Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question "Are you in favor of an increase in state spending on the arts?" An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference

Answer:

[tex]\$0.26[/tex] has to be paid more if the coupon is applied first

Step-by-step explanation:

Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.

To find: how much more would be paid if the coupon is applied first

Solution:

Let $ x denotes cost of hand soap

Case 1:

If the discount is given first,

cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]

If the coupon for $2.00 off is applied,

Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]

Case 2:

If the coupon for $2.00 off is applied first,

cost of hand soap = [tex]\$(x-2)[/tex]

If the discount is given then,

final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]

Here,

[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]

So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.

Answer:

$0.26

Step-by-step explanation: I took the test

Answer:

[tex]5(3x-2y-2)[/tex] i think. i am sorry if i am wrong

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Probability of the captain hitting the pirate ship [tex]=\dfrac{1}{2}[/tex]

Probability of the pirate hitting the captain's ship [tex]=\dfrac{1}{6}[/tex]

If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship

=P(Captain Hits AND Pirate Hits)

=P(Captain Hits) X P(Pirate Hits)

[tex]=\dfrac{1}{2} X \dfrac{1}{6}\\\\=\dfrac{1}{12}[/tex]

Answer:

589

Step-by-step explanation:

l x w

19x11

5x31

5x45

589

Answer:

589 is the answer

Answer:

24 beads

Step-by-step explanation:

beads in 4 sheet=32

beads in 1 sheet=32/4=8

beads in 3 sheet=8*3=24

Answer:

Assuming that you can make the same number of beads with 1 sheet of paper, Tameka can make 24 beads with 3 sheets of paper.

Answer:

1/4845

Step-by-step explanation:

The probability of selecting a defective cog first is

1/5

The second cog is

3/19

The third cog is

1/9

And the fourth cog is

1/17

Multiplying these together we get

1/5 * 3/19* 1/9 * 1/17  = 1/4845

The probability of selecting 4 cogs from the 20 produced where all are defective is approximately 0.000206.

Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.

The probability of selecting 4 defective cogs from the 20 produced can be calculated as follows:

P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20)

The number of ways to select 4 defective cogs can be found by selecting 4 defective cogs out of the 4 defective cogs produced, and 0 non-defective cogs out of the remaining 20-4=16 non-defective cogs. This can be expressed mathematically as:

Number of ways to select 4 defective cogs = (4 choose 4) * (16 choose 0) = 1

The total number of ways to select 4 cogs from 20 can be found by selecting 4 cogs out of the 20 produced. This can be expressed mathematically as:

Total number of ways to select 4 cogs from 20 = (20 choose 4) = 4845

Therefore, the probability of selecting 4 defective cogs from the 20 produced is:

P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20) = 1/4845

Thus, the probability of selecting defective cogs is approximately 0.000206.

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Answer:

[tex]20.25 \: m^2[/tex]

Step-by-step explanation:

Use the formula for the area of a square.

[tex]A=s^2[/tex]

Where [tex]s=4.5[/tex]

[tex]s^2\\(4.5)^2\\20.25[/tex]

The area of the square is 20.25 square meters as per the concept of the square.

To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.

First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.

Next, we square the side length:

[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].

To simplify the fraction, we can divide the numerator by the denominator:

81 ÷ 4 = 20 remainders 1.

Therefore, the area of the square is 20 1/4 square meters.

However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:

20 1/4

= 20 + 1/4

= 20 + 1/4

= 20 + 0.25

= 20.25.

Therefore, the area of the square is 20.25 square meters.

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Answer:

26.68% probability that exactly three will end up being replaced under warranty

Step-by-step explanation:

For each telephone under warranty, there are only two possible outcomes. Either they need to be replaced, or they do not need to be replaced. Each telephone is independent of other telephones. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

30% must be replaced with new units

This means that [tex]p = 0.3[/tex]

If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty

This is [tex]P(X = 3)[/tex] when [tex]n = 10[/tex]. So

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

[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]

26.68% probability that exactly three will end up being replaced under warranty

The Answer is 1/4

Step-by-step explanation:

The required constant of variation for given data is k = 1/4

The correct option is (a)

In a direct variation, the product of two variables; in an inverse variation, the ratio of two variables, is called constant of variation

Formula:

k = [tex]\frac{n}{fg}[/tex]

Here we have given that n = 4, f = 2 and g = 8

Substitute the given values into above formula

k = [tex]\frac{4}{2(8)} =\frac{1}{4}[/tex]

The required constant of variation is 1/4

Therefore the correct option is (a)

This is the conclusion to the answer.

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Answer:

The z score when x =72 is:

[tex] z = \frac{72-58}{11}= 1.273[/tex]

The mean is 58

This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.

Step-by-step explanation:

Assuming the following info for the question: Suppose John's words per minute on a typing test are normally distributed. Let X -the number of words per minute on a typing test. Then X N(58, 11) If necessary, round to three decimal places.

Provide your answer below rds per minute in a typing test on Sunday. The z score when x =72 is

For this case we know that the variable of interest is modelled with the normal distribution:

[tex]X \sim N (\mu= 58, \sigma=11)[/tex]

And the z score is given by:

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

And replacing we got:

[tex] z = \frac{72-58}{11}= 1.273[/tex]

The mean is 58

This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.

Answer:

0.004% probability the student will pass

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 50, p = \frac{1}{4} = 0.25[/tex]

So

[tex]\mu = E(X) = np = 50*0.25 = 12.5[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.25*0.75} = 3.06[/tex]

If a student guesses on every question, what is the probability the student will pass

Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5. So

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

[tex]Z = \frac{24.5 - 12.5}{3.06}[/tex]

[tex]Z = 3.92[/tex]

[tex]Z = 3.92[/tex] has a pvalue of 0.99996

1 - 0.99996 = 0.00004

0.004% probability the student will pass

Answer:

160 yards

Step-by-step explanation:

P=2l+2w

P=2(3w-8)+2(w)

432=2(3w-8)+2(w)

432=6w-16+2w

432=8w-16

432+16=8w

448=8w

w=448/8

w=56yards

l=3(56)-8

l=168-8=160yards

Answer:

Graph 2

Step-by-step explanation:

You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!

The question is incomplete. Here is the complete qeustion.

In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15

(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.

(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?

Answer: (a) 0.089 ≤ μ ≤ 0.171

(b) No

Step-by-step explanation:

(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample

X = [tex]\frac{0.1+0.13+0.16+0.15+0.14+0.08+0.15}{7}[/tex]

X = 0.13

s = [tex]\sqrt{\frac{(0.1-0.13)^{2} + (0.13 - 0.13)^{2} + ... + (0.15 - 0.13)^{2}}{7-1} }[/tex]

s = 0.029

The degrees of freedom is

N - 1 = 7 - 1 = 6

And since the confidence is of 99%:

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

The t-test statistics for [tex]t_{6,0.005}[/tex] is 3.707

(Value found in the t-distribution table)

Now, calculate Error:

E = [tex]t_{6,0.005}[/tex] . [tex]\frac{s}{\sqrt{N} }[/tex]

E = 3.707. [tex]\frac{0.029}{\sqrt{7} }[/tex]

E = 0.041

The interval will be:  

0.13 - 0.041 ≤ μ ≤ 0.13+0.041

0.089 ≤ μ ≤ 0.171

(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.

Answer:

[tex]y=\frac{3}{2} x-4[/tex]

Step-by-step explanation:

The graph I provided shows it passes thru (4,2) and that it is parallel

Answer:

y = 3/2x -4

Step-by-step explanation:

3x - 2y = - 6

First find the slope by putting it in slope intercept form

Subtract 3x from each side

-2y = -3x-6

Divide by -2

y = -3x/-2  -6/-2

y = 3/2x +3

The slope is 3/2

Parallel lines have the same slope

We have the slope 3/2 and a point (4,2)

y = mx+b where m is the slope and b is the y intercept

y =3/2x+b

Substitute the point into the equation

2 = 3/2(4) +b

2 = 6 +b

Subtract 6

2-6 = 6-6+b

-4 =b

y = 3/2x -4

Answer:

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

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Step-by-step explanation:

We have the following equation given:

[tex] 2x^2 +3x -5=0[/tex]

And if we use the quadratic formula given by:

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

Where a = 2 , b= 3, c= -5, replacing we have this:

[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]

And simplifying we got:

[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]

And the two solutions are:

[tex] x_1 = \frac{-3+7}{4}= 1[/tex]

[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]

And the correct options are:

B and C

Answer:

B and C

Step-by-step explanation:

Answer:

Option (A).

Step-by-step explanation:

We choose a point from table of f(x), that is (-2, -31)

1). If this point is reflected across x-axis, rule to be followed,

(x, y) → (x, -y)

That means y coordinate of the point gets changed with opposite notation.

If (-2, -31) is reflected over the x-axis,

(-2, -31) → (-2, 31) ----------(1)

2). When a point is reflected over the y-axis,

Rule to be followed,

(x, y) → (-x, y)

(-2, -31) → (2, -31) ----------(2)

3). When a point is reflected over the line y = x

Rule to be followed,

(x, y) → (y, x)

(-2, -31) → (-31, -2) -----------(3)

By comparing f(x) and g(x) we find the relation between the functions as,

f(-2, -31) → g(2, -31)

Rule between the functions f and g matches with the rule number (2).

Therefore, function 'f' has been reflected across y axis to get the function 'g'.

Option (A) will be the answer.

Answer: Option A.

Step-by-step explanation:

Here we have two equations for the circumference, one for each circle:

C = 2*pi*r

C' = 2*pi*r'

now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:

C/C' = 2*pi*r/(2*pi*r') = r/r'

So we have the relation:

C/C' = r/r'

And this is obtained for the division property of equality.

IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.

Then the correct option is A.

Answer:

  $2756 million

Step-by-step explanation:

  2.756×10⁹ = 2756×10⁶

Sales in 2014 were $2756 million.

_____

Comment on the question

In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.

Answer:

-3 ( x+2i) (x-2i)

Step-by-step explanation:

-3x^2-12

Factor out a -3

-3(x^2 +4)

Rewrite

-3 ( x^2 - -4)

-3 ( x^2 - (-2i)^2)  This is the difference of squares ( a^2 -b^2 ) = (a-b)(a+b)

-3 ( x- -2i) (x+2i)

-3( x+2i) (x-2i)

Answer:

y = x + 5

Step-by-step explanation:

Perpendicular slope is opposite inverse so the perpendicular slope to -1x would be 1x

Then find b in y=mx+b

Plug in all the number

y=-9

x=-4

m=1

So, -4=1(-9)+b

1×-9=-9

+9 to both sides

5=b

Therefore,

y=x+5

Answer:

A=12 feet²

Step-by-step explanation:

1/2*base*height=area

(1/2)*4*6=12

Answer: idk

Step-by-step explanation:

idk

Answer:

$4,000,000

Step-by-step explanation:

20,000*200=4,000,000

Answer:

The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.

CV smokers: 0.387

CV non-smokers: 0.234

Step-by-step explanation:

We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).

Then, first we calculate the mean and standard deviation for the smokers data:

Mean: 43.7

Standard deviation: 286.5

[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]

The mean and standard deviation for the non-smokers is:

Mean: 30.3

Standard deviation: 50.9

[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]

Now, we can calculate the coefficient of variation:

CV smokers:

[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]

CV non-smokers:

[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]

Answer:

3

I used to be an olimpic runner and I ran the 400 all the time and I did cross country

Answer:

x =30.4 seconds

Step-by-step explanation:

We can use ratios to solve

20 drops           8 drops

---------------  = ----------------

76 seconds      x seconds

Using cross products

20x = 8*76

20x =608

Divide each side by 20

20x/20 = 608/20

x =30.4 seconds

Answer:

30.4 secs = 30secs

Step-by-step explanation:

20 drops fall in 76s

Hence 1 drop is 76/20

Therefore 8 drops would be ;

76/20 × 8 = 30.4 secs

Answer:

61%

Step-by-step explanation:

16/26 x 100 = 61.538461

You have to round it up if the question tells you to round it up.

hope it helps! :)

Answer:

62%

Step-by-step explanation:

42 x 62% = 26.04

I am sorry if you get this wrong. I really hope this helps.

Answer:

The correct answer would be F. 7.8

Step-by-step explanation:

the line is more or less a reflection of segment ON

so they are more or less the same.

I hope this helped you!