Which expression shows that the quotient {Read Attachment for full question}

Answer:

y = 2/3x + 4

Step-by-step explanation:

Step 1: Find slope

m = (4-0)/(0+6)

m = 2/3

Step 2: Write in y-int (0, 4)

y = 2/3x + 4

Answer:

A reflection and a dialation

Step-by-step explanation:

In this case a rotation is not nessasary, so I would suggest a reflection in the y-axis and a dialation to shrink the triangle to A'B'C'

So for the transformations that could have occurred to map ABC to A'B'C' you should choose the answer

a reflection and a dialation

The transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation

Thus, in the transformation shown, figure ABC was reflected over the y-axis and then dilated to give A'B'C'.

Therefore, the transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation

Learn more about transformation on:

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Answer:

Answer:

Option 2nd is correct.

=0.

Step-by-step explanation:

Given the function:

Solve:

First calculate:

f[g(x)]

Substitute the function g(x)

Replace x with x-8 in the function f(x) we get;

The distributive property says that:

Using distributive property:

⇒

Put x = 6 we get;

Therefore, the value of   is 0.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

f(x) = 6x + 12

g(x) = x − 8

f(g(6))=?

g(6)=6-8= -2

f(-2)= -2*6+12= -12+12=0

f(g(6))= f(-2)=0

Answer:

[tex]\mu_1 \neq \mu_2 \neq \mu_3[/tex]

Where [tex]\mu_1[/tex] is the average effect of strength training

[tex]\mu_2[/tex] is the average effect of aerobic training

[tex]\mu_3[/tex] is the average effect of yoga

Step-by-step explanation:

The aim of this study is to confirm whether the strength training, aerobic training, and yoga have equal effect on the decreasing rates of injury and absenteeism or not. The null hypothesis suggests that these three training have equal effect on the decreasing rates of injury and absenteeism because according to the null hypothesis, there is no statistical difference between observed variables.

The alternative hypothesis on the other hand suggests a statistical difference between the observed variables. In this case, the alternative hypothesis suggests that the observed variables have different effects on the decreasing rates of injury and absenteeism.

My alternative hypothesis as the director of the employee wellness and productivity program is [tex]\mu_1 \neq \mu_2 \neq \mu_3[/tex]

Where [tex]\mu_1[/tex] is the average effect of strength training

[tex]\mu_2[/tex] is the average effect of aerobic training

[tex]\mu_3[/tex] is the average effect of yoga

The alternative hypothesis is, [tex]\mu_1 \neq \mu_2 \neq \mu_ 3[/tex].

Where, [tex]\mu_1[/tex] is the average effect of strength training,

[tex]\mu_2[/tex] is the average effect of aerobic training.

[tex]\mu_3[/tex] is the average effect of yoga.

Given that,

As director of the employee wellness and productivity program in your company,

you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism.

The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga.

We have to determine,

Your alternative hypothesis is.

According to the question,

The effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism.

The aim of this study is to confirm whether strength training, aerobic training, and yoga have equal effects on decreasing rates of injury and absenteeism or not.

The null hypothesis suggests that these three pieces of training have an equal effect on the decreasing rates of injury and absenteeism because according to the null hypothesis,

There is no statistical difference between observed variables.

The alternative hypothesis on the other hand suggests a statistical difference between the observed variables.

In this case, the alternative hypothesis suggests that the observed variables have different effects on the decreasing rates of injury and absenteeism.

The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga.

Therefore, The alternative hypothesis as the director of the employee wellness and productivity program is,

Where [tex]\mu_1[/tex] is the average effect of strength training,

[tex]\mu_2[/tex] is the average effect of aerobic training.

[tex]\mu_3[/tex] is the average effect of yoga.

To know more about the Hypothesis click the link given below.

https://brainly.com/question/23056080

Answer:

Test statistic z = 2.3839.

P-value = 0.0086.

At a signficance level of 0.05, there is enough evidence to support the claim that the percentage of residents who favor construction is above 56%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is above 56%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.56\\\\H_a:\pi>0.56[/tex]

The significance level is 0.05.

The sample has a size n=900.

The sample proportion is p=0.6.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.56*0.44}{900}}\\\\\\ \sigma_p=\sqrt{0.000274}=0.017[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.56-0.5/900}{0.017}=\dfrac{0.039}{0.017}=2.3839[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.3839)=0.0086[/tex]

As the P-value (0.0086) 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 percentage of residents who favor construction is above 56%.

Answer:

3/10

Step-by-step explanation:

Answer:

The value of y that would make O P parallel to L N = 36

Step-by-step explanation:

This is a question on similar triangles. Find attached the diagram obtained from the given information.

Given:

The length of O L = 14

the length of O M = 28

the length of M P = y

the length of P N = 18

Length MN = MP + PN = y + 18

Length ML = MO + OL = 28+14 = 42

For OP to be parallel to LN,

MO/ML = MP/PN

MO/ML = 28/42

MP/PN= y/(y+18)

28/42 = y/(y+18)

42y = 28(y+18)

42y = 28y + 18(28)

42y-28y = 504

14y = 504

y = 504/14 = 36

The value of y that would make O P parallel to L N = 36

Answer:

D-36

Step-by-step explanation:

Answer:

I hope this help

Step-by-step explanation:

Answer:

Correct statement: "the number is divisible by 3".

Step-by-step explanation:

The statement provided is:

When a number is divisible by 9, the number is divisible by 3.

The general form of a conditional statement in if-then form is:

[tex]p\rightarrow q[/tex]

This implies that if p, then q.

The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.

The if-then form of the provided statement is:

If a number is divisible by 9, then the number is divisible by 3.

So, the conclusion is:

"the number is divisible by 3"

Answer:

a

Step-by-step explanation:

Answer:

( 3.5 , -2 )

Step-by-step explanation:

Answer:

( 3.5 , -2)

Explanation:

On edge

Answer:

25%

Step-by-step explanation:

The last percentile always contains 25% of the observations.

Answer:

Volume of the cone is 1883.7 cm³

Step-by-step explanation:

The circumference of the full circle with radius 18 cm :

360 := 2*π*18 = 36π cm

125 := 125/360 * 36π

The new circumference is maller:

36π - 125/360 * 36π

36π * 0.652(7)

Calculate the new r based on the new circomference:

2*π * r = 36π * 0.652(7)

r = 36π/2π * 0.652(7)

r = 18 * 0.652(7)

r = 11.75 cm

Based on this radius you can calculate the area of the base of the cone.

area base = π*(11.75)²

The Volume V of this cone = 1/3 π r² * h

You can calculate the height h by using Pythagoras theorum.

The sector is the hypothenusa= 18 cm

The h is the height, which is the "unknown"

The r is the new radius = 11.75 cm

s² = r² + h²

h² = s² - r²

h = √(s² - r²)

h = √(18² - 11.75²)

h = 13.6358901432946 cm

h = 13.636 cm

V cone

V = 1/3 π 11.75² * h

V = 1/3 π 11.75² * √(18² - 11.75²)

V = 1/3 π 11.75² * 13.636

V = 1883.7 cm³

Answer:

0.143

Step-by-step explanation:

1/7 means 1 divided by 7. 1 divided by 7 is approximately 0.143.

Hope this helps!

area =πr²

6.5²xπ=132.73

2.3²xπ=16.62

132.73-16.62= 116.11

116cm^2

i think its this anyway

Answer:

116 cm^2 to 3 s f's.

Step-by-step explanation:

The area of the shaded part = area of the outer circle - area of the inner circle

= π * 6.5^2 - π *  2.3^2

=  132.732 - 16.619

= 116.113  cm^2.

Answer:  b) the tiles are not similar because both SP:SR is 5:4 and MJ:ML is 5:2

Step-by-step explanation:

We are given that the tiles are rectangular which implies that they both have a 90° angle.

In order to prove similarity, We need to show that the lengths and widths are proportional.

P Q R S

J  K L M

a) PQ : QR         JK : LM

  w=4  L=5        w=2 w=2

                                  ↓

                                 We need Length (not width)

b) SP : SR         MJ : ML

  L=5  w=4        L=5 w=2

      5 : 4               5 : 2

When comparing length to width they do not have the same ratio so the rectangles are not similar.

c) PQ : QR         JK : KL

  w=4  L=5        w=2 L=5

      4 : 5               2 : 5

When comparing width to length they do not have the same ratio so the rectangles are not similar.

d) SR : ML         PQ : JK

  w=4  w=2        w=4 w=2

           ↓                     ↓

  We need Length (not width)

Answer:

The value of the sample mean resonance frequency is 112Hz

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 111.6

Upper bound: 112.4

Sample mean: (111.6 + 112.4)/2 = 112Hz

The value of the sample mean resonance frequency is 112Hz

The value of the sample mean resonance frequency is 112 Hz.

The value of the sample mean resonance frequency is equivalent to the average of the upper limit and the lower limit.

The sample mean resonance frequency = (lower limit + upper limit) / 2

(111.6 +112.4) / 2

= 224 / 2

= 112 Hz

To learn more about confidence interval, please check: https://brainly.com/question/15905477

Answer:

I'm not completely sure what you mean by a, "single fraction," but I'm pretty sure the answer you are looking for is [tex]\frac{5-4}{a-b}[/tex]

Step-by-step explanation:

Answer:

[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]

[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]

Step-by-step explanation:

Notation

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

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

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case the 9% confidence interval is given by:

[tex] 8.8104 \leq \mu \leq 11.1248[/tex]

We can calculate the mean with the following:

[tex]\bar X = \frac{8.8104 +11.1248}{2}= 9.9676[/tex]

And we can find the margin of error with:

[tex] ME= \frac{11.1248- 8.8104}{2}= 1.1572[/tex]

The margin of error for this case is given by:

[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE[/tex]

And we can solve for the standard error:

[tex] SE = \frac{ME}{t_{\alpha/2}}[/tex]

The critical value for 95% confidence using the normal standard distribution is approximately 1.96 and replacing we got:

[tex] SE = \frac{1.1572}{1.96}= 0.5904[/tex]

Now for the 98% confidence interval the significance is [tex]\alpha=1-0.98= 0.02[/tex] and [tex]\alpha/2 = 0.01[/tex] the critical value would be 2.326 and then the confidence interval would be:

[tex] 9.9676 - 2.326*0.5904 =8.594[/tex]

[tex] 9.9676 + 2.326*0.5904 =11.341[/tex]

Answer:

91 employees

Step-by-step explanation:

To find the number of employees absent fewer than six days...add the frequency of those absent for 0 to 3 days and that of 3 to 6 days

The frequency of 0 to 3 days = 60

The frequency of 3 to 6 days = 31

Thus, the numbers of employees absent fewer than 6 days is 60+31 = 91

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\[/tex]

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=500\\\\H_a:\mu< 500[/tex]

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=5-1=4[/tex]

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.1)=0.166[/tex]

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

Answer:

  (x, y) = (7, 4) meters

Step-by-step explanation:

The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.

The perimeter of the floor is the sum of all side lengths, so is 4x +2y.

The given dimensions tell us ...

  x^2 -y^2 = 33

  4x +2y = 36

From the latter equation, we can write an expression for y:

  y = 18 -2x

Substituting this into the first equation gives ...

  x^2 -(18 -2x)^2 = 33

  x^2 -(324 -72x +4x^2) = 33

  3x^2 -72x + 357 = 0 . . . . write in standard form

  3(x -7)(x -17) = 0 . . . . . factor

Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.

  y = 18 -2(7) = 4

The floor dimension x is 7 meters; the inset dimension y is 4 meters.

Answer:

Step-by-step explanation:

given a point [tex](x_0,y_0)[/tex] the equation of a line with slope m that passes through the  given point is

[tex]y-y_0 = m(x-x_0)[/tex] or equivalently

[tex] y = mx+(y_0-mx_0)[/tex].

Recall that a line of the form [tex]y=mx+b [/tex], the y intercept is b and the x intercept is [tex]\frac{-b}{m}[/tex].

So, in our case, the y intercept is [tex](y_0-mx_0)[/tex] and the x  intercept is [tex]\frac{mx_0-y_0}{m}[/tex].

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph [tex](x_0,\frac{1}{x_0})[/tex]. Which means that [tex]y_0=\frac{1}{x_0}[/tex]

The slope of the tangent line is given by the derivative of the function evaluated at [tex]x_0[/tex]. Using the properties of derivatives, we get

[tex]y' = \frac{-1}{x^2}[/tex]. So evaluated at [tex]x_0[/tex] we get [tex] m = \frac{-1}{x_0^2}[/tex]

Replacing the values in our previous findings we get that the y intercept is

[tex](y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}[/tex]

The x intercept is

[tex] \frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0[/tex]

The triangle in consideration has height [tex]\frac{2}{x_0}[/tex] and base [tex]2x_0[/tex]. So the area is

[tex] \frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2[/tex]

So regardless of the point we take on the graph, the area of the triangle is always 2.

Answer:

Sry, i dont know all of the numbers. Hope this helps!

Here are the first:

Step-by-step explanation:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382

Pls mark Brainliest

Answer:

The probability that Bronson gets just spinach is;

P = 1/7

or

P = 0.1429

Step-by-step explanation:

There are three possibilities;

- just one topping

- two topping

- three topping

For just one topping, the number of possible outcomes is;

N1 = 3C1 = 3!/(1!2!) = 3 possible outcomes

For two topping, the number of possible outcomes is;

N2 = 3C2 = 3!/(2!1!) = 3 possible outcomes

For three topping, the number of possible outcomes is;

N3 = 3C3 = 3!/3! = 1 possible outcomes

Total number of possible outcomes;

N = N1+N2+N3

N = 3+3+1 = 7

The probability that Bronson gets just spinach is;

Getting spinach is one out of seven possible outcomes, so;

P = 1/N = 1/7

P = 1/7 or 0.1429

Answer:

P(7 or 11) = 0.2222

Step-by-step explanation:

First let's find the cases where we get a sum of 7 and a sum of 11:

The cases where we get a sum of 7 are:

(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

And the cases where we get a sum of 11 are:

(5,6), (6,5)

So we have a total of 8 cases among the 36 total possible outcomes.

So the probability of the sum of the two dice being 7 or 11 is:

P(7 or 11) = 8 / 36 = 0.2222

Answer:

Present value is $993.47

Step-by-step explanation:

PV = present value

Fv = future value = $1,600

Discount (i) = 10%

N = Years = 5

The formula for this is given by:

PV = FV/(1 + i)^N

PV = $1600/(1 + 0.10)^5

PV = $1600/1.1^5

PV = $1600/1.61051

PV = $993.47

Answer:  d) SR and S'R' have the ratio 1:3

Step-by-step explanation:

In order for the polygons to be similar, they must have congruent angles and proportional side lengths.

a) ∠Q and ∠Q' have the ratio 1:3          

  FALSE - The angles must be congruent (not proportional)

b) TS and T'S' have equal lengths

 FALSE - We can see that there is a dilation so they cannot be congruent.

c) RT and R'T' have equal lengths

 FALSE - We can see that there is a dilation so they cannot be congruent.

d) SR and S'R' have a ratio of 1:3

 TRUE! - The sides are proportional so we can use this to prove similarity.

Answer:

D- The lengths of side SR and side S'R' are in the ratio 1:3.

Step-by-step explanation:

I took the test and it was right

Answer: The solution  is [tex](-2,\frac{5}{3} )[/tex]

Step-by-step explanation:

it already gives you the solution for x so just plot it into the equation to solve for y.

y= [tex]\frac{2}{3} *\frac{-2}{1}+3[/tex]  

y= [tex]\frac{-4}{3}+\frac{3}{1}[/tex]

y= [tex]\frac{5}{3}[/tex]

Answer: -2 5/3

Step-by-step explanation:

y= 2/3*-2/1+3

y= -4+3/1

-2 5/3

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, [tex]H_0[/tex] : p = 0.013      {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, [tex]H_A[/tex] : p > 0.013      {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion faulty modems= [tex]\frac{10}{367}[/tex] = 0.027

           n = sample of modems = 367

So, the test statistics  =  [tex]\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }[/tex]

                                     =  2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.