n=400 people under the age of 25 was asked whether they check social media sites right after they wake up. 42% check social media sites in the morning and 58% said that they don’t. Using a 5% significance level, test to see if there is evidence that less than 50% of people under the age of 25 check social media sites right after they wake up.

Answer:

Null hypothesis:[tex]p_{1} \leq p_{2}[/tex]    

Alternative hypothesis:[tex]p_{1}> p_{2}[/tex]  

[tex]z=\frac{0.117-0.08}{\sqrt{0.0979(1-0.0979)(\frac{1}{230}+\frac{1}{250})}}=1.363[/tex]    

Since is a right tailed test the p value would be:    

[tex]p_v =P(Z>1.363)= 0.0864[/tex]    

Comparing the p value and the significance level given we see that [tex]p_v <\alpha=0.1[/tex] so then we have enough evidence to reject the null hypothesis and then the proportion of defectives for the retailer is significantly higher than the proportion of defectives for the competitor at a 10% of significance level used.

Step-by-step explanation:

Data given

[tex]X_{1}=27[/tex] represent the number of defectives from the retailer

[tex]X_{2}=20[/tex] represent the number of defectives from the competitor

[tex]n_{1}=230[/tex] sample for the retailer

[tex]n_{2}=3377[/tex] sample for the competitor

[tex]p_{1}=\frac{27}{230}=0.117[/tex] represent the proportion of defectives for the retailer

[tex]p_{2}=\frac{20}{250}=0.08[/tex] represent the proportion of defectives for the competitor

[tex]\hat p[/tex] represent the pooled estimate of p

z would represent the statistic (variable of interest)    

[tex]p_v[/tex] represent the value for the test (variable of interest)  

[tex]\alpha=0.1[/tex] significance level given  

System of hypothesis

We need to conduct a hypothesis in order to check if the percentage of defective cellular phones found among his products, ( p1 ), will be no higher than the percentage of defectives found in a competitor's line, ( p2 ), the system of hypothesis would be:    

Null hypothesis:[tex]p_{1} \leq p_{2}[/tex]    

Alternative hypothesis:[tex]p_{1}> p_{2}[/tex]    

The statistic is given by:

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)  

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{27+20}{230+250}=0.0979[/tex]  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:    

[tex]z=\frac{0.117-0.08}{\sqrt{0.0979(1-0.0979)(\frac{1}{230}+\frac{1}{250})}}=1.363[/tex]    

P value

Since is a right tailed test the p value would be:    

[tex]p_v =P(Z>1.363)= 0.0864[/tex]    

Comparing the p value and the significance level given we see that [tex]p_v <\alpha=0.1[/tex] so then we have enough evidence to reject the null hypothesis and then the proportion of defectives for the retailer is significantly higher than the proportion of defectives for the competitor at a 10% of significance level used.

Answer:20%

Step-by-step explanation:

Answer:

We accept H₀  the weaning weights of cows at this ranch is 610 lbs

Step-by-step explanation:

We assume normal distribution

Population mean      μ₀  = 610  lbs

Population standard deviation     unknown

sample size  n = 41

degree of fredom    df = n - 1    df  =  41 - 1   df = 40

Sample mean    X = 578  lbs

Sample standard deviation   s  =  87

As we don´t know standard deviation of the population we will use t- student test, furthemore, as  we are looking for any difference upper and lower we are in presence of a two tails test

Test Hypothesis    Null  hypothesis    H₀                X  =  μ₀

Alternative hypothesis                         Hₐ                X  ≠  μ₀

Now at α  = 0,01 ,   df  = 40   and two tail test we find   t = 2,4347

We have in t table

30 df           t  =  2,457        for       α  = 0,01

60 df           t  = 2,390         for      α   = 0,01

Δ = 30               0,067

     10                    x  ??       x = 0,022

then  2,457  -  0,022  =  2,4347

t = 2,4347

Now we compute the interval:

X ±  t * ( s/√n)    ⇒   578  ±  2,4347 * ( 87/√41)

578  ±  2,4347 * 13,59

578  ±  33,09

P [ 578 + 33,09  ;  578 - 33,09 ]

P ( 611,09 ; 544,91]

We can see that vale 610 = μ₀   is inside the iinterval , so we accept H₀ the weaning weight of cows in the ranch is 610 lbs

It's a goofy question.  These sides satisfy the triangle inequality, 7 < 4+5, so we can draw as many triangles as we care to with those sides.

The more interesting question is how many non-congruent triangles can we draw with those sides?   The answer is only 1, because by SSS all triangles with those sides will be congruent.

If we're asking about how many triangles with these sides cannot be mapped to each other through translation and rotation, the answer is two, basically a pair of reflected copies.

So much for deconstructing this lousy question.  Let's go with

Answer: 1

When two triangles are congruent, corresponding sides and angle both are equal.

Only one triangle can be drawn that fit the given description.

it is given that, A triangle has sides of length 7 cm, 4 cm, and 5 cm.

Two triangles that have corresponding congruent sides are congruent (SSS).

If triangle ABC has the sides AB=7 cm, AC=4 cm, BC=5 cm  and the triangle MNP has MN=7 cm, MP=4 cm, and PN=5 cm then

                    [tex]AB=MN=7 cm\\\\AC=MP=4 cm\\\\BC=PN=5cm[/tex]

Hence,  based on the axiom of congruent triangles side–side–side (SSS) triangle ABC is congruent with triangle MNP.

Learn more about the triangles here:

https://brainly.com/question/1058720?referrer=searchResults

The requried, water depth is less than the minimum required depth of 4 inches, and the water is not deep enough for the flowers.

To determine if the water depth in the spherical vase is sufficient for the flowers, we need to compare the height of the water to the minimum required depth of 4 inches.

Given that the surface of the water forms a circle with a diameter of 5 inches, we can calculate the radius of this circle by dividing the diameter by 2.

Radius = Diameter / 2

Radius = 5 inches / 2

Radius = 2.5 inches

Since the shape of the vase is spherical, the water depth will be equal to the radius.

Therefore, the water depth in the spherical vase is 2.5 inches.

Since the water depth is less than the minimum required depth of 4 inches, the water is not deep enough for the flowers.

Learn more about circle here:
https://brainly.com/question/15541011

#SPJ12

Final answer:

Given that the spherical vase’s surface water diameter is 5 inches, translating to a radius of 2.5 inches at the water's surface level, the maximum depth at the center might be close to 2.5 inches, falling short of the 4 inches required for fresh cut flowers. Therefore, the water is not deep enough for the flowers.

Explanation:

The question asks if the water in a spherical vase, with a surface diameter of 5 inches, is adequate (at least 4 inches deep) for fresh cut flowers. To determine this, we need to consider the properties of a sphere and how the depth of water relates to its diameter.

Since the diameter of the water's surface is given as 5 inches, the radius of the spherical vase (at the water's surface level) is 2.5 inches. The depth of the water in a spherical vase does not evenly translate to its diameter because the shape curves upwards from every point on its surface. However, considering that the vase is filled to a level where the diameter is 5 inches, we must acknowledge that the depth in the very center might be more but decreases as we move towards the edge of the water's surface.

Given the spherical shape, the maximum depth of the water could be close to the radius of 2.5 inches in the center, assuming the vase is filled to exactly half its height. This depth is less than the required 4 inches for fresh cut flowers. Therefore, without a specific height indication of the water level relative to the vase's total height, and based on the central depth potentially being 2.5 inches at most, it is unlikely the flowers would have the required 4 inches of water depth across the entirety of the vase's base.

Answer:

0.95

Step-by-step explanation:

Let's convert this into a fraction that has a denominator of 100. In order to do so, we need to multiply the numerator and denominator both by 5 (because 20 * 5 = 100):

[tex]\frac{19}{20}* \frac{5}{5} =\frac{95}{100}[/tex]

So, we have 95/100, which is technically 95 divided by 100. Whenever we divide something by a power of 10, like [tex]10^n[/tex], where n is any integer, we move the decimal point of the dividend n places to the left.

Here, we have 100, which is [tex]10^2[/tex], so we want to move the decimal point of 95 (which equals 95.0) 2 places to the left:

0.95

Hope this helps!

Answer:95 degrees

Step-by-step explanation: That’s what it is closest to

Answer:

base : ¼

three points : (¼,1), (1,0), (4,–1)

domain : x>0

range : all real number

asymptote : x=0

Answer:

your answer would be x=0

Step-by-step explanation:

I nee to write a 5-paragraph eassy, so please help me it is base on an article name "Schools in Maryland Allow Elementary Students to Carry Cellphones, by Amanda Lenhart, The Washington Post" here are some pic. I just need help writing two paragraph. I already have my Introduction, Body Paragraph #1 and my Body paragraph #2 just need my Body paragraph #3 and my Conclusion I will give brainlis and 30 pnt.

Prompt:

Write an argumentative essay answering the questions: Should students be allowed to carry cellphones on campus? You must support your claim with evidence from the text. You may also use relevant examples from your own experience, observations, and other readings.

Directions:

Before you begin, read the text below, which presents information about the advantages and disadvantages of carrying a cell phone at school. Use the Student Writing Checklist on the back of this page to plan and write a multi-paragraph essay that addresses the prompt. Use your own words, except when quoting directly from the text.

PLEASE DONT WAST THEM

Complete question:

CHECK ATTACHMENT FOR THE DIAGRAM.

Answer:

Angle 7 is 76°

Step-by-step explanation:

From the diagram, notice that angle 4 = angle 5

That is,

Δ4 = Δ2

Because vertically opposite angles are equal.

Δ4 = 7x

Δ2 = 126

So

126 = 7x

Divide both sides by 7

x = 126/7 = 18

Again, angle 5 = angle 7

Δ5 = Δ7

Because vertically opposite angles are equal.

Since Δ5 = (4x + 4)°

And x = 18

Then

Δ7 = 4(18) + 4 = 72 + 4 = 76°

Answer:

The distribution of sample proportion Americans who can order a meal in a foreign language is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

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

The sample size of Americans selected to disclose whether they can order a meal in a foreign language is, n = 200.

The sample selected is quite large.

The Central limit theorem can be applied to approximate the distribution of sample proportion.

The distribution of sample proportion is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

Answer:

73.90%

Step-by-step explanation:

Let Event D=Defective,  D' = Non Defective

Let Event N=New Machine, N' = Old Machine

From the given information:

[tex]P(D|N')=0.25\\P(D|N)=0.09\\P(N)=0.7\\P(N')=0.3[/tex]

We are required to calculate the probability that a widget was manufactured by the new machine given that it is non defective.  

i.e. [tex]P(N|D')[/tex]

[tex]P(D'|N')=1-P(D|N')=1-0.25=0.75\\P(D'|N)=1-P(D|N)=1-0.09=0.91[/tex]

Using Baye's Law of conditional Probability

[tex]P(N|D')=\dfrac{P(D'|N)P(N)}{P(D'|N)P(N)+P(D'|N')P(N')} \\=\dfrac{0.91*0.7}{0.91*0.7+0.75*0.3}\\ =0.73897\\\approx 0.7390[/tex]

Therefore given that a selected widget is non-defective, the probability that it was manufactured by the new machine is 73.9%.

Answer:

82%

Step-by-step explanation:

Final answer:

The probability that Sophia was assigned Golem given that her software crashed is approximately 82%, calculated using Bayes' Theorem.

Explanation:

When software crashes and we want to know the likelihood Sophia was using Golem, we need to consider both the probability of being assigned Golem and the probability of that software crashing. This is known as the application of Bayes' Theorem, which is a way to find conditional probabilities. In this case, we calculate as follows:

We want to find the probability that Sophia was assigned Golem given that her software crashed (P(G|C)). We use the formula:

P(G|C) = (P(C|G) * P(G)) / (P(C|G) * P(G) + P(C|F) * P(F))

Inserting the above probabilities yields:

P(G|C) = (0.10 * 7/10) / ((0.10 * 7/10) + (0.05 * 3/10))

P(G|C) = 0.07 / (0.07 + 0.015)

P(G|C) = 0.07 / 0.085

P(G|C) = 0.8235 or approximately 82%

Expressed as a whole-number percentage, the probability that Sophia was using Golem is 82%.

Answer:

11.69% probability that it will weigh between 523 grams and 534 grams

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 551, \sigma = 20[/tex]

If you pick one fruit at random, what is the probability that it will weigh between 523 grams and 534 grams

This is the pvalue of Z when X = 534 subtracted by the pvalue of Z when X = 523. So

X = 534

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{534 - 551}{20}[/tex]

[tex]Z = -0.85[/tex]

[tex]Z = -0.85[/tex] has a pvalue of 0.1977

X = 523

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{523 - 551}{20}[/tex]

[tex]Z = -1.4[/tex]

[tex]Z = -1.4[/tex] has a pvalue of 0.0808

0.1977 - 0.0808 = 0.1169

11.69% probability that it will weigh between 523 grams and 534 grams

Answer:

[tex]P(523<X<534)=P(\frac{523-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{534-\mu}{\sigma})=P(\frac{523-551}{20}<Z<\frac{534-551}{20})=P(-1.4<z<-0.85)[/tex]

And we can find this probability with this difference:

[tex]P(-1.4<z<-0.85)=P(z<-0.85)-P(z<-1.4)[/tex]

And in order to find these probabilities we can use the table for the normal standard distribution, excel or a calculator.  

[tex]P(-1.4<z<-0.85)=P(z<-0.85)-P(z<-1.4)=0.198-0.0808=0.1172[/tex]

Step-by-step explanation:

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

[tex]X \sim N(551,20)[/tex]  

Where [tex]\mu=551[/tex] and [tex]\sigma=20[/tex]

We are interested on this probability

[tex]P(523<X<534)[/tex]

We can solve the 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(523<X<534)=P(\frac{523-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{534-\mu}{\sigma})=P(\frac{523-551}{20}<Z<\frac{534-551}{20})=P(-1.4<z<-0.85)[/tex]

And we can find this probability with this difference:

[tex]P(-1.4<z<-0.85)=P(z<-0.85)-P(z<-1.4)[/tex]

And in order to find these probabilities we can use the table for the normal standard distribution, excel or a calculator.  

[tex]P(-1.4<z<-0.85)=P(z<-0.85)-P(z<-1.4)=0.198-0.0808=0.1172[/tex]

Answer:

£155

Step-by-step explanation:

look at the formula

first solve 12 minutes per light switches

12*10(lightswitches)= 120 minutes

we know that 120 minutes = 2 hours

the task says that she charges £30 per hour

so, 2 hours+ 2 hours= 4 hours

now do

4*30= £120

120+35(call-out fee)= £155

I really hope this helped.

Answer:

x = 2.298

Step-by-step explanation:

we have to use the sin formula which is sin = opp / hyp

sin 50 = x / 3

x = 3 sin 50

x = 2.298

Given:

The graph of [tex]f(t)=4 \cdot 2^t[/tex] shows the value of a rare coin in year t.

We need to determine the meaning of the y - intercept.

Meaning of the y - intercept:

Here, t represents the x - axis and f(t) represents the y - axis.

The value of y - intercept is the value of y when x = 0.

Hence, the the value of f(t) can be determined by substituting t = 0 in the function [tex]f(t)=4 \cdot 2^t[/tex]

Thus, we have;

[tex]f(0)=4 \cdot 2^0[/tex]

[tex]f(0)=4[/tex]

Thus, the value of the y - intercept is 4.

The y - intercept represents the value of the rare coin in year 0.

Therefore, the meaning of the y - intercept is "When it was purchased (year 0), the coin was worth $4".

Hence, Option B is the correct answer.

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the dresser is in shape of a rectangular prism

Note that, a rectangular prism has a shape of a cuboid

So, area of the rectangular prism is same as area of a cuboid

A = (2LB + 2LH + 2BH)

Where

L is length

B is breadth

H is height

Then, given the dimension of the rectangular prism to be

2ft by 2ft by 6ft

Then, you can assume that,

Length L = 2ft

Breadth B = 2ft

Height H = 6ft.

NOTE: you can take you assumption anyhow, there is no standard, you will get the same answer.

Then,

A = (2LB + 2LH + 2BH)

A = (2×2×2 + 2×2×6 + 2×2×6)

A = (8 + 24 + 24)

A = 56 ft²

The total surface area of the dresser is 56ft²

Answer:

Surface area of the dresser is 56ft²

Step-by-step explanation:

Surface area of a rectangular prism is expressed as S = 2(LW+LH+WH)

L is the length the prism

W is the width

H is the height

If the rectangular prism measures 2 feet by 2 feet by 6 feet

L = 2feet, W = 2feet, height = 6feet

S = 2{(2)(2)+2(6)+2(6)}

S = 2{4+12+12}

S = 2×28

S = 56ft²

Answer:

a) "This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) "They will decide the stands are safe when they're not."

c) "They will decide the stands are unsafe when they are in fact safe."

Step-by-step explanation:

a) As the alternative hypothesis Ha is μ>575, the rejection region lays in the upper tail. Then, it is an upper-tail test.

They are testing the claim that the stand supports an average of 575 pounds or more, and are looking for statistical evidence for that claim.

"This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b)  A Type I error happens when a true null hypothesis is rejected.

This would mean that a stands that doesn't really hold 575 pounds or more has passed the test. The stand would appear more safe than it is.

"They will decide the stands are safe when they're not."

c) A Type II error happens when a false null hypothesis failed to be rejected. In this case, a safe stand, that suports 575 pounds or more, does not pass the test.

"They will decide the stands are unsafe when they are in fact safe."

Final answer:

The hypothesis test in question is an upper-tail test aiming to prove that the stands can support more than 575 pounds. A Type I error would misclassify safe stands as unsafe, while a Type II error would incorrectly certify unsafe stands as safe.

Explanation:

a) This is an upper-tail test because the goal is to show that the metal stand can support more than the standard set weight (>575 pounds). This is vital to ensure that the product holds significantly more weight than the heaviest TVs, thereby providing a safety margin.

b) A Type I error occurs if the inspectors reject the null hypothesis when it is actually true. In this context, it means they will incorrectly deem the stands to be unsafe when they are actually safe.

c) A Type II error occurs if the inspectors fail to reject the null hypothesis when it is false. In this scenario, it means that the inspectors will wrongfully certify the stands as safe when they are, in fact, not capable of holding the standard weight.

Answer:

36 degrees.

Step-by-step explanation:

Total Sum of the Exterior Angle of a Regular Polygon[tex]=360^0[/tex]

One Exterior Angle of a n-sided regular polygon[tex]=\dfrac{360^0}{n}[/tex]

A decagon has 10 sides.

One Exterior Angle of a decagon[tex]=\dfrac{360^0}{10}=36^0[/tex]

Therefore, the measure x of the angle between the house and the pool is 36 degrees.

Final answer:

To find the measure x of the angle between the house and a pool shaped as a regular decagon, calculate the exterior angle of the decagon, which is 36 degrees. This is the angle measure sought in the question.

Explanation:

The question involves finding the measure x of the angle between the house and the pool, where the pool is in the shape of a regular decagon.

First, let's recall that a regular decagon is a ten-sided polygon with all sides and angles equal. The sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180, where n is the number of sides. For a decagon, n = 10, so the sum of the interior angles is (10-2) × 180 = 1440 degrees. Since all angles in a regular decagon are equal, each interior angle measures 1440 ° / 10 = 144 °.

Now, to find the measure x of the angle between the house and the pool, we need to understand that the exterior angle of the decagon will be involved, as this is the angle made between one side of the decagon (lying against the house) and an extension of an adjacent side. The measure of an exterior angle of a regular polygon is 360 ° / n. For our decagon, this is 360 ° / 10 = 36 °.

Therefore, the measure x of the angle between the house and the pool is 36 °, which is the measure of the exterior angle of the regular decagon.

Answer:i think is [tex]30r2[/tex]

Step-by-step explanation:

Answer:

30r^3

Step-by-step explanation:

The answer is 30r^3 because first you multiply 5r and 6r and then you add the exponents of them together.

5r * 6r=30r

the exponent of 5r is two and the exponent of 6r is one so you add those together.

hope this helped

Answer:

Check the explanation

Step-by-step explanation:

Scatter plot

x---square feet

y---rent

SolutionA:

Kindly check the attached image below:

THERE EXISTS A WEAK POSITIVE RELATIONSHIP BETWEEN SQUARE FEET AND RENT .

AS SQUARE FEET INCREASES RENT INCREASES

SolutionB:

Rent=0.4932(squarefeet)+992.99

slope=m=0.4932

Y intercept=992.99

SolutionC:

Interpretation of slope:

slope =m=change in rent/change in square foot

For a unit increase in square feet rent increases by 0.4932

Interpretation of y intercept:

when square feet=0 rent is 992.99

Solutiond:

when squarefeet=800

Rent=0.4932(squarefeet)+992.99

=Rent=0.4932(800)+992.99

=1387.55

Answer:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

[tex] s=1.09[/tex]

Step-by-step explanation:

For this case we have the following data given:

2.3 3.1 2.8

1.7 0.9 4.0

2.1 1.2 3.6

0.2 2.4 3.2

Since the data are assumedn normally distributed we can find the standard deviation with the following formula:

[tex]\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}[/tex]

And we need to find the mean first with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

And then we can calculate the deviation and we got:

[tex] s=1.09[/tex]

Answer:

X ~ Norm ( 2.29167 , 1.09045^2 )

Step-by-step explanation:

Solution:-

- The (GPA) for 12 randomly selected college students are given as follows:

            2.3 , 3.1 , 2.8 , 1.7 , 0.9 , 4.0 , 2.1 , 1.2 , 3.6 , 0.2 , 2.4 , 3.2

- We are to assume the ( GPA ) for the college students are normally distributed.

- Denote a random variable X: The GPA secured by the college student.

- The normal distribution is categorized by two parameters:

- The mean ( u ) - the average GPA of the sample of n = 12. Also called the central tendency:

                        [tex]Mean ( u ) = \frac{\sum _{i=1}^{\ 12 }\: Xi }{n}[/tex]

Where,

           Xi : The GPA of the ith student from the sample

           n: The sample size = 12

          [tex]Mean ( u ) = \frac{2.3 + 3.1 + 2.8 + 1.7 + 0.9 + 4.0 + 2.1 + 1.2 + 3.6 + 0.2 + 2.4 + 3.2}{12} \\\\Mean ( u ) = \frac{27.5}{12} \\\\Mean ( u ) = 2.29167[/tex]

- The other parameter denotes the variability of GPA secured by the students about the mean value ( u ) - called standard deviation ( s ):

          [tex]s = \sqrt{\frac{\sum _{i=1}^{\ 12 }\: [ Xi - u]^2}{n} } \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = ( 2.3 - 2.29167)^2 + ( 3.1 - 2.29167)^2 + ( 2.8 - 2.29167)^2 + ( 1.7\\\\ - 2.29167)^2+ ( 0.9 - 2.29167)^2 + ( 4 - 2.29167)^2 + ( 2.1 - 2.29167)^2 + ( 1.2 - 2.29167)^2 +\\\\ ( 3.6 - 2.29167)^2 + ( 0.2 - 2.29167)^2 + ( 2.4 - 2.29167)^2 + ( 3.2 - 2.29167)^2 \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = 14.26916 \\\\\\s = \sqrt{\frac{ 14.26916 }{12} } \\\\s = \sqrt{1.18909 } \\\\s = 1.09045[/tex]

- The normal distribution for random variable X can be written as:

                 X ~ Norm ( 2.29167 , 1.09045^2 )

Answer:

The lateral surface area of cube = 4

Step-by-step explanation:

Explanation:-

Given perimeter of the cube is 12

let 'a' be the base of cube

we know that the perimeter of cube formula = 12 a

        12 a= 12

           a = 1

The side of cube = 1cm

The lateral surface area of cube = 4 × a²

                                                      = 4 X (1)²

                                                      = 4

Final answer:-

The lateral surface area of cube = 4

Answer:

Check the explanation

Step-by-step explanation:

The fundamentals

A continuous random variable can take infinite values in the range associated function of that variable. Consider [tex]f\left( x \right)f(x)[/tex] is a function of a continuous random variable within the range [tex]\left[ {a,b} \right][a,b][/tex] , then the total probability in the range of the function is defined as:

[tex]\int\limits_a^b {f\left( x \right)dx} = 1 a∫b​ f(x)dx=1[/tex]

The probability of the function [tex]f\left( x \right)f(x)[/tex] is always greater than 0. The cumulative distribution function is defined as:

[tex]F\left( x \right) = P\left( {X \le x} \right)F(x)=P(X≤x)[/tex]

The cumulative distribution function for the random variable X has the property,

[tex]0 \le F\left( x \right) \le 10≤F(x)≤1[/tex]

The probability density function for the random variable X has the properties,

[tex]\\\begin{array}{c}\\{\rm{ }}f\left( x \right) \ge 0\\\\\int\limits_{ - \infty }^\infty {f\left( x \right)dx} = 1\\\\P\left( E \right) = \int\limits_E {f\left( x \right)dx} \\\end{array} f(x)≥0[/tex]

Kindly check the attached image below to see the full explanation to the question above.

Answer:

   £1800

Step-by-step explanation:

The lower price is 80% of the original, so the original price is ...

   £1440 = 0.80×original

   £1440/0.80 = original =  £1800

The price before the decrease was  £1800.

Answer:

8-4x= 0 has only 1 solution

Step-by-step explanation:

This can only have one solution because there will only be one value that can set the equation equal to 0 that number is 2. -2 on the other hand will not work because you will get 8+8=0 which does not make sense so you can only have 1 solution.

Hope this helps

Answer:

in fraction form: -1/36, 1/216, -1/1296

in decimal form: -.03, .005, -.0008

Step-by-step explanation:

Each term is the previous term divided by -6:

-36 ÷ -6= 6

6 ÷ -6= -1

and so on...

-1/36

The numbers divide by -6 each time

Answer:

[tex]7.3-1.440\frac{1.2}{\sqrt{830}}=7.240[/tex]    

[tex]7.3+1.440\frac{1.2}{\sqrt{830}}=7.360[/tex]    

So on this case the 85% confidence interval would be given by (7.2;7.4)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=7.3[/tex] represent the sample mean

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

[tex]\sigma =1.2[/tex] represent the population standard deviation

n=830 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)

Since the Confidence is 0.85 or 85%, the value of [tex]\alpha=0.15[/tex] and [tex]\alpha/2 =0.075[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.075,0,1)".And we see that [tex]z_{\alpha/2}=1.440[/tex]

Now we have everything in order to replace into formula (1):

[tex]7.3-1.440\frac{1.2}{\sqrt{830}}=7.240[/tex]    

[tex]7.3+1.440\frac{1.2}{\sqrt{830}}=7.360[/tex]    

So on this case the 85% confidence interval would be given by (7.2;7.4)    

Answer:

The answer is [tex]\pi(\pi-6)[/tex]

Step-by-step explanation:

Recall that green theorem is as follows: Given a field F(x,y) = (P(x,y),Q(x,y)) and a closed curve C that is counterclockwise oriented. If P and Q are continuosly differentiable, then

[tex]\oint_C F\cdot dr = \int_{R} \frac{\partial P }{\partial y}-\frac{\partial P }{\partial x} dA[/tex]

where R is the region enclosed by the curve C.

In this particular case, we have the following field [tex]F(x,y) = (4xy^2,2x^3+y)[/tex]. We are given the description of the region R as [tex]0\leq y \leq \sin(x), 0\leq x \leq \pi[/tex]. So, in this case (calculations are omitted)

[tex]\frac{\partial P}{\partial y} = 8xy, \frac{\partial Q}{\partial x} = 6x[/tex]

Thus,

[tex]\oint_C F\cdot dr =\int_{0}^{\pi}\int_{0}^{\sin(x)}(8xy-6x)dydx[/tex]

So,

[tex] \int_{0}^{\pi}\int_{0}^{\sin(x)}(8xy-6x)dydx=\int_{0}^{\pi}4x\left.y^2\right|_{0}^{\sin(x)}-6x\left.y\right|_{0}^{\sin(x)} = \int_{0}^{\pi} 4x\sin^2(x)-6x\sin(x)dx[/tex]

Since [tex]\sin^2(x) = \frac{1-\cos(2x)}{2}[/tex], then

[tex] \int_{0}^{\pi} 4x\sin^2(x)-6x\sin(x)dx = \int_{0}^{\pi} 2x(1-\cos(2x))-6x\sin(x)dx[/tex]

Consider the integrals

[tex] I_1 = \int_{0}^{\pi} x\cos(2x)dx, I_2 = \int_{0}^{\pi}x\sin(x)dx[/tex]

Then, by using integration by parts (whose calculations are omitted) we get

[tex]\int_{0}^{\pi} x\cos(2x) = \left.\frac{x\sin(2x)}{2}+\frac{\cos(2x)}{4}\right|_{0}^{\pi} = \frac{\pi\sin(2\pi)}{2}+\frac{\cos(2\pi)}{4}- \frac{0\sin(2\cdot 0)}{2}+\frac{\cos(2\cdot 0)}{4}=0[/tex]

[tex] \int_{0}^{\pi}x\sin(x) = \left.-x\cos(x)+\sen(x)\right |_{0}^{\pi} = -\pi\cos(\pi)+\sen(\pi)- (-0\cdot \cos(\pi)+\sin(0)) = \pi[/tex]

Then, we have that

[tex]\int_{0}^{\pi} 2x(1-\cos(2x))-6x\sin(x)dx = \left.x^2\right|_{0}^{\pi} -2I_1-6I_2 = \pi^2-2\cdot 0 -6\pi = \pi(\pi-6)[/tex]

Answer:

QS + QR > RS

QR + RS > QS

RS + QS > QR    

Step-by-step explanation:

    ∧ ∧

( Ф∨Ф)

Answer:

hm here <3

Step-by-step explanation:

1 RS

2 QS

3 QR

<3

Answer:

they can get at most 6 drinks

Step-by-step explanation:

5 (17.5) + 2x ≤100

87.5 + 2x≤100

2x≤ 12.5

x≤6.25

Answer:

0 to 6 drinks, but no more.

Step-by-step explanation: