minutes. This means that the majority of response times will cluster around the average of 13 minutes.

Furthermore, we know that 95% of the response times fall within the range of 10 to 16 minutes. This suggests that the response times are relatively consistent, with only a small percentage of outliers falling outside this range.

In summary, the average response time for this ambulance company is 13 minutes, and 95% of their response times fall between 10 and 16 minutes.

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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 correct answer is: The median is the best measure of center, and it equals 19.

A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.

The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.

The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).

The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.

A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.

The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.

In light of this, the answer is "The median is the best measure of center, and it equals 19."

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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

After considering all the given data we conclude that the total distance traveled by the car is 285m, under the condition that the given car starts from rest and moves with an acceleration of 1m/s2 for 15.

The distance traveled during this time can be evaluated using the formula

[tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u =  initial velocity (0),

a = acceleration (1m/s2)

t = time (15s).

Placing in these values we get

s = 0 + (1/2) × 1 × 15²

= 112.5m .

After this, the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. The distance traveled during this time can be evaluated applying  the formula

[tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (10s).

Placing in these values we get

s = 112.5 + (1/2) × (-0.05) × 10²

= 87.5m.

Finally, brakes are applied and it stops after 5s. The distance traveled during this time can be evaluated using the formula [tex]s = ut + (1/2)at^2[/tex]

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (5s).

Placing in these values we get s = 87.5 + (-0.05)× 5² = 85m.

Therefore, total distance traveled by car can be calculated by adding all three distances together which gives us

112.5m + 87.5 + 85

= 285m.

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The complete question is

A car starts from rest and moves with an acceleration of 1m/s2 for 15. Then the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. then the brakes are applied and it stops 5s after calculating the total distance traveled?