Water is being pumped into a pool at a constant rate P(t):
P(t)
=1170 gal/hour
- for 10 hours, where t is the number of hours since pumping began. The pool contained 1200 gallons of water at t= 0. However, there is a crack in the pool that is
getting larger over time. Water leaks from the pool at a rate L(t):
L(t)=0.3e' gal/hour
_during the same 10 hours.
a. What is the rate of change of water in the pool at t=5 hours?
b. Write an integral expression to calculate the total volume of water in the pool at t= 10 hours. Calculate the volume of water in the pool at t= 10 hours in
gallons.
c. What is the average rate of change of water in the pool over the 10 hours? Indicate units.
d. Find the absolute maximum volume of water, in gallons, in the pool over the interval, 0

The required equation function j which is the transformation of [tex]f(x)= x^{1/2}[/tex] is  [tex]j(x)= (x+2)^{1/2}[/tex] .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  [tex]j(x)= (x+2)^{1/2}[/tex]  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of [tex]f(x)= x^{1/2}[/tex] is  [tex]j(x)= (x+2)^{1/2}[/tex] .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

The HCF of each of the pair of numbers are 2, 6 and 4

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

The HCF of each of the pair of numbers is calculated as follows

Pair 1

2 = 2

36 = 2 * 2 * 3 * 3

The highest common factor above is

HCF = 2

Pair 2

42 = 2 * 3 * 7

24 = 2 * 2 * 2 * 3

The highest common factor above is

HCF = 2 * 3

Evaluate

HCF = 6

Pair 3

8 = 2 * 2 * 2

12 = 2 * 2 * 3

The highest common factor above is

HCF = 2 * 2

Evaluate

HCF = 4

Hence, the HCF of each of the pair of numbers are 2, 6 and 4

The venn diagrams are also attached

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Mathis's rate of return on his investment of $1,000 in a mutual fund that sold for $1,250, including taxes, inflation, and administrative costs of $8 was 24.2%.

The rate of return represents the percentage of the net gain an investment generates.

The rate of return is determined using the quotient of the division operation between the return and the initial investment.

The return or net return is the difference between the final value and the initial value after taking into account taxes, inflation, and other administrative costs.

The initial investment = $1,000

The final sales value = $1,250

Taxes, inflation, and other costs = $8

Net sales proceeds = $1,242 ($1,250 - $8)

Returns = $242 ($1,242 - $1,000)

Rate of return = 24.2% ($242 ÷ $1,000 x 100)

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The probability of selecting a checkered fabric sample is determined by dividing the number of checkered fabric samples by the total number of fabric samples. In this case, Lacey has 10 fabric samples and 4 of them are checkered. Therefore, the probability of selecting a checkered fabric sample is 4/10 or 0.4.

In other words, there is a 40% chance that Lacey will choose a checkered fabric sample for her bedroom. It is important to note that probability is always expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In conclusion, the probability of selecting a checkered fabric sample from Lacey's options is 0.4 or 40%.
Hi! The probability of Lacey selecting a checkered fabric sample can be calculated using the formula: probability = number of successful outcomes / total number of outcomes. In this case, there are 4 checkered fabric samples and a total of 10 fabric samples. So, the probability of selecting a checkered fabric is:

Probability = 4 (checkered samples) / 10 (total samples) = 2/5 or 0.4.

Therefore, the probability that a randomly selected fabric sample will be checkered is 0.4 or 40%.

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The domain to plot the growth function is 0 ≤ x < 7

Given that

f(d) = 11(1.01)ᵇ

When the radius is approximately 1179 mm

We have

11(1.01)ᵇ = 11.79

Divide

(1.01)ᵇ = 1.072

Take the logarithm

d = log(1.072)/log(1.01)

Evaluate

d = 6.99

So, the reasonable domain is 0 ≤ x < 7

Here, we have

f(d) = 11(1.01)ᵇ

The y-intercept is 11

This means tha the initial radius of the algae is 11 mm

For the average rate, we have

f(7) = 11(1.01)⁷ = 11.79

f(2) = 11(1.01)² = 11.22

So, we have

Rate  = (11.22 - 11.79)/(2 - 7)

Evaluate

Rate  = 0.114

So, the average rate of change from day 2 to day 7 is 0.114 mm per day

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Answer:

8.4

Step-by-step explanation:

C^2-B^2=A^2

12.3^2=151.29

9^2=81

151.29-81=70.29

square root of 70.29

is 8.38

Rounded to the nearest tenth is

8.4 or B

Answer:

8 meters

Step-by-step explanation:

4(16)=64

They have the same area so the area of the square is also 64.

x^2=64

x=8

The best definition of the test statistic is the number of standard errors above or below the expected outcome that our sample z-score corresponds to. In other words, the test statistic measures how far our sample mean deviates from the expected population mean in terms of standard deviation units.

The test statistic is a crucial element in hypothesis testing as it helps us determine the probability of obtaining our sample mean by chance. We use the test statistic to calculate the p-value, which is the probability of obtaining a result as extreme as our sample mean under the null hypothesis.

The boundary value corresponding to the p-value is determined by the level of significance we choose for our test. If our p-value is less than the level of significance (usually 0.05), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

In summary, the test statistic is a measure of how far our sample mean deviates from the expected population mean in standard deviation units. It is used to calculate the p-value and determine the level of significance for our hypothesis test.
The best definition of the test statistic among the given terms is: the number of standard errors above or below the expected outcome that our sample represents. A test statistic is a value calculated from sample data that is used to determine whether to reject or fail to reject a null hypothesis in hypothesis testing. It measures how far the sample statistic is from the hypothesized population parameter, considering the sample's variability.

In simpler terms, the test statistic helps us understand how likely our sample results are, given the null hypothesis. It does this by comparing the sample's outcome to what we would expect under the null hypothesis, considering the variability within the sample. By calculating the test statistic, we can then determine the corresponding p-value, which represents the probability of obtaining the observed results or more extreme results, assuming the null hypothesis is true.

In summary, the test statistic quantifies the difference between the sample outcome and the expected outcome under the null hypothesis, expressed in terms of the number of standard errors. It helps us make decisions about the null hypothesis based on the calculated p-value.

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The solution of the equations is (6, 1).

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Using the substitution method.

We can start by setting the two expressions for Y equal to each other since they both represent the same value of Y:

-Y + 7 = (3/2)X - 3

Next, we can isolate Y on one side of the equation by subtracting 7 from both sides:

-Y = (3/2)X - 10

Then, we can multiply both sides of the equation by -1 to isolate Y and make it positive:

Y = -(3/2)X + 10

Now we have expressions for Y in terms of X for both equations. We can set them equal to each other to find the value of X that satisfies both equations:

-X + 7 = -(3/2)X + 10

To solve for X, we can start by adding (3/2)X to both sides:

(1/2)X + 7 = 10

Next, we can subtract 7 from both sides:

(1/2)X = 3

Finally, we can multiply both sides by 2 to solve for X:

X = 6

Now that we have found the value of X, we can substitute it back into one of the original equations to find the corresponding value of Y.

Let's use the first equation:

Y = -X + 7

Y = -6 + 7

Y = 1

Therefore,

The solution of the equations is (6, 1).

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Answer: it would be 13 beeps

Step-by-step explanation:

The method used to determine the probability that a football team will win the next game is subjective.

The subjective method involves relying on personal judgment, experience, or expert opinion to estimate the probability of an event. In this case, the sports analyst has assessed various factors such as team performance, player injuries, historical data, and other relevant information to form their subjective opinion that the team's probability of winning is 0.37.

This method is based on the analyst's subjective assessment and may vary from one analyst to another. It does not involve any formal calculations or statistical techniques. The probability estimate is derived from the individual's knowledge, expertise, and perception of the situation.

It's important to note that subjective probabilities can be influenced by biases or personal opinions, and they may not always accurately reflect the true probability of an event. However, they can provide valuable insights and serve as a useful starting point for decision-making or further analysis.

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The point B is 27 meters east of point A.

Since we want to find the distance east, we need to consider the horizontal component of the displacement between the two points.

Using trigonometry, we can determine the eastward distance using the cosine function:

Eastward distance = 54 m x cos(061°)

Eastward distance ≈ 54 m x cos(61°)

                                ≈ 54 m * 0.500

                                ≈ 27 m

Therefore, point B is 27 meters east of point A.

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Answer:

Let's start by assigning variables to the unknown ages:Trisha's age = TAge of Trisha's first brother = T + 3Age of Trisha's second brother = T - 3Age of Trisha's third brother = T/3Age of Trisha's father = 3TWe know that the sum of all their ages is 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95Combining like terms, we can simplify this equation:8T + T/3 = 92Multiplying both sides by 3 to get rid of the fraction:24T + T = 276Simplifying again:25T = 276Dividing both sides by 25:T = 11.04So Trisha is 11.04 years old.We can check our answer by plugging it back into the original equation and verifying that the sum of all their ages is indeed 95:T + (T + 3) + (T - 3) + T/3 + 3T = 95

11.04 + (11.04 + 3) + (11.04 - 3) + 11.04/3 + 3(11.04) = 95

95 = 95The sum of their ages is 95, so our answer is correct. Therefore, Trisha is 11.04 years old.

Step-by-step explanation:

The missing value in the chart will be 1/9.

From the chart, the given function is an exponential function,

Since the function is 3ⁿ.

Thus, the value of the function at n= -2 will be,

=> 3ⁿ=3⁻²

=> 3ⁿ= 1/3²

=> 3ⁿ= 1/9

Therefore, the value of the function at n = -2 will be 1/9.

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[tex]3x + 2y^{2} + xy + x + 7x[/tex]

first, you combine like terms:

[tex]11x + 2x^{2} + xy[/tex]

next, rearrange the terms:

[tex]xy + 2y^{2} + 11x[/tex]

...which brings us to the answer! hope this helps, and please give me brainliest :)

To calculate the incidence of breast cancer in the unexposed group (i0) per 1,000, we need to first calculate the total number of mothers in the unexposed group. The total number of mothers in the study is 1,628 + 4,450 = 6,078.
We know that among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer.

Therefore, the incidence of breast cancer in this group is 65/4,450 = 0.0146.

To convert this incidence rate to a per 1,000 basis, we multiply by 1,000: 0.0146 x 1,000 = 14.6.

Therefore, the incidence of breast cancer in the unexposed group (i0) per 1,000 is 14.6.

It's important to note that we cannot directly calculate the incidence rate of breast cancer in the exposed group since we do not have information on the total number of mothers in that group who did not develop breast cancer. However, we can still compare the incidence rates between the exposed and unexposed groups to see if there is a significant difference.

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The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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The least number 456xy that is divisible by 20 and where x and y are different digits is 45652.

For a number to be divisible by 20, it must be divisible by both 4 and 5. Therefore, the least number 456xy that is divisible by 20 must end in a 0 and be divisible by 4.

We have:

4 + 5 + 6 + x + 2 = 17 + x

For the sum to be divisible by 4, x must be either 1 or 5.

If we choose x = 1, we get the number 45621, which is not divisible by 4.

If we choose x = 5, we get the number 45652, which is divisible by 4 and ends in 0.

Therefore, the least number 456xy that is divisible by 20 and where x and y are different digits is 45652.

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part A.

The equation of the ellipse is:

x² / 280900 + y² / 198025 = 1

part B.

The area of the ellipse at the White House is found to be  741,022.16 square feet.

The standard form equation for an ellipse is given as :

(x² / a²) + (y² / b²) = 1

Where "a" =  half the length of the major axis

b =   half the length of the minor axis.

length of the major axis = 1060 feet,

a = 1060 / 2 = 530 feet.

The length of the minor axis is 890 feet,

b = 890 / 2

b= 445 feet.

x² / 530² + y² / 445² = 1

x² / 280900 + y² / 198025 = 1

B.

a = 530 feet and b = 445 feet.

Area = π * 530 * 445

A = 741,022.16 square feet

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It will cost approximately $1,715.20 to carpet a room with 360 square feet of floor area, assuming the carpet costs $42.88 per square yard.

To calculate the cost of carpeting a room with a floor area of 360 square feet, we need to convert the area into square yards and then multiply it by the cost per square yard.

There are 9 square feet in a square yard (1 square yard = 3 feet x 3 feet = 9 square feet). Therefore, the room's floor area in square yards is:

360 square feet / 9 = 40 square yards

Next, we multiply the area (40 square yards) by the cost per square yard ($42.88) to find the total cost of carpeting the room:

Total cost = 40 square yards * $42.88 per square yard

Calculating this gives us the final result:

Total cost = $1,715.20

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The statement "NOT(MyAge > YourAge)" is true if MyAge is not greater than YourAge, which is not the case in this scenario because 30 is less than 40.

Therefore, option (a) is false.

The statement "MyAge >= YourAge" is also false because MyAge (30) is less than YourAge (40). Therefore, option (b) is also false.

Option (c) states that none of the above statements are true, which is also false because statement (a) is false.

Option (d) is irrelevant because it compares the values of MyAge and YourAge with string values, which is not the correct way to compare integers. Therefore, option (d) is also false.

The correct answer is (c) None of the above are a true statement.

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Answer:

I believe it would be 3/10 simplified, 30/100 not simplified

Step-by-step explanation:

because it is 30%, 30% in a fraction form is 3/10, or 30/100

Answer:

8 1/15 meters of ribbon left.

Step-by-step explanation:

To find this, we have to find the difference. 16-7 14/15=8 1/15. So, Beth has 8 1/15 meters of ribbon left.

The function, f(x) = 10x - 2x² can be evaluated for f(4) by substituting the value of x for 4 to get the answer: f(4) = 8.

A function is an equation that gives an output for every specific input. To evaluate a function for a given input (x), we have to plug in the value of the input into the equation to get the output of the function.

Given the equation of a function as, f(x) = 10x - 2x², to find f(4) means to plug in the value of x = 4 into the equation:

f(4) = 10(4) - 2(4²)

Evaluate:

f(4) = 40 - 32

f(4) = 8

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Answer:

gradient = 1 , y- intercept = - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

y = x - 4 ← is in slope- intercept form

with gradient m = 1 and y- intercept c = - 4