2) A prime number is an integer greater than 1 with exactly two different positive factors, 1nd the number itself. There are three children in a family. Each of their ages is a prime number. The sum of their ages if 41 and at least two of the children have ages that differ by 16. Determine all possibilities for the ages of the children.​

Answer:

see below

Step-by-step explanation:

5x+5+4x=4-3x+6

Combine like terms

9x+5 = 10-3x

Add 3x to each side

9x+3x +5 = 10-3x+3x

12x+5 = 10

Subtract 5 from each side

12x+5-5 = 10-5

12x = 5

Divide each side by 12

12x/12 = 5/12

x=5/12

The cost of cementing the walls of the cuboidal well is Rs 3640.

A three-dimensional solid form with six rectangular sides is called a cuboid. It also goes by the name rectangular prism. The shapes and sizes of the faces on either side of each other are identical.

A cuboid's surface area is the sum of all of its faces. We can determine the area of each face and put them together to determine the cuboid's surface area.

Given that, the cost of cementing the walls of the well at the rate Rs 52 per square m.

Thus,

Area of one rectangular face = length x height = 2 x 10 = 20m².

Area of the other rectangular face = width x height = 1.5 x 10 = 15m².

Total surface area of the walls = 2(20) + 2(15) = 70m².

Now, the cost of cementing the walls of the well at the rate of Rs 52 per m² is:

Cost = 70m x Rs 52 = Rs 3640

Hence, the cost of cementing the walls of the well is Rs 3640.

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Lee painted 63 feet of fence in 3 days

The natural response of the given transfer function is \(y_n(t) = c_1e^{-t} + c_2e^{-2t} + c_3e^{-2t}\sin(2t) + c_4e^{-2t}\cos(2t)\), \(y_n(t) = c_1e^{-t} + c_2e^{-2t} + c_3e^{-2t}\sin(\omega t) + c_4e^{-2t}\cos(\omega t)\)

We have:

\((s + 1)^2(s^2 + 4)(s + 8) = 0\)

The roots of the denominator polynomial are:

\(s_1 = -1\) (double pole),

\(s_2 = 2j\) (double pole),

\(s_3 = -2j\) (double pole),

\(s_4 = -8\) (single pole).

The first root is a double pole at \(s=-1\), which gives an exponential term of \(e^{-t}\). The second and third roots are a complex conjugate pair of double poles at \(s=2j\) and \(s=-2j\), which give two exponential terms \(e^{-2t}\cos(2t)\) and \(e^{-2t}\sin(2t)\). Finally, the last root is a single pole at \(s=-8\), which gives an exponential term of \(e^{-8t}\).

Therefore, the natural response of the given system is:

\(y_n(t) = c_1 e^{-t} + c_2 e^{-2t}\cos(2t) + c_3 e^{-2t}\sin(2t) + c_4 e^{-8t}\).

Thus ,the natural response of the given transfer function is \(y_n(t) = c_1e^{-t} + c_2e^{-2t} + c_3e^{-2t}\sin(2t) + c_4e^{-2t}\cos(2t)\),

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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The events U and V are mutually exclusive, which means they cannot occur at the same time. Therefore, the probability of both events happening together, P(U and V), is 0. On the other hand, to calculate the probability of either U or V occurring, we can add the individual probabilities of U and V. Given that P(U) is 0.26 and P(V) is 0.37, we can determine that the probability of either U or V happening, P(either U or V), is 0.63

Mutually exclusive events are events that cannot occur at the same time. In this case, U and V are mutually exclusive events. When two events are mutually exclusive, the probability of both events occurring together (P(U and V)) is always 0 because they cannot happen simultaneously. Therefore, the probability of U and V occurring together is 0.

To calculate the probability of either U or V occurring (P(either U or V)), we need to add the individual probabilities of U and V. In this case, P(U) is given as 0.26 and P(V) as 0.37. By adding these probabilities, we get 0.26 + 0.37 = 0.63. So, the probability of either U or V occurring is 0.63.

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Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so,  when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.\(\sum(x - \bar x) = 0\)

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.

Answer:

30

any more help just ask

Answer:

28

Step-by-step explanation:

You have to add 22 to 6 to get your answer. Hope this helps you!

Answer:

D.

Step-by-step explanation:

Focus on one point and see how it shifts.

Now just count the unit shifts.

Answer:

5:6

Step-by-step explanation:

The correct interpretation of the confidence interval is: "We can estimate with 95% confidence that the true population mean pizza delivery time is between 33.78 and 38.22 minutes."

The confidence interval represents a range of values within which the

population mean delivery time is likely to fall, based on the sample data.

It does not provide information about the delivery times of individual pizzas

or restaurants.

The confidence level refers to the percentage of times that the true

population mean would be expected to fall within the interval if the same

sampling procedure were repeated many times.

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Thus, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

The equation of exchange is an economic equation that relates the money supply (M) with the price level (P), the velocity of money (V), and the real output of the economy (Q). The equation is M x V = P x Q.

Using the given values of M = $1.5 trillion, V = 7, and P = 1.05, we can solve for Q by rearranging the equation as Q = M x V / P.

Plugging in the numbers, we get:

Q = ($1.5 trillion x 7) / 1.05 = $10 trillion

Therefore, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

It's worth noting that the equation of exchange is a theoretical model and may not reflect actual economic conditions. In practice, changes in any one of the variables (M, V, P, or Q) can affect the others, and there may be other factors at play that influence the economy.

Nonetheless, the equation of exchange provides a useful framework for thinking about the relationship between the money supply, prices, and economic activity.

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Complete question

in the equation of exchange, if m = $1.5 trillion, v = 7, and p = 1.05, then:

Find real output.

a) The probability that the first toss is heads is simply 0.5 or 50%.

b) The probability that the first two tosses landed heads is 0.25 or 25%.

c) The probability that at least two of the first five tosses landed heads is 0.8125 or 81.25%.

a) To find the chance that the first toss landed heads, we can use the fact that each toss is independent and has a 50-50 chance of being heads or tails.

b) Similarly, the probability that the first two tosses landed heads is calculated by considering that each toss is independent, so the probability of both being heads is simply the product of the probabilities of each toss being heads, which is:

P(first two tosses are heads) = P(first toss is heads) * P(second toss is heads) = 0.5 * 0.5 = 0.25 or 25%

c) To find the probability that at least two of the first five tosses landed heads, we can use the binomial distribution. The number of heads in the first five tosses follows a binomial distribution with n = 5 trials and p = 0.5 probability of success (heads).

Using the binomial distribution formula, we can calculate the probability of getting exactly 0 or 1 heads in the first five tosses:

P(0 heads in first 5 tosses) = (5 choose 0) * (0.5)^0 * (0.5)^5 = 0.03125

P(1 head in first 5 tosses) = (5 choose 1) * (0.5)^1 * (0.5)^4 = 0.15625

Then, we can use the complement rule to find the probability of getting at least two heads in the first five tosses:

P(at least two heads in first 5 tosses) = 1 - P(0 heads in first 5 tosses) - P(1 head in first 5 tosses) = 1 - 0.03125 - 0.15625 = 0.8125 or 81.25%

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The probability that a dancer performs first in the talent competition can be calculated by dividing the number of favorable outcomes (a dancer performing first) by the total number of possible outcomes (all possible orderings of the acts). The answer is a simplified fraction.

There are a total of 20 acts consisting of 4 instrumentalists, 10 singers, and 6 dancers. Since we want to find the probability of a dancer performing first, we can consider the first act as the dancer, and the remaining acts can be arranged in any order.

The total number of possible orderings of the 20 acts is 20!, which represents the factorial of 20 (20 factorial).

The number of favorable outcomes is 6 * 19!, which means fixing one dancer as the first act and arranging the remaining 19 acts in any order.

Therefore, the probability can be calculated as:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

= (6 * 19!) / 20!

The expression (6 * 19!) / 20! can be simplified by canceling out the common factors:

Probability = 6 / 20

Hence, the probability that a dancer performs first is 6/20, which simplifies to 3/10.

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The number of ways to select a committee of four Republicans, three Democrats, and two Independents from a group of 10 distinct Republicans, 12 distinct Democrats, and four distinct Independents is: 277,200.

This can be calculated using the formula for combinations, which states that the number of ways to choose k objects from a set of n distinct objects is given by

nCk = n! / (k! * (n-k)!),

where ! denotes the factorial function.

In this case, we use this formula to calculate the number of ways to choose four Republicans from a group of 10, three Democrats from a group of 12, and two Independents from a group of 4.

We then multiply these values together to get the total number of possible committees:

(10C4) x (12C3) x (4C2) = 210 x 220 x 6 = 277,200

The final answer is 277,200.

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Answer:

19/25

Step-by-step explanation:

7/10 + 6/100

= 70/100 + 6/100

= 76/100

= 19/25

So, the answer is 19/25

Answer: A. 2   B. 2    C. 1/2

Step-by-step explanation:

Hello there!

-4/-2=2 because if we divide a negative by a negative, we get a positive.

-2/-1=2. Keep in mind that a negative number divided by a negative number always equals a positive number

-24/-48=\(\frac{1}{2}\)

Hope this helps you!

~Just a joyful teen

\(SilentNature\)

The volume of the rectangular pyramid with a length of 8m, width of 5m and height of 12m is 160 m³.

A rectangular pyramid is simply a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

From the diagram:

Length l = 8 meters

Width w = 5 meters

Height h = 12 meters

Volume V = ?

Plug the given values into the above formula and solve for the volume:

V = (1/3) × l × w × h

V = (1/3) × 8 × 5 × 12

V = 160 m³

Therefore, the volume of the pyramid is 160 m³.

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Answer:

------------------------

Each triangle face has height of 7 ft and base of 0.6 ft and the base of the pyramid is the square with side of 0.6 ft.

Total surface area includes a square base and four triangular faces and the measure of it is:

The matching choice is B.

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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Option B is correct. The statement that is true about the values we have been given here is that They are the only values that make both equations true.

We have been given two equations

The first equation is

4y-3x=16

We have to plug in the values (-5, 0.25) in this equation

4(0.25) -3(-5) =16

Then we have

1 + 15 = 16

Hence 16 = 16 This satisfies the equation.

In the second equation we have to follow the same step

-x-8y=3

Such that

-(-5)-8*0.25 = 3

5-2 = 3

3 = 3 This also satisfies the equation.

Therefore the correct answer option is B

a. They satisfy equation 8 but not equation A.

B. They are the only values that make both equations true.

C. They show that the equations represent the same line.

D. They satisfy equation A but not equation B.

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(a) The variable educ might be endogenous

(b) The variable brthord is birth order (one for the first-born child, two for a second-born child and so on) could be used as an instrument for educ in equation

a) The variable instruction might be endogenous because as compensation increases the income expansions which additionally make able to an individual more educating himself. So there is an opportunity for the instruction might be an endogenous variable.

The indigeneity may involve the 32 the coefficient of knowledge as well different variables like married, black, south, urban, etc.

b) There is a substantial high relationship exists between birth order and the status of teaching. it is more possible to have higher schooling with less the order of child-born and the birth order is autonomous of the error term as well with wage. So the variable "birth order" is a good variable to use as an agency for the endogenous variable instruction.

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Answer:

8

Step-by-step explanation:

4*8=32

6*8=48

9*8=72

They are all multiples of 8

Answer: 8

Step-by-step explanation: You can factor out 32, 48, and 72 by using prime factorization which is listing all of the PRIME factors for each number

32: 2 x 2 x 2 x 2 x 2

48: 3 x 2 x 2 x 2 x 2

72: 3 x 3 x 2 x 2 x 2

If you look at all the prime factors, 2 appears in every number 3 times, so you do 2x2x2 to get the final answer, which is 8.

The likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%

When dealing with normally distributed data, we use the mean and standard deviation to determine the likelihood of certain events occurring. In this case, the mean weight of bags of cement is 53 with a standard deviation of 2.

To find the likelihood that a randomly selected bag has a weight greater than 50, we need to calculate the z-score for 50. The z-score tells us how many standard deviations away a particular value is from the mean.

z = (X - μ) / σ

where X is the value we're interested in (50), μ is the mean (53), and σ is the standard deviation (2).

z = (50 - 53) / 2 = -1.5

A z-score of -1.5 means that a weight of 50 is 1.5 standard deviations below the mean. To find the likelihood of a bag weighing more than 50, we can use a z-table or a calculator to find the area to the right of this z-score.

Looking up a z-score of -1.5, we find that the area to the left is approximately 0.0668, which means the area to the right (the likelihood of a bag weighing more than 50) is:

1 - 0.0668 = 0.9332

Thus, the likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%.

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Answer: (5,5)

Step-by-step explanation:

The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is \(y=-x+10\).

Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.

If x=5, then y=5 as well.

So, F has coordinates (5,5).

Answer:

60th percentile = 23.5

Step-by-step explanation:

Put numbers in order from lowest to highest:

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

Formula:

60th percentile = 60% x Total number of elements

We have 20 scores,

60th percentile = 60% x 20

                          = 0.60 x 20

                          = 12

the 60th percentile is the 12th number on the list

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

The 60th percentile is between 23 and 24

23 + 24 / 2 = 23.5

Answer:

its B ok sana makatulong

The development of a 95% confidence interval for average wage rates in a random sample of 40 workers illustrates the characteristic of sampling error.

Sampling error refers to the fact that there will always be differences between a sample and the population from which it is drawn. These differences can occur due to chance, and they can affect the estimated characteristics of the sample, such as average wage rates.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of certainty or probability. In this case, a 95% confidence interval means that if we were to take many samples of size 40 from the same population and calculate a confidence interval for each one, approximately 95% of those intervals would contain the true population parameter.

The fact that the confidence interval is developed based on a random sample of 40 workers is an example of how sampling error can affect the estimate of the population parameter. Since the sample is just one possible subset of the population, there is some degree of uncertainty involved in estimating the true population parameter based on the sample data. The confidence interval helps to quantify that uncertainty and provide a range of possible values for the population parameter.

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