The time it takes in minutes for a leaky barrel to empty varies inversely with the rate at which the liquid is leaking on gallons per minute. The leaking rate of a certain liquid is 2 gallons per minute and it takes a barrel full of the liquid 30 minutes to empty. Co.plete the table foe the time it takes to empty the barrel foe the given rates.

Ronald will need 128π square feet to paint all the surfaces of the 8 Columns.

The formula for the total surface area of a cylinder is given by:

A = 2πr(r + h)

Where r is the radius and h is the height

In this case, each wooden cylindrical columns is 7 feet tall and have a diameter of 2 feet. Thus:

r = 2/2 = 1 feet and h = 7 feet

Thus, the total surface area of each wooden cylindrical columns will be:

A = 2π * 1 * (1 + 7)

A =  2π * 1 * 8

A = 16π square feet

Then the total surface areas of all the 8 Columns will be:

A = 8 * 16π

A = 128π square feet

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Answer:

C

Step-by-step explanation:

To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:

(2x-1)/(7x+x+2) + (x-2)/(8x-2)

Simplifying the denominators, we get:

(2x-1)/(8x+2) + (x-2)/(8x-2)

Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:

[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)

Simplifying the numerator, we get:

[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)

Combining like terms, we get:

(24x²-2) / (64x²-4)

Factoring out a 2 from the numerator and denominator, we get:

2(12x²-1) / 2(32x²-2)

Simplifying further, we get:

(12x²-1) / (16x²-1)

Therefore, the sum of the rational expressions is:

12x²-1

-----------

16x²-1

So, the answer is option C.

Assuming the Social Security contribution rate is 6.2% of the wage, Ted's contribution to Social Security can be calculated as follows:

Ted's total wage for the month = 160 hours * $10/hour = $1600

Social Security contribution = 6.2% * $1600 = $99.20

Therefore, the answer is option C. $99.20.

The estimate the number of pieces of food collected by mice is 96 and closest estimate to 24 is given by option b. 20.

Number of pieces of food collected by mice every day = 24 pieces

Total number of days mice collects the food = 4 days

To estimate the total number of pieces of food collected,

Now, multiply the number of pieces collected each day by the number of days,

Total number of pieces

= 24 pieces/day × 4 days

= 96 pieces

To estimate the answer closest to 24, we can round 24 to the nearest tens.

The nearest tens to 24 is 20.

Therefore, the estimate of collection of food pieces in 4 days by mice is equal to 96 and the closest estimate to 24 is option b. 20.

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The above question is incomplete , the complete question is:

A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?

a. 10

b. 20

c. 30

d. 40

Answer:

7

Step-by-step explanation:

All of the numbers are going up by 4 so what times 4 gives 28

thats 7

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Being male and preferring Brand A are independent, as:

P(male|Brand A) = P(male).

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.

From the table, we are already given the relative frequencies, hence the probability of being male is given as follows:

0.5 + 0.15 = 0.65.

The conditional probability of being male, given that the person prefers brand A, is given as follows:

P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 =  0.625.

As the probabilities are equal, the events are independent.

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The number of adult that paid is 234 and the number of seniors that pad is 60.

A movie theatre charges 11$ for adults and 9$ for seniors. On a particular day when 294 people paid an admission, the total receipts were 3114.

Therefore, let's find how many paid for adult and for seniors.

Let

x = number that paid for adult

y = number that paid for senior

Hence, the situation forms the following equation.

x + y = 294

11x + 9y = 3114

multiply equation(i) by 11

11x + 11y = 3234

11x + 9y = 3114

subtract the equation

2y = 120

y = 120 / 2

y = 60

Let's find x

x = 294 - 60

x = 234

Therefore,

number of adults that paid= 234

number of seniors that paid = 60

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Answer:

Step-by-step explanation: its c

The probability distribution for X is given below:

Probability of no even number, (X = 0)= 1/2

Probability of one even number, (X = 1) = 1/2

Probability of two even numbers, (X = 2) = 1/8

The probability distribution for X is found as follows:

The probability that an even number is not selected i.e. X = O

P(X = 0) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 0) = 1/2

The probability that an even number is selected once i.e. X = 1

P(X = 1) =  (2/4 * 2/4) + (2/4 * 2/4)

P(X = 1) = 1/2

The probability that an even number is selected twice i.e. X = 2

P(X = 2) = 2/4 * 2/4

P(X = 2) = 1/8

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The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Each of the other three clerks have to complete 3 reports each.

The top employee finishes 40% of the reports, or: 0.40 x 15 = 6 reports.

Therefore, the other three clerks must finish the remaining 60% of the reports.

Total reports to be completed by the other clerks = 0.60 x 15 = 9 reports

We may distribute the remaining reports evenly among the other clerks since they all have an equal number of reports to complete:

Number of reports each of the other clerks have to complete = 9 reports ÷ 3 clerks = 3 reports

Therefore, each of the other three clerks have to complete 3 reports each.

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

Answer:(−1,−4π/3)

Step-by-step explanation:Note that the point is on the circle whose radius is labeled 1, so r=1 or r=−1. Of the choices available, only an angle of −4π3, drawn from the negative x axis plots at the point Q.  So θ=−4π3, and r must be negative, as the angle is measured from the negative x axis. Thus, the polar coordinates are (−1,−4π3).

The mean is approximately 9, the median is 9, the mode is 8, and the range is 7.

To find the mean, we add up all the numbers in the data set and divide by the total number of numbers:

Mean = (7 + 6 + 8 + 12 + 9 + 13 + 8) / 7 = 63 / 7 ≈ 9

So the mean is approximately 9.

To find the median, we need to arrange the numbers in order from smallest to largest:

6, 7, 8, 8, 9, 12, 13

Since there are an odd number of values in the data set, the median is the middle value, which is 9.

To find the mode, we need to look for the value that occurs most frequently in the data set. In this case, 8 occurs twice, which is more than any other value, so the mode is 8.

To find the range, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value = 13 - 6 = 7

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The sequence of steps that translates figure W to figure X are -

Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -

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The values that make the inequality true are given as follows:

-4, -3, -2, -1,  0.

The equivalent inequality is given as follows:

b ≥ -4.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The inequality for this problem is given as follows:

b/2 ≥ -2.

b ≥ -4.

Which is composed by numbers that are greater than or equal to -4.

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Marcus jogged approximately 2 1/2 miles over the weekend.

We need to discover a common denominator to add the miles run on Saturday and Sunday. Because 10 is the least common multiple of 5 and 2,

we may convert the fractions to have a denominator of 10:

1 2/5 = 1 + 4/5 = 5/5 + 4/5 = 9/5

9/10 = 0.9 = 9/10

Now we can add the two distances:

9/5 + 9/10 = 18/10 + 9/10 = 27/10

Rounding 27/10 to the nearest 1/2 gives:

27/10 ≈ 2 1/2

Therefore, Marcus jogged approximately 2 1/2 miles over the weekend.

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Answer: (B)

Step-by-step explanation:

To determine which point is a solution to the system of inequalities, we must test each point to see if it satisfies both inequalities. Starting from point A, we plug in its coordinates (2, 9) into both inequalities. However, it does not satisfy y < 1 over 2x − 2. We then move on to point B, which has coordinates (3, 0). Plugging this into both inequalities, we find that it satisfies both of them. Therefore, the point that is a solution to the system of inequalities is point B.

Jenny earns $36 in interest in one year in her savings account.

To calculate the interest that Jenny earns in one year on her savings account, we can use the formula for simple interest:

I = P x r x t

where I is the interest earned, P is the principal amount (in this case, $1200), r is the interest rate (in decimal form), and t is the time period (in years).

In this case, the interest rate is 3% per year, which can be written as 0.03 in decimal form. The time period is one year. So we have:

I = 1200 x 0.03 x 1

I = $36

Therefore, Jenny earns $36 in interest in one year in her savings account.

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The graph of the inequality is on the image at the end.

To graph this, we need to do a solid graph of the linear equation:

y = -(7/2)x + 4

And because the symbol ≥  (and that is why we will use a solid line instead of a dashed line) is used, we need to shade all the region above that line graph.

Then the graph of the inequality will be something like the one of the graph at the end.

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The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

�

=

1.154701

Step-by-step explanation:

12x sqaured - 2 = 14

so first add 2 to make it 16 in the other side.

12x sqaured =16 then divide the sqaured and get 4 on the other side

so 12x = 4 then the answer is 4/12 or 1/3

Answer:

Step-by-step explanation:

12x²-2=14              add 2 to both sides

12x²=16                  divide both sides by 12

x² = 16/12             reduce by dividing top and bottom by 4

x²=4/3                  take square root of both sides to cancel square

                            when you take sq root you also get ±

x=±[tex]\sqrt{\frac{4}{3} }[/tex]                    you can take square root of 4

= ±  [tex]\frac{2}{\sqrt{3} }[/tex]                        you can never leave root on bottom so multiply by

                              root on top and bottom  to simplify

= ± [tex]\frac{2}{\sqrt{3} } \frac{\sqrt{3} }{\sqrt{3} }[/tex]

= ±  [tex]\frac{2\sqrt{3} }{3}[/tex]

The graph which represents the number of months it will take Talia to save at least $200 is Line B.

Given that,

Talia tutors and wants to save money.

Talia currently has $60 and plans to save an additional $35 per month.

Current amount = $60

Additional amount each month = $35

Let n be the number of months taken to at least save $200.

60 + 35n ≥ 200

35n ≥ 140

n ≥ 4

So the graph will be a number line which has a closed circle on 4 and pointing to the right, because number of months should be either equal to or greater than 4.

Hence the correct option is B.

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The solution is:

(a) A (20, 60), B = (0, 0) and C = (80, 0).

(b) The values of x and y that maximize the objective function are

(20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

We have,

The set of all possible points of an optimization problem that satisfy the problem's constraints—which may include inequalities, equalities, and integer constraints—is referred to in mathematics as a feasible region, feasible set, search space, or solution space.

Given,

x ≥0, y ≥ 0

x + y ≤ 80

y ≤ 3x

Objective function: z = 250x + 300y

(a) For the given constraints the feasible region is attached below.

The feasible region is ABC.

where, A (20, 60), B = (0, 0) and C = (80, 0).

(b) Now to find the values of x and y which maximize the objective function.

z = 250x + 300y

At A = (20, 60)

z = 250(20) + 300(60) = 5000 + 18000 = 23000

At B = (0, 0)

z = 250(0) + 300(0) = 0

At C(80, 0)

z = 250(80) + 300(0) = 2000 + 0 = 2000

Therefore, the values of x and y that maximize the objective function are (20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

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The value of x for the intersecting chords is derived to be 14 which makes option C correct.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x × 32 = 16 × 28

32x = 448

32x/32 = 144/32 {divide through by 32}

x = 14

Therefore, the value of x for the intersecting chords is derived to be 14

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