Write the value of the money in dollars 4-8 Brainliest Awnser gets 7 points for greatness

Write The Value Of The Money In Dollars 4-8 Brainliest Awnser Gets 7 Points For Greatness

Answers

Answer 1

4. 12 cent

5. $2.06

6. $1.56

7. $1.30

8. 86 cent


Related Questions

Please answer this correctly

Answers

Answer:

0

Step-by-step explanation:

3 cards

P( odd) = 1 odd/ 3 cards = 1/3

No replacement

2 cards 6,8

No odds

P( odd) = 0/2

P( odd, no replacement, odd) = 1/2 * 0 = 0

What tool is used to draw circles

Answers

Answer:

Pair of compasses.

Step-by-step explanation:

These are used to inscribe circles/arcs.

Compasses are used in maths, navigation,e.t.c.

Hope it helps.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.

Answers

Answer:

to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]

The resulting function can be written as

[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]

Step-by-step explanation:

Hello,

f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0

and [tex]f(x)\geq 0[/tex]

so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]

and then we can write

[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]

hope this helps

A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?

Answers

Answer:

  41°, 56°, 83°

Step-by-step explanation:

We can find the largest angle from the law of cosines:

  c² = a² +b² -2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°

Then the second-largest angle can be found the same way:

  B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°

Of course the third angle is the difference between the sum of these and 180°:

  A = 180° -82.8192° -55.7711° = 41.4096°

Rounded to the nearest degree, ...

  the angles of the triangle are 41°, 56°, 83°.

Find the value of x that makes A||B

Answers

Answer:

For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15°

How would I Evaluate 8×5÷10?

Answers

Answer:

4

Step-by-step explanation:

8×5÷10

PEMDAS says multiply and divide from left to right

40÷10

4

Answer:

4

Step-by-step explanation:

Follow the PEMDAS order of operations

8*5=40

40÷10=4

=4

OR

8x5÷10

8x0.5=4

=4

Have a good day and stay safe!

What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4

Answers

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

[tex]4+4\times \text{log}_2(x)=14[/tex]

By subtracting 4 from both the sides of the equation.

[tex]4\times \text{log}_2(x)=14-4[/tex]

Now divide the equation by 4

[tex]\text{log}_2(x)=\frac{10}{4}[/tex]

[tex]\text{log}_2(x)=2.5[/tex]

[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]

[tex]x=(2)^{2.5}[/tex]

[tex]x = 5.657[/tex]

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

In geometry the set of all points is called ---- ?​

Answers

Answer:

it may be locus. because is a set of point and line is formed the locus of points.

In geometry, the set of all points is called space.

What are collinear points?

In Mathematics and Geometry, collinear points can be defined as three or more points that all lie on the same straight line (single line). This ultimately implies that, two (2) planes intersect at a line.

For example, we can infer and logically conclude that a sphere would have all points in space that are 4 units from a point.

Generally speaking, the set of all points is referred to as a space in geometry.

Read more on collinear points here: brainly.com/question/24391959

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Do class limits and class marks make sense for qualitative data classes? Explain
your answer.
NEED QUICKLY

Answers

Answer: NO, class limits and class marks are not meaningful to qualitative data.

Step-by-step explanation: Qualitative data are non-numerical data. They are collected mostly through observation. They include; sex, name and soon.

Class limits and class marks are groupings used in numerical data (quantitative data). They are not relevant and are meaningless to qualitative data classes as these data class are non- numerical.

A club has 20 women and 17 men and needs to form a committee of six members. How many committees are possible if the committee must have at least two men?

Answers

Answer:

2,022,456 committees

Step-by-step explanation:

From the above question, we are given the following information:

Number of women = 20

Number of men = 17

In order to form a committee of six members with at least 2 men, the number of ways we can do this is 5 ways and they are:

a) A committee of 6 men

b) A committee of 5 men and 1 woman

c) A committee of 4 men and 2 women

d) A committee of 3 men and 3 women

e) A committee of 2 men and 4 women

To solve for this we use the combination formula which is given as:

C(n, r) = nCr = n!/r!(n - r)!

Hence, the number of committees that are possible if the committee must have at least two men is calculated as

A committee of 6 men or A committee of 5 men and 1 woman or A committee of 4 men and 2 women or A committee of 3 men and 3 women or A committee of 2 men and 4 women

=[C(17, 6)]+ [C(17,5) × C(20,1)] + [C(17,4) × C(20,2)] + [C(17,3) × C(20,3)] + [C(17,2) × C(20,4)]

= [17!/6!(17 - 6)!] + [17!/5!(17 - 5)! × 20!/1!(20 - 1)!] + [17!/4!(17 - 4)! × 20!/2!(20 - 2)!] + [17!/3!(17 - 3)! × 20!/3!(20 - 3)!] + [17!/2!(17 - 2)! × 20!/4!(20 - 4)!]

= [12376] + [ 6188 × 20] + [2380 × 190] + [680 × 1140] + [ 136 ×4845]

= 2,022,456 committees


Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.

Answers

Answer:

m∠A = 17 degrees       m∠B = 73 degrees     m∠C = 90 (given)    a =   12 (given)    b =  40           c = 42 (given)

Step-by-step explanation:

Use sin to solve m∠A

sin x = 12/42     Simplify

sin x = 0.2857   Use the negative sin to solve for x

sin^-1 x =  17 degrees

Add together all of the angle measures to solve for m∠B

17 + 90 + x = 180    Add

107 + x = 180

-107        -107

x = 73 degrees

Use Pythagorean Theorem to solve for b

12^2 + x^2 = 42^2     Simplify

144 + x^2 = 1764

-144            -144

x^2 = 1620               Take the square root of both sides

x = 40

a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red

Answers

Answer:

0.42

Process:

1 - 0.58

0.42

Jimmie invested $13,000 at 5.23% compounded monthly.

What will Jimmie's account balance be in 42 years?

Answers

Answer:

116370.197$

Step-by-step explanation:

Jimmie invested $13,000 at 5.23% compounded monthly.

Jimmie's account balance (B) after 42 years:

B = principal x (1 + rate)^time

  = 13000 x (1 + (5.23/100)/12)^(42 x 12)

  = 116370.197$

what is 18576939*47 Thanks!!!!!

Answers

Answer:

873116133

Step-by-step explanation:

18576939 × 47

Multiply the numbers.

= 873116133

Answer: 873116133

Step-by-step explanation:

‘Hope this helps:)

A tabletop has an area of 12 square feet and a perimeter of 16 ft. What are the dimensions of the table? 2 ft by 6 ft 2 ft by 8 ft 4 ft by 3 ft 4 ft by 4 ft

Answers

Answer:

2 ft by 6

Step-by-step explanation:

The dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Since, the area of a rectangle is:

Area = length x width

We know that the area of the table is 12 square feet,

So, we can write:

12 = length x width

And, use the formula for the perimeter of a rectangle:

Perimeter = 2 x length + 2 x width

We know that the perimeter of the table is 16 feet, so we can write:

16 = 2 x length + 2 x width

Now we have two equations with two variables (length and width), which we can solve simultaneously as.

Let's rearrange the second equation to solve for length:

16 = 2 x length + 2 x width

16 - 2 x width = 2 x length

8 - width = length

Now we can substitute this expression for length into the first equation:

12 = length x width

12 = (8 - width) x width

12 = 8w - w²

We can rearrange this equation into standard quadratic form:

w² - 8w + 12 = 0

Now we can use the quadratic formula:

where a = 1, b = -8, and c = 12

w = (-(-8) ± √((-8)² - 4(1)(12))) / 2(1)

w = (8 ± √(16)) / 2

w = 4 ± 2

Hence, w = 2

w = 6

So the possible values for the width are 2 and 6.

If the width is 2 feet, then the length is:

length = 8 - width = 6 feet

If the width is 6 feet, then the length is:

length = 8 - width = 2 feet

Therefore, the dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.

Learn more about the rectangle visit:

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A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?

Answers

Answer:

50 miles

Step-by-step explanation:

hello,

let's note x the number of miles travelled heading west,

it takes 1 hour to travel 25 miles

so it takes x/25 hours to travel x miles

we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles

so in 7-x/25 hours it travels 19(7-x/25) miles

we can write, as the total distance is 145 miles

[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]

we can verify

50 miles heading West takes 2 hours

in 5 hours it travels 19*5 = 95 miles

the total is 145 miles

so this is correct

hope this helps

Help me plzzzzz!!!!

Answers

Answer:124

Step-by-step explanation:

2x + 8 + x - 2 = 180

Add like terms

3x + 6 = 180

Subtract the 6 from both sides

3x + 6 - 6 = 180 - 6

3x = 174

Divide by 3

x = 58

Now we have to find the measure of angle ACD

2(58) + 8 = 124

Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?

Answers

Answer:

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

Uniform distribution from 0 to 4.8 seconds.

This means that [tex]a = 0, b = 4.8[/tex]

61% of the time a person will wait at least how long before the wave crashes in?

This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]

[tex]x = 4.8*0.39[/tex]

[tex]x = 1.872[/tex]

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.

Answers

Answer:

The height of the hill is 116.9 meters.

Step-by-step explanation:

The diagram depicting this problem is drawn and attached below.

From Triangle ABC

[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]

From Triangle XBC

[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]

Therefore:

[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]

Therefore, the height of the hill

[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]

The height of the hill is 116.9 meters.

A farmer divided his land into 2 groups of sections randomly. There is no difference in the quality of the soil between the 2 groups of land. He used Type A seeds in the first group and Type B seeds in the second group. After 3 months, the heights of the crops are measured across the two groups of land sections. Is the study observational or experimental? If it is an experiment, what is the controlled factor?

Answers

Answer:

Experiment

Time..

Step-by-step explanation:

It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.

The control factor in this case may includes the time...before measurements.

Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:

Quality of the soil.Wheater.Hours of daylight.

What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.

After 3 months, he measures the height of the crops.

The questions are:

Is the study observational or experimental?

It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.

If it is an experiment, what are the controlled factor?

The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:

Quality of the soil.Wheater.Hours of daylight.

If you want to learn more about experiments, you can read:

https://brainly.com/question/11256472

A survey of enrollment at 35 community colleges across the United States yielded the following figures:

6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."

b. Construct a histogram of the data.

c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?

d. Calculate the sample mean.

e. Calculate the sample standard deviation.

f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?

Answers

Answer: (a) The chart is in the first attachment named table frequency.

(b) The histogram is in the second attachment named frequency vs. enrollment

(c) Mode

(d) x = 9071.4

(e) s = 6677.64

(f) It is -0.16 standard deviation away

Step-by-step explanation:

(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.

(d) To calculate sample mean of a frequency data:

1) Find the midpoint for each interval;

2) Multiply each midpoint for its correspondent frequency;

3) Sum up each multiplication obtained in the previous step;

4) Sum up all the frequencies;

5) Divide the sum in step 3 by the sum in step 4;

For this chart:

x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]

x = 9071.4

(e) To find the standard deviation:

1) With each midpoint, calculate its square;

2) Multiply the midppoint square by its correspondent frequency;

3) Use the following formula to determine the sample standard:

s = √∑f.M²  - n(μ)² / n-1

For this chart:

s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]

s = 6677.64

(f) To find how many standard deviations away is the enrollment:

z = [tex]\frac{8000-9071.4}{6677.64}[/tex]

z = - 0.16

8000 enrollments are -0.16 standard deviations away from the mean.

there are 11 people in an office with 6 different phone lines. if all the lines begin to ring at once, how many groups of 6 people can answer these lines?

Answers

T_11

Expect_6 phones

This is a permutation problem

Therefore 11p6= 11!/(11-6)! = (5!*6*7*8*9*10*11)/5! = 6*7*8*9*10*11 (ANSWER)

Answer:

one group

Step-by-step explanation:

there is only one group of six people in the office since the office only has 11 people.

Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?

Answers

Hey there! :)

Answer:

x = 18 minutes.

Step-by-step explanation:

To solve this equation, set up a ratio.

# of towels over time taken:

[tex]\frac{6}{3} = \frac{36}{x}[/tex]

Cross multiply:

6x = 108

Divide both sides by 6:

6x/6 = 108/6

x = 18 minutes.

Answer:

In eighteen minutes she will have folded all 36

Please answer this correctly

Answers

Answer:

100%

Step-by-step explanation:

First, let's determine the probability for each of the conditions.

For P(greater than 2), we will have the cards 3, 4, 5, 6, 7, and 8.

For P(less than 3), we will have the cars 2.

In other words, every single card fits the conditions.

Thus, P(greater than 2 or less than 3)=7/7=100%

100%

Answer:

100%

Step-by-step explanation:

Greater than 2 is 3, 4, 5, 6, 7, 8

And less than 3 is 2 so that’s all the numbers which is 100%

Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9

Answers

Answer:

Hello, your answer is:

B. 3²×5

Step-by-step explanation:

Prime factorization of 45 is:

45 = 9 x 5

= 3²×5

Hope this helps you.. Good Luck

Answer:

B. 3² × 5

Step-by-step explanation:

45 can be written as a product of its prime factors.

45 = 3 × 3 × 5

45 = 3² × 5

[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!

Answers

Answer:

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

Step-by-step explanation:

[tex]\frac{5x-11}{2x^2+x-6}[/tex]

Factor the denominator.

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

The fraction cannot be simplified further.

Answer:

[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]

solution,

[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]

Hope this helps..

A​ penny, a​ nickel, a​ dime, and a quarter are tossed. What is the probability of obtaining exactly two tails on the​ tosses?

Answers

Assuming all the coins are fair coins with equal probability =0.5
p
=
0.5
of heads or tails, we can model the probability of X out of N coins landing head side up with the binomial distribution:

(=∣)=()(1−)−
P
(
x
=
X

p
)
=
(
N
X
)
p
X
(
1

p
)
N

X


Substituting the probability =0.5
p
=
0.5
and =4
N
=
4
into this pdf, we get:

(=)=(4)0.50.54−
P
(
x
=
X
)
=
(
4
X
)
0.5
X
0.5
4

X


To get the probability that three or more heads are obtained, we sum all the probabilities for ≥3
x

3
, i.e.

(≥3)=∑=34(4)0.50.54−
P
(
x

3
)
=

x
=
3
4
(
4
X
)
0.5
X
0.5
4

X


(≥3)=(43)0.54+(44)0.54
P
(
x

3
)
=
(
4
3
)
0.5
4
+
(
4
4
)
0.5
4


(≥3)=4(0.54)+0.54
P
(
x

3
)
=
4
(
0.5
4
)
+
0.5
4


(≥3)=5(0.54)
P
(
x

3
)
=
5
(
0.5
4
)


(≥3)=5(116)
P
(
x

3
)
=
5
(
1
16
)


(≥3)=516=0.3125
P
(
x

3
)
=
5
16
=
0.3125


Note: This particular question is simple enough to do without the above equation. One must recognize that there are 24
2
4
possible outcomes in the sample space of this four coin flip. Four of these outcomes have one coin which landed tails (one outcome for each different value of coin) i.e. three heads, and only one outcome exists where all coins are heads. These make up 5 of the 16 possible outcomes. Each are equally likely due to the equal probability of heads or tails for each coin, so we get the same answer as above.

Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?

Answers

Answer:

Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion that support the candidate has significantly changed.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=800 has a proportion of p1=0.58.

[tex]p_1=X_1/n_1=460/800=0.58[/tex]

The sample 2, of size n2=1000 has a proportion of p2=0.52.

[tex]p_2=X_2/n_2=520/1000=0.52[/tex]

The difference between proportions is (p1-p2)=0.05.

[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]

As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers

Answers

Answer: 5182

To get the value of all 100 numbers you would need to multiply.

Step-by-step explanation:

51.82x100= 5182

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 130
x = 69; 90% confidence

a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603

Answers

Answer:

d. 0.459 < p < 0.603

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.531.

[tex]p=X/n=69/130=0.531[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]

The 90% confidence interval for the population proportion is (0.459, 0.603).

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