Graph the equation y = 1/8x-7

Answer:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

Step-by-step explanation:

The info given is:

[tex] X= 21[/tex] number of students who said that they planned to work in a rural community

[tex] n= 380[/tex] represent the sample size selected

[tex]\hat p =\frac{21}{380}= 0.0553[/tex] the estimated proportion of students who said that they planned to work in a rural community

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replpacing we got:

[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]

[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]

A mean for estimation is the minimum-maximum variation estimate's C.I. The % of pupils planning to work in a rural community alters between 0.0323 and 0.0783.

Confidence interval:

Let's [tex]p^{}[/tex] represent the sampling fraction of the people who promised to work in a rural area.

Sample size:

[tex]n = 380[/tex]

x: the large number the pupils expected to work in a rural setting

[tex]p^{} = \frac{x}{n} \\\\p^{} = \frac{21}{ 380} = 0.0553\\\\(1- \alpha)\ \ 100\%[/tex]confidence for true proportion:

[tex]( p^{}\ \pm Z_{\frac{\alpha}{2}} \times \sqrt{p^{} \times \frac{(1-p^{})}{n}} ) \\\\[/tex]

For [tex]95\%[/tex]confidence interval:

[tex]\to 1 - \alpha = 0.95[/tex]

When:

[tex]\to \alpha = 0.05[/tex]

Calculating the value of Z by using the table:

[tex]\to Z_{0.025} = 1.96[/tex]

When the  [tex]95\%[/tex] of the confidence interval:

[tex]\to (0.0553 \pm Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}})\\\\\to (0.0553 - Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380})},0.0553 + Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}))}\\\\[/tex]

by solving the value we get:

[tex]\to ( 0.0323 , 0.0783 )[/tex]

Find out more about the Confidence interval here:

brainly.com/question/2396419

The slope greater than one would be the last image, because for every step in x, you get more than one y step.

The slope between 1 and 0 would be the second image

And the slope less than 0 would be the third image

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Answer:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=25, p=0.85)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)[/tex]

And replacing using the mass function we got:

[tex]P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156[/tex]  

[tex]P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211[/tex]  

[tex]P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217[/tex]  

[tex]P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161[/tex]  

[tex]P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759[/tex]  

[tex]P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172[/tex]  

And adding the values we got:

[tex] P(X\geq 20) = 0.8381[/tex]

Options

Answer:

[tex](E)0.7+0.4-0.2=0.9[/tex]

Step-by-step explanation:

In probability theory

[tex]P$(A or B)=P(A)+P(B)$-$P(A and B)[/tex]

Let the event that the show had animals in it = A

P(A)=0.7

Let the event that the show aired more than 10 times =B

P(B)=0.4

P(A and B)= 0.2

[tex]P$(A or B)$=0.7+0.4-0.2=0.9[/tex]

Therefore, the equation which  shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:

[tex]0.7+0.4-0.2=0.9[/tex]

The correct option is E.

Answer:

The area formula of a triangle is (base * height) / 2 and the area of a square is s² where s is the length of one side.

Answer:

246000 in scientific notation is 2.46e5, or 2.46 x 10^5

Step-by-step explanation:

246000, move the decimal place 5 places to the left.

2.4x10^5

Answer:

2.46 × 10⁵

Step-by-step explanation:

The decimal point is after the first non-zero digit.

⇒ 2.46

Multiply the number with base 10 and an exponent which will equal to 246,000.

⇒ 10⁵

Answer:

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

Step-by-step explanation:

Confidence interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]

Percentage:

Proportion multplied by 100.

0.8546*100 = 85.46%

0.9454*100 = 94.54%

The 99​% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.

Based on the​ result, does the method appear to be​ effective?

Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.

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▹ Answer

Area = 9

▹ Step-by-Step Explanation

A = b * h ÷ 2

A = 9 * 2 ÷ 2

A = 9

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

B

Step-by-step explanation:

area of top on triangle=1/2×4×3=6m²

area of four top triangles=6×4=24 m²

area of bottom square=4×4=16 m²

area of four side rectangles=4×(4×5)=80 m²

Total area= 24+16+80=120m²

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▹ Answer

15.75

▹ Step-by-Step Explanation

3 ÷ 4 = .75

15 + .75 = 15.75

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

z = 1.476

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.86}{2} = 0.07[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.07 = 0.93[/tex], so [tex]z = 1.476[/tex]

The answer is z = 1.476

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Answer:

B. (-0.5, 5.75)

Step-by-step explanation:

Use a graphing calc and analyze the graph for the minimum value (vertex).

Answer:

D

Step-by-step explanation:

Parallel lines are those that have the same slope, or coefficient of x.

Here, let's calculate the slope of the given line. Slope is the difference in the y-coordinates divided by the difference in the x-coordinates, so given the two coordinates (12, 6) and (0, -4):

slope = m = (-4 - 6) / (0 - 12) = -10 / (-12) = 10/12 = 5/6

So the slope is 5/6. That means the equation we want should also have a slope of 5/6. Already, we can eliminate A, B, and C, leaving D as our answer. But, let's check.

The equation of a line can be written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is the coordinates of a given point.

Here, our slope is 5/6 and our given point is (12, -2). So plug these in:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-2)=(5/6)(x-12)[/tex]

[tex]y+2=\frac{5}{6} x-10[/tex]

[tex]y=\frac{5}{6} x-12[/tex]

This matches D, so we know that it's the correct answer.

~ an aesthetics lover

The answer is D I just took the test

Answer:

if m is supposed to be the equals (=) sign then x = 25

Step-by-step explanation:

45 = (2x-5)

+5         +5

50 = (2x)

÷2     ÷2

25 = x

Answer: 70

Step-by-step explanation:

Answer: d) 95 degrees

Step-by-step explanation:

To find this solution, simply subtract -20 from 75, to get 95.  In reality, you would take the absolute value of one temperature - another, but all you need to remember is to always subtract the smaller temperature from the larger.

Answer:

95 degrees(answer d)

Step-by-step explanation:

when you have a negative temp. and a positive temp., you add the two numbers to find the difference.

that means, 20+75=95 degrees(take away the negative sign when adding only.)

That means the difference between the two temperatures is 95 degrees.

Answer:

1. Point estimate M (sample mean): 83.33

2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.

3. A. The researcher could decrease the level of confidence.

Step-by-step explanation:

A point esimate for the population mean travel tax can be done with the sample mean.

We can calculate the sample mean as:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]

2. We have to calculate a 95% confidence interval for the mean.

The sample mean is M=83.33.

The sample size is N=8.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

We calculate the sample standard deviation as:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]

The standard error is:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=8-1=7[/tex]

The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.

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

[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]

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

[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]

The 95% confidence interval for the mean travel tax is (73.36, 93.30).

We can be 95% confident that the true mean travel tax is within this interval.

3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.

The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.

Step-by-step explanation:

[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The quadratic formula is honestly the most straightforward way of solving here.

Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:

1) a=1, b=0, c=8

This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)

2) a=-9, b=4, c=-10

This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.

3) a=1, b=8, c=17

This reduces to x=(-4+i), (-4-i)

So those are the answers for each.

Please Refer to the screenshot. Hope this helps!

Answer: 7/100

Step-by-step explanation:

In this question, ignore the 8 and the 3 and focus on the 7.  Isolate it and you will get 0.07.  0.07 in fraction from is 7/100.

The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Given the decimal,

0.873

8 → Tenth place (Fraction value 8/10)

7 → Hundredth place(Fraction value 7/100)

3 → Thousandth place (Fraction value 3/1000)

Since 7 is at hundredth place thus it will be 7/100.

Hence "The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07".

For more about the number system,

https://brainly.com/question/22046046

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Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

p > α

0.7038 > 0.05

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of  cloth.

Step-by-step explanation:

We are given that a chemist wishes to test the effect of four chemical agents on the strength of a particular type of  cloth.

Since we are given data for four independent chemical agents to determine the effect on the strength of a particular type of cloth, therefore, a one-way analysis of variance may be used for the given problem.

ANOVA:

The one-way analysis of variance (ANOVA) may be used to find out whether there is any significant difference between the means of two or more independent categories of data.

Set up hypotheses:

Null hypotheses = H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternate hypotheses = H₁: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

Set up decision rule:

We Reject H₀ if p ≤ α

OR

We Reject H₀ if F > F critical

ANOVA in Excel:

Step 1:

In the data tab, select data analysis

Step 2:

Select "Anova single factor" from the analysis tools

Step 3:

Select the destination of input data in the "input range"

Step 4:

Select "rows" for the option "Group By"

Step 5:

Tick the option "labels in first row"

Step 6:

Set alpha = 0.05

Step 7:

Select the destination of output data in the "output options"

Conclusion:

Please refer to the attached results.

The p-value is found to be

p = 0.7038

The F value is found to be

F = 0.475

The F critical value is found to be

F critical = 3.238

Since p > α

0.7038 > 0.05

We failed to reject H₀

Also since F < F critical

0.475 < 3.238

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a difference among the four chemical agents on the strength of a particular type of cloth.

Answer:

x = 5 and y = -4

Step-by-step explanation:

y = - 3x + 11 ______(1)

5x + y = 21______(2)

Substitute (1) into (2).

5x + (-3x + 11) = 21

5x - 3x + 11 = 21

2x = 21-11

2x = 10

x = 10/2

x = 5

Now substitute x = 5 into (1).

y = -3(5) + 11

y = -15 + 11

y = -4

Hence, x = 5 and y = -4

Answer:

Option C is correct.

The discriminant of the function is negative since the function doesn't have real roots as evident from the graph.

Step-by-step explanation:

The discriminant of a quadratic equation is the part of the quadratic formula underneath the square root symbol, that is, (b² - 4ac).

The discriminant tells us whether there are two solutions, one solution, or no solutions.

- When the discriminant is positive or greater than zero, that is, (b² - 4ac) > 0, the quadratic function has 2 real distinct roots.

- When the discriminant is equal to zero, that is, (b² - 4ac) = 0, the quadratic function has 1 repeated root.

- When the discriminant is negative or lesser than zero, that is, (b² - 4ac) < 0, the quadratic function has no real roots.

For this question, the graph of the quadratic function shows that it doesn't have real roots (this is evident because the graph doesn't cross the x-axis), hence, the duscriminant of this quadratic function has to bee negative.

Hope this Helps!!!

Answer:

true

Step-by-step explanation:

doesn't over lap each other

Answer:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0.635,0.082)[/tex]  

Where [tex]\mu=0.635[/tex] and [tex]\sigma=0.032[/tex]

We are interested on this probability

[tex]P(X<0.4375)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<0.4375)=P(\frac{X-\mu}{\sigma}<\frac{0.4375-\mu}{\sigma})=P(Z<\frac{0.4375-0.635}{0.082})=P(z<-2.41)[/tex]

And we can find this probability using the z table and we got:

[tex]P(z<-2.41)=0.0080[/tex]