[1/3 Points) DETAILS PREVIOUS ANSWERS Find the Nth partial sum of the infinite series and evaluate its limit to determine whether the series converges or diverges. 1 Σ. n +7 + SN - X converges O diverges If the series is convergent, find its sum. (If an answer does not exist, enter DNE.)

The age of Michael as of now is 6 years old as the age pf Norman will be 12 years. So option (B) 6 is correct answer.

Let N = Norman’s age now; (N + 6) = Norman’s age in 6 years.

Let M = Michael’s age now; (M + 6) = Michael’s age in 6 years.

Translate the first two sentences into equations. Note that the second equation deals with Norman and Michael’s ages in 6 years:

N=M+12

(N+6)=2(M+6)

The question asks for M, so substitute (M + 12) for N in the second equation:

(M+12)+6=2(M+6)

M+18=2M+12

M=6

Therefore, the age of Michael as of now is 6 years old. So option (B) 6 is correct answer.

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We can use the z-score associated with the 80th percentile to calculate the upper bound of the interval using the formula: sample mean + 0.84*(σ/√n).

To round the answer to at least two decimal places, we need to know the values of n and σ. Without that information, we can't provide a specific numerical answer.

To find the 80th percentile of the sample mean, we first need to calculate the sample mean and standard deviation. Let's assume we have a sample of size n and we know the population standard deviation σ.

Using the central limit theorem, we know that the sample mean follows a normal distribution with mean μ and standard deviation σ/√n. Since we don't know the population mean μ, we can use the sample mean as an estimate.

Next, we need to find the z-score associated with the 80th percentile. We can use a z-table or a calculator to find that z = 0.84.

Finally, we can use the formula for the confidence interval of the sample mean:

sample mean ± z*(standard deviation/√n)

Plugging in the values, we get:

sample mean ± 0.84*(σ/√n)

Since we're looking for the upper bound of the 80th percentile, we only need to consider the positive value of the interval:

sample mean + 0.84*(σ/√n)

This represents the value that separates the top 20% of sample means from the bottom 80%.

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When Gregory adds these two numbers, the greatest sum Gregory can get will be 975.

From the information, Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get?

The greatest 3-digit number that can be formed with the digits 1, 2, 3, 4, 5, and 6 is 654 and the smallest is 123. If Gregory forms these two numbers, the sum of these numbers is 654 + 321 = 975, which is the greatest sum he can get.

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Answer:975

Step-by-step explanation:

uyygu

The two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is -4.08 (rounded to two decimal places).

To calculate the two-sample z-test statistic, we need to compare the proportions of students who support capital punishment in 1970 and 2005. The null hypothesis states that the percentage of students who support capital punishment did not change.

Let p1 be the proportion of students who support capital punishment in 1970, and p2 be the proportion in 2005. We can calculate the sample proportions as p1 = 590/1000 = 0.59 and p2 = 350/1000 = 0.35.

The formula for the two-sample z-test statistic is given by z = (p1 - p2) / sqrt((p(1 - p)(1/n1 + 1/n2))), where p is the pooled proportion and n1 and n2 are the sample sizes.

To calculate p, we compute the pooled proportion as p = (p1n1 + p2n2) / (n1 + n2) = (0.591000 + 0.351000) / (1000 + 1000) = 0.47.

Substituting the values into the formula, we have z = (0.59 - 0.35) / sqrt((0.47*(1 - 0.47)(1/1000 + 1/1000))) = -4.08.

Therefore, the two-sample z-test statistic for evaluating the null hypothesis is -4.08 (rounded to two decimal places).

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Answer:

2\(x^{2}\)+2\(y^{2}\)

Step-by-step explanation:

\((x+y)^{2}\) + (\(x^{2}\) -2xy+\(y^{2}\))

(x+y)(x+y)+(\(x^{2}\) -2xy+\(y^{2}\))

\(x^{2}\)+ xy + xy+\(y^{2}\)+\(x^{2}\)-2xy+\(y^{2}\)

\(x^{2}\)+2xy+\(y^{2}\)+\(x^{2}\)-2xy+\(y^{2}\) (cancel 2xy)

The answer is  -      2\(x^{2}\)+2\(y^{2}\)

Answer:

2 x 3 x 5

Step-by-step explanation:

30/2 = 15

15/3 = 5

5/5 = 1

See the attached picture

Answer:

hope this helps! Feel free to clarify!

b(i) The probability that a randomly selected graduate will have a starting salary of less than £15,600 is 0.2912.

b(ii) 3,000 students graduated from the university this year.

b(iii) 93.14% of the graduates will have starting salaries between £4,320 and £35,680.

(i) To find the probability that a randomly selected graduate will have a starting salary of less than £15,600, we use the standard normal distribution.

Standardize the value of £15,600 using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (15,600 - 20,000) / 8,000

z = -0.55

Using a calculator, the probability of a z-score of -0.55 is  0.2912.

(ii) First, we standardize the value of £32,240:

z = (32,240 - 20,000) / 8,000

z = 1.53

Using a calculator, the probability is 0.9370.

The probability of graduates with salaries less than £32,240:

1 - 0.9370 = 0.0630

Total Number of Graduates = 189 / 0.0630

Total Number of Graduates ≈ 3,000

(iii) First, we standardize the value £4,320:

z1 = (4,320 - 20,000) / 8,000

z1 = -1.71

Next, we standardize the value £35,680:

z2 = (35,680 - 20,000) / 8,000

z2 = 1.96

The cumulative probability for z1 is approximately 0.0436, and for z2, it is approximately 0.9750.

The probability of starting salaries between £4,320 and £35,680, we will be:

0.9750 - 0.0436 = 0.9314

The percentage of graduates with starting salaries between £4,320 and £35,680:

0.9314 * 100 = 93.14%

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It is true that studying sampling distributions can help to better understand the concepts of 99% confidence, confidence intervals, standard error, and margin of error.

Sampling distributions refer to the distribution of sample statistics, such as the mean or standard deviation, obtained from multiple random samples of the same size from a population. The central limit theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the population distribution.

The concept of 99% confidence refers to the likelihood that a population parameter, such as the population mean, falls within a specific range of values based on the sample mean and standard deviation. This range is known as the confidence interval, and its width is determined by the sample size and level of confidence. By studying the sampling distribution, we can understand how the width of the confidence interval is affected by sample size and level of confidence.

The standard error is the standard deviation of the sampling distribution of the mean. It represents the variability of sample means around the population mean. By studying the sampling distribution, we can understand how the standard error is affected by sample size and population variability.

The margin of error is the range of values that the true population parameter is likely to fall within based on the sample statistic and a specific level of confidence. It is determined by the standard error and level of confidence. By studying the sampling distribution, we can understand how the margin of error is affected by sample size and level of confidence.

Therefore, studying sampling distributions can provide valuable insights into the concepts of 99% confidence, confidence intervals, standard error, and margin of error

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Recall that a periodic function is a function that repeats itself at regular intervals, and the period is the distance between the repetitions.

Notice that the given graph repeats itself regularly, then it must be periodic.

From the given diagram we get that the period of the given graph is:

Answer: Option C.

Answer:

The factors of a^2b is a×a×b.

\(\\ \sf\longmapsto (-42)+15+(-63)\)

\(\\ \sf\longmapsto -42+15+(-63)\)

\(\\ \sf\longmapsto -27+(-63)\)

\(\\ \sf\longmapsto -27-63\)

\(\\ \sf\longmapsto -90\)

Answer:

42 + 15 + (-63) = -90

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

B. (-3, -17)

Step-by-step explanation:

Plotting them out on a graph, the other 3 points are able to be connected as a parallelogram. If you don't have graph paper at home, you can do an online search for "online graph paper" and use that. I personally find it very helpful to be able to see these kinds of things with my eyes.

The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.

The length of the first secant in the image is x + 18, and the second is 24 + 16.

x + 18 times 18 = 40 times 16

18x + 324 = 640

18x = 316

x= approximately 17.6

After 15 more years of contributions of $4,000 at the end of each quarter, the retirement account will be worth approximately $760,514.47.

To calculate this, we need to use the formula for the future value of a lump sum. A lump sum is a one-time payment made at the beginning or end of a specific period. In this case, we're looking at the future value of the retirement account after 15 more years of contributions.

Using the given information, we can plug in the values and solve for FV:

PV = $150,000

Pmt = $4,000

r = 10%

n = 4 (since interest is compounded quarterly)

t = 15 years

First, we need to calculate the future value of the current investment of $150,000:

FV1 = $150,000 x (1 + 0.1/4)⁴ ˣ ¹⁵ = $548,534.24

Then, we can calculate the future value of the quarterly contributions of $4,000 over 15 years:

FV2 = $4,000 x [(1 + 0.1/4)⁶⁰ - 1] / (0.1/4) = $211,980.23

Finally, we can add FV1 and FV2 to get the total future value of the retirement account after 15 more years:

Total FV = FV1 + FV2 = $548,534.24 + $211,980.23 = $760,514.47

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The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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Answer:

Step-by-step explanation:

Answer:

9 on its own can not be simplified. It needs to be a fraction.

Answer:

0.75

Step-by-step explanation:

use the scale to get the width

The constant of proportionality is given as follows:

k = 3/4.

Hence the value of y when x = 10 is given as follows:

y = 7.5.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For this problem, we have that when x = 4, y = 3, hence the constant is given as follows:

4k = 3

k = 3/4.

Hence the equation is:

y = 3x/4.

The numeric value at x = 10 is given as follows:

y = 3 x 10/4

y = 30/4

y = 15/2

y = 7.5.

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The number of ways are = 1867866560

According to our question-

The passwords contain only digits and lower-case letters.

Length is 6 and the password must contain at least one digit.

There are 26 lower case and 10 digits.

Total = 26+10=36

Length is 6 and the password must contain at least one digit.

Hence, The number of ways are = 1867866560

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Answer:

interest money is the amount of money a lender or a financial institution receives for lending out money

The function that calculates the total principal through a specified number of payments is the PMT function.

This function is mainly used in Microsoft Excel and is widely used for calculating loan payments, and other related financial calculations. The PMT function returns the payment amount for an investment that is based on constant payments and a constant interest rate.The main answer to the question is the PMT function. This function is used for calculating the total principal through a specified number of payments. The function takes into account constant payments and a constant interest rate to arrive at the payment amount for the investment.The PMT function in Excel uses three arguments: Rate, Nper, and Pv. Where,Rate: It is the interest rate per period.

It is the rate at which the investment earns interest.Nper: It is the total number of payments for the investment.Pv: It is the present value of the investment. It is the amount of money that is being invested.The function also includes optional arguments like Fv, Type. Where, Fv: It is the future value of the investment. Type: It specifies when payments are due, whether they are at the beginning or the end of the period.The above explanation comprises more than 100 words and covers the necessary information related to the PMT function.

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Step-by-step explanation: The first thing you're going to probably

try to do here is to factor out a greatest common factor.

The problem is, there is no factor that is in common

to all three of these terms so you may think it's unfactorable.

However, this trinomial is in a special form.

We have an x squared term, an x term, and a constant term.

When a trinomial is in this form, it can be

factored as the product of two binomials.

So start by setting up two sets of parentheses.

Inside each set, we will have the two terms that compose each binomial.

So we have (    )(    ).

The first term is a factor of the x² term, x · x.

For the second term, we need factors of 12 that add to -7.

Since the middle term is negative, we use the negative factors of 12.

Notice that -4 and -3 add to -7 and multiply to be 12.

So our answer is (x - 4)(x - 3).

Answer: 199263

Step-by-step explanation: do I even need an explanation for simple multiplication?

Answer:

1.

5/3 h

5/3 h

Les résultats sont égaux

2.

5/3

3.

-5/3

Step-by-step explanation:

1.

Femmes: 5 h / 3 = 5/3 h

Hommes: 15 h / 9 = 15/9 h = 5/3 h

Les résultats sont égaux

2.

3 × ... = 5

3 × 5/3 = 5

3.

45 × ... = -75

-75/45 = -5/3

45 × (-5/3) = -75

Answer:

\(22\)

Step-by-step explanation:

Similar shapes must have corresponding sides in a constant proportion. Therefore, we can set up the following equation and solve for \(?\):

\(\frac{28}{42}=\frac{?}{33}\) (divide corresponding sides)

\(\frac{28}{42}=\frac{?}{33},\\\\?=\frac{28\cdot 33}{42}=\boxed{22}\)