How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515…

Answers

Answer 1

The process of converting repeating, non-terminating decimal to a fraction has been explained below. On conversion of 0.1515…, we get the fraction as 5/33.

What is a non-terminating decimal?

Non-terminating decimals are those decimal numbers that never reach an end since there is no endpoint in their decimal digits.

We are given a repeating, non-terminating decimal as 0.1515…

So, let x = 0.1515151515  ...(1)

Here, .15 is repeating

So, we will move one set of the repeating digits in front of the decimal.

By this, we get

100x = 15.1515151515     ...(2)

Now, on subtracting (1) from (2), we get

⇒100x - x = 15.1515151515 - 0.1515151515

⇒99x = 15

⇒x = 15/99

⇒x = 5/33

Hence, this way we can convert repeating, non-terminating decimal to a fraction.

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Related Questions

 write a function to describe the following scenario. A taxi driver charges a flat rate of 7.25+0.65 per mile. y=(?)+(?)x

Answers

The function that describes the scenario is y = 7.25 + 0.65x

How to determine the linear function

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

Initial = 7.25

Rate = 0.65

Represent the number of miles with x

So, we have the following representation

y = 7.25 + 0.65x

Where the total cost is y

Hence, the function is represented above

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the town of pleasantville conducted a 5-year crime prevention program. based on the graph, what was the percent of change in the number of crimes from year 1 to 5

Answers

The requried percentage change in crimes from years 1 to 5 is given as    60.86%.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
From the table.

Crime in year 1 = 23
Crime in year 5 = 9

Percentage change = 23 - 9 / 23 ×100%
                              = 60.86%

Thus, the requried percentage change in crimes from years 1 to 5 is given as 60.86%.

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in the number 652.12, how does the value of the 2 in the hundredths place compare to the value of the 2 in the ones place?

Answers

In the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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In the number 652.12, the 2 in the hundredth place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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jamie drove 61 miles jamie car used 4 gallons of gas, how many miles per gallon did jamie car get

Answers

The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

What is the rate?

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Jamie drove 61 miles Jamie's car used 4 gallons of gas.

The number of miles per gallon that Jamie's car get will be given as,

Rate = 61 / 4

Rate = 15.25 miles per gallon

The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.

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Amy wins a $200 gift card from a local store during its grand opening. If the card is not used within the year, a 10% fee is deducted from the balance at the end of each year. The following table shows Amy's gift card balances (y) for an inactive gift card at the end of year x

Answers

Answer:

20 dollars will be deducted if the card is not used. I am not sure what your question is but this is what I understood sorry it it isn't what you are asking for

Please look at photo
The pointer shown to the right can land on every number, and
the respective probability that the pointer can land on is
shown in the table below. Compute the expected value for the
number on which the pointer lands.
The expected value for the number on which the pointer lands
Question Viewer
(Type an integer or a decimal.)
CHI
N
Outcome Probability
a

Answers

The expected value for the number on which the pointer lands is 21/8.

What is probability?

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given the pointer shown to the right can land on every number, and

the respective probability that the pointer can land is

shown in the table below,

table for probability,

outcome        probability

1                           1/4

2                          1/4

3                           1/8    

4                           3/8

expected value is given by,

E(x) = ∑ [tex]x_i.p(x_i)[/tex]

  = 1(1/4) + 2(1/4)  + 3(1/8)  + 4(3/8)

 = 1/4 + 1/2 + 3/8 + 3/2

   =  (2 + 4 + 3 + 12)/8

 =  21/8 = 2.625

Hence expected value is 21/8 or 2.625.

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Q. Mr X had income from salary of 200000. Income from Capital Gain of
150000 and income from other sources is 250000. Contribution to PF
is *40000, PPF 70000, and LIC is 40000. Calculate Income Tax Liability of mr x

Answers

The income tax liability of Mr. X is 450,000 rupees.

What is subtraction?

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

Mr X had income from salary of 200000.

Income from Capital Gain of, 150000 and income from other sources is 250000.

Contribution to PF is 40000, PPF 70000, and LIC is 40000.

Income Tax liability = total income - total deductions

= 600,000 - 150,000

= 450,000

Therefore, the tax liability is 450,000 rupees.

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A company is printing 250 calendars. In one hour, 75 calendars are printed.

What percent of the calendars are printed in 1 hour?

Answers

Answer:

In one hour, 75 calendars were printed, which is 30% of the total number of calendars (250). Therefore, the percent of the calendars printed in one hour is 30%.

Answer: 30

Step-by-step explanation: The answer would be 30 because if you took 75 and divided by 200 you would end up with a product of about 30! Hopefully this helped you!!

solve for h.
h/6 - 1 = -3

Answers

H= -12

Because

-12/6=-2

-2-1=-3

Good luck hope this helps


:)))

experimental insight 2.1 describes data on the kernel color distribution of bicolor corn, collected by a genetics class like yours. to test the hypothesis that the kernel color of bicolor corn is the result of the segregation of two alleles at a single genetic locus, the class counted 9882 kernels and found that 7506 were yellow and 2376 were white. use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.

Answers

To test the hypothesis that the kernel color of bicolor corn using  chi-square analysis to evaluate the fit between the segregation hypothesis and the class results as the ratio 0.01:0.05 and degree of freedom is 4.82.

Formula for Chi square is,

[tex]x^2 = \frac{(O - E)^2}{E}[/tex]

O = Observed Value

E = Expected Value

So x = 9882/2376 = 4.82.

And after getting a ratio of the yellow and white from the chi diagram we have class ratio of 0.01:0.05

When the sample sizes are large, a chi-squared test (also known as a chi-square or 2 test) is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine if two categorical factors (two dimensions of the contingency table) have independent effects on the test statistic (values within the table).

The test, specifically Pearson's chi-squared test and its variations, is valid if the test statistic is chi-squared distributed under the null hypothesis. If there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table, it can be determined using Pearson's chi-squared test. A Fisher's exact test is used as an alternative for contingency tables with smaller sample sizes.

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How much is 40 minutes in decimal?

Answers

40 minutes in decimal is 0.666.

How do you convert minutes to decimals?The conversion is not complicated, there is a simple formula for it:Number of minutes/60 => Conversion from hours and minutes to decimal.Decimal time * 60 => Conversion from decimal to hours and minutes.Convert minutes to decimal hours to calculate time sheets and payroll hours worked. Includes rounding to 2, 3, 4 or more decimal places.If your number of minutes is less than 60 divide by 60. The decimal is minutes in decimal hours.If your number of minutes is greater than or equal to 60, divide by 60 and carry the whole number to hours. The remaining decimal is minutes in decimal hours.Round the decimal to your level of accuracy.

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a hospital director believes that 46% of the lab reports contain errors. a sample of 250 tubes found 95 errors. is there sufficient evidence at the 0.05 level to refute the hospital director's claim? state the null and alternative hypotheses for the above scenario.

Answers

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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the radius of a circle is 10.4 ft. find the circumference \textit{to the nearest tenth}to the nearest tenth.

Answers

The circumference with radius of 10.4 ft is 65.3 ft. The result is obtained by using the formula for circumference.

What is circumference?

Circumference is also called the perimeter of a circle. It can be expressed as

P = 2πr

Where

Radius of the circle = m.π = 22/7 or 3.14 ft.

The circumference with the radius = 10.4 ft.

We have

Radius of a circle, r = 10.4 ft

Find the circumference! (to the nearest tenth)

The circumference will be

P = 2πr

P = 2(3.14)(10.4)

P = 65.3 ft

Hence, the perimeter of the circle to the nearest tenth is 65.3 feet.

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use a double number line to solve eache equation​

Answers

Answer: x = -2

Step-by-step explanation:

find each value of k for which the lines y=9kx-1 and kx 4y=12 are perpendicular

Answers

The value of k in the equations is 2/3

How to determine the value of k

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

y = 9kx - 1

kx + 4y = 12

This can be expressed as

y = 9kx - 1

y = -kx/4 + 3

The slopes of perpendicular lines are opposite reciprocal

This means that

9k * -k/4 = -1

So, we have

k^2 = 4/9

Evaluate

k = 2/3

Hence, the value of k is 2/3

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You own a hat shop. Your total monthly cost
is $1,850. Each hat costs $50. How many hats
must you sell to break even each month?

Answers

Answer:

The Answer is 37

Step-by-step explanation:

Just do 1850/50 and then do 50*37 to confirm

37 hats all you have to do is 1850/50

Determine whether the following statement is true or false. Every graph represents a function. Choose the correct answer below. A. The statement is true because every graph associates a unique y-value for each x-value. B. The statement is false because a graph that crosses the x-axis two times does not represent a function. C. The statement is true because every graph associates a unique x-value for each y-value. D. The statement is false because a graph that crosses the y-axis two times does not represent a function.

Answers

"Every graph represents a function" - statement is false.

Correct option: D

What is function?

The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x.

If for a particular x, and y values are coming it means it is not a function.

Hence, every graph is a function is false.

Because if it crosses y axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function

Hence option D is correct: The statement is false because a graph that crosses the y-axis two times does not represent a function.

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find the area bounded by the graphs of the indicated equations over the given interval. y; y0;

Answers

The area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

The area bounded by the graphs of the indicated equations y and y0 over the given interval can be calculated using the formula A=∫y0 dy. To calculate the area, we need to first find the antiderivative of y0, which is F(y0) = ∫y0 dy. Then, we need to evaluate the integral from the lower limit of the given interval to the upper limit of the given interval. For example, if the given interval is from x=0 to x=2, then the area bounded by the two graphs would be A=F(y0)|2-0 = ∫y0 dy|2-0. Once we have evaluated the integral, we can calculate the area of the graph by subtracting the lower limit result from the antiderivative In this example, A=F(y0)|2-0 = ∫y0 dy|2-0 = F(y0)|2-F(y0)|0 = ∫y0 dy|2-∫y0 dy|0. Thus, the area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

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a group has 400 members only 5/8 have paid there fees what percent have paid there fees

Answers

Answer:

400

Step-by-step explanation:

percent means per one hundred so

p/100=5/8

p=500/8

p=62.5%

so, 62.5% have paid their yearly fees .

400(5/8) =200

250 member paid their fees .

Answer:

250

Step-by-step explanation:

If a group contains 400 members

Then the 5/8 of 400 who didn't pay the fees are as follows:-

=5/8*400

=5*50

=250 out of 400

So, the fees is only paid by 250 members out of 400.

(2 points) match the slope fields shown below with the differential equations a 1. y′=cos(x) d 2. y′=4−y c 3. y′=x e 4. y′=y f 5. y′=x−y b 6. y′=sin(x)

Answers

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

a. y'=cos(x): This differential equation describes the slope field shown in figure A. To calculate the slope of a given point (x,y), we can use the formula y'=cos(x). For example, if x=π/2 and y=1, the slope of the line at that point is y'=cos(π/2)=-1.

b. y'=sin(x): This differential equation describes the slope field shown in figure B. To calculate the slope of a given point (x,y), we can use the formula y'=sin(x). For example, if x=0 and y=1, the slope of the line at that point is y'=sin(0)=0

c. y'=4-y: This differential equation describes the slope field shown in figure C. To calculate the slope of a given point (x,y), we can use the formula y'=4-y. For example, if x=0 and y=2, the slope of the line at that point is y'=4-2=2.

d. y'=x: This differential equation describes the slope field shown in figure D. To calculate the slope of a given point (x,y), we can use the formula y'=x. For example, if x=3 and y=2, the slope of the line at that point is y'=3.

e. y'=y: This differential equation describes the slope field shown in figure E. To calculate the slope of a given point (x,y), we can use the formula y'=y. For example, if x=3 and y=4, the slope of the line at that point is y'=4.

f. y'=x-y: This differential equation describes the slope field shown in figure F. To calculate the slope of a given point (x,y), we can use the formula y'=x-y. For example, if x=2 and y=1, the slope of the line at that point is y'=2-1=1.

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

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Ten more than 32% of a number is 26

Answers

Answer:

16.

Step-by-step explanation:

Let x be the number.

32% of x = (32/100)x = 0.32x.

Ten more than 32% of x = 0.32x + 10.

0.32x + 10 = 26.

0.32x = 16.

x = 50.

So the number is 50, and 32% of it is 0.32 * 50 = 16.

Lat week, Zachary' Diner old 28 milkhake with whipped cream on top and 72 milkhake without whipped cream. What percentage of the milkhake had whipped cream?

Answers

Zachary' Diner old 28 milkshake with whipped cream on top and 72 milkshake without whipped cream,  percentage of the milkshake had whipped cream is 28%.

Zachary ordered 28 milkshake with whipped cream on top and 72 milkshake without whipped cream.

So total number of milkshake is 100

So percentage of milkshake had whipped cream will be,

28/100 x 100

=28%

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied.

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(-3,9) (4,6) (6,-3)

find the fourth vertex of the parallelogram

Answers

Answer: (-1, 0)

not sure

Step-by-step explanation:

ex 1: create a function that will return the product of two integers.

Answers

The code that creates a function that will return the product of two integers is given below:

#include <iostream>

using namespace std;

/* Your code goes here */

int main() {

  int input1, input2;

  int result;

  cin >> input1;

 cin >> input2;

  result = ComputeVal(input1, input2);

  cout << result << endl;

  return 0;

}

In mathematics, whole numbers and negative numbers are grouped together as integers. Integers, like whole numbers, do not include the fractional portion.

Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all mathematical operations, including addition, subtraction, multiplication, and division.

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For numbers 3-6 state if the triangles are congruent and if so what method proves they are congruent?​

Answers

The congruence postulates used for each triangle are as follows;

3) AAS

4) None

5) HL congruence

6) None

How to Identify the triangle congruence postulate?

Some of the triangle congruence postulate in geometry are;

SAS; Side Angle Side Congruence Postulate

SSS; Side Side Side Congruence Postulate

ASA; Angle Side Angle Congruence Postulate

AAS; Angle Angle Side Congruence Postulate

HL; Hypotenuse Leg Congruence Postulate

3) W e can see that we are given two triangles with two corresponding congruent angles and corresponding non-included side. Thus, the congruence postulate used is AAS.

4) We are given two triangles with two corresponding congruent angles but the sides given are not congruent to each other and so the triangles are not congruent.

5) We are given two triangles with their corresponding hypotenuse and leg being congruent and so the HL congruence postulate is used.

6) The angles shown don't match each other. It is just two congruent sides and this is insufficient to conclude the triangles are congruent.

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HELP EMERGENCY A printing company charges $8.95, plus an additional $.15 for each print over 50. Write an equation that can be used to determine the cost, C, to print an order of p, prints
Answer choices:

c (p) =.15 (x+50) +. 8.95
c (p) = 8.95 (x + 50) + 0.15
c (p) =.15 (x- 50) + 8.95
c (p) = 8.95 (x- 50) +0.15

Answers

Answer:

  (c)  C(p) =.15 (p- 50) + 8.95

Step-by-step explanation:

You want an equation for the cost of prints that are $0.15 for each print over 50 plus an additional $8.95.

Translating English

The number of prints over 50 will be (p -50). At $0.15 for each of these, their cost will be ...

  0.15(p -50)

When the $8.95 charge is added, the total comes to ...

  c(p) = 0.15(p -50) +8.95

__

Additional comment

The problem statement asks for the function to be written C(p). The answer choices use c(p) with the variable x in the equation where p should be. In effect, none of the answer choices is correct.

a survey is conducted and the following results are recorded 360 students are taking a math course 280 are taking a physics course 300 are taking a biology course 100 are taking math and physics 120 are taking math and biology 110 are taking physics and biology 40 are taking math, physics and not biology 40 are not taking any of the courses a. how many are taking only math? b. how many are in the survey? c. how many are taking exactly two of the courses?

Answers

A) The total no. of students taking only maths is 220 students.

let's say the total no. of students taking only maths = M

M = 360 - (100 + 40) = 220 students.

B) The total no. of students in the survey is 960 students.

let's say the total no. of students in the survey = S

S = 360 + 280 + 300 - (100 + 120 + 110) + 40 = 960 students.

C) The total no. of students who are taking exactly two of the courses is 330 students.

let's say the total no. of students who are taking exactly two of the courses = T

T = 100 + 120 + 110 = 330 students.

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Two secretarial students, AGYEMANG and IKE, are used- Typewriter dealers. They found that the length of time before a major repair is required on Typewriter sold is normally distributed, with a mean equal to 11 months and a standard deviation of 2 months. If the dealers want only 5% of the cars to fail before the end of the guarantee period, for how many months should the Typewriters be guaranteed?

Answers

The Typewriters should be guaranteed for 7.72 months, which would give a 5% chance of requiring a major repair before the end of the guarantee period.

Typewriter repair times have a normal distribution, with a mean of 11 months and a standard deviation of 2 months. To find the warranty period at which only her 5% of typewriters fail before the warranty expires, we need to find the corresponding z-score and solve it after the warranty period.

Using the standard normal distribution table, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.64.

This means that 95% of typewriters will need major repairs after 11 + 1.64 * 2 = 14.28 months.

To ensure that only 5% of typewriters fail before the warranty expires, the warranty period should be set to 11 - 1.64 * 2 = 7.

72 months.

Finally, the typewriter still has about 7.72 months of warranty, and only 5% of cars fail before the warranty runs out.

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What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
a) 3127
b) 3133
c) 3137
d) 3139
e) 3149

Answers

The smallest positive integer that is neither prime nor square and that has no prime factor less than 50 is 3137.

This can be determined by using the prime factorization method. Prime factorization is a process of breaking down a number into its prime factors. The prime factors of a number are the factors that are only divisible by one and itself. For 3137, the prime factors are 3, 7, 17 and 37 since these are the only prime numbers that can divide 3137 evenly. Since none of the prime factors are less than 50, 3137 is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50.

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Find the perimeter of triangle FGL, if the perimeter of triangle MHQ is 70.4 centimeters.

Answers

Answer:

The perimeter of triangle FGL is unknown.

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