Robyn adopted a child who is exactly 28 years younger than her.
In one year's time, Robyn will be 3 times as old as her child will be.
How old is Robyn now?

To find the derivative of the function y = ∫(6t² + e^t) dt using Part 1 of the Fundamental Theorem of Calculus, we apply the derivative to the integrand.

Part 1 of the Fundamental Theorem of Calculus states that if a function y(x) is defined as the integral of a function f(t) with respect to t from a constant a to x, then the derivative of y(x) with respect to x is equal to the integrand evaluated at x. In this case, we have y(x) = ∫(6t² + e^t) dt. To find dy/dx, we differentiate the integrand with respect to t, yielding dy/dx = d/dx(6t² + e^t) = 12tx + e^t.

Part 2 of the Fundamental Theorem of Calculus states that if a function F(u) is defined as the integral of a function f(u) with respect to u from a constant a to x, then the integral of f(u) from a to b can be evaluated as F(b) - F(a). In this case, we have ∫(5u + 7)(3u - 1) du. To evaluate this integral, we expand the integrand and find the antiderivative: ∫(15u² - 2u + 21u - 7) du = ∫(15u² + 19u - 7) du. The antiderivative is F(u) = 5u³/3 + 19u²/2 - 7u. Evaluating F(u) at the endpoints a and b, we have F(b) - F(a) = (5b³/3 + 19b²/2 - 7b) - (5a³/3 + 19a²/2 - 7a).

In summary, using Part 1 of the Fundamental Theorem of Calculus, the derivative of y = ∫(6t² + e^t) dt is dy/dx = 12tx + e^t. Using Part 2 of the Fundamental Theorem of Calculus, the integral ∫(5u + 7)(3u - 1) du can be evaluated as (5b³/3 + 19b²/2 - 7b) - (5a³/3 + 19a²/2 - 7a)

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Answer:

A

Step-by-step explanation:

Step-by-step explanation:

The expression that represents the perimeter of the triangle is 13a + 5c + 2b + 46 centimeters.

So, the expression for the perimeter of the triangle is:

(7a + 2b) + (6a + 3c) + (3c + 46)

Simplifying and combining like terms, we get:

13a + 5c + 2b + 46

Rational functions can also have holes in their graphs, which  do when a factor in the numerator and denominator cancel out.

For  illustration, the function

\(h( x) = ( x2- 4)/(x^{2} )( x- 2)\)has a hole at x =  2,

where the factor ( x- 2) cancels out in the numerator and denominator.  

Graphing rational functions can be tricky, but it helps to identify the  perpendicular and vertical asymptotes, any holes in the graph, and the  of the function near these points.

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One of the benefits of representing data sets using frequency distributions is; Organizing the data into a frequency distribution can make patterns within the data more evident.

Frequency distributions are usually portrayed as frequency tables or graphs or charts. Frequency distributions may likely show either the actual number of observations falling in each range or the percentage of observations and this distribution is called a relative frequency distribution.

There are three types of frequency distributions namely;

Looking at the options, the most appropriate one showing a benefit of using graphs of frequency distributions is; Option A

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Answer:

self selected

Step-by-step explanation:

i hope it is helpful for you

Answer:

$36 in change

Step-by-step explanation:

book cost total: 64

100-64=36

If you aren't sure how to read the chart, each "X" represents one book and the numbers below represent the price.

The probability that, if driven normally, the car will get 75 miles per gallon or better is approximately 0.5000 or 50%.

To find the probability that the car will get 75 miles per gallon or better, we need to calculate the area under the normal distribution curve to the right of the value 75.

Given information:

Mean (μ) = 75 miles per gallon

Standard deviation (σ) = 10 miles per gallon

To calculate this probability, we can use the standard normal distribution table or standardize the value and use the standard normal distribution.

Standardize the value:

To standardize the value 75, we use the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

Standardized value:

Z = (75 - 75) / 10

Z = 0

Calculate the probability:

Now, we need to find the probability corresponding to the standardized value of 0. We can use the standard normal distribution table to find this probability.

From the standard normal distribution table, the area to the right of the standardized value 0 is 0.5000. Since we want the probability to the right of 0 (or greater than 0), we subtract this value from 1.

Probability = 1 - 0.5000

Probability = 0.5000

Therefore, the probability that, if driven normally, the car will get 75 miles per gallon or better is approximately 0.5000 or 50%.

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Answer:

x= 3

Step-by-step explanation:

Move all the terms that do not contain x to the right side and solve.

Hope this helped!

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Answer:

We can approach this problem using combinatorics.

First, we need to find the total number of ways to rank the 4 men and 6 women. This is given by 10! (10 factorial), which is the number of permutations of 10 distinct items.

Next, we need to find the number of ways in which a woman can achieve the highest ranking (x = 1). This can be done by fixing the highest ranking to one of the 6 women, and then permuting the remaining 9 people. This gives us 6*9! ways to arrange the people such that a woman achieves the highest ranking.

Therefore, p(x = 1) = (6*9!)/10! = 6/10 = 0.6

For x = 3, we need to choose 2 women (out of 6) who will get the top 3 rankings, and then permute the remaining 8 people. This gives us (6 choose 2)*8! ways to arrange the people such that 2 women get the top 3 rankings. Therefore, p(x = 3) = [(6 choose 2)*8!]/10! = 15/54 = 0.2778

For x = 4, we need to choose 3 women (out of 6) who will get the top 4 rankings, and then permute the remaining 7 people. This gives us (6 choose 3)*7! ways to arrange the people such that 3 women get the top 4 rankings. Therefore, p(x = 4) = [(6 choose 3)*7!]/10! = 20/54 = 0.3704

For x = 6, all the women will have the lowest rankings. This can be done by permuting the 4 men and then permuting the 6 women. This gives us 4!*6! ways to arrange the people such that all women have the lowest rankings. Therefore, p(x = 6) = (4!*6!)/10! = 0.01296

Note that the sum of probabilities for all possible values of x should be equal to 1.

Step-by-step explanation:

If the expected counts are less than 5, then the chi-square test cannot be performed.

To perform the appropriate chi-square test using the data from this study, the following conditions must be satisfied:

i. The population distribution is approximately normal.

ii. The treatments were randomly assigned.

iii. The expected counts are all at least 5.

The chi-square test is a statistical method that examines whether observed data matches with the expected data.

The chi-square test is used to compare the categorical data between two or more groups. It is a non-parametric test of the statistical hypothesis.

In order to perform the appropriate chi-square test using the data from this study, the following conditions must be satisfied:

1. The population distribution is approximately normal: This means that the population data should be distributed normally. The normal distribution should be checked using a normal probability plot, which shows the data points relative to the standard normal distribution curve.

If the data is not normally distributed, then the chi-square test cannot be performed.

2. The treatments were randomly assigned: The treatments should be randomly assigned to the study participants in order to ensure that the results are not biased.

If the treatments are not randomly assigned, then the chi-square test cannot be performed.

3. The expected counts are all at least

4: The expected counts for each category should be at least

5. This means that there should be a sufficient number of observations in each category. If the expected counts are less than 5, then the chi-square test cannot be performed.

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For maximum strength training, it is recommended to perform 1 to 5 repetitions per set, with heavier weights and longer rest periods between sets. This type of training focuses on increasing muscle strength and power.

Maximum strength training is a type of resistance training that is designed to increase muscle strength and power. The number of repetitions per set is an important factor in developing maximum strength, and the recommended range is between 1 and 5 repetitions. For this type of training, heavier weights and longer rest periods between sets are used. This allows the muscles to recover and build strength. During each set, the goal is to lift the weight as fast and explosively as possible, to help increase muscle power. It is important to also keep proper form and technique when performing exercises, as any incorrect movements can result in injury. Maximum strength training should be done with a gradual increase in weight, so that the body can properly adjust to the new load. It is also important to vary the exercises and the intensity level to help the body adapt to the training and to avoid plateaus in progress. To ensure optimal results, it is recommended to consult with a professional trainer or physical therapist.

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2.4645×10⁴ gallons of milk do United States dairy cows produce each year.

We need scientific notation reason is large number can be written in compact form.

According to the given question There are approximately 9.3 x 106 dairy cows in the United States.

Which is 985.8 cows in the united states.

Also given each cow produces 2.5×10 = 25 gallons of milk per year.

∴ United state cows will produce (985.8×25) gallons of milk each year which is = 24645 gallons of milk per year.

Now 24645 can be represented as 2.4645×10⁴ gallons of milk.

We have raised it to the 4th power of 10 because we have moved the decimal 4 digits before to balance the number and we know that in scientific notation base should be greater than 1 and less than 4 so moving the decimal to some other place is not valid.

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The total length of wire used to construct the frame of the square-bottomed rectangular box is 12x, where l represents the total length of wire and x denotes the length of each segment of wire.

The total length of the wire used to construct the frame of a square-bottomed rectangular box can be represented by l.

In a square-bottomed rectangular box, there are twelve edges that need to be constructed with wire. Each edge consists of two segments of equal length, resulting in a total of six pairs of edges. Let's denote the length of each segment of wire as **x**.

Therefore, the total length of wire used, **l**, can be calculated by multiplying the number of pairs of edges by the length of each segment of wire:

l = 2x + 2x + 2x + 2x + 2x + 2x

l = 12x

Hence, the total length of wire used to construct the frame of the square-bottomed rectangular box is 12x, where **l** represents the total length of wire and **x** denotes the length of each segment of wire.

It's important to note that the exact value of **l** will depend on the specific dimensions of the square-bottomed rectangular box and the chosen length of each segment of wire.

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The expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

To express the area under the graph of f(x) as a limit, we divide the interval [2, 4] into n subintervals of equal width Δx = (4 - 2)/n = 2/n.

Let xi be the right endpoint of each subinterval, with i ranging from 1 to n. The area of each rectangle is given by f(xi)Δx.

By summing the areas of all the rectangles, we obtain the Riemann sum: A = Σ[f(xi)Δx], where the summation is taken from i = 1 to n.

To find the expression for the area under the graph of f(x) as a limit, we let n approach infinity, making the width of the rectangles infinitely small.

This leads to the definite integral: A = ∫[2, 4] f(x) dx.

In this case, the expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

Evaluating this limit would yield the actual value of the area under the curve.

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Answer:

4x^3

Step-by-step explanation:

4x^3 goes into both number and when you divide you get

10+9x^2

Answer:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

10/1÷5/6

Applying the fractions formula for division,

  10×6  

= --------

    1×5

=60/5

Simplifying 60/5, the answer is

=12

Answer:

1.2

Step-by-step explanation:

5/6=8.333

10/8.3333

The hotel will need 32 feet of tiling in order to add this border.

The given figure represents a water fountain. A hotel needs to retile part of a water fountain. They plan to make a one -inch tile border around the edge of the pool. Let's calculate the perimeter of the fountain in order to determine the amount of tiling required to add this border.Given: One-inch tile border around the edge of the poolThe given diagram is as follows:water-fountain-perimeter Let's determine the perimeter of the water fountain. Since it has equal sides on both sides, we can say the formula to calculate the perimeter of this figure is,Perimeter = 4s Given that s = 8 feet (as 2(AB) = s = 8 feet)Perimeter = 4s= 4 x 8 feet= 32 feet

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Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we consider:

Hence the costs for x hours of moving from each company are given as follows:

For 7 hours, the costs are given as follows:

Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.

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Answer:

(x-2)^2+4.

Hope this helps!

The probability that at least one calculator will be defective is 0.7305.

The probability that at least one of the calculators is defective can be calculated using the formula:

P(at least one defective calculator) = 1 - P(no defective calculator)

The probability of selecting a defective calculator from the group of defective calculators is 16/46.

Since the calculators are selected randomly, the probability of selecting a non-defective calculator is 30/46.

Therefore, the probability of selecting 4 non-defective calculators from the group of 46 calculators is:

30/46 × 29/45 × 28/44 × 27/43 = 0.2695 (rounded to 4 decimal places)

Using the formula above, we can calculate the probability that at least one calculator will be defective:

P(at least one defective calculator) = 1 - P(no defective calculator)P(no defective calculator)

                                                         = 1- 0.2695 P(at least one defective calculator)

                                                         = 1 - 0.2695

                                                         = 0.7305

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Answer:

x=6

Step-by-step explanation:

6(x-3)=18

Then divide both sides by 6

x-3=3

Add 3 to both sides

x=6

Answer:

x = 6

Explanation:

use distributive property: a(b + c) = ab + ac

change sides

add integers

divide both sides by 6

Answer:

this is the answer r≈19.42in

because you radius with a circumference of 122in

and that's your answer

Step-by-step explanation:

hope it works

Answer:

So M is the midpoint of RS lmbo

Step-by-step explanation:

What you have here are lengths of two equal segments, expressed as different algebraic expressions.

you just set those two expressions equal, and solve for x.  Then plug that x into EITHER of the two expressions, to get the equal lengths of RM & MS.

Answer:

50

Step-by-step explanation: