Jack and his cousin Emma are picking apples in their grandparents' orchard. Jack has filled 11 baskets with apples and is filling them at a rate of 5 baskets per hour. Emma has 8 full baskets and will continue picking at 6 baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?

Total distance represented by the simplified expression for which the car was tested equals option c. x² + 2x - 4 .

Total distance drive on flat road = x miles

Total distance drive on downhill =  (x²+ 3) miles

Total distance drive on uphill =  ( x - 7 ) miles

Simplified expression which is equivalent to total distance drive by a car

= Distance drive on ( flat road + downhill + uphill )

= ( x +  x²+ 3 + x - 7 ) miles

= ( x² + 2x - 4 ) miles

Therefore, the simplified expression equivalent to the total distance drive by a tested car is equal to option c.  ( x² + 2x - 4 ) miles.

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The above question is incomplete , the complete question is:

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road,    (x²+ 3) miles downhill, and (x - 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

a.3x² _ 4

b. 3x² + 10

c. x² + 2x - 4

d. x² + 2x + 10

Answer:

what are the questions

Step-by-step explanation:

Therefore, the equation of the line passing through (3, 2) that minimizes the area bounded by the line, the x-axis, and the y-axis is: y = (2/3)x.

The area bounded by the line, the x-axis, and the y-axis is a right-angled triangle. To minimize the area, we need to find the line that maximizes the length of the altitude (perpendicular distance) from the origin to the line.

Let the equation of the line passing through (3, 2) be y = mx + c, where m is the slope and c is the y-intercept.

Since the line passes through (3, 2), we have the point (3, 2) satisfying the equation:

2 = m(3) + c

To maximize the length of the altitude, we want the line to pass through the origin (0, 0), which gives us the point (0, 0) satisfying the equation:

0 = m(0) + c

c = 0

Substituting c = 0 into the equation 2 = m(3) + c, we get:

2 = 3m

Solving for m, we find m = 2/3.

Therefore, the equation of the line passing through (3, 2) that minimizes the area bounded by the line, the x-axis, and the y-axis is:

y = (2/3)x

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After simplifying the algebraic expression (5t - 4t²) + 11(7t + 3), we obtain -4t² + 82t + 33. The number multiplied by t in the simplified expression is 82.

To simplify the expression (5t - 4t²) + 11(7t + 3), we can distribute the 11 to the terms inside the parentheses:

(5t - 4t²) + 11(7t + 3) = 5t - 4t² + 77t + 33

Next, we can combine like terms by adding or subtracting the coefficients of the same degree of t:

= (-4t² + 5t + 77t) + 33

Combining the terms with t:

= (-4t² + 82t) + 33

Now, the simplified expression is -4t² + 82t + 33.

To find the number that is multiplied by t in the simplified expression, we look for the coefficient of t, which is 82.

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The pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

To determine the sample size needed for estimating a proportion, we can use the formula:

n = (Z^2 * p * q) / E^2

where:

n is the sample size

Z is the z-value corresponding to the desired confidence level (96 percent confidence corresponds to a z-value of approximately 1.75)

p is the estimated proportion (since we don't have an initial estimate, we can assume a conservative estimate of 0.5)

q is 1 - p (complement of the estimated proportion)

E is the desired margin of error (0.02)

Plugging in the values, we have:

n = (1.75^2 * 0.5 * 0.5) / 0.02^2

n ≈ 2627

Therefore, the pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

This sample size calculation ensures that the estimate of the true proportion will have a margin of error (E) of 0.02 or less, providing a high level of confidence (96 percent) in the accuracy of the estimate.

In conclusion, by using the formula for sample size estimation, the pollster should survey 2627 voters to achieve a 96 percent confidence level with a margin of error of 0.02 when estimating the true proportion of U.S. voters opposing capital punishment.

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The area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

From the information given, we have the formula for area to be;

A = 3.14r²

Where 'r' is the radius of the shape

The radius of Jupiter = 2 * 5^2 * 11 * 79

This is simplified to = 2 × 25 × 11 × 79 = 43, 450

Substitute into the formula

Area = 3. 14 × (43, 450)²

Area = 3. 14 × 1. 89 × 10^9

Area = 5. 92 × 10^9 square miles

Thus, the area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles

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Answer:

5,928,013,850

Answer:

3.75 or 3 3/4

Step-by-step explanation:

(3/4) times 5 equals 3.75

The arrivals calls will follow the poisson distribution then

a) The average number of people in line is equals to 64.

b) The average number of people in the system is equals to 64.

c) The average amount of time that a person can expect to spend in line is 64 calls per hour.

d) On average, the time a person will spend in the system is 64 calls per hour.

e) increase in the typical number of persons who are waiting in line when arival rate become 80 calls per hour.

We have a call center has analyzed the calls received in the last month.

Average of calls received = 64 calls per hour

Assume that call arrivals follow the poisson distribution and service times follow an exponential distribution with an average of 45 seconds per call served. Also, the queue length can be infinite with fcfs discipline.

a) The average length of time spent waiting in line is 45 seconds. This is due to the fact that the pace of calls coming in is 45 seconds each call, yet the arrival rate is 64 calls per hour.

b) The typical number of users is 64, according to the system. This is due to the fact that the pace of calls coming in is 45 seconds each call, yet the arrival rate is 64 calls per hour.

c) A person should anticipate waiting in line for a total of two minutes on average. This is the typical wait time. This is due to the fact that the pace of calls coming in is 45 seconds each call, yet the arrival rate is 64 calls per hour.

d) The typical wait time for a person to be processed via the system is four minutes. This is due to the fact that the pace of calls coming in is 45 seconds each call, yet the arrival rate is 64 calls per hour.

e) There will be an increase in the typical number of persons who are waiting in line to . This is due to the fact that the pace of calls coming in is 45 seconds each call, yet the arrival rate is 64calls per hour.

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Answer:

3 of the pyramids

Step-by-step explanation:

Given:

Hexagonal Prism

Hexagonal based pyramid

Required

How many of the pyramid will fill up the prism

To do this, we start by calculating the volumes of both shapes.

Let V1 be the volume of the hexagonal prism

\(V_1 = \frac{3\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

Let V2 be the volume of the hexagonal based pyramid

\(V_2 = \frac{\sqrt{3}}{2}a^2h\)

Where: a = base and h = height

The number of the pyramid that can occupy the prism is calculated by dividing V1 by V2

\(Number = \frac{V_1}{V_2}\)

\(Number = \frac{3\sqrt{3}}{2}a^2h /\frac{\sqrt{3}}{2}a^2h\)

Convert division to multiplication

\(Number = \frac{3\sqrt{3}}{2}a^2h * \frac{2}{\sqrt{3}a^2h}\)

\(Number = \frac{3\sqrt{3}}{2} * \frac{2}{\sqrt{3}}\)

\(Number = \frac{3\sqrt{3}}{1} * \frac{1}{\sqrt{3}}\)

\(Number = \frac{3*1}{1} * \frac{1}{1}\)

\(Number = 3\)

There are 2 ways to make a series of 11 moves.

Since the checker can move to either the blue or yellow space in each move, there are 2 possibilities for each move. We want to find the number of sequences of 11 moves that result in the checker returning to the red space, i.e., a sequence of moves that alternates between the red and one of the other two spaces.

There are 2 possible sequences of 11 moves: RBYB...BYBR and BYBY...YBRB, where R represents the red space, B represents the blue space, and Y represents the yellow space.

So, in total there are 2 ways to make a series of 11 moves which result in the checker returning to the red space.

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Answer:

y = 0x +6 or y = 6 if simplified

Step-by-step explanation:

y=mx+b is slope intercept formula

m is the slope which we know ( 0 ) and we know the line passes through (5,6) so all we need to figure out is b

so plug it in and solve:

6 = 0(5) +b

6 = b

so 6 is b and now we know the equation

y = 0x +6 or y = 6 if simplified

Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer:

C. log(25)+log(18)

Step-by-step explanation:

This is because the log rules say when you multiply logs with the same base you can essentially add them.

Answer:

Step-by-step explanation:

Answer:

13p

Step-by-step explanation:

because the P it have 1 hidden there

12p + 1p = 13p

On solving the provided question, we can say that by linear equation  $249.67  money was raised from the raffle

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here,

the linear equation that can be formed is

200x + 24 y = 3.50

125 x + 20y = 5

ratio = 8:1

so,  $249.67  money was raised from the raffle

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Answer:

Step-by-step explanation:

look at the screenshot

please mark me brainlist

Answer:

280m

Step-by-step explanation:

Work rate would be (210m)/(45people)(60days)=7/90 m/(people)(day)

7/90 m/(people)(day) * 72people * 50days =280m

The two tow trucks are exerting forces of 2,850 N and 2,655 N on a stuck truck via 12 m long towing straps attached to its hitch. The angle between the two trucks is 42. We have to determine the magnitude of the resultant force.

The formula to find the magnitude of the resultant force is given below:\(F = √(F₁² + F₂² + 2F₁F₂cosθ) where, F₁ = 2,850 NF₂ = 2,655 Nθ = 42 degrees F = √(2,850² + 2,655² + 2(2,850)(2,655)cos(42))F = 4,325 N (rounded off to th\)e nearest whole number) Hence, the magnitude of the resultant force is 4,325 N.

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The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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The graph of the reflection of the function is g(x) = -1/3(9)x

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

f(x) = 1/3(9)x

The rule of reflection across the x-axis is

g(x) = -f(x)

Using the above as a guide, we have the following:

g(x) = -1/3(9)x

Hence the function is g(x) = -1/3(9)x

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Answer:

CD = 48

Step-by-step explanation:

Find the value of x using the two equations

9x - 15 = 7x - 1

9(7) - 15 = 7(7) - 1

63 - 15 = 49 - 1

48 = 48

Answer: x = 7

Then get the result of both equations

CD = 48

The length of CD is 48 units.

Isosceles triangles are those triangles which has the length of two sides or angles are equal to each other.

Given triangle ABC is an isosceles triangle since the length of sides AB and BC are given to be equal.

BD is the altitude of the triangle from the vertex B.

We know that, altitude of an isosceles triangle from the non equal angle bisect the opposite side, which is base.

So, AC is bisected at D.

AD = CD

9x - 15 = 7x - 1

Solving,

9x - 7x = -1 + 15

2x = 14

x = 7

Length of CD = 7x - 1 = 49 - 1 = 48

Hence 48 units is the length of CD.

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The countermeasures to avoid potential human errors are   Visual aids & work instructions, education and/or discipline, work standardization and discipline and TPM and skill building etc.

Many major accidents, such as Texas City, Piper Alpha, and Chernobyl, were caused by potential human error. Companies must manage human failure as rigorously as they manage technical and engineering measures to avoid accidents and illness.

There are several countermeasures for amateur or beginner mistakes. Potential human errors can be avoided by some measures including training, skill development, work standardisation, visual aids, and work instructions. Every human being makes mistakes, whether they are professional or not.

Thus, Visual aids and work instructions, education and/or discipline, work standardisation and discipline, TPM and skill building, and other counter measures are used to avoid potential human errors.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Approximation of 12.0 by rounding off the number is 12.

Anything similar to something else but not precisely the same is called an approximation. By rounding, a number may be roughly estimated. By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.

Rounding is a very basic estimating technique. The main ability you need to swiftly estimate a number is frequently rounding. In this case, you may simplify a large number by "rounding," or expressing it to the tenth, hundredth, or a predetermined number of decimal places.

In the given problem, we are asked to approximate the value of 12.0 which is equal to 12.

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Answer:

Step-by-step explanation:

1.  Interchange x and y.  We get:  x = y^2 - 5

2. Solve for y:  y^2 = x + 5, so that y = ±√(x + 5)

The measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.

"It states that the sum of any two sides must be greater than the third side."

For given question,

we have been given the measures 3.1, 4.8, and 10.2  

We need to check whether given measures can be the side lengths of a triangle.

First we check whether the given measures obey triangle inequality or not.

3.1 + 4.8 = 7.9

7.9 < 10.2

This means, the measures 3.1, 4.8, and 10.2 do not obey triangle inequality

Therefore,  the measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.

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The proof by mathematical induction that all horses are the same color is flawed because the basis step does not make any sense. Because the basis step is invalid, the proof is incorrect overall.

Specifically, for the basis step, we cannot start with a set of 1 horse, as there is no other horse to compare it to. Hence, we cannot make any definitive claims about a single horse, and the basis step cannot be completed. The inductive step, on the other hand, is correct, assuming that the basis step was valid. By assuming that all horses in a set of n horses are the same color, we can show that horses 1 through n + 1 must be the same color. This is because the sets of horses from 1 to n and from 2 to n + 1 overlap, and therefore, by the transitive property of equality, all horses in the set from 1 to n + 1 must be the same color. However, because the basis step is invalid, the proof is incorrect overall.

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