2.The distance needed to stop a car after applying the brakes varies directly with the square of the car's speed. Thetable below shows stopping distances for various speeds.60Speed (mph) 10 20 30 40 5070Distance (ft) 6.25 25 56.25 100 156.25 225 306.25Determine the average rate of change in braking distance, in ft/mph, between one car traveling at 50 mph and onetraveling at 70 mph. Explain what this rate of change means as it relates to braking distance.

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:

Calculating the absolute change:

Absolute change = Final value - Initial value

= 57.7 pounds - 67.8 pounds

= -10.1 pounds

Step 2: Calculate the relative change:

Relative change = (Absolute change / Initial value) * 100

= (-10.1 pounds / 67.8 pounds) * 100

≈ -14.9%

The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

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It can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.

Let the hypothesis be:

H₀: The difference in the mean is less than or equal to 0.

H₁: The difference in the mean is greater than 0.

Here, the sample size, n = 8.

Assume, α = 0.05.

First, find the mean of the differences.

\(\bar{d}=\frac{(283-215)+(299-206)+...+(277-196)}{8}\)

  \(=79.375\)

Now, the standard deviation of the difference is:

\(s_d=\sqrt{\frac{(68-79.375)^2+...+(81-79.375)^2}{8-1}}\)

   \(=13.3838\)

The t value is:

\(t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}\)

 \(=16.7745\)

Now, the degree of freedom is 8 - 1 = 7.

The p-value corresponding to this is 0.0005, which is less than the value of 0.05.

So, reject H₀.

Hence, it can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.

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The Solution.

The given probability distribution is

The expected value for the random variable X is given by the formula below:

This implies that:

So, the expected value of X is 30c.

Thus, the correct answer is 30c.

Answer:

6.3 ft

Step-by-step explanation:

The ladder lying on the wall with an elevation of 39° forms a right angled triangle.

Hypotenuse = length of ladder = 10 ft

Opposite = x = ?

θ = 39°

Use trigonometric ratio formula to find, x, which is how far the ladder goes up the wall.

The trigonometric ratio formula to use is:

sin(θ) = opposite/hypotenuse

Sin(39) = x/10

Multiply both sides by 10

10*sin(39) = x

x = 10*sin(39)

x = 6.29 ≈ 6.3 ft (to nearest tenth)

Answer:

6.3 ft

Step-by-step explanation:

did the quiz got it right

Answer:

176

Step-by-step explanation:

8+8+64+64+16+16

Answer: Angle D= 0.51 radians or 29.05°

Step-by-step explanation:

For this problem, we can use our trigonometry to find the measure of angle D.

Since this is a right triangle, we know we can use sine, cosine, and tangent. We are focusing on angle D, so we would see which trigonometric function best fits angle D. Looking at where 25 ft and 45 ft are labeled, we can use tangent. Tangent of opposite/adjacent. Now that we know this, we can set up an equation. Let's use θ in place for angle D.

tan(θ)=25/45

tan(θ)=5/9

Since we want to find θ, we would do inverse tangent.

θ= \(tan^-^1(\frac{5}{9} )\)

θ=0.507

θ=0.51

This answer is in radians. In degrees, it is 29.05°.

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Answer:

Step-by-step explanation:

\( \space\)

A = b × h

=> 154.5 = b × 15

=> b = \( \sf{\frac{154.5}{15} }\)

=> 10.3 cm

\( \space\)

Hope it helps!

Have a great day! :)

Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

Answer: The sample might not be a representative of the population because it only included lunch customers.

Step-by-step explanation:

Answer:

The sample might not be representative of the population because it only included lunch customers.

Step-by-step explanation:

Since she is only picking lunch customers and not breakfast and dinner it doesn't show all the people only the people who order lunch

Answer:

21.01 cubic metres

Step-by-step explanation:

We have to find the value of 1 cubic foot and then convert to cubic metre.

1 foot = 0.3048 m

1 cubic foot = \((0.3048)^3\) = 0.02832 cubic metre

A volume of 742 cubic foot will therefore be:

742 * 0.02832 = 21.01 cubic metres

The volume in cubic metres is 21.01 cubic metres

A) x=-5

Explanation

Step 1

add like terms

Step 2

now, add 9 in both sides. (If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.)

Step 3

finally, divide both sides by -3

so, the answer is A) x=-5

I hope this helps you

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

A set that includes all or a portion of another set's elements is known as a subset. For instance, because every even integer is also an integer, the set of even integers is a subset of the set of integers. A subset that contains some, but not all, of the members of another set is said to be a proper subset. Because it contains some, but not all, of the positive integers, the set of positive integers less than 10 is a valid subset of the set of positive integers.

A function's codomain is a subset of its range. Although it is not a true subset, it is conceivable for the range to be equal to the codomain, in which case it is also a subset of the codomain.

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Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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Answer:

87 / 100 I do believe will be your answer.

Step-by-step explanation:

1 is the greatest common divisor of 87 and 100, and therefore the result can't be further reduced. I hope this helps!

Answer:

\(4i \sqrt{6} \)

Answer:

60 km

Step-by-step explanation:

the line is constant around 3

The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

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When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.

Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.

We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:

Using the formula V = \(Pe^rt\)

Principal (P) = $48,800.00

Annual Rate (R) = 3.1%

Compound (n) = Compounding Continuously

Time (t in years) = 13 years

Result:

V = $73,019.78

V = P + I where

P (principal) = $48,800.00

I (interest) = $24,219.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.1/100

r = 0.031 rate per year,

Solving the equation for V:

V = \(Pe^rt\)

V = \(48,800.00(2.71828)^(0.031)(13)\)

V = $73,019.78

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Answer:

904.78 \(in^{3}\)

Step-by-step explanation:

The volume formula for a sphere is the following:
\(v=\frac{4}{3} \pi r^{3}\)
\(d = 2r\)
Replace with values and the answer is 904.78

Answer:

O = 16.7 degrees

A = 73.3 degrees

Step-by-step explanation:

used a triangle calculator

The number of people is 10%

The number of people is 66%

Percentage is a way of expressing a fraction or proportion as a number out of 100. The term "percent" means "per hundred," so if you say that something is "20 percent," it means that 20 parts out of 100 are being referred to.

Total number = 15 + 36 + 73 + 26

= 150 people

The percentage that arrived before 7 am = 15/150 * 100/1

= 10%

After 7:59 = 99/150 * 100/1

= 66%

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Answer:

the height the ladder can reach up the building to save the cat = 13.9feet

Question:

The question didn't state the height of the building. If the ladder was initially 12feet and then it was extended to another length to reach the top of the roof, we need the height of the building to enable us calculate how high the ladder can reach up the building the save the cat.

Let's consider the following question:

A cat gets stuck on the roof. If the ladder is 12 feet long and must be placed 7 feet away from the building. How high can the ladder reach up the building to save the cat if the height of the building is 12feet.

Step-by-step explanation:

The distance between the foot of the ladder to foot of the building = 7feet

adjacent = 7feet

The height of the building = 12feet

Opposite = 12feet

The length of the ladder is unknown

To find how high can the ladder reach up the building to save the cat, we would apply Pythagoras theorem

Using Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent²

Hypotenuse ² = 12² + 7²

Hypotenuse ² = 144 + 49

Hypotenuse ² = 193

Hypotenuse = √193

Hypotenuse = 13.9feet

The height of the ladder to reach up the building to save the cat = 13.9feet

Step-by-step explanation:

Plug

\( {x}^{2} + 1\)

for x.

\(( {x}^{2} + 1) {}^{2} + 1\)

Note that

\((a + b) {}^{2} = 2ab\)

So we have

\( {x}^{4} + 2 {x}^{2} + 2\)

Answer:

B, because thats dividing, which equals 3. for the answer A, did you mean 15*5?

Step-by-step explanation:

The total number of yards the friends who paddle the Adventure Mid travel is 8,580 yards

Number of friends who paddle Adventure Mid Trip = 40% of 15

= 0.4 × 15

= 6 friends

Total yards the friends who paddle the Adventure Mid Trip travel = Total length of travel

= 4 7/8 miles

Recall,

1 mile = 1760 yards

Total yards the friends who paddle the Adventure = 4 7/8 × 1,760

= 39/8 × 1,760

= (39 × 1,760) / 8

= 68,640 / 8

= 8,580 yards

Consequently, the task content is solved by converting number of miles to yards.

Complete question:

Great Adventures Canoe and Kayak company offers 3 different options as shown in the table. This afternoon a group of 15 friends paddle the different options in individual kayaks and 40% of the group paddle the Adventure Mid Trip. How many total yards will the friends who paddle the Adventure Mid Trip travel? (Hint: 1 mile = 1760 yards)

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Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.

Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).

To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.

After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.

In conclusion, it is represented by the equation y = -x + 3.

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Answer:

median is 14, and mean is 5.5

Step-by-step explanation: