express 4.3242424.... in vulgar fraction

Answer:

1. 3 cookies

2. 2 cups

3. 300 calories

4. $35 per month

5. k = y/x

6. If there is no constant (k)

Step-by-step explanation:

1. The number of cookies the factory makes in one minute = (The number of cookies the factory makes in 12 minutes)/(12 minutes)

∴ The number of cookies the factory makes in one minute = 36 cookies/(12 minutes) = 3 cookies/minute

The correct answer is 3 cookies

2. The number of cups of water that leak every minute = (The number of cups of water that leak in 1/4 minute) × (The number of 1/4 minute per minute)

The number of cups of water that leak every minute = 1/2 cup per 1/4 minute × 4_1/4 minute per minute

The number of cups of water that leak every minute = 1/2  × 4 = 2

The number of cups of water that leak every minute = 2 cups

3. 5 glazed donuts contains 750 calories

∴ 1 glazed donuts contains 750/5 = 150 calories

2 = 2 × 1 glazed donuts will contain 2 × 150 = 300 calories

4. The charge of the cell phone company for 2 months = $70

The charge of the cell phone company for 6 months = $210

The constant rate per month = The rate of change of the cell phones companys charges

∴ The constant rate per month = (210 - 70)/(6 - 2) = 140/4 = 35

The constant rate (per month) for the service = $35 per month

5. The formula to find the constant of a chart, k = y/x

6. A chart is not considered proportional if there is no constant (k)

3. The current price of the common stock is $40.

4. The stock price considering the company quitting business after 25 years is $46.81.

5. The stock price assuming constant dividends is $26.67.

6. The stock price assuming constant dividends and the company quitting business after 25 years is $25.88.

3. The current price of the common stock can be calculated using the dividend discount model. The formula for the stock price is P = D / (r - g), where P is the stock price, D is the dividend, r is the required return, and g is the growth rate. In this case, the dividend is $4, the required return is 15% (0.15), and the growth rate is 5% (0.05). Plugging these values into the formula, we get P = 4 / (0.15 - 0.05) = $40.

4. If the company quits business after 25 years, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / (r - g) * (1 - (1 + g)^-n), where PV is the present value, D is the dividend, r is the required return, g is the growth rate, and n is the number of years. In this case, D = $4, r = 15% (0.15), g = 5% (0.05), and n = 25. Plugging these values into the formula, we get PV = 4 / (0.15 - 0.05) * (1 - (1 + 0.05)^-25) = $46.81. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $46.81 + $0 = $46.81.

5. Assuming constant dividends, the stock price can be calculated using the formula P = D / r, where P is the stock price, D is the dividend, and r is the required return. In this case, the dividend is $4 and the required return is 15% (0.15). Plugging these values into the formula, we get P = 4 / 0.15 = $26.67.

6. If the company quits business after 25 years and assuming constant dividends, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / r * (1 - (1 + r)^-n), where PV is the present value, D is the dividend, r is the required return, and n is the number of years. In this case, D = $4, r = 15% (0.15), and n = 25. Plugging these values into the formula, we get PV = 4 / 0.15 * (1 - (1 + 0.15)^-25) = $25.88. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $25.88 + $0 = $25.88.

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Answer:

\(y = \frac{8}{3} x-5\)

Step-by-step explanation:

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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Given:

The graph of triangle PQR and triangle P'Q'R'.

To find:

The transformation that will map the triangle PQR onto P'Q'R'.

Solution:

From the given graph it is clear that the triangle PQR is formed in II quadrant and its base lies on the negative direction of x-axis.

The triangle P'Q'R' is formed in IV quadrant and its base lies on the positive direction of x-axis.

This is possible it the figure is rotated 180 degrees about the origin.

Therefore, the correct option is A.

The statement holds for k + 1. By the principle of mathematical induction, the original equation is proven for all positive integers n greater than or equal to 1.

To prove the given statement using mathematical induction, we first establish the base case. When n = 1, the equation becomes s(1) = 1 * 1! = 1. On the other hand, (1-1)! - 1 = 0 - 1 = -1. Since these values are not equal, the base case is invalid.

Next, we assume that the equation holds true for some positive integer k, denoted as s(k) = (k-1)! - 1. This is known as the induction hypothesis. Now we need to prove that the statement holds for k + 1.

Considering s(k+1), we can rewrite it as s(k+1) = (k+1) * (k+1)! and simplify it further.

s(k+1) = (k+1) * (k+1)!

= (k+1) * (k+1)! * k/k

= (k+1) * (k!) * k/k

= (k+1)! * k

= (k+1)! * (k+1 - 1)

= (k+1)! * k!

Now we can substitute the induction hypothesis into the equation:

s(k+1) = (k+1)! * k!

= (k+1 - 1)! - 1 (by induction hypothesis)

= k! - 1

Thus, the statement holds for k + 1. By the principle of mathematical induction, the original equation is proven for all positive integers n greater than or equal to 1.

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Answer:

f'(x)=6x+8

Step-by-step explanation:

Alternative hypothesis may be one-sided or two-sided.

b) alternative hypothesis.

In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis. However, the research hypothesis is sometimes congruent with the null hypothesis.

In statistics, alternative hypotheses are frequently denoted as Hₐ or H₁. In a statistical hypothesis test, hypotheses are developed to be compared.

In the field of inferential statistics, two competing hypotheses can be compared using explanatory and predictive power.

This is the two tailed test .

alternative hypothesis is ,

Hₐ :μ≠

For the left tail is

Hₐ : μ<

For the right tail is

Hₐ :  μ >

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The complete question is :

"In hypothesis testing, which hypothesis can be either one-sided or two sided?

Group of answer choices

a.) null hypothesis

b.) alternative hypothesis"

Answer:

x−5=11−3x

Group all the constants at one side

That's

x + 3x =11 + 5

4x = 16

Divide both sides by 4

4x/4 = 16/4

x = 4

Hope this helps you

Answer:

x=4

Step-by-step explanation:

x−5=11−3x

take care of all the variables

you want to put the variables on one side and the numbers on the other

x−5=11−3x

+3x     +3x

4x-5=11

+5    +5

4x=16

÷4  ÷4

x=4

hope this helps :)

Answer:

(0,1)(4,9)

Step-by-step explanation:

Step-by-step explanation:

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\( \underline{ \underline{ \large{ \tt{T \: O \: \: F \: I \: N \: D}}}} : \)

\( \underline{ \underline{ \large{ \tt{S\: O\: L \: U \: T \: I \: O \: N}}}} : \)

Firstly , Find the cost of 1 cushion. Fo the cost of 1 cushion , the cost of 11 cushions is divided by 55.

⟼\( \large{ \tt{Cost \: of \: 1 \: cushion = \frac{55}{11} = £ 5}}\)

Since , the cost of 19 cushions is more than that of 1 cushion. So, the cost of 1 cushion is multiplied by 19.

⟼\( \large{ \tt{Cost \: of \: 19 \: cushion = 19 \times 5 = £ 95 }}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : { \boxed{ \boxed{ \underline{ \large\tt{ £ 95}}}}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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9514 1404 393

Answer:

  -4.2

Step-by-step explanation:

The linear term is missing from the quadratic, which means it is symmetrical about the vertical line x=0. For each x-intercept greater than 0, another is its opposite. The opposite of 4.2 is -4.2

The other x-intercept is -4.2.

__

Consider the parent function ...

  y = x^2

which is symmetrical about the y-axis.

Transforming it to ax^2 +k causes it to be scaled vertically by a factor of 'a', and shifted vertically up k units. Neither of these transformations affects the horizontal position of the curve, so it remains symmetrical about the y-axis. Attached is one example of a quadratic of this form with an x-intercept of 4.2.

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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So, the gradient vector field of f is (∇f) = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2).

To find the gradient vector field of the function f(x, y, z) = x cos(5y/z), we need to calculate the partial derivatives with respect to each variable and combine them into a vector.

The gradient vector is defined as:

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Taking the partial derivatives of f(x, y, z) with respect to each variable:

∂f/∂x = cos(5y/z)

∂f/∂y = -5x sin(5y/z)/z

∂f/∂z = 5xy sin(5y/z)/z^2

Putting these partial derivatives together, we have:

∇f = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2)

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Answer:8534.46

Step-by-step explanation:

The depreciated value of the bike after 12 years is $8534.46

Depreciated value is the minimum amount that an asset is worth after depreciation.

Given that, the value of a motorcycle is depreciating by 2.8% each year, the bike was purchased for $12,000,

We know that, the depreciation value is given by,

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = rate

n = years or time

Therefore,

A = 12000(1-0.028)¹²

A = 12000(0.972)¹²

A = 8534.46

Hence, the depreciated value of the bike after 12 years is $8534.46

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Hey there! I'm happy to help!

We have twice the number.

2n

We want the sum of that and 13. Sum means to add.

2n+13

And this is 75.

Equation: 2n+13=75

We subtract 13 from both sides.

2n=62

We divide both sides by 2.

n=31

Have a wonderful day! :D

An equation is formed of two equal expressions. The value of n is 31.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the sum of twice a number and 13 is 75. Therefore, the equation for this situation can be written as,

\(2n+13 = 75\)

Solving the above equation for n we will get,

\(2n+13 = 75\\\\2n = 75 -13\\\\2n= 62\\\\n = \dfrac{62}{2} \\\\n= 31\)

Hence, the value of n is 31.

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Answer:

60 degrees

Step-by-step explanation:

The total angles of a circle add up to 360 so to find a missing angle, subtract the figures already given from 60. The angles given total to (140+125+35) = 300. To find angle a, you subtract the 300 from 360. 360-300 = 60 degrees. Therefore, angle a is 60 degrees

You have $2.30 and would like to buy some rice flour buy 9.2 ounces of rice flour with $2.30.

To arrive at this answer, we need to first convert the price per pound to price per ounce. There are 16 ounces in a pound, so the price per ounce is $4/16 = $0.25 per ounce.

Next, we divide the amount of money you have ($2.30) by the price per ounce ($0.25).

$2.30/$0.25 = 9.2 ounces.

Therefore, the conclusion is that you can buy 9.2 ounces of rice flour with $2.30.
Hi! I'm happy to help you with your question.


You can buy 9.2 ounces of rice flour.


1. First, we need to find out how many dollars you have per ounce of rice flour: $4 per pound / 16 ounces per pound = $0.25 per ounce.
2. Next, we'll determine how many ounces of rice flour you can buy with $2.30: $2.30 / $0.25 per ounce = 9.2 ounces.


With $2.30, you can buy 9.2 ounces of rice flour at the given price of $4 per pound.

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A two-sample proportion test is used to analyze whether "liking cats" is a different proportion for males vs. females at the 0.10 level of significance. The p-value is the probability of obtaining a test statistic as extreme as the observed one.

To analyze whether "liking cats" is a different proportion for males vs. females at the 0.10 level of significance, we can use a two-sample proportion test. Here are the steps to perform the analysis:

Step 1: State the hypotheses The null hypothesis (H0) is that there is no difference in the proportion of males and females who like cats. The alternative hypothesis (Ha) is that there is a difference in the proportion of males and females who like cats.H0: p1 = p2Ha: p1 ≠ p2, where p1 is the proportion of males who like cats and p2 is the proportion of females who like cats.

Step 2: Check the assumptions Before proceeding with the test, we need to check whether the assumptions are met. The following assumptions must be satisfied: Independence: The samples of males and females must be independent of each other. This means that the response of one person should not influence the response of another person. Randomness: The samples of males and females must be selected randomly from the population. Success-Failure Condition: Both samples must have at least 10 successes and 10 failures.

Step 3: Calculate the test statisticWe can use the following formula to calculate the test statistic:

\(z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))\) , where p_hat is the pooled proportion, n1 is the sample size of males, and n2 is the sample size of females.p_hat = (x1 + x2) / (n1 + n2), where x1 is the number of males who like cats, and x2 is the number of females who like cats.

Step 4: Find the p-valueThe p-value is the probability of obtaining a test statistic as extreme as the one we observed, assuming the null hypothesis is true. We can find the p-value using a normal distribution table or a calculator. The p-value for a two-tailed test is:P-value = P(z < -z_alpha/2) + P(z > z_alpha/2), where z_alpha/2 is the z-value corresponding to the level of significance alpha/2.

Step 5: Make a decision and interpret the resultsFinally, we compare the p-value to the level of significance alpha. If the p-value is less than alpha, we reject the null hypothesis and conclude that there is evidence of a difference in the proportion of males and females who like cats. If the p-value is greater than alpha, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference in the proportion of males and females who like cats.

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Answer:

Step-by-step explanation:

An equation contains a sign equality (=) between two expressions.

And an expression is a simple algebraic statement.

By these definitions,

          Equations                          Expressions

         x = 2x + 5                            21x - 13 + 11x

         \(\frac{1}{2}x=5+3\)                           -3.7x - 13  

         3x + 1 = -2.1                          \(\frac{1}{2}x+5\)

Answer: the true answer is A

Step-by-step explanation:

Good luck, give Brainliest

Using the normal distribution, it is found that the probability that more than 524 customers will come to the store on a given day is given by:

A. 0.15%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by:

\(\mu = 428, \sigma = 32\).

The probability that more than 524 customers will come to the store on a given day is one subtracted by the p-value of Z when X = 524, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{524 - 428}{32}\)

Z = 3

Z = 3 has a p-value of 0.9985.

1 - 0.9985 = 0.0015 = 0.15%.

Hence option A is correct.

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Answer:

x>=9

Step-by-step explanation:

so, we can plot this on a number line

the point at 9 is a solid dot, since brackets (not parenthasis) indicates that we including the number. the shaded part of the line extends all the way to positive infinity. the shaded part means that it is a solution, while the un-shaded parts aren't solutions to [9,infinity) it is x>=9 and not x>9 because 9 is included.

x>=9 is the answer

Answer:

3/216

Step-by-step explanation:

The sample space for this experiment is 6^3 which is 216

there are three prime numbers on  die

namely 2 , 3 and 5

so the probability of getting a prime number on all three roles would be

(3/6)^3

Answer:

sp with vat=9040

d=20%

vat=13%

mp=?

Step-by-step explanation:

sp with vat=9040

sp+vat%of sp=9040

sp(1+13/100)=9040

sp=9040/1.13=8000

Answer:

-1 C

Step-by-step explanation:

Mean = Average

To find the mean simply add all the values and then divide that by the number of given values

So first add the 4 values together

1.5 + -2.6 + -3.4 + .5 = -4

Then divide the sum by the number of values ( there are 4 values )

-4 / 4 = -1

The mean temperature is -1

By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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There are 52 cards in the deck.

Picking the 6 of spades or 9 of clubs are two of the possible cards you could pick.

Your probability is 2/52 or 1/26 or 3.8461538461538%.