What is the equivalent of 27/5 in decimal form?

Answers

Answer 1
5.4 is equivalent to 27/5.
Answer 2

Answer: 5.4

Step-by-step explanation: 27/5, so 5x5 makes 25 and 2 remaining so 5x0.4=2 so answer is 5+0.4 which equals to 5.4


Related Questions

Select the correct graph.

Answers

Answer:

Graph 1

Step-by-step explanation:

The only graph that could be possible would be graph 1.

As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.

PLS HELP:Find the side length, C.
Round to the nearest tenth.

Answers

Answer:

[tex]\huge\boxed{c = 14.9}[/tex]

Step-by-step explanation:

Using Cosine Rule

[tex]c^2 = a^2 + b^2 -2abCosC[/tex]

Where a = 11 , b = 7 and C = 110

[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]

[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]

Taking sqrt on both sides

c = 14.9

​34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.

Required:
Construct a binomial distribution using n= 0.6 and p=0.34

Answers

Answer:

solution below

Step-by-step explanation:

The question says 6 working mother's were selected so n = 6 not 0.6

We are expected to find

P(X = 0,1,2,3,4,4,6)

1. When x = 0

6C0*(0.34)⁰*(0.66)⁶

= 1 *1* 0.827

= 0.0827

2. When X = 1

6C1*(0.34)¹*(0.66)⁵

= 6 x 0.34 x 0.252

= 0.2555

3. When X = 2

6C2*(0.34)²*(0.66)⁴

= 15 x 0.1156 x 0.1897

= 0.3289

4. When x = 3

6C3*(0.34)³*(0.66)³

20 x 0.039304 x 0.2875

= 0.2599

5. When X = 4

6C4*(0.34)⁴*(0.66)²

= 15 x 0.01336 x 0.4356

= 0.8729

6. When x = 5

6C5*(0.34)⁵*(0.66)¹

= 6 x 0.0045 x 0.66

= 0.01782

7. When x = 6

6C6*(0.34)⁶*(0.66)⁰

1 x 0.0015 x 1

= 0.0015

Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.

Answers

Answer: Jake is 9 and his dad is 33.

Step-by-step explanation: 9x3=27+6=33 9+33=42

Answer:

Jake is 9 and Jake's dad is 33

Step-by-step explanation:

To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake

J+D=42

3J+6=D

Solve by substitution

Consider the following sample data: 12, 13, 7, 5, 15, 18. Which one of the following represents the value of the standard deviation?
A. 11.67
B. 4.89
C. 2.52
D. 23.87

Answers

Answer:

Standard deviation= 4.46

B) 4.89 is the nearest answer

Step-by-step explanation:

Standard deviation √variance

Variance= (summation (x-mean)²)/n

Mean= summation of numbers/total

Mean =( 12+13+ 7+5+15 18)/6

Mean= 70/6

Mean= 11.67

Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6

Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6

Variance= 119.3334/6

Variance= 19.8889

Standard deviation= √variance

Standard deviation= √19.8889

Standard deviation= 4.46

Which of the following statements is TRUE about the stepwise selection procedure?
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
B. Backward stepwise procedure and forward stepwise procedure would end up with the same "best" model.
C. The "best" model determined by the stepwise selection method is the same model as what would be selected by complete search but stepwise method is usually faster.
D. Different choices of alpha limits for variable selection may end up with different final models.

Answers

Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Assume that random guesses are made for ​multiple-choice questions on a test with choices for each​ question, so that there are n ​trials, each with probability of success​ (correct) given by p. Find the probability of no correct answers

Answers

Complete Question

Assume that random guesses are made for 7 ​multiple-choice questions on a test with 5 choices for each​ question, so that there are n=7 ​trials, each with probability of success​ (correct) given by  p=0.20. Find the probability of no correct answers.

Answer:

The  probability is [tex]P(X = 0 ) = 0.210[/tex]

Step-by-step explanation:

From the question we are told that

    The number of trial is  n =  7

    The  probability of  success is  p =  0.20

   

Generally the probability of failure is

       [tex]q = 1- 0.20[/tex]

       [tex]q = 0.80[/tex]

Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure

Then the probability is mathematically represented as

          [tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]    

          [tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]

Here   [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]

=>      [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]

=>     [tex]P(X = 0 ) = 0.210[/tex]

Simplify the following expression.X^1/3 * X^1/5

Answers

Answer:

[tex] X^{\frac{8}{15}} [/tex]

Step-by-step explanation:

[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]

To multiply two powers with the same base, write the base and add the exponents.

[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]

[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]

[tex] = X^{\frac{8}{15}} [/tex]

Original price of a soda: $800 tax 7% selling price: $

Answers

Answer:

$856

Step-by-step explanation:

Find 7% of $800 and then add it to $800

FIND THE VALUE OF NT
PLEASE HELP ASAP :(

Answers

Answer:

NT = 14 units

Step-by-step explanation:

In this question we will apply the theorem of intersecting chords.

Two chords MY and TN are intersecting each other inside a circle at a point H.

Theorem states,

MH × HY = TH × HN

12(x) = 8(x + 2)

12x = 8x + 16

12x - 8x = 16

4x = 16

x = 4

Therefore, measure of chord NT = NH + HT

                                                       = 8 + (x + 2)

                                                       = x + 10

                                                       = 4 + 10

                                                       = 14 units

5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution

Answers

Answer:

C. Infinitely many solutions

Step-by-step explanation:

First, simplify the second equation by dividing it by 2

2y = 6x + 2

y = 3x + 1

Now, we can see that both equations are the same, both y = 3x + 1.

Since they are the same line, this means that there are infinitely many solutions.

So, the correct answer is C.

Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) Find the probability of the event that exactly one of the colors that appears face up is red.

Answers

Answer:

12/27

Step-by-step explanation:

Step 1

We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.

Where

R = Red

B = Blue

Y = Yellow

RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR

We have 27 Total outcomes for this 6 faced die

Step 2

The event that exactly one of the colors that appears face up is red.

RBY, RYB, YBR, YRB, RBB, RYY, BBR,

BRB, BRY, YRY, BYR, YYR

Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12

The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes

= 12/27

Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below.a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.b. If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?A. Since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.B. Since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.C. Since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Answers

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information

Answers

Answer: B. Always

Explanation:

Two points always create a line. The correct answer is option B.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the two points always create a line. The correct answer is option B.

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(x+1)(x−1)(x−5)=0 HELP

Answers

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5


[tex]4x - 2x = [/tex]

Answers

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.

0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8

Answers

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

Reading a Tape Measure
Measure the green bar using the provided image of a tape measure

Answers

Answer:

3 inches

Step-by-step explanation:

The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.

On a map 1 cm represents 4.5km. What is the actual distance between two towns which are 4cm apart on the map?

Answers

Answer:

18km

Step-by-step explanation:

1cm:4.5km/4cm then get the answer as 18km

1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.

Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]

Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.

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Point A is at (2, -8) and point C is at (-4, 7).
Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.

Answers

Answer:

(-2, 2)

Step-by-step explanation:

Given:

Point A is at (2, -8) and point C is at (-4, 7)

Difference of coordinates:

Δx = 2 - (-4) = 6Δy = - 8 - 7 = - 15

The ratio of AB to AC is 2:1. So:

AB = 2*AC/3 and BC = AC/3

Then coordinates of point B should be 2/3 from the point A:

x = 2- 6*2/3 = 2 - 4 = -2y = - 8 - (-15)*2/3 = -8 + 10 = 2

So point B has coordinates of (-2, 2)

PLEASE SOLVE THE ABOVE PROBLEM you’ll get 43 POINTS

Answers

heya friend

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

and 10 is not zero

so it is sacrificed

hope this helps u

Answer:

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

10 is not 0

Step-by-step explanation:

1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident​

Answers

Answer:

math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.

The mathematics assessment defines as "the process of gathering evidence about a content performance of capacity to use, as well as comportment away from traditional maths, as well as of making presumptions from that proof for a range of functions". In several inferences could be derived from the information in the Educational section. In order to enhance a program that promotes learning outcomes, assessment involves the use of empirical evidence on student learning. As just a result, students' learning is improved.As per my opinion, the given question is an opinion question and in the education sector some student likes math and some aren't. In this, I will select the "excited and confident" choice because I love maths.

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Find the values of x which satisfy the following inequation:
x3 – x² <12x​

Answers

Answer:

x< -3 and 0 < x < 4

Step-by-step explanation:

x^3 – x² <12x​

Subtract 12x from each side

x^3 -x^2 - 12x< 0

Factor

x( x^2 -x-12) <0

Factor

x( x-4) ( x+3) < 0

Using the zero product property

x=0   x=4  x=-3

We have to check the signs regions

x < -3

-( -) (-) < 0   True

-3 to 0

-( -) (+) < 0   False

0 to 4

+( -) (+) < 0   True

x>4

+( +) (+) < 0   False

The regions this is valid is

x< -3 and 0 < x < 4

will rate you brainliest

Answers

Answer:

A

Step-by-step explanation:

f(x)→g(x)

(0, 0) → (3, -4)

Therefore it increases it x-axis from 0 to 3

And decreases in y-axis from 0 to -4

Please help. I’ll mark you as brainliest if correct!

Answers

Answer: x= -1, z=2, y= -4

Step-by-step explanation:

System of equations:

-5x - 4y - 3z= 15  +

-10x + 4y + 6z= 6

-15x         + 3z = 21  ------>  3 (-5x + z) = 7.3

-5x + z = 7

now,

-10x + 4y + 6z= 6

2(-5x + z) + 4y + 4z = 6

14 + 4y + 4z = 6

7 + 2y + 2z = 3

2y + 2z= -4

y+z=-2

Now we were using the equation: 20x + 4y + 4z = -28

20x + 4(y+z) = 20x -8= - 28

20 x = -20

x= -1

With this we can find y and z

X=-1

-5x + z = 7

z= 2

y+z=-2

y=-4

Finally we have: x= -1, z=2, y= -4

I hope this can help you.

Thank you

The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?

Answers

Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

f(x) = x^2 + 2x + 1, then for what values of x, f(x)=f(x+2) step by step plz​

Answers

Answer:

x = -2

Step-by-step explanation:

given f(x) = x² + 2x + 1

f(x+2) = (x+2)² + 2(x+2) + 1

= x² 4x+4+2x+4+1

= x² + 6x + 9

for f(x) = f(x+2), simply equate the two expressions and solve for x

f(x) = f(x+2)

x² + 2x + 1 = x² + 6x + 9      (x² terms cancel out)

2x + 1 = 6x + 9  (subtract 1 from both sides)

2x  = 6x + 9 - 1

2x  = 6x + 8  (subtract 6x from both sides)

2x - 6x = 8

-4x = 8 (divide both sides by -4)

x = 8 / (-4)

x = -2

I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.

Answers

Answer:

C. It is the product of the prime factors that are either unique to or shared by the polynomials.

Step-by-step explanation:

LCM of polynomials is:

=> Finding the factors of all the numbers and variable in the expression

=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.

So, C is the correct answer.

The LCM of a set of polynomials  is the product of the prime factors that are either unique to or shared by the polynomials.  

What is LCM of polynomial?

To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.

Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.

Factorizing 4a2 - 25b2 we get,

(2a)2 - (5b)2, by using the identity a2 - b2.

= (2a + 5b) (2a - 5b)

Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get

= 3a(2a + 5b)

L.C.M.  is 3a(2a + 5b) (2a - 5b)

According to the question

The LCM of a set of polynomials is

 is the product of the prime factors that are either unique to or shared by the polynomials.  

(from above example we can see that )

Hence,  It is the product of the prime factors that are either unique to or shared by the polynomials.  

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Can someone please help me?

Answers

Negative Integers are :

Less than zeroTo the left of zero on a number line.

In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?

Answers

Answer:

a

  [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

b

  [tex]P( X >0.025 ) = 0.99379[/tex]

Step-by-step explanation:

From the question we are told that

   The  population proportion is  [tex]p = 0.10[/tex]

    The sample size is  [tex]n = 100[/tex]

Generally the standard error is mathematically represented as

       [tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]

=>   [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]

=>   [tex]SE =0.03[/tex]

The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178

   [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]

  Generally  [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]

    [tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]

   [tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]

From the z-table  

      [tex]P(Z < 2.6 ) = 0.99534[/tex]

     [tex]P(Z < 2.4 ) = 0.9918[/tex]

[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]  

 [tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]  

the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as

        [tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]

        [tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]

From the z-table  

        [tex]P (Z > -2.5 ) = 0.99379[/tex]

Thus

      [tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]

Other Questions
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