The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration. A test of
H0:μ=20 versus Ha:μ is greater than 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)
a. n = 17, t = 3.1, α=0.05
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
b. n = 10, t = 1.8, α=0.01
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
c. n = 24, t = -0.4, p-value =

Answer:

B

Step-by-step explanation:

Took the test edge2021

The function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

A function which is at x = 2 mapped to 32

The above statement means that at x = 2

The value of the function will be 32

The given functions:

f(x) = -3x² - 4

Plug x = 2

f(2) = -3(2)² - 4

f(2) = -16

g(x) = 4(x + 3)² - 68

Plug x =2

g(2) = 4(2 + 3)² - 68

g(2) = 100 - 68

g(2) = 32

Thus, the function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

Learn more about the function here:

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Answer:

There is enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

Given the cilindrical configuration of the tank and supposing that only external face must be painted, the surface area of the section (lateral wall + lid) can be calculated by the following expression:

[tex]A_{s} = 2\pi\cdot r\cdot h + \pi\cdot r^{2}[/tex]

Where [tex]r[/tex] and [tex]h[/tex] represent the radius and the height of the cube, respectively.

If [tex]r = 0.55\,m[/tex] (a diameter is two times the length of radius) and [tex]h = 1.4\,m[/tex], the intended surface area is:

[tex]A_{s} = 2\pi\cdot (0.55\,m)\cdot (1.1\,m)+\pi\cdot (0.55\,m)^{2}[/tex]

[tex]A_{s} \approx 4.751\,m^{2}[/tex]

It is known that 250 mL of paint are needed to cover a square meter of the surface area, the needed amount of paint to cover the required area is estimated by simple rule of three:

[tex]Q = \frac{4.751\,m^{2}}{1\,m^{2}}\times (250\,mL)[/tex]

[tex]Q = 1187.75\,mL\,(1.188\,L)[/tex]

In consequence, there is enough paint to cover the tank with one layer of paint.

Answer:

Probability = 0.10565

Step-by-step explanation:

Given:

Mean, u = 2

x = 2.5

CV = 20% = 0.2

To find standard deviation [tex] \sigma[/tex] use the formula:

[tex] CV = \frac{\sigma}{u} [/tex]

[tex] 0.2 = \frac{\sigma}{2} [/tex]

[tex] \sigma = 0.2 * 2 [/tex]

[tex] \sigma = 0.4 [/tex]

Find Z, using the formula:

[tex] Z = \frac{x - u}{\sigma} [/tex]

[tex] Z = \frac{2.5 - 2}{0.4} [/tex]

[tex] Z = \frac{0.5}{0.4} [/tex]

[tex] Z = 1.25 [/tex]

Using the p value table,

P(x > 1.25) = 0.10565

Therefore, The probability that this building will settle more than 2.5 inches is 0.10565

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:

sorry but are you dyin why do u need help why do you need someone to save you just say i need answers to this equation pls

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:

-4/8

Step-by-step explanation:

Using rise over run would give you -4/8. Since the rise is going downward four times the number would be negative. Since the run is going to the right 8 times it would be positive.

Answer:  the slope is -1/2

Step-by-step explanation:  The rise is -4. Easy to see from the y-intercept, 4 below the origin. The run is 8, again easy to see from the distance between the x-intercept at -8, 8 unite away from the origin.

So slope = rise/run -4/8   simplify (by LCM, 4) So you get slope = -1/2

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

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:

[tex]\large \boxed{\text{-1.8$^{\circ}$F/1000 ft}}[/tex]

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

[tex]\begin{array}{cccc}\textbf{Alt/1000 ft} & \textbf{B.p.$/^{\circ}$F} & \Delta\textbf{B. p}& \Delta\textbf{B.p/1000 ft}\\0 & 212.0 & & \\& &-0.9 & -1.8\\0.5 & 211.1 & & \\& &-0.9 & -1.8\\1.0 & 210.2 & & \\& &-1.8 & -1.8\\2.0 & 208.4 & & \\& &-1.8 & -1.8\\3.0 & 206.6 & & \\& &-1.8 & -1.8\\4.0 & 204.8 & & \\& &-0.9 & -1.8\\4.5 & 203.9 & & \\\end{array}[/tex]

[tex]\text{ The change in boiling point per thousand feet of altitude is $\large \boxed{\textbf{-1.8$^{\circ}$F/1000 ft}}$}[/tex]

Answer:

Answer:

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

Step-by-step explanation:

Answer:

Hey there!

The solutions to a system are where the lines, or graphs intersect each other.

We see that the graphs intersect at (0, -4) and (2, 0).

Thus, the solutions are (0, -4) and (2, 0).

Hope this helps :)

Answer:

A. (0,2) and (7,23)

Step-by-step explanation:

To solve, we set both equations equal to each other (because both equations equal y).

3x + 2 = x^2 -4x + 2

x^2 - 7x = 0

x(x-7)

so the x values are 7 and 0.

Plugging x back into the linear equation (because it’s easier)

3(7) + 2 = 23

3(0) + 2 = 2

so the answers are (7, 23) and (0,2)

Answer:

Validation

Step-by-step explanation: Validation is a term used to describe the processes involved when we compare a set of values and observations against a set standard or rules to ensure that they meet certain expectations or criteria.

Validation is meant to prove that something, a data set etc are acceptable based on known rules, the rules or standards which is used to evaluate what can be described as valid.

━━━━━━━☆☆━━━━━━━

▹ 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!

━━━━━━━☆☆━━━━━━━

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:

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Answer:

x = 5, AB=5, BC = 15

Step-by-step explanation:

AC = AB + BC (Segment Addition)

AC= 20, AB =x Bc = 3x,

20= x+3x 20=4x

x=5

AB=x, AB =5

BC=3x BC= 15

The segment addition postulate states gives the value of x as 5, given

that the sum of x and 3·x is 20.

Responses:

From the given diagram, we have;

[tex]\overline{AB}[/tex] = x

[tex]\overline{BC}[/tex] = 3·x

According to segment addition postulate we have;

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches

Which gives;

x + 3·x = 20

Therefore;

4·x = 20

[tex]x = \dfrac{20}{4} = 5[/tex]

[tex]\mathbf{\overline{BC}}[/tex] = 3·x  

[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15

Learn more about segment addition postulate here:

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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%.

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:

Step-by-step explanation:

Given the 3* 3 matrices [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex], to compute the determinant using the first row means using the row values [0 4 1 ] to compute the determinant. Note that the signs on the values on the first row are +0, -4 and +1

Calculating the determinant;

[tex]= +0\left[\begin{array}{cc}-3&0\\3&1\\\end{array}\right] -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] +1\left[\begin{array}{cc}5&-3\\2&3\\\end{array}\right] \\\\= 0 - 4[5(1)-2(0)] +1[5(3)-2(-3)]\\= 0 -4[5-0]+1[15+6]\\= 0-20+21\\= 1[/tex]

The determinant is 1 using the first row as co-factor

Similarly, using the second column [tex]\left[\begin{array}{c}4\\-3\\3\end{array}\right][/tex] as the cofactor, the determinant will be expressed as shown;

Note that the signs on the values are -4, +(-3) and -3.

Calculating the determinant;

[tex]= -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\5&0\\\end{array}\right] \\\\= -4[5(1)-2(0)] - 3[0(1)-2(1)] -3[(0)-5(1)]\\= -4[5-0] -3[0-2]-3[0-5]\\= -20+6+15\\= -20+21\\= 1[/tex]

The determinant is also 1 using the second column as co factor.

It can be concluded that the same value of the determinant will be arrived at no matter the cofactor we choose to use.

Answer: 52.8

Step-by-step explanation: it’s on khan ,

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 statistic for this case would be:

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

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

Step-by-step explanation:

For this case we have the following info:

[tex] n =700[/tex] represent the sample size

[tex] X= 305[/tex] represent the number of employees that earn more than 50000

[tex]\hat p=\frac{305}{700}= 0.436[/tex]

We want to test the following hypothesis:

Nul hyp. [tex] p \leq 0.4[/tex]

Alternative hyp : [tex] p>0.4[/tex]

The statistic for this case would be:

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

And replacing we got:

[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]

And the p value would be given by:

[tex] p_v = P(z>1.922)= 0.0274[/tex]

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:

We have this original function given:

[tex] g(x) =-x^2 +5[/tex]

And we want to transtale vertically downward 4 units this function and we will get the new fnction h(x) and on this case we have to do this transformation:

[tex] h(x)= g(x) -4[/tex]

And replacing we got:

[tex] h(x) = -x^2 +5 -4 =-x^2 +1[/tex]

Step-by-step explanation:

We have this original function given:

[tex] g(x) =-x^2 +5[/tex]

And we want to transtale vertically downward 4 units this function and we will get the new fnction h(x) and on this case we have to do this transformation:

[tex] h(x)= g(x) -4[/tex]

And replacing we got:

[tex] h(x) = -x^2 +5 -4 =-x^2 +1[/tex]

Answer:

[tex]\boxed{Costing Price = $675}[/tex][tex]\boxed{Costing Price = $675}[/tex]Costing Price = $675

Step-by-step explanation:

Selling Price = $432

Discount = 36% of the costing price (36/100 * CP)

Then, Costing Price:

Let costing price be x

=> x - 0.36 x = 432

=> 0.64 x = 432

Dividing both sides by 0.64

=> x = $675

So, the costing Price is $675

Answer:

I think its

             T

 R--------Q----------A

             U

Step-by-step explanation:

Because RA as a line bisects TU

Answer:

true

Step-by-step explanation:

doesn't over lap each other

Answer:

  134 degrees

Step-by-step explanation:

Right so far. To find the numerical measure of the angle, you need to use x=7 in your expression for the angle measure:

  m∠STU = -27 +23(7) = 134 . . . 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.