A water tower holds 26,400 gallons of water. The water company can fill the tower at a rate of 20 gallons per minute. How many hours would it take the water company to fill the tower if it is completely empty?

Given:

Multiply equation(1) by 2 and add with equation(2)

Option B is the final answer

If 15 carpenters can build 3 houses in 3 hours, it means that each house takes 1 hour to complete with their combined effort. Therefore, it would take 5 carpenters the same amount of time, 1 hour, to build 1 house.

Given that 15 carpenters can build 3 houses in 3 hours, we can determine their collective rate of work. Since 3 houses are built in 3 hours, it means each house takes 1 hour to complete with the combined effort of the 15 carpenters. Now, if we reduce the number of carpenters to 5 while keeping the rate of work constant, it stands to reason that 5 carpenters would take the same amount of time, 1 hour, to build 1 house. The number of carpenters is inversely proportional to the time taken to complete a task, assuming the rate of work remains constant. Therefore, by reducing the number of carpenters from 15 to 5, we can still maintain the same rate of work and complete 1 house in 1 hour.

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Answer:

28 of the student do not snowboard

Step-by-step explanation:

Answer:

They spent 2hrs and 30min

Step-by-step explanation:

If you cut 5 in half you get 2.5

60 cut in half equals 30

In other words... 2.5 = 2hrs and 30min

The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. In this case, we have two different hypothesis tests with null hypotheses of μ2 - μ1 = 3 and μ2 - μ1 = 4. If the difference between the sample means is 5, we can determine the p-values, denoted as p1 and p2 respectively, for these hypothesis tests.

The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.

Therefore, in this context, we can infer that p1 would be smaller than p2 since the difference between the sample means is larger (5) compared to the hypothesized difference of 3. This suggests that the evidence against the null hypothesis of μ2 - μ1 = 3 is stronger than the evidence against the null hypothesis of μ2 - μ1 = 4, given the observed data.

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The p-value is a measure of the evidence against the null hypothesis in a hypothesis test. We have two hypothesis tests with different null hypotheses regarding the difference between two population means.  The difference between the sample means is 5, compare the p-values (p1 and p2) for each hypothesis test.

The p-value represents the probability of obtaining a test statistic as extreme as the observed difference between the sample means, assuming the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.

In the first hypothesis test, where H0: μ2 - μ1 = 3, the p-value (p1) measures the probability of observing a difference of 5 or greater, assuming the true difference is 3. If p1 is small (e.g., p1 < 0.05), it suggests strong evidence against the null hypothesis, indicating that the observed difference of 5 is unlikely to occur by chance alone.

In the second hypothesis test, where H0: μ2 - μ1 = 4, the p-value (p2) measures the probability of observing a difference of 5 or greater, assuming the true difference is 4. The p2 value may be smaller or larger than p1, depending on the specific data and test statistics used. Again, a smaller p-value (e.g., p2 < 0.05) suggests stronger evidence against the null hypothesis.

Therefore, by comparing the p-values (p1 and p2) obtained from the respective hypothesis tests, we can determine the strength of evidence against the null hypotheses and make conclusions about the difference between the population means.

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There isn't enough evidence to indicate that the percentage of Americans who own American-made cars is more than 53 percent.

A representative of a car manufacturer in the United States claimed that 53 percent of Americans owned American-made cars ten years ago.

However, today, the percentage is higher.

A research group conducted a study to find out whether the statement was true.

They found out that 56 percent of a random sample of car owners in the United States owned American-made cars. The appropriate hypothesis test produced a p-value of 0.283.

Assuming the conditions for inference were satisfied, is there sufficient evidence to conclude, at the level of significance of α = 0.05

At α = 0.05, we want to see if there is enough evidence to reject the null hypothesis.

Therefore, since α = 0.05, the null hypothesis (H0) should be tested against the alternative hypothesis (Ha).

H0: μ ≤ 0.53 (The percentage of Americans who own American-made cars is no higher than 53%).

Ha: μ > 0.53 (The percentage of Americans who own American-made cars is higher than 53%).

It is clear that the researcher's claim was not supported by the evidence since the p-value of 0.283 was far above the significance level of α = 0.05.

Therefore, there is no statistically significant evidence to reject the null hypothesis (H0).

The research group discovered that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars.

The null hypothesis states that the percentage of Americans who own American-made cars is no higher than 53 percent.

Since the p-value was greater than 0.05, we failed to reject the null hypothesis.

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After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

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The P-value in this case is approximately 0.1131.

In the given problem, we are given a test statistic t = 1.212, a sample size n = 6, and an alternative hypothesis H1: μ > μ0.

To calculate the P-value, we need to find the area to the right of the test statistic t in the t-distribution with n - 1 degree of freedom (df), assuming the null hypothesis is true.

Using a t-table or calculator, we can find that the area to the right of t = 1.212 with 5 degrees of freedom is approximately 0.1131. This means that if the null hypothesis were true (i.e., if the population mean were equal to the hypothesized value μ0), we would expect to observe a test statistic as extreme as t = 1.212 or more extreme in about 11.31% of random samples of size 6.

Since the P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming that the null hypothesis is true, we can conclude that the P-value in this case is approximately 0.1131.

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Answer:

x>5

Step-by-step explanation:

-11>-1-2x

2x>-1+11

2x>10

x>5

Answer:

5 > x

Step-by-step explanation:

-11 > -1 -2x ---> plus one on each side---> -10 > -2x ----> divide by -2 --> 5 > x

The expected number of failures in 1 year is 8.9948.

The authors calculate a failure rate for PVC pipe of 0.0081 per 100 miles of pipe per day in 2008. Think of a 100-mile section of this pipe.

(I)

Given;

Mean failures per day = 0.0081

So,

Expected number of failures in 1 year = 0.0081 * 365

                                                               = 8.9948

(II)

Poisson Distribution with λ = 8.9948 is given by:

\(P(x) =\frac{e^-^8^.^9^9^4^8 8.9948^0}{x!}\)

             ⇒ for x = 0, 1, 2,. . . .

P(At least 1 failure) = 1- P(X=0);

\(P(x) = \frac{e^-^8^.^9^9^4^8 8.9948^0}{0!} = \frac{0.00012*1}{1}\)

        = 0.00012    

So,

P(At least 1 failure) = 1 - 0.00012 = 0.99988

Hence, the expected number of failures in 1 year is 8.9948.

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Answer:

28

Step-by-step explanation:

Basically, x has to be a number where it is the average of the given sides since it is the middle

So 35 + 21 = 36

x = 36 ÷ 2 = 28

Answer:

Step-by-step explanation:

Let x be the random variable representing the height of the students. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 68.5

σ = 2.7

the probability that a student's height is between 67.5 and 71.0 inches exclusive is expressed as

P(67.5 < x < 71.0)

For x > 67.5,

z = (67.5 - 68.5)/2.7 = - 0.37

Looking at the normal distribution table, the probability corresponding to the z score is 0.36

For x < 71.0

z = (71.0 - 68.5)/2.7 = 0.93

Looking at the normal distribution table, the probability corresponding to the z score is 0.82

Therefore,

P(67.5 < x < 71.0) = 0.82 - 0.36 = 0.46

The number of students whose height is between 67.5 and 71.0 inches is

0.46 × 1000 = 460 students

The probability that a student's height is greater than or equal to 74.0 inches is expressed as P(x ≥ 74)

P(x ≥ 74) = 1 - P(x < 74)

For x < 74,

z = (74 - 68.5)/2.7 = 2.04

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

P(x ≥ 74) = 1 - 0.98 = 0.02

The number of students whose height are greater than or equal to 74.0 inches is

0.02 × 1000 = 20 students

Answer:

300 beats in 5 minutes

180/3

180/3=60   3/3=1

60/1*5

60*5=300

1*5=5

300/5

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

180 divided by 3 = 60

60 times in 1 minutes  

60 times 5 = 300

Answer = heart beats 300 times in 5 minutes

Determining the number of electrons on a charged object requires information about the charge magnitude, the charge of an electron (1.602 x 10^-19 Coulombs), and any other relevant details about the system.

To calculate the charge on the pith balls for each rod/soft material combination and determine the number of electrons residing on each pith ball, we need additional information about the specific conditions and measurements.

The charge on an object can be calculated using Coulomb's law, which depends on factors such as the distance between the objects, the nature of the materials involved, and the applied voltage or potential difference.

Similarly, determining the number of electrons on a charged object requires information about the charge magnitude, the charge of an electron (1.602 x 10^-19 Coulombs), and any other relevant details about the system.

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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Answer:

m∠1 = 54° m∠2 = 63° m∠3 = 117°

Step-by-step explanation:

We know that 117 + m∠2 = 180°, which when calculated is equal to 63. Now, we know that 63 + 63 + m∠1 = 180°. This comes out to be 54°. Finally, we know that m∠3 has to equal 117° because they are same side interior angles.

The measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively

The sum of angle in a straight line is 180 degrees, hence:

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63 degrees

For the diagram, m<2 - m<3 = 63 degrees (alternate angle.)

Also, the sum of interior angle of the triangle is 180 degrees, hence:

m<2 + m<2 + m<1 = 180

63 + 63 + m<1 = 180

126 + m<1 = 180

m<1 = 180 -126

m<1 = 54degrees

Hence the measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively

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Answer:

Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer: Liters would be the better unit of capacity for the amount of water in a bathtub.

Step-by-step explanation:

Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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If the equation is wx + wz = -3, then the value of w = -3 / (x + z)

The equation is given that

wx + wz = -3

The equation is defined as the mathematical statement that show the relationship between two expression with an equal sign. The inequality cannot be the part of equation. It consist of mathematical operators, different types of variable and numbers .

The equation is

wx + wz = -3

Take common term outside from the equation

w(x+z) = -3

Move the (x+z) to the right hand side of the equation

w = -3 / (x+z)

Hence, if the equation is wx + wz = -3, then the value of w = -3/(x+z)

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Answer:

\(-6-22i\)

Step-by-step explanation:

\((1-5i)(4-2i)\\\\(1)(4)+(1)(-2i)+(-5i)(4)+(-5i)(-2i)\\\\4-2i-20i+10i^2\\\\4-22i+10(-1)\\\\4-22i-10\\\\-6-22i\)

Recall that \(i^2=-1\)

Answer:

The pink angle is half the angle subtended by the blue arc.

Step-by-step explanation:

Given

See attachment for circle

Required

Compare the pink angle to the blue arc

Let the pink angle be x and the angle subtended by the blue arc be y.

So, we have:

\(x \to\) angle at circumference

\(y \to\) angle subtended by arc

The relationship between x and y is:

\(y =2x\)

Make x the subject

\(x = \frac{1}{2}y\)

Answer:Option D

Step-by-step explanation:Can't be asked to explain.

Hope it helps :)

Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

The perimeter of ABCD in inches is 30 in.

Perimeter is the measurement of the total distance around an object.

To calculate the perimeter of ABCD, we use the formula below

Formula:

Where:

To find /BC/ we use Pythagoras theorem

Substitute these values into equation 1

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In this case, the mean is 5.5 cm and the standard deviation is 0.1 cm. So, one standard deviation below the mean is 5.4 cm and one standard deviation above the mean is 5.6 cm. Therefore, about 68% of the data falls between 5.4 cm and 5.6 cm, which includes the range of 5.3 cm to 5.7 cm.

Your question involves a normal distribution with a mean (µ) of 5.5 cm and a standard deviation (σ) of 0.1 cm. You want to find the percentage of data between 5.3 cm and 5.7 cm.

First, we need to standardize the scores using the z-score formula: z = (x - µ) / σ

For 5.3 cm: z1 = (5.3 - 5.5) / 0.1 = -2
For 5.7 cm: z2 = (5.7 - 5.5) / 0.1 = 2

Now, referring to a standard normal distribution table or using a calculator, we find the area between these z-scores:

This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean

P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 0.9544

Converting it to a percentage, we get 95.44%, which is approximately 95%.

So, the answer is A. 95%.

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Answer:

60%

Step-by-step explanation:

10+12+5+3= 30

10+5+3=18

18 out of 30 is 60%

Answer: 4c+32

Step-by-step explanation: