-2 x + 4 =2 x - 4 solve .

The average rate of change for a function over an interval can only be determined with two endpoints. The formula to calculate the average rate of change is (f(b) - f(a)) / (b - a),This expression calculates the average slope of the line joining the points (0, f(0)) and (t, f(t)) on the graph of the function f(x) over the interval [0,t].

Rate refers to the measure of how fast something changes over time, distance, or any other unit of measurement. It is expressed as a ratio of the change in a quantity over a given interval.

A function is a mathematical relationship between two quantities, typically represented as f(x), where x is the independent variable and f(x) is the dependent variable determined by a set of rules or operations applied to x.

According to the given information:

The average rate of change for the interval a to b is a measure of how much a quantity has changed, on average, per unit of time or distance during that interval. Specifically, for a function f(x), the average rate of change over the interval [a,b] is calculated as the difference in the function values at the endpoints divided by the length of the interval:

Average rate of change = (f(b) - f(a)) / (b - a)

In the given problem, if the interval is [0,t], where t is some positive value, then the average rate of change for the function f(x) over that interval is given by:

Average rate of change = (f(t) - f(0)) / t

This expression calculates the average slope of the line joining the points (0, f(0)) and (t, f(t)) on the graph of the function f(x) over the interval [0,t]. This concept is useful in many areas of mathematics, physics, and engineering, where it can help us understand how a quantity changes over time or distance.

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The best measure of variability for this data is the range, and its value is 10.

The range, which is the difference between the dataset's largest and smallest values, is the appropriate variable for the data at hand.

We simply subtract the smallest value from the largest value to determine the range:

Range = 12 - 2 = 10

Therefore, the best measure of variability for this data is the range, and its value is 10.

Variability, not mean and median, are measures of central tendency. Another way to measure variability is the IQR (interquartile range), but it's not the best option for this dataset because it only takes into account the middle half of the data and may not cover the whole range of values.

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To simplify 6x8y ÷ -3x2y2, we first need to divide the coefficients and simplify the variables separately.

Dividing 6 and -3 gives us -2.

For the variables, we subtract the exponents of x and divide them, which gives us x^(8-2) or x^6.

We also subtract the exponents of y and divide them, which gives us y^(1-2) or y^-1. To simplify y^-1, we move the variable to the denominator and make it y^1 or simply y.

Therefore, our final answer is -2x^6y.

So, 6x8y ÷ -3x2y2 = -2x^6y

Answer:

82,000

Step-by-step explanation:

The linear regression equation for the data in the table is given as follows:

y = 3x - 2.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

From the table, the points of the data-set in this problem are given as follows:

(1, 4), (2, 1), (3, 5), (4, 10), (5, 16), (6, 19), (7, 15).

Using a calculator, the line of best fit is given as follows:

y = 3x - 2.

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Answer:

To find the time it takes for the two SUVs to pass each other, we can use the formula:

time = distance / relative speed

The relative speed is the sum of the speeds of the two SUVs, as they are moving towards each other. Let's calculate it:

Relative speed = speed of first SUV + speed of second SUV

Relative speed = 39 mph + 32 mph

Relative speed = 71 mph

Now, we can plug in the values into the formula to find the time it takes for the SUVs to pass each other:

time = 639 miles / 71 mph

Using division, we get:

time = 9 hours

So, it will take 9 hours for the two SUVs to pass each other.

The width of the rectangular garden is 10 feet using the formula of the perimeter of a rectangle.

The perimeter of a rectangle is the sum of the lengths of all its sides. If the length of a rectangle is l and the width is w, then the perimeter is given by the formula:

Perimeter = 2l + 2w

In other words, the perimeter is twice the length plus twice the width.

Let's denote the width of the garden with "w".

The perimeter of the garden is the sum of the lengths of all sides:

P = 2w + 2l

where "l" is the length of the garden. We know that the perimeter of the garden (i.e., the length of the fence) is 60 feet, and the length of the garden is 20 feet. So we can plug these values into the equation:

60 = 2w + 2(20)

Simplifying the equation:

60 = 2w + 40

Subtracting 40 from both sides:

20 = 2w

Dividing both sides by 2:

w = 10

Therefore, the width of the garden is 10 feet.

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The lower bound of B is all elements of A that are below all elements of B. In this case, the lower bound of B is {a, b}.

Lower Bound of B: The lower bound of B is a set of elements that are less than or equal to every element of B. In this case, the lower bound of B is {a, b}; these are the elements which are less than or equal to every element of B.

Greatest Lower Bound of B: The greatest lower bound of B is an element which is less than or equal to every element of B, and is greater than any other element that is less than or equal to every element of B. In this case, the greatest lower bound of B is c. It is the element which is less than or equal to every element of B, and it is greater than a and b, which are also less than or equal to every element of B.

Therefore, the lower bound of B is all elements of A that are below all elements of B. In this case, the lower bound of B is {a, b}.

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Okay, let's do this step-by-step:

1) We have in-state tuition amounts and out-of-state tuition amounts for some state colleges.

2) We want to find a linear model that relates the in-state and out-of-state tuition.

3) Once we have the linear model, we can use it to predict the out-of-state tuition for an in-state tuition of $6,000.

Let's assume the data points are:

In-state tuition | Out-of-state tuition

$3,000 | $9,000

$5,000 | $11,000

$7,000 | $13,000

$9,000 | $15,000

To find the linear model:

1) Find the slope:

Slope = (Out-of-state tuition for $9,000 in-state tuition) - (Out-of-state tuition for $3,000 in-state tuition)

= $15,000 - $9,000 = $6,000

Slope = $6,000

2) Find the y-intercept:

y-intercept = Out-of-state tuition when In-state tuition = 0

= $9,000

So the linear model is:

Out-of-state tuition = Slope * In-state tuition + y-intercept

= $6,000 * In-state tuition + $9,000

To predict Out-of-state tuition for $6,000 In-state tuition:

Out-of-state tuition = $6,000 * $6,000 + $9,000

= $36,000 + $9,000

= $45,000

Rounding to the nearest choice:

Out-of-state tuition for $6,000 In-state tuition = $45,000

So the answer is c. about $12,450

Let me know if you have any other questions!

Answer:

0.73,0.71 this is the answer

Step-by-step explanation:

put in 'a+2' where 'x' is and compute:

( 3 + (a+2) )  / ((a+2) -3)    = (5+a) / (a-1)    

Answer:

The sin B got canceled and the one left same as on the other parenthesis inside the parenthesis I canceled the cos so one left now 1*1=1 and 1 over tan b plus 1 over tan b- we extract the tan to opp/adj then opp and adjacent got canceled and the one too so just only one left so 1=1

A) Expansion of the given fraction expression gives: ⁵/₆x - 1

B) The given fraction expression is not the same as that of part A

A) We are given the expression:

¹/₂x + 3 + ¹/₃x - 4

Regrouping this to get like terms together gives:

(¹/₂x + ¹/₃x) + (3 - 4)

x(¹/₂ + ¹/₃) - 1

= ⁵/₆x - 1

B) We are given the expression:

¹/₂(x + 3) + ¹/₃(x - 4)

Expanding the bracket gives:

¹/₂x + ³/₂ + ¹/₃x - ⁴/₃

= ¹/₂x + ¹/₃x + ³/₂ - ⁴/₃
= ⁵/₆x + ¹/₉

This is not the same as the answer in Part A.

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It will take 16.84 minutes for the two pools to have the same amount of water and when the two pools have the same amount of water, each pool will have 385.84 liters of water.

The amount of water in the first pool is 770 liters, since no water is being added to it.

The amount of water in the second pool is 45.75t liters, since water is being added to it at a rate of 45.75 liters per minute.

To find the time at which the two pools have the same amount of water, we can set these two expressions equal to each other and solve for t:

770 = 45.75t

t = 770 / 45.75

t = 16.84 minutes

So it will take approximately 16.84 minutes for the two pools to have the same amount of water.

To find the amount of water in each pool when they have the same amount, we can substitute t = 16.84 into either expression.

Using the expression for the second pool, we have:

Amount of water in second pool = 45.75t

= 45.75(16.84)

= 771.69 liters

Therefore, when the two pools have the same amount of water, each pool will have 771.69 / 2 = 385.84 liters of water.

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The relations that are functions are (d) the table of values and (e)  f(x) = x^3 - 3x + 2

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

The list options

Option A has two y values for the x-value of 1, so it does not satisfy the vertical line test, which is a necessary condition for a relation to be a function.

Option D represents a function.

The third option, the function f(x) = x^3 - 3x + 2, is a function by definition.

The ordered pair and the graph are not functions

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The radius are already given and hidden in the images. For example:

7) Radius = 4.1

8) Radius = 8.7

9)  Radius = 3

10) Radius = 7

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more recent use, it is also their length. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.

The diameter is the distance across a circle via its center. The radius is the distance from the center of a circle to any point on its edge. 2r=d; the radius is half the diameter. 2 r = d .

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The probabilities for this problem are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The number of cars with purchase prices less than $20,000 is given as follows:

86 + 67 + 35 = 188.

Of those 188 cars, 86 had repair costs less than $10,000, hence the probability is given as follows:

p = 86/188

p = 0.4574.

The number of cars with repair costs less than $10,000 is given as follows:

86 + 71 + 40 = 197.

Of those, 40 had a purchase price of more than $40,000, hence the probability is given as follows:

p = 40/197

p = 0.203.

The table is given by the image presented at the end of the answer.

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The image of (-12, 4) after a dilation by a scale factor of 1/4 centered at the origin is (-3, 1).

What is image of points?

In geometry, the image of a point is the position of that point after a transformation. The transformation can be a translation, rotation, reflection, dilation or any combination of these.

When we apply a transformation to a point, the resulting image may be located at a different position in the plane, or it may be the same point if the transformation is an identity transformation (i.e., no change occurs).

For example, if we translate a point (x, y) by a distance of (a, b), then its image (x', y') can be found using the formula,

x' = x + a

y' = y + b

Similarly, if we rotate a point (x, y) by an angle of θ degrees around the origin, then its image (x', y') can be found using the formula:

x' = xcos(θ) - ysin(θ)

y' = xsin(θ) + ycos(θ)

Likewise, if we reflect a point (x, y) about the x-axis, then its image (x', y') can be found using the formula,

x' = x

y' = -y

And if we dilate a point (x, y) by a scale factor of k with respect to a center of dilation (h, k), then its image (x', y') can be found using the formula,

x' = h + k(x - h)

y' = k(y - k)

In summary, the image of a point is its position after a transformation, and it can be found using the appropriate formula for the specific type of transformation.

Here to find the image of the point (−12, 4) after a dilation by a scale factor of 1/4 centered at the origin, we can use the following formula,

(x', y') = (1/4)(x, y) where (x, y) is the original point, and (x', y') is its image after dilation.

Substituting the values of the original point,

(x', y') = (1/4)(-12, 4)

Simplifying,

(x', y') = (-3, 1)

Therefore, the image of (-12, 4) after a dilation by a scale factor of 1/4 centered at the origin is (-3, 1).

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Correct question is "what is the image of (−12,4) after a dilation by a scale factor of 1/4 centered at the origin?"

The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

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Answer:

Step-by-step explanation:

a

Answer: D

Step-by-step Explanation:

Circumference of a circle is : 2 [tex]\pi \\[/tex] r

Radius: diameter/2

Plug into equation and round.

2[tex]\pi[/tex](6) = 37.7 or 38.

Answer:

D. 96

Step-by-step explanation:

1/2 (82 + 110)

1/2 (192) = 96

Answer:

96 D

Step-by-step explanation:

Step-by-step explanation:

Let X be the amount invested in CDs, Y be the amount invested in bonds, and Z be the amount invested in stocks.

We know from the problem that:

X + Y + Z = 135000 ---(1) (the total amount invested is $135000)

0.0375X + 0.035Y + 0.097Z = 6337.5 ---(2) (the total annual income from the investments is $6337.5)

Y = X + 60000 ---(3) (the amount invested in bonds is $60000 more than the amount invested in CDs)

We can use equation (3) to substitute for Y in equations (1) and (2), then solve for X and Z as follows:

X + (X + 60000) + Z = 135000

2X + Z = 75000

0.0375X + 0.035(X + 60000) + 0.097Z = 6337.5

0.0725X + 0.097Z = 8550

Using the system of equations 2X + Z = 75000 and 0.0725X + 0.097Z = 8550, we can solve for X and Z to get:

X = 22500

Z = 78000

Substituting back into equation (3), we get:

Y = X + 60000 = 82500

Therefore, the amounts invested in CDs, bonds, and stocks were $22500, $82500, and $78000 respectively.

The correct answer is option A. That is the average cost of gasoline, Clinton and Stacy will spend on gasoline for the round trip to Yellowstone National Park and back home is $1,166.40.

Miles and gallons are two different units of measurement and cannot be converted directly to each other. Miles measure distance, while gallons measure volume. However, it is possible to calculate the number of gallons of gasoline used for a given distance traveled if you know the fuel efficiency of the vehicle in miles per gallon.

To calculate the number of gallons used, you can divide the number of miles traveled by the fuel efficiency in miles per gallon. For example, if you travel 100 miles and your vehicle gets 25 miles per gallon, you will use 4 gallons of gasoline (100 miles / 25 miles per gallon = 4 gallons).

Given that the distance from their home to Yellowstone National Park is 1,701 miles. And on average the RV gets 10.5 miles per gallon and on average the cost of a gallon of gasoline is $3.60.

The round trip from their home near Austin, Texas, to Yellowstone National Park and back is a distance of 2 x 1,701 = 3,402 miles.

Since the RV gets 10.5 miles per gallon, the total gallons of gasoline required for the round trip would be 3,402/10.5 = 324 gallons.

The total cost of gasoline for the round trip would be 324 x $3.60 = $1,166.4.

Therefore, the answer is option A. $1,166.40.

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The person must leave the money in the bank for approximately 10.6 years (rounded to the nearest tenth of a year) for it to reach 8700 dollars.

To solve this problem,  the compound interest formula:

[tex]A = P(1 + r/n)^{nt}[/tex]

where:

A = the future worth of the speculation

P = the underlying speculation (present worth)

r = the yearly loan cost (as a decimal)

n = the times the interest is accumulated each year

t = the quantity of years

We need to find the worth of t that will make An equivalent to 8700 bucks. We are aware that P is $3,500 and that r is 6.25 percent, or 0.0625 in decimal form. The value of n is unknown, but the fact that the interest is compounded annually indicates that n is 1.

Substituting these values into the formula, we get:

[tex]8700 = 3500(1 + 0.0625/1)^{1t}[/tex]

Simplifying the right side, we get:

[tex]8700 = 3500(1.0625)^t[/tex]

Dividing both sides by 3500, we get:

[tex]2.485714286 = 1.0625^t[/tex]

Taking the logarithm of both sides (with any base), we get:

[tex]log(2.485714286) = log(1.0625^t)[/tex]

Using the power rule of logarithms, we can bring the exponent t down:

[tex]log(2.485714286) = t log(1.0625)[/tex]

Dividing both sides by log(1.0625), we get:

[tex]t = log(2.485714286) / log(1.0625)[/tex]

Using a calculator, we get:

t ≈ 10.6

Therefore, to reach $8700, the individual must keep the money in the bank for approximately 10.6 years (rounded to the nearest tenth of an year).

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Answer:

tan D = 4.9/9.1 = 7/13

tan F = 9.1/4.9 = 13/7

The volume of the leaning regular hexagonal prism is 396.90 cubic inches.

The volume of a leaning regular hexagonal prism can be calculated using the formula

V = (P×h×sin(a))/2, where P is the perimeter of the base, h is the slanted height of the prism, and a is the angle at which the prism is leaning.

In the given problem, P = 36 inches, h = 11 inches, and a = 70°.

Substituting these values in the formula, we get:

V = (36×11×sin(70°))/2

= 396.90 inches³

Therefore, the volume of the leaning regular hexagonal prism is 396.90 cubic inches.

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A) The monthly payment (PMT) for the loan is $-244.13.

B) The total interest for the loan is $1,718.20 (rounded to the nearest cent).

To find the monthly payments (PMT) and the total interest for the loan, we use the formula for calculating the PMT for a loan with a fixed interest rate, known as the Amortizing Loan Payment Formula:

PMT = P × r × (1 + r)^n / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate divided by 12)

n = Number of months in the loan term

Given:

No of periods = 48

Principal amount (P) = $10,000

Annual interest rate = 8%

Loan term = 4 years

First, let's calculate the monthly interest rate (r):

r = Annual interest rate / 12 months

r = 8% / 12

r = 0.08 / 12

r = 0.00667 (rounded to 5 decimal places)

Next, we calculate the number of months in the loan term (n):

n = Loan term in years × 12 months/year

n = 4 years × 12

n = 48

Let's put the values into the formula to calculate the monthly payment (PMT):

PMT = $10,000 × 0.00667 × (1 + 0.00667)^48 / ((1 + 0.00667)^48 - 1)

PMT = $-244.13 (rounded to the nearest cent)

B) To calculate the total interest, we can multiply the monthly payment by the number of months in the loan term, and then subtract the principal amount:

Total interest = (PMT × n) - P

Total interest = ($157.08 × 48) - $10,000

Total interest = $1,718.20

Thus, the total interest for the loan is  $1,718.20 (rounded to the nearest cent).

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There is sufficient evidence at 0.10 because Yes, because 0.001 < 0.10

Alana is running a test to analyze if the amount of messages transmitted between them surpasses an average of 100 daily.

The given α, or significance level, is 0.10, which requires proof strong enough to affirm the alternative hypothesis (H: μ > 100) while negating the null hypothesis (H0: μ = 100), supposing P < 0.10.

As the P-value is approximately 0.001 and hence lower than 0.10, it is sufficient evidence prohibitting acceptance of the null hypothesis and proposing that they usually dispatch more than 100 communications each day.

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Alana and her friends have been using a group messaging app for over a year to chat with each other. She suspected that, on average, they sent each other more than 100 messages per day. She took a random sample of 30 days from their chat history and recorded how many messages were sent on those days. The sample data had a mean of 127 messages and a standard deviation of 44 messages.

Alana used those results to test Hoμ= 100 messages versus H: > 100 messages, where is the average number of messages sent per day. She calculated a test statistic of t≈ 3.36 and a P-value of approximately 0.001. Assume that the conditions for inference were met.

Is there sufficient evidence at the a = 0.10 level to conclude that, on average, they sent each other more than 100 messages per day?

Choose 1 answer:

No, because 0.001 < 0.10.

Yes, because 0.001 < 0.10.

No, because 0.001 < 3.36.

Yes, because 0.001 < 3.36.

The possible number of minutes Pablo has used his phone in a month is given by the inequality m ≥ 1009 minutes

Given data ,

Let's assume that the number of minutes Pablo has used his phone in a month is denoted by "m". Given that he pays a monthly fee of $24 and an additional $0.06 per minute, the total cost of his phone service in a month can be expressed as:

Total cost = Monthly fee + (Per minute charge x Number of minutes used)

Total cost = $24 + ($0.06 x m)

On simplifying , we get

$ 84.54 = $24 + ($0.06 x m)

Subtracting 24 on both sides , we get

m = $60.54 / $0.06

m = 1009 minutes

Hence , the inequality is m ≥ 1009 minutes

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