The table shows how many Calories Lance burns jogging on a treadmill for different lengths of time. Lance's goal today is to burn 380 Calories. If he has been jogging for 25.5 minutes, for how many more minutes does he still need to jog? Assume the situation is proportional.

Answer:b

Step-by-step explanation:b

The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as follows:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

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The average gas mileage of the cars traded is 15.8 miles per gallon round to the nearest.

Let's assume that the average gas mileage of the cars traded in is x miles per gallon. According to the problem, the average increase in gas mileage for the new car purchased versus the car traded in was 61%. This means that the new car gets 61% more miles per gallon than the car traded in. We can express this relationship mathematically as:

25.4 = x + 0.61x

Simplifying the right-hand side of the equation, we get:

25.4 = 1.61x15.78

Dividing both sides by 1.61, we get:

x = 15.78

Therefore, the average gas mileage of the cars traded in was approximately 15.8 miles per gallon, rounded to the nearest tenth.

To understand this result, we can interpret it as follows: for the first week of the "Cash for Clunkers" program, the average gas mileage of the new cars purchased was 25.4 miles per gallon, which is 61% higher than the average gas mileage of the cars traded in. This suggests that the program was successful in incentivizing people to trade in their old, less fuel-efficient cars for new, more fuel-efficient cars.

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[tex]\cos(40^o )=\cfrac{\stackrel{adjacent}{32}}{\underset{hypotenuse}{x}} \implies x=\cfrac{32}{\cos(40^o)}\implies x\approx 41.77[/tex]

Make sure your calculator is in Degree mode.

if we will divide 137 with 100 and then multiply it with 680 you will gett your answer

the answer is 931.6

Answer:

931.6

Step-by-step explanation:

We need to change the percent to decimal form.

137%  = 1.37

Multiply this by 680.

1.37 * 680

931.6

The solutions of the given equations are x = 0 and x = -36.

We have,

To solve these equations:

9x - 7 = -7

We can add 7 to both sides to isolate the variable:

9x - 7 + 7 = -7 + 7

Simplifying the left-hand side and the right-hand side, we get:

9x = 0

Finally, dividing both sides by 9, we get:

x = 0

Next, to solve:

-1 = 5 + x/6

We can begin by subtracting 5 from both sides:

-1 - 5 = 5 + x/6 - 5

Simplifying the left-hand side and the right-hand side, we get:

-6 = x/6

Finally, multiplying both sides by 6, we get:

-36 = x

Thus,

The solutions of the given equations are x = 0 and x = -36.

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The complete question.

9x - 7 = -7

-1 = 5  + x/6

Answer:

The domain of a function is the set of all possible input values for the function. In this case, the function is a graph, so the domain is the set of all possible x-values that correspond to points on the graph.

To find the domain, we need to consider all of the points on the graph. We can see that the graph extends infinitely to the left and right, so all real numbers are possible input values. Therefore, the domain of the function is all real numbers, or R.

Here is a more formal definition of the domain of a function:

The domain of a function is the set of all real numbers x for which the function f(x) is defined.

In other words, the domain is the set of all input values for which the function produces a valid output value.

Step-by-step explanation:

The measure of value of ∠5 is 83°.

Now, It is given that;

Two Lines m and n are parallel with each other and l is the transversal crossing the two given parallel lines.

And, m∠6 = 97°,

Since, Two rays combined into an angle have a single terminal. The point is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Hence, Then by using the property of liner pair angles, we have

⇒ m∠5 + m∠6=180°

(Because they form a linear pair angles.)

⇒ m∠5 + 97 = 180

Subtract 97 both side, we get;

⇒ m∠5 + 97 - 97 = 180 - 97

⇒m∠5 = 180 - 97

⇒m∠5 = 83°.

Therefore, the value of the measure of ∠5 is,

⇒ ∠5 = 83°.

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Answer

I think it's acute scalene triangle

Step-by-step explanation:

All the angles are less than 90 degrees, which is acute.

The two answers that describe the unit rate at which Darrell walks are 1.5 seconds per meter and 1.5 meters per second

To find the unit rate at which Darrell walks, we need to determine how many meters he walks per second. We are given that he walks 90 meters in 60 seconds.
Step 1: Divide the total distance by the total time to find the unit rate.
Unit rate = (total distance) / (total time)
Step 2: Plug in the given values and calculate.
Unit rate = 90 meters / 60 seconds
Step 3: Simplify the fraction.
Unit rate = 1.5 meters per second
The two answers that describe the unit rate at which Darrell walks are:
1. 1.5 meters per second
2. 30 seconds per meter (the reciprocal of the unit rate)

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The size tray of plants which is the best value for money is large tray.

A small tray of 10 plants costs £2.50

Cost per unit = Total cost / number of plants

= £2.50 / 10 plants

= £0.25 per plant

A medium tray of 40 plants costs £8.40

Cost per unit = Total cost / number of plants

= £8.40 / 40 plants

= £0.21 per plant

A large tray of 90 plants costs £12.60

Cost per unit = Total cost / number of plants

= £12.60 / 90 plants

= £0.14 per plant

Hence, the large tray of 90 plants costs £12.60 is the best buy for your money.

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Answer: We can use both formulas to calculate the interest on an investment of $3500 at 2.75% for 3 years.

Using the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years, we have:

A = 3500(1+0.0275/1)^(1*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

Using the formula A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828, we have:

A = 3500e^(0.0275*3) ≈ $3843.84

Therefore, the interest earned is:

Interest = A - P = $3843.84 - $3500 = $343.84

The interest earned is $343.84 in both cases.

Using the secant-secant theorem, the possible values of x are x = 6 and x = -10. -10 cannot be a value of x because length cannot be negative.

From the question, we are to determine the value of x in the given diagram.

The Secant-secant theorem states that

"Given two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other segment and its external segment"

Thus,

We can write that

5 × (5 + 7) = x × (x + 4)

Simplifying

5 × 12 = x² + 4x

60 = x² + 4x

x² + 4x - 60 = 0

Solve the quadratic equation

x² + 4x - 60 = 0

x² + 10x - 6x - 60 = 0

x(x + 10) - 6(x + 10) = 0

(x - 6)(x + 10) = 0

x - 6 = 0 or x + 10 = 0

x = 6 or x = -10

Since x cannot be negative,

x = 6

Hence, the value of x is 6

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Step-by-step explanation:

[tex]f'(x)=[(3x^2-4x+1)^4]'=4(3x^2-4x+1)^3*(3x^2-4x+1)'=4(3x^2-4x+1)^3*(6x-4)=8(3x^2-4x+1)^3(3x-2);[/tex]

The required derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

We can use the chain rule and power rule of differentiation to find the derivative of f(x).

Let u = 3x² - 4x + 1, then we have:

f(x) = u⁴

Using the chain rule, we get:

f'(x) = 4u³ * u'

To find u', we can differentiate u with respect to x using the power rule:

u' = d/dx (3x² - 4x + 1) = 6x - 4

Substituting u' and u into f'(x), we get:

f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

Therefore, the derivative of f(x) = (3x² - 4x + 1)⁴ is f'(x) = 4(3x² - 4x + 1)³ * (6x - 4)

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The probability of drawing a red or green M&M is 29/74.

The probability of drawing an M&M that is not blue or green is 36/74.

the probability of drawing an M&M that is not brown is 69/74.

The probability of drawing a red or green M&M is the sum of their probabilities, since they are mutually exclusive events (meaning that an M&M can't be both red and green at the same time):

P(red or green) = P(red) + P(green) = 8/74 + 21/74 = 29/74

The probability of drawing an M&M that is not blue or green is the complement of the probability of drawing a blue or green M&M:

P(not blue or green) = 1 - P(blue or green) = 1 - (P(blue) + P(green)) = 1 - (17/74 + 21/74) = 36/74

The probability of drawing an M&M that is not brown is the complement of the probability of drawing a brown M&M:

P(not brown) = 1 - P(brown) = 1 - 5/74 = 69/74

To determine which is more likely, drawing a red M&M or drawing an orange M&M, we need to compare their probabilities:

P(red) = 8/74

P(orange) = 12/74

Since 12/74 is greater than 8/74, it is more likely to draw an orange M&M than a red M&M.

The color with the highest chance of being drawn is the one with the highest probability, which is green with a probability of 21/74.

The probability of drawing any M&M is 1, since there is a 100% chance of drawing an M&M when you draw from the bag.

Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

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the x coordinates are matched as follows

For y = √110/11  x = ± 1/√(11)

For y = 7/11  x = ± 6√(2) /11

For y = 5/11   x = ±4√(6) /11

For y = 9/11:   x = ±2√(10) /11

Using the equation of the unit circle

x² + y² = 1

For y = √110 / 11

x² + (√110/11)² = 1

x² + 110/121 = 1

x² = 1 - 110/121

x² = 11/121

x = ±√(11)/11

x = ± 1/√(11)

For y = 7/11

x² + (7/11)² = 1

x² + 49/121 = 1

x² = 1 - 49/121

x² = 72/121

x = ±√72/11

x = ± 6√(2) /11

For y = 5/11

x² + (5/11)² = 1

x² = 1 - 25/121

x² = 96/121

x = ±4√(6) /11

For y = 9/11

x² + (9/11)² = 1

x² = 1 - 81/121

x² = 40/121

x = ±√40/11

x = ±2√(10) /11

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Answer:

Squaring positive and negative numbers always yields a positive number; the product of two negative numbers is always a positve number.  Using √4 as an example, we know the positive answer is 2 since 2 * 2 = 4.  However, the negative answer is -2 since -2 * -2 = 4 also.

The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

In a scenario where there are 2 defective screws out of 100 packs, each containing 500 screws, we can calculate the probability of obtaining 15 defective screws. Let's assume that each pack is independent of the others.

The probability of a single screw being defective is 2/500, as there are 2 defective screws out of 500 in each pack.

Conversely, the probability of a screw being non-defective is 498/500.

To find the probability of obtaining exactly 15 defective screws, we can use the binomial distribution formula. The probability (P) can be calculated as follows:

P = (100 C 15) * (2/500)^15 * (498/500)^85

The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

By plugging these values into the formula and performing the calculations, the probability of obtaining exactly 15 defective screws can be determined. However, I am unable to perform the calculation for you within the given word limit.

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The solution is it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

Here,

we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.

C(5) = 25(5) + 75 = 125 + 75 = 200

We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.

Hours Cost

1          $90

2         $130

3         $170

We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.

It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.

It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.

In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

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complete question:

19) The function C(x) = 25x+75 represents the labor cost (in dollars) for Bob's Auto Repair to replace

your alternator, where x is the number of hours. The table below shows sample labor costs from its main

competitor, Budget Auto Repair. The alternator is estimated to take 5 hours of labor. Which company

would you hire? Explain.

Hours 1,2,3

Cost

$90 $130 $170

Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

To calculate the amount of cardboard needed to construct the square pyramid, we need to find the surface area of each individual face and then add them together.

Given that the base of the pyramid is a square with side length [tex]\(b = 9\) inches[/tex] and the height of the triangular sides is [tex]\(a = 14\) inches[/tex], we can proceed as follows:

The surface area of the square base is [tex]\(b^2 = 9^2 = 81\)[/tex] square inches.

Each triangular face has a base equal to the side length of the square base, [tex]\(b = 9\) inches[/tex], and a height of [tex]\(a = 14\) inches[/tex]. Therefore, the surface area of each triangular face is [tex]\(\frac{1}{2} \times b \times a = \frac{1}{2} \times 9 \times 14 = 63\)[/tex] square inches.

Since there are four triangular faces in a square pyramid, the total surface area of the triangular faces is [tex]\(4 \times 63 = 252\)[/tex] square inches.

Adding the surface area of the square base and the total surface area of the triangular faces, we get [tex]\(81 + 252 = 333\)[/tex] square inches.

Therefore, Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

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If the volume of an open rectangular object or space is 24.3m³ with a height of 2.7m, the surface area is 9m.

The surface area can be determined by dividing the volume by the height.

This is because the product of the surface area and the height gives the volume.

The surface area is a product of the length and width, while the volume is the product of the length, width, and height.

Volume = 24.3m³

Height = 2.7m

Surface area = 9m (24.3m³ ÷ 2.7)

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Answer:

Step-by-step explanation:

Pneumonoultramicroscopicsilicovolcanoconiosis

Answer: Supercalafragilisticexpialadocious

Step-by-step explanation:

The area of the pentagon using the composite area formula is 37 in².

A pentagon is one of the many types of polygon having five sides and five angles.

To calculate the area of the pentagon, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

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The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Answer:

i'm pretty sure it is "the graph forms a parabola"

Step-by-step explanation:

There is a bias because the question suggests a particular answer. Option B

A systematic inaccuracy or departure from the true value that causes inaccurate conclusions to be drawn about a population or topic under study is referred to as bias in research. Any step of the research process, including study design, data collecting, analysis, and interpretation, is susceptible to bias.

It may be caused by a number of variables, including the sample strategy, participant selection, measuring methods, the researcher's own ideas and preconceptions, or the influence of outside variables like funding sources or political motivations.

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Answer: 5(x - 12) = 3x

Step-by-step explanation:

       We can cross-multiply to answer this question.

[tex]\frac{5}{x} =\frac{3}{x-12}[/tex]

5 * (x - 12) = 3 * x

5(x - 12) = 3x

Answer:

b) 5(x - 12) = 3x

Step-by-step explanation:

Given expression,

→ 5/x = 3/(x - 12)

Now we have to,

→ Find the equivalent expression.

Let's find the required answer,

→ 5/x = 3/(x - 12)

Cross multiplying both sides:

→ 5(x - 12) = 3(x)

→ 5(x - 12) = 3x

Applying Distributive property:

→ 5(x) - 5(12) = 3x

→ 5x - 60 = 3x

Solving for the value of x:

→ 5x - 3x = 60

→ 2x = 60

→ x = 60/2

→ [ x = 30 ]

Hence, the value of x is 30.