A pool can be filled by one pipe in 4 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill the pool?

Answer:

a. f(6)/f(5) = 60.75/81 = 3/4

b. f(n) = f(n-1) x 3/4 or f(n) = 3/4f(n-1)

Step-by-step explanation:

We have 256, 192, 144, 108, 81

common ratio r = f(n) / f(n-1) = 192/256 = 3/4

so f(n) = f(n-1) x 3/4

f(1) = 256

f(2) = 256 x 3/4 = 192

f(3) = 192 x 3/4 = 144

f(4) = 144 x 3/4 = 108

f(5) = 108 x 3/4 = 81

f(6) = 81 x 3/4 = 60.75

a. f(6)/f(5) = 60.75/81 = 3/4

b. f(n) = f(n-1) x 3/4 or f(n) = 3/4f(n-1)

Answer:

i believe itś y=2x+8

i apologize if it is wrong

Therefore, the potential likelihood of selecting a blue stone is roughly 0.1333 or 13.33%.

Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.

To find the theoretical probability of choosing a blue marble, we need to divide the number of blue marbles by the total number of marbles in the bag.

Total number of marbles = 3 green + 2 blue + 5 red + 5 yellow = 15

Number of blue marbles = 2

Therefore, the theoretical probability of choosing a blue marble is:

P(Blue) = Number of blue marbles / Total number of marbles = 2 / 15

= 0.1333 (rounded to 4 decimal places)

So, the theoretical probability of choosing a blue marble is approximately 0.1333 or 13.33%.

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Answer:

$0.75 per pound

Step-by-step explanation:

On the graph, the x is the number of pounds of tomato, and the y is the price.

We see when the x is 1 pound of tomato; the y is $0.75. So the unit rate is $0.75 per pound.

Answer:

1 mile = 1,609344 km

250 miles = X

X= 250 x 1,609344

X= 402,336km

So 500 km > 250 miles

Step-by-step explanation:

1 mile = 1,609344 km

250 miles = X

X= 250 x 1,609344

X= 402,336km

So 500 km > 250 miles

We can conclude that the figure is a square as all 4 sides are equal with all angles being 90°.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral.

The square's angles are at a straight angle or 90 degrees. Additionally, the diagonals of the square are equal and intersect each other at 90 degrees.

Therefore, we can conclude that the figure is a square as all 4 sides are equal with all angles being 90°.

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Answer:

shortened height = h(1 - tan(20))

Step-by-step explanation:

To solve this problem, we need to use trigonometry to find the height that the airplane reaches at a 20° angle, and then subtract this height from the height of the cell tower to determine how short it needs to be.

Let's assume that the cell tower has a height of "h", and that the airplane takes off at a 20° angle. We can use trigonometry to find the height "x" that the airplane reaches above the ground:

tan(20) = x / h

Multiplying both sides by "h", we get:

x = h * tan(20)

So the airplane reaches a height of "x" above the ground. To find how short the cell tower needs to be, we simply subtract this height from the original height of the tower "h":

shortened height = h - x

Substituting the expression we found for "x", we get:

shortened height = h - h * tan(20)

Simplifying, we get:

shortened height = h(1 - tan(20))

So, the cell tower needs to be shortened by "h(1 - tan(20))" to ensure that the airplane can take off safely at a 20° angle.

The first term of the geometric sequence is 1/2 and the common ratio is 2.

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed number called the common ratio. The general form of a geometric sequence is:

a, ar, ar², ar³, ar⁴, ...

where 'a' is the first term, 'r' is the common ratio, and the subscripts represent the position of the term in the sequence.

Let's denote the first term of the geometric sequence by "a" and the common ratio by "r".

We know that the third term of the sequence is 2, which means that:

a * r² = 2 (1)

We also know that the sixth term of the sequence is 16, which means that:

a * r⁵ = 16 (2)

Now we can solve for "a" and "r" by dividing equation (2) by equation (1):

(a * r⁵)/(a * r²) = 16/2

Simplifying, we get:

r³ = 8

Taking the cube root of both sides, we get:

r = 2

Now we can use equation (1) to solve for "a":

a * 2² = 2

Simplifying, we get:

4a = 2

a = 1/2

Therefore, the first term of the geometric sequence is 1/2 and the common ratio is 2.

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Answer:

a)168.725

b)168.735

168.725≤x<168.735

Step-by-step explanation:

a)168.73 - 0.005

168.725

b) 168.73 + 0.005

168.735

With wait times of 12 and 15 minutes for the most popular ride, bimodal distribution is the best way to describe the form of the data for

The line plot shows the wait time in line for a ride at a local fair, with the number of dots above each time interval representing the frequency of wait times falling in that interval.

The data is not symmetric, according to the provided line plot, which shows that there are more dots above 12 and 15 minutes than at other time intervals. This shows that the data is not normally distributed, and that the symmetric distribution assumption is consequently incorrect.

The claim that "the wait times were less than 13 minutes for all the rides" is untrue is further supported by the absence of dots over time intervals of less than 10 minutes. While there are dots above time intervals less than and equal to 13 minutes, it is equally untrue to say that "the wait times were over 13 minutes for all the rides."

Because there are two peaks in the distribution with wait times of 12 and 15 minutes for the most popular ride, bimodal distribution is the best way to describe the form of the data. This may indicate the existence of two popular rides with distinct wait times, or it may indicate that the popularity of some rides fluctuated over time, resulting in a bimodal distribution.

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Answer:it B

Step-by-step explanation:

Answer:

a) 0.0281

b) 0.6924

c) 0.3081

Step-by-step explanation:

Probability that one of those sampled saying that Roosevelt was the best president since World War II = 345/2055 = 0.17

Probability that one of those sampled don't mention Roosevelt = (2055 - 345)/2055 = 1710/2055 = 0.83

a) The probability that both adults picked say Franklin Roosevelt was the best president since World War II = (345/2055) × (344/2054) = 0.0281

b) The probability that neither of the two adults say Franklin Roosevelt was the best president since World War II = (1710/2055) × (1709/2054) = 0.6924

c) The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = Probability that one of the two adults mention Roosevelt + Probability that the two adults mention Roosevelt

Probability that one of the adults mention Roosevelt = [(345/2055) × (1710/2054)] + [(1710/2055) × (345/2054)] = 0.280

Probability that two of the adults mention Roosevelt has been done in (a) and it is equal to 0.0281

Probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = 0.280 + 0.0281 = 0.3081

The solution to the system of equations given as y = 7/3x - 2 and y = x + 2 is (3, 5).

Given that

y = 7/3x - 2

y = x + 2

To solve this system of equations using substitution, we need to isolate one of the variables in one equation and substitute the resulting expression into the other equation.

Let's start by isolating y in the second equation:

y = x + 2

Now we can use this expression for y in the first equation:

y = 7/3x - 2

We substitute x + 2 for y

x + 2 = 7/3x - 2

Next, we can solve for x by isolating it on one side of the equation:

x - 7/3x = -2 - 2

-4/3x = -4

So, we have

x = 3

Now that we have an expression for x in terms of y, we can substitute it into either of the original equations to solve for y. Let's use the second equation:

y = x + 2

Substituting

y = 3 + 2

Simplifying, we get:

y = 5

Therefore, the solution to the system of equations is (x, y) = (3, 5).

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Answer:

A

Step-by-step explanation:

B: would lead to g being in the same spot

C: would still be missing the rotation

D:It would be the flipped version of H

With mean=2.2, the training program was effective in increasing the production rates.

What is mean?

In mathematics, the mean represents the average value of a dataset. It is calculated by summing all the values in a dataset and dividing by the total number of values. The mean is often used as a standard measure of the central location of a dataset

Now,

The hypotheses for this problem are:

Null hypothesis (H0): The training program did not have any effect on the production rates. In other words, the mean difference in production rates (d) is equal to zero.

Alternative hypothesis (Ha): The training program was effective in increasing the production rates. In other words, the mean difference in production rates (d) is greater than zero.

To compute the test statistic, we first need to find the sample mean and standard deviation of the differences:

d = After - Before

Worker Before After   d

1            6           9         3

2           10          12        2

3           9            10       1

4           8             11       3

5           7            9        2

The sample mean of the differences is:

mean(d) = (3+2+1+3+2)/5 = 2.2

The sample standard deviation of the differences is:

s = √(sum((d - mean(d))²)/(n-1)) = √((1.04)/4) = 0.57

The test statistic for testing the null hypothesis is:

t = (mean(d) - 0)/(√(n)) = (2.2 - 0)/(0.57/√(5)) = 6.07

Using a t-distribution with n-1 = 4 degrees of freedom and a significance level of 0.05, the critical value is 2.776.

Since the calculated t-value (6.07) is greater than the critical value (2.776), we reject the null hypothesis and conclude that the training program was effective in increasing the production rates.

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Correct Question:-

The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before.

Worker Before After

1 6 9

2 10 12

3 9 10

4 8 11

5 7 9

We want to determine if the training program was effective.

Give the hypotheses for this problem.

Compute the test statistic.

At 95% confidence, test the hypotheses. That is, did the training program

actually increase the production rates? Please, I need the work for this problem.

The distance between E and the bottom of the tree, given the distance above the ground, is 7 m.

We are told that the tree is midway between points E and F. We are also told that points E and F are 14 meters away from each other.

The distance between E and the bottom of the tree would be half of the distance between E and point F because the tree is located midway between both points.

The distance between E and the bottom of the tree is therefore:

= 14 / 2

= 7 m

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Answer:

-13

Step-by-step explanation:

The term in the polynomial which doesn't have any variables is called constant.

So, (-13) is the constant.

The length of m is 15.6 cm.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

113/7.5

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Answer:

The best measure of center for the data shown is the median, and its value is 11.

Step-by-step explanation:

In statistics, measures of central tendency are used to summarize a set of data and provide a single value that represents the center or typical value of the data. The three commonly used measures of central tendency are the mean, median, and mode.

The mean is calculated by adding up all the values in the data set and dividing by the total number of values. The mean is affected by outliers and can be heavily skewed by extreme values.

The median is the middle value of the data set when the values are arranged in order. It is not affected by extreme values and is a more robust measure of central tendency compared to the mean.

In the given box plot, the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, which is the middle value of the box. Therefore, the best measure of center for the data shown is the median, and its value is 11.

The best measure of the center for the data shown is the median, and its value is 11 thus the correct option is  C.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

In statistics, the measures of central tendency are used to summarize a set of data and provide a single value that shows the center or typical value of the data. Also, it is known that three commonly used measures of central tendency are the mean, median, and mode.

The median is not affected by extreme values and is a more robust measure of central tendency compared to the mean.

In the given box plot, we can conclude that the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, that is the middle value of the box. the median, value is 11.

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Vaccinations can prevent various infectious diseases including measles, mumps, rubella, polio, tetanus, pertussis, hepatitis A and B, varicella, HPV, and influenza.

One should consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and individual factors.

Vaccinations can prevent many infectious diseases, including:

Measles

Mumps

Rubella

Polio

Tetanus

Pertussis (whooping cough)

Hepatitis A and B

Varicella (chickenpox)

Human papillomavirus (HPV)

Influenza (flu)

Pneumococcal disease (pneumonia, meningitis, blood infections)

Rotavirus (diarrhea and vomiting)

Haemophilus influenzae type b (meningitis, pneumonia, and other infections)

Meningococcal disease (meningitis and blood infections)

Hepatitis A and B (liver infections)

and many others. It is important to consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and other individual factors

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Using the expression 2/7 × 28 it is obtained that Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The total number of pencils Professor Elena bought is  28 pencils.

If Professor Elena bought 28 pencils, and she distributed 5/7 of them to her students.

The fractional expression will be -

1 - 5/7

Simplifying the expression we get -

(7 - 7) / 2

2/7

Then she kept 2/7 of the pencils for herself.

The number of pencils she has with her will be -

2/7 × 28 = 8 pencils

Therefore, Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.

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Professor Elena bought 28 pencils and distributed 5/7 of the pencils to her students. How many pencils did teacher Elena have left?​

Answer:

Enter your answer as a decimal in the b

Using the appropriate statistical relation, the confidence interval estimate for the net worth of the wealthiest celebrities is (150.35; 204.77).

Given the samples :

X = 256,196,190,166,163,162,148,148,143.

Using a calculator, we could obtain the sample mean and sample standard deviation is-

Mean, μ = [tex]\sum\frac{x}{n}[/tex] = 174.55

Standard deviation, σ = 38.8

The confidence interval can be defined thus :

Mean ± standard error

Standard Error = Tcritical × σ/√n

Tcrit ; 95% ; df = n - 1 = 9 - 1 = 8; T-critical = 2.26

Standard Error = (2.26 × 38.06/√10) = 27.20

Lower confidence boundary = 177.55 - 27.20 = 150.35

Upper confidence boundary = 177.55 + 27.20 = 204.77

Therefore, the confidence interval is (150.35; 204.77)

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The answer is A. 12.0. The mean absolute deviation MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units.

To calculate the Mean Absolute Deviation (MAD), we need to find the absolute difference between the actual demand and forecast demand, then take the average of those differences. The formula for MAD is:

[tex]MAD = (1/n) * Σ|A - F|[/tex]

where A is the actual demand, F is the forecast demand, and n is the number of observations.

Using the provided data, we can calculate the MAD for each week:

Week 1: |100 - 120| = 20

Week 2: |120 - 130| = 10

Week 3: |110 - 120| = 10

Week 4: |130 - 125| = 5

Week 5: |160 - 145| = 15

To calculate the MAD at the end of week 5, we need to add up the absolute differences and divide by the total number of observations:

MAD = (20 + 10 + 10 + 5 + 15) / 5 = 12

Therefore, the answer is A. 12.0. The MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units. This question is related to the topic of forecasting and measures of forecast accuracy. Specifically, it involves calculating the mean absolute deviation (MAD) as a measure of forecast error.

The MAD provides a measure of forecast accuracy and can be used to evaluate the performance of forecasting methods and to make adjustments to improve the accuracy of future forecasts.

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According to the given information, the cyclists will meet after x hours of riding, and the distance from the orchard where they meet is given by either A(x) or B(x)

What is speed?

Speed is defined as the distance traveled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance/time

where "distance" is the distance traveled by the object, and "time" is the time it takes for the object to travel that distance.

Let's assume that the distance function for cyclist A is given by: A(x) = ax + b, where a and b are constants that depend on the cyclist's speed and initial distance from the orchard, respectively.

Similarly, let's assume that the distance function for cyclist B is given by: B(x) = cx + d, where c and d are constants that depend on the cyclist's speed and initial distance from the orchard, respectively.

Since both cyclists left home at the same time, we know that their initial distance from the orchard must be the same. Therefore, we can set b = d and rewrite the distance functions as:

A(x) = ax + b

B(x) = cx + b

The cyclists will meet when their distances from the orchard are equal, so we can set A(x) = B(x) and solve for x:

ax + b = cx + b

ax - cx = b - b

x(a-c) = 0

Since x cannot be zero (they are riding for some positive amount of time), we know that a - c must be zero, which means that their speeds are equal:

a - c = 0

a = c

Therefore, we know that the cyclists are traveling at the same speed. To find the meeting point, we can set A(x) = B(x) = D, where D is the distance from the orchard where they meet, and solve for x:

ax + b = Dx

cx + b = Dx

ax + b = cx + b

ax - cx = 0

x(a-c) = 0

Since a = c, we can simplify this equation to:

x = 0 or x = D/(a-c)

Since we know that x cannot be zero (they left home at the same time and met later), we can conclude that:

x = D/(a-c)

Therefore, the cyclists will meet after x hours of riding, where x is given by the above formula, and the distance from the orchard where they meet is given by either A(x) or B(x) (they are equal at the meeting point).

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The percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.

When compared to the real number and expressed in percent format, percentage error seems to be the variance between the projected amount and the actual number.

By deducting the actual value from the estimated value, you may get the percentage error. Then, divide the real number's absolute value by the absolute value of the error. You will receive the error in decimal form as a result. The percentage error can then be calculated by multiplying the result by 100%.

Given data:

Required height of cake =  78.25 inches

Actual height = 75.5 inches.

Thus,

percent error = (Required height - Actual height)/actual height *100%

percent error = (78.25 - 75.5)/75.5 * 100

percent error = 3.64 %

Thus, the percent error in Abigail 's calculation for the height of the cake to the nearest tenth is 3.64 %.

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Answer:

Any number greater than 10;   11, 12, 15, 20, 100...etc

Step-by-step explanation:

Order the data from least to greatest and strikethrough numbers on each side until you reach the middle 1 or 2 numbers. In this case there are 9 numbers, so the middle number is our median.

8, 8, 8, 8, 10, v, 18, 18, 18

the variable v can be many numbers, but in order for the median to be 10, v must be a number greater than 10. If v = 11, the median is 10. Likewise, if v = 100000, the median is still 10 because it is the middle of the set.

Answer:

Step-by-step explanation:

R.E.F image

f(x)=x+6

X -3 -2 -1 0 1 2

Y 3 4 5 6 7 8

Given equation is −x+y=6

That can be written as f(x)=x+6

The required graph is drawn in the figure.

solution

Answer:

Step-by-step explanation: 412+x-6 is also 412+8-6

If you do this by pemdas it would equal to  414

To start, denote x as the number of lbs utilized per each coffee type (type A and type B). Further, let ax be the quantity of lbs for type A coffee and bx be the quantity of lbs for type B coffee. So, ax and bx are in units of quantity*lbs.

The cost of type A and type B coffee can be equated as follows:

Cost (A) = 5.95/lb and Cost (B) = 4.65/lb

The key information given ("This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00") can be represented algebraically as follows:

Cost (Blend) = Cost(A)*ax + Cost(B)*bx = $796.00. Since the quantity of type B coffee is 3 times the quantity of type A coffee, it follows that a = 1 and b = 3.

Therefore, 5.95/lb*(x) + 4.65/lb*(3x) = 796--> 5.95/lb*(x) + 13.95/lb*(x) = 796 or (5.95+13.95)(x) = 796.

Therefore, quantity (lbs) = 796/(13.95+5.95) = 796/(19.9) = 40.

Using the previous relation, we know that 3x + x = 40 or 4x = 40. So, the number of lbs for type A coffee utilized in the blend equates to the following:

x = 10 lbs.