Jeremy reads 3 books each week. How many books will Jeremy read in 5 weeks?

We have proved that if 2|n and 4 is not a factor of n, then μ∗φ(n) = 0.To prove that if 2|n and 4 is not a factor of n, then μ∗φ(n)=0, we need to use the properties of the Möbius function (μ) and Euler's totient function (φ).

First, let's define the properties of the Möbius function (μ):
1. If p is a prime number and \(p^2\) divides n, then μ(n) = 0.
2. If n is square-free (i.e., it is not divisible by any square greater than 1), then μ(n) = 1 if n has an even number of prime factors, and μ(n) = -1 if n has an odd number of prime factors.
Now, let's consider the given conditions:
1. 2|n: This means that n is divisible by 2.
2. 4 is not a factor of n: This means that n is not divisible by 4.

Since 2|n, n has at least one prime factor of 2. Therefore, n has an even number of prime factors.
Since 4 is not a factor of n, n cannot have any prime factors greater than 2. Therefore, n has only prime factors of 2.
From the properties of the Möbius function, we can conclude that μ(n) = 1, as n has an even number of prime factors, all of which are 2.Now, let's consider Euler's totient function (φ):
φ(n) represents the number of positive integers less than or equal to n that are coprime (relatively prime) to n.
Since n only has prime factors of 2, any number less than or equal to n will either be divisible by 2 or have a common factor with n. Therefore, φ(n) = 0.
Finally, we can prove that μ∗φ(n) = 0 by substituting the values we found:

μ(n) = 1 and φ(n) = 0.

Therefore, 1 * 0 = 0.
Hence, we have proved that if 2|n and 4 is not a factor of n, then

μ∗φ(n) = 0.

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The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)

What is an exponential function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Mathematical functions with exponents include exponential functions. f(x) = bx, where b > 0 and b 1, is a fundamental exponential function.

Here, we have

Given: The value of a car that depreciates over time can be modeled by the function M(t) = 10000\((0.9)^{3t}\)

An exponential function is in the form

y = abˣ

where y and x are variables, a is the initial value of y, and b is the multiplier.

Let m(t) represent the value of the car after t years, hence the exponential decay is given by:

m(t) = \(10000(0.9)^{3t}\)

m(t) = 10000\((0.9)^{3(t)}\)

m(t) = 10000\((0.729)^{t}\)

Hence, The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)

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Answer:

It's B

Step-by-step explanation:

Step-by-step explanation:

\(\displaystyle\\12-15x > 22\\12-15x+15x > 22+15x\\12 > 22+15x\\12-22 > 22+15x-22\\-10 > 15x\\Divide\ both\ parts\ of \ the \ equation\ by\ 15:\\-\frac{10}{15} > x\\\\-\frac{5*2}{5*3} > x\\\\-\frac{2}{3} > x \\\\Thus,\\\\x < \frac{-2}{3}\)

Answer: A

\(\displaystyle\\4\leq 3x+10 < 19\\\\4-10\leq 3x+10-10 < 19-10\\\\-6\leq 3x < 9\\\\Divide\ the\ inequality\ by \ 3:\\\\-2\leq x < 3\\\\Answer:\ -2\leq x < 3\)

For an a normally distributed the length of a pregnancy, with mean of 280 days and a standard deviation of 13 days,

a) the probability that he was NOT the father is equals to the 0.9762.

b) The probability that he could be the father is equals the 0.0238.

We have an expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed. Let variable X has normal distribution, Mean, μ = 280 days

standard deviations, σ = 13 days

An alleged father was out of the country from 240 to 306 days before the birth of the child. So, the variable value varies X < 240 or X> 306. Using Z-Score formula for normal distribution,

\(z= \frac{x -μ}{σ}\)

For x = 240

=> z =( 240 - 280)/13

= -40/13 = - 3.07

For x = 306

=> z = (306 - 280)/13

= 26/13 = 2

a) Probability that he not be the father , P ( 240< x < 306) or P(E)

= \( P ( \frac{240 - 280}{13 }< \frac{x - \mu}{\sigma} < \frac{306 - 280}{13})\)

= P (- 3.07 < z < 2 )

= P( x< 2) - P(z< - 3.07)

Using the normal distribution table value of probabilities for z < 2 and z< - 3.07 are determined, = 0.9762

= P(240<x <306)

b) Probability that he could be the father,

\(P( \bar E) \) = 1 - P(E)

= 1 - 0.9762

= 0.0238

Hence, required value is 0.0238.

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Answer:

−

-11

Step-by-step explanation:

The required, we can be 95% confident that the true difference in battery life between the model 10 and model 9 phones is between 0.25 and 2.95 hours longer for model 10 phones.

The appropriate inference procedure to be used to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone is a t-confidence interval for a difference in means.

The reason we use a t-test is that we are dealing with small sample sizes (n₁ = n₂ = 40) and do not know the population standard deviations.

We use a confidence interval instead of a hypothesis test because the question is asking for an estimate of the difference in battery life, rather than testing a specific hypothesis.

We can use the following formula to calculate the confidence interval:

( X₁ - X₂ ) ± t* ( Sqrt( s₁²/n₁ + s₂²/n₂ ) )

where:

X₁ and X₂ are the sample means of the battery life for model 10 and model 9, respectively

s₁ and s2 are the sample standard deviations of the battery life for model 10 and model 9, respectively

n₁ and n₂ are the sample sizes for model 10 and model 9, respectively

t is the critical t-value for the desired confidence level (degrees of freedom = n₁ + n₂ - 2)

Plugging in the given values, we get:

( 14.4 - 12.8 ) ± t* ( √( 2.1²/40 + 2.3²/40 ) )

= 1.6 ± t* 0.573

To find the critical t-value, we need to determine the degrees of freedom:

df = n₁ + n₂ - 2 = 78

Using a t-table or a calculator, for a 95% confidence level with 78 degrees of freedom, the critical t-value is approximately 1.99.

Plugging this into the formula above, we get:

1.6 ± 1.99 * 0.573

= ( 0.25, 2.95 )

Therefore, we can be 95% confident that the true difference in battery life between the model 10 and model 9 phones is between 0.25 and 2.95 hours longer for model 10 phones.

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The length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

What do you mean by length?

The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, the length and width of a rectangle define its dimensions.

According to data in the given question,

We have the given information:

The height of the person is 7 ft.

The person is walking away from the post at a rate of 5ft/sec.

The height of the lamppost is 20ft.

Let the person's distance from the bottom of the light post be x ft.

And his shadow's length is y ft.

Form the similar triangles,

\(\frac{x+y}{20}=\frac{y}{7}\\\)

7(x+y) = 20y

7x+7y = 20y

20y-7y = 7x

13y = 7x

y = \(\frac{7}{13}x\)

Now, we will differentiating wrt t,

\(\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}................(1)\)

We know that,

\(\frac{dx}{dt}=5\frac{ft}{sec}\)

Putting the value of  \(\frac{dx}{dt}\)  in equation (1),

\(\frac{dy}{dt}=\frac{7}{13}.5=\frac{35}{13}=2.69\frac{ft}{sec}\)

Therefore, the length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

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Answer:

$ 8902.72

Step-by-step explanation:

We would like to calculate the money which we need to invest at 3.3% rate compounded annually for two years . We know that ,

\(\longrightarrow \boldsymbol{ A = P \bigg(1+\dfrac{R}{100}\bigg)^n } \)

where the symbols have their usual meaning . So here ,

\(\longrightarrow \$ 9500 = P \bigg( 1+\dfrac{3.3}{100}\bigg)^2\\ \)

Simplify RHS ,

\(\longrightarrow \$ 9500 = P \bigg(\dfrac{100+3.3}{100}\bigg)^2\\\)

Simplify Nr . in RHS ,

\(\longrightarrow \$ 9500 =P\bigg(\dfrac{103.3}{100}\bigg)^2\\ \)

Isolate P ,

\(\longrightarrow P = \dfrac{ \$9500\times 100\times 100}{103.3\times 103.3}\\\)

Simplify ,

\(\longrightarrow \underline{\underline{\boldsymbol{ P = \$ 8902.72 }}}{} \)

And we are done !

\(\bold{Formula: A = P(1 + \frac{r}{100})^{(n)}}\)

Where

\( \bold{Solution : } \\ \\ \: \: \: \: \tt \: A = 9,500(1+\frac{3.3\%}{100})^{(2)} \\ \: \: \: \: \: \: \tt \: A = 9,500(1+ 0.033)^{(2)} \\ \tt \: A = 9,500(1.033)^{(2)} \: \: \\ \tt \: A = 10,137.34 \qquad \: \: \: \)

therefore,I need $10,137.34 if would like to purchase the car.

Answer:

it's a

Step-by-step explanation:

for these questions try each option till u find the correct one

so since x=5/2 y=4/3

\(3( \frac{5}{2} ) + 5( \frac{4}{3} ) = 14 \\ 7.5 + 6.66 = 14 \\ 14.16 = 14\)

which is nearly 14 and same way for the other equation

The mean can be calculated by adding all the data points and dividing the sum by the total number of data points. Therefore, the mean, median, and modes of the given data are 35.4, 39, and none, respectively.

The given stem-and-leaf plot represents the following data:2 | 4 62 | 4 7 9 9 1The stem values are 2 and 3, and the corresponding leaves represent the following data:24, 26, 47, 49, and 31.

The data is arranged in ascending order as follows: 24, 26, 31, 47, and 49.

Using the given data, Mean = (24 + 26 + 31 + 47 + 49) / 5= 177/5= 35.4

Therefore, the mean of the given data is 35.4.

The median is the middle value when the data is arranged in ascending or descending order. Since there are 5 data points, the median will be the average of the two middle values.

Hence, the median is given as:(31 + 47)/2= 39

Therefore, the median of the given data is 39.

The mode is the most frequently occurring data value in the dataset. There are no repeated data values in the given dataset.

Hence, the dataset does not have a mode. Thus, there are no modes of the given data.

Therefore, the mean, median, and modes of the given data are 35.4, 39, and none, respectively.

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Answer: 50-50

Step-by-step explanation:

Answer:

there will be 176 seats in the 40th row

Answer:

8576×7=60032

Step-by-step explanation:

Answer:

XDDDDDDDD

Step-by-step explanation:

Answer:

2915

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Answer:

5/6 and 75 1/3%

Step-by-step explanation:

8 1/3 = 25/3

25/3 pages of a book in 10 minutes

Multiply both numbers by the reciprocal of 10, which is 1/10

25/3 x 1/10 = 25/30 = 5/6

So, Charlotte reads 5/6 pages of a book in 1 minute.

Which is equal to 75 1/3%

hope this helps! :)

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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The value of y when x = 28 is y = 112. Since y is directly proportional to the value of x, we can write y = kx.

When a quantity 'p' is increasing with an increase in the other quantity 'q' or decreases with a decrease in 'q', both quantities are said to be directly proportional.

I.e., p ∝ q ⇔ p = kq

Where k is the proportionality constant.

It is given that, the value of y is directly proportional to the value of x.

I.e., y ∝ x

Then, y = kx

If x = 3.5 and y = 14, then k is

k = y/x = 14/3.5 = 4

So, if k = 4 and x = 28, then y is

y = kx = 4 × 28 = 112

Therefore, the value of y is 11.

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Answer:

Identity (a) can be re-written as

\(sec x\ cosec x - cot x = tan x\)

which we already proven in another question, while for idenity (b)

\((A)\frac 1 {sin x} -sin x = cos x \frac{cos x}{sin x}\\\\(B)\frac {1-sin^2x}{sin x} = \frac {cos^2x} {sin x} \\\\(C) \frac {cos^2x}{sin x} =\frac {cos^2x} {sin x}\)

step A is simply expressing each function in terms of sine and cosine.

step B is adding the terms on the LHS while multiplying the one on RHS.

step C is replacing the term on the numerator with the equivalent from the pithagorean identity \(cos^2x + sin^2x = 1\)

The first option, A BC^2 - AB^2 = AC^2, is true. This is a special case of the Pythagorean Theorem, which states that for a right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In this case, BC^2 - AB^2 = AC^2.

The first option, A BC^2 - AB^2 = AC^2, is true. This special case of the Pythagorean Theorem states that for any right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In other words, BC^2 - AB^2 = AC^2. This theorem has been used for centuries by mathematicians and builders, as it is a reliable way to measure and construct the sides of a triangle. The theorem is also useful in applications such as computer graphics, where it is used to calculate the dimensions of a triangle on a two-dimensional plane. By understanding the principles of the Pythagorean Theorem, one can accurately measure and construct triangles of any size and shape.

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The first option, A BC^2 - AB^2 = AC^2, is true. This is a special case of the Pythagorean Theorem, which states that for a right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In this case, BC^2 - AB^2 = AC^2.

The first option, A BC^2 - AB^2 = AC^2, is true. This special case of the Pythagorean Theorem states that for any right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In other words, BC^2 - AB^2 = AC^2. This theorem has been used for centuries by mathematicians and builders, as it is a reliable way to measure and construct the sides of a triangle. The theorem is also useful in applications such as computer graphics, where it is used to calculate the dimensions of a triangle on a two-dimensional plane. By understanding the principles of the Pythagorean Theorem, one can accurately measure and construct triangles of any size and shape.

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Answer: Answer: A

Explanation:

Just plug in numbers since you know the unknown values,

x + r = 4 + 5

4 + 5 = 9

Step-by-step explanation:

Based on the information provided, it appears that a study will be conducted to compare the mean weights of two populations of raccoons.

To do so, random samples will be selected from each population, and the mean weight of each sample will be calculated. By comparing the mean sample weights of the two populations, researchers can determine whether there is a significant difference in the mean weights between the two groups.

It is important to note that the use of random samples helps to ensure that the results are representative of the entire population and reduces the risk of bias in the study.

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The sequence's eighth partial total, then, is zero.

A series is a collection of things that is in order in mathematics. (or events). Similar to a group, it has individuals. (also called elements, or terms). The total length of the series is the number in ordered components (possibly endless).

The sequence is: 24, -24, 24, -24, ...

To find the 8th partial sum, we need to add the first 8 terms of the sequence.

S8 = 24 + (-24) + 24 + (-24) + 24 + (-24) + 24 + (-24)

Simplifying this expression, we see that every pair of adjacent terms cancels each other out, leaving us with:

S8 = 0 + 0 + 0 + 0

Therefore, the 8th partial sum of the sequence is 0.

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Answer:

It c

Step-by-step explanation:

She applied the exponent Negative 2 to 4 (negative 2) instead of applying the exponent to just Negative 2.