If EG = 28 and F is the midpoint of
segment EG, the length of EF =
E
F.
G

The 45 mi/h is equal to the 2640 ft/min.

To convert 30 miles per hour to feet per minute, we use dimensional analysis in the process.

We have given that, rate using dimensional analysis.

1 hour = 60 minutes.

1 mile is equal to 5280 feet and 1 hour is equal to 60 minutes.

Hence the formula of conversion is 30 miles / hour *(5280 ft/ mile) * (1 hour / 60 min).

The answer is 2640 ft/min.

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Answer: The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line.

Step-by-step explanation:

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot.

The normal probability plot is a graphical method for determining whether or not a data set is roughly normally distributed . The points in the data are displayed against a hypothetical normal distribution such that they should roughly form a straight line.

The sorted data are shown with an approximation to the means or medians of the associated order statistics to create the normal probability plot. It is applied to ascertain if a tiny amount of data is representative of a normal distribution.

A graphical method for locating significant deviations from normalcy is the normal probability plot. Outliers, skewness, kurtosis, the requirement for transformations, and mixes are some examples of this. The raw data, residuals from model fits, and estimated parameter values are used to create normal probability charts.

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Answer:

x = 8

Step-by-step explanation:

We can use the Pythagorean theorem to solve this.

15^2 + x^2 = (x+9)^2

225 + x^2 = x^2 + 18x + 81

144 = 18x

x = 8

Answer:

of coure. this is alternative B.

The solution to the equation 3 = -4g - 53 is g = -14. By adding 53 to both sides, we eliminated the constant term on the right side, resulting in 56 = -4g. Finally, by dividing both sides by -4, we found that g = -14.

The equation 3 = -4g - 53 can be solved to find the value of g.

To begin, let's isolate the variable g by performing the necessary operations step by step.

First, let's add 53 to both sides of the equation to eliminate the constant term on the right side:

3 + 53 = -4g - 53 + 53

This simplifies to:

56 = -4g

Next, we can divide both sides of the equation by -4 to solve for g:

56 / -4 = (-4g) / -4

This gives us:

-14 = g

Therefore, the solution to the equation 3 = -4g - 53 is g = -14.

In the supporting explanation, we performed the necessary steps to isolate the variable g in the equation 3 = -4g - 53. By adding 53 to both sides, we eliminated the constant term on the right side, resulting in 56 = -4g. Finally, by dividing both sides by -4, we found that g = -14.

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Answer:

The answer is x = 25.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

15

Step-by-step explanation:

24*5=120 / 8 = 15

15 is answer.

Answer: 92°

Step-by-step explanation:

180-88=92

Step-by-step explanation:

and one of these day I must get straigh and drip all over you

Answer:

17

a. 5^4 = 625

b. 3^4 = 81

18

a. log base 10000 , 10 = -4

b. log base 2, 1/2 = -1

19. Inverse represent opposite functions, when you plug one into the other using variables, the result should be x.

Step-by-step explanation: Remember that when converting, use the base of the log function as the base of exponent. The answer to the log function represents the value of the exponent. Hope this helps!

The probability that a family with 4 children has no more than 3 boys is 15/16.

To find the probability that a family with 4 children has no more than 3 boys, we can use the binomial distribution.

The binomial distribution is used to calculate the probability of obtaining a certain number of successes (boys in this case) in a fixed number of trials (children in this case), where each trial has only two possible outcomes (boy or girl) and the trials are independent.

Let X be the number of boys in the family. We want to find P(X ≤ 3), which is the probability of having no more than 3 boys. Since the probability of having a boy is 1/2 and the trials are independent, we can use the binomial distribution formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (1/2)⁴ + 4(1/2)⁴ + 6(1/2)⁴ + 4(1/2)⁴

= 15/16

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Answer:

50; 25; 105

Step-by-step explanation:

Sum of the angles of triange is 180, so we have 2x + x + 2*2x + 5 = 180 (x is number of degrees of second angle), if I understood word 'twice' correctly.

Next, let me solve this:

2x + x + 4x + 5 = 180

7x + 5 = 180

7x = 175

x = 25

So, second angle is 25 degrees, first is 25*2=50 degrees and third is 50*2+5=105 degrees.

Hope that this was helpful.

Answer:

D = 272 ft

Step-by-step explanation:  hope this helps. pls mark me brainliest

Answer:

17 160 inches

Step-by-step explanation:

Area = width x length

so 165 x 104 which is 17 160

Therefore, the area of the rectangle is 17 160 inches

hope this helps, give brainliest?

Using mathematical induction, it can be proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

Base Case: For n = 2, we have 13 = 3 and 24 = 8. Since 3 <= 8, the inequality holds true.

Induction Hypothesis: Assume that 13...(2k-1) <= 24*...*(2k-2) holds true for some positive integer k >= 2.

Induction Step: We need to show that the inequality also holds for k+1, i.e., 13...(2k+1) <= 24*...(2k).

To do this, we start with the left-hand side of the inequality:

13*...(2k+1) = (13*...(2k-1))(2k+1) <= (24...(2k-2))(2k+1)

(Using the induction hypothesis and the fact that 2k+1 is greater than or equal to 2).

Next, we simplify the right-hand side:

24...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1))

Finally, we can conclude that:

13...(2k+1) <= 24*...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1)) <= 24...*(2(k+1)-2)

(Since k+1 is greater than or equal to 2, we can use the induction hypothesis again.)

Therefore, by the principle of mathematical induction, we have proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.

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Answer:

96

Step-by-step explanation:

64 x 1.4 = 96

V = 115999.674 cm3

Answer:

x=60

Step-by-step explanation:

this is an isosceles triangle. so angle D and F are equal. D= x and F=x. so 58+x+x=180

2x+58=180

2x=122

x=60

Answer:

90%

Step-by-step explanation:

1 = 10%

10 - 1 = 9

9 x 10 = 90

=90%

Answer:

f(7)=-4

Step-by-step explanation:

f(7)=10-2(7)

f(7)=-4

Answer:

-4

Step-by-step explanation:

f(7)=10-2(7)

f(7)= 10-14

f(7)= -4

Prime factorization of 10 x 4  is 2 x 5 x 2 x 2.

Finding the prime numbers that are multiplied together to produce the original number is the process of prime factorization. The prime factors of 16, for instance, are 2 x 2 x 2 x 2.

Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 x 3 x 3. Here, the two main factors of 18 are 2 and 3. For instance, 72 = 2 x 3 x 3  x 2 can be written as a product of prime factors. The prime factorization of 72 is said to be the expression 2 x 3 x 3  x 2.

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Answer:

Step-by-step explanation:

The correct answer is: The median of 14 is the most accurate to use, since the data is skewed.

Explanation: Since the data is skewed to the right, meaning there are some larger donations that pull the mean up, the median is a more accurate measure of center. It represents the middle value of the data when it is ordered from smallest to largest, and is not affected by extreme values.

The correct answer is: The IQR is the best measure of variability, and it equals 3.

Explanation: The IQR (interquartile range) is the best measure of variability for this data because it shows the range of the middle 50% of the data. The range, which is the difference between the minimum and maximum values, is affected by outliers and extreme values. In this case, the IQR is equal to 20-17=3.

The correct answer is: There is an outlier at 22.

Explanation: To determine if there are outliers in the data, we can use the rule: an outlier is any value more than 1.5 times the IQR below the first quartile or above the third quartile. The first quartile is 9.5 and the third quartile is 18, so the IQR is 18-9.5=8.5. Therefore, any value less than 9.5-1.5(8.5)= -4.25 or greater than 18+1.5(8.5)=30.25 would be considered an outlier. The value of 22 is greater than 30.25, so it is an outlier.

The correct answer is: The IQR is the best measure of variability, and it equals 18.5.

Explanation: The IQR (interquartile range) is the best measure of variability for this data because it shows the range of the middle 50% of the data. The range, which is the difference between the minimum and maximum values, is affected by outliers and extreme values. In this case, the IQR is equal to the difference between the third quartile (25) and the first quartile (6.5), which is 18.5.

The correct answer is: Player A is the most consistent, with an IQR of 1.5.

Explanation: The IQR (interquartile range) is the best measure of variability for this data because it shows the range of the middle 50% of the data. To find the IQR, we first need to find the first and third quartiles. For Player A, the first quartile is 2 and the third quartile is 3, so the IQR is 3-2=1. For Player B, the first quartile is 2 and the third quartile is 5, so the IQR is 5-2=3.

The correct answer is: The median is the best measure of center, and it equals 7.3.

Explanation: Since the data is not strongly skewed, either the mean or the median could be used as a measure of center. However, the median is often preferred because it is less affected by extreme values. The median for this data is the value that is in the middle when the data is ordered from smallest to largest. In this case, we have 10 data points, so the median is the average of the 5th and 6th values, which are both equal to 7. Therefore, the median is 7, and not 7.3. The mean is also 7.3, but it is affected by the extreme values.

Answer:

See below, please.

Step-by-step explanation:

Question 1

The median of 14 is the most accurate to use, since the data is skewed.

Question 2

The IQR is the best measure of variability, and it equals 3.

Question 3

There is an outlier at 22.

Question 4

The IQR is the best measure of variability, and it equals 18.5.

Question 5

Player A is the most consistent, with an IQR of 1.5.

Question 7: The median is the best measure of center, and it equals 7.3.

A) 24 machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days..

Let's analyze the given information and use it to determine the number of machines required to produce 3x units of product P in 4 days.

We are told that 4 machines can produce a total of x units of product P in 6 days. This means that the rate at which these 4 machines produce the product is x/(4 * 6) units per day.

To find the number of machines required to produce 3x units of product P in 4 days, we can set up a proportion based on the rates:

(x units / (4 machines * 6 days)) = (3x units / (N machines * 4 days))

Simplifying the proportion:

1/(4 * 6) = 3/(N * 4)

Multiplying both sides by 4:

1/24 = 3/N

Cross-multiplying:

N = 24/1

N = 24

Therefore, the number of machines required to produce 3x units of product P in 4 days is 24.

The answer is option A. 24.

Correct Question :

Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?

A. 24

B. 18

C. 16

D. 12

E. 8

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No, there is no commutative property of subtraction for rational numbers. The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers.

The commutative property states that the order of the operands does not affect the result of an operation. For addition and multiplication, the commutative property holds true. However, for subtraction, the order of the operands does matter, and thus, the commutative property does not apply.

Let's consider an example to demonstrate this:

Take the rational numbers 3/4 and 1/2.

If we subtract 3/4 from 1/2, we have: 1/2 - 3/4 = (2/4) - (3/4)

= -1/4.

If we subtract 1/2 from 3/4, we have: 3/4 - 1/2 = (3/4) - (2/4)

= 1/4.

As you can see, the results are different when the order of subtraction is changed, indicating that subtraction does not follow the commutative property for rational numbers.

The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers. Changing the order of subtraction changes the result, making subtraction non-commutative for rational numbers.

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The commutative property does not apply to the operation of subtraction with rational numbers. This is because changing the order of the numbers in a subtraction operation will give a different result.

In mathematics, the commutative property refers to the idea that the order in which numbers are used in an operation does not change the result of that operation. This property holds true for addition and multiplication but, unfortunately, it does not hold true for subtraction and division. For example, in subtraction, if we take two rational numbers such as 5 and 3, 5 - 3 is equal to 2, but 3 - 5 equals to -2. As you can see, changing the order of the numbers gives us different results, demonstrating that there is no commutative property of subtraction for rational numbers.

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To calculate the z-score for a person who received a score of 81 on the recent quiz, we use the formula z = (x - μ) / σ, where x is the individual's score, μ is the mean of the class, and σ is the standard deviation of the class. Plugging in the values, we get z = (81 - 70) / 3.6, which simplifies to z ≈ 3.06. The z-score indicates how many standard deviations away from the mean the individual's score is. A z-score of 3.06 suggests that the person's score is quite high relative to the class mean.

To calculate the z-score, we first subtract the mean of the class from the individual's score (81 - 70) to sure the distance between the two values. Then, we divide this difference by the standard deviation of the class (3.6) to standardize the score. The resulting z-score of approximately 3.06 indicates that the individual's score is around 3 standard deviations above the mean. In a normal distribution, z-scores beyond ±2 are generally considered unusual or uncommon. Therefore, a z-score of 3.06 suggests that the person's score is quite exceptional and falls into the category of unusual performance in comparison to the class.

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The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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The value of the expression 8/(4 - d) when d - 2 is 4

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

8/(4 - d)

Also, in the question, we have

d = 2

Substitute the known values in the above equation, so, we have the following representation

8/(4 - d) = 8/(4 - 2)

So, we have

8/(4 - d) = 8/2

When evaluated, we have

8/(4 - d) = 4

Hence, the solution to the expression is 4

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Answer:

a. 15%

b. 60%

Explanation:

Part a.

The absolute change in percentage points can be calculated as

So, by replacing the final value with 40% and the initial value with 25%, we get

Therefore, the absolute change is 15%

Part b.

The relative change can be calculated as

Replacing the final value with 40% and the initial value with 25%, we get

Therefore, the relative change is 60%