A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.

Answer:

  point B

Step-by-step explanation:

The names of the lines, AB and BE, tell you that point B is on both lines.

Point B will be the point of intersection.

Answer:

point b

Step-by-step explanation:

i took the test and got it right

Answer:

8

Step-by-step explanation:

Hello,

[tex]x=3y^2<=>y=\sqrt{\dfrac{x}{3}} \ \ for \ x\geq 0[/tex]

And for y = 2, x = 3 * 2 * 2 = 12 so first, let's compute

[tex]\displaystyle \int\limits^{12}_0 {\sqrt{\dfrac{x}{3}}} \, dx =\dfrac{1}{\sqrt{3}} \int\limits^{12}_0 {\sqrt{x}} \, dx\\\\=\dfrac{1}{\sqrt{3}} \left[ \dfrac{2}{3}x^{3/2}\right]_0^{12}\\\\=\dfrac{1}{\sqrt{3}} *\dfrac{2}{3}*12*\sqrt{12}\\\\=\dfrac{2*12*2*\sqrt{3}}{3*\sqrt{3}}\\\\=2*4*2=16[/tex]

The area which is asked is 12*2 - 16 = 24 - 16 = 8

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Using integrals, it is found that the area of the region enclosed by the curves in the interval is of 27 units squared.

In this problem:

Then, the integral for the area is:

[tex]A = \int_{0}^{2} 3y^2 dy[/tex]

[tex]A = y^3|_{y = 0}^{y = 3}[/tex]

[tex]A = 3^3 - 0^3[/tex]

[tex]A = 27[/tex]

The area of the region enclosed by the curves in the interval is of 27 units squared.

You can learn more about the use of integrals to calculate an area at https://brainly.com/question/15127807

Answer:

(-2, 2)

Step-by-step explanation:

Given:

Difference of coordinates:

The ratio of AB to AC is 2:1. So:

Then coordinates of point B should be 2/3 from the point A:

So point B has coordinates of (-2, 2)

Answer:

Graph 1

Step-by-step explanation:

The only graph that could be possible would be graph 1.

As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.

heya friend

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

and 10 is not zero

so it is sacrificed

hope this helps u

Answer:

0.2

0.2**10/10

=2/10

in 2/10 2 and 10 are integers

10 is not 0

Step-by-step explanation:

Answer:

5:8

Step-by-step explanation:

If I understand your question correctly, we have 1500/2400=15/24=5/8, so we have Lynn:Bo is 5:8, however, in the future please be more clear.

What is "estimates roof jon"? And, instead of saying "ratio to lynn to bo" say "What is the ratio of the estimates?" or whatever you're asking. If this answer is wrong, you only have yourself to blame.

Answer: x=8/3 or x= 2.6666....

Step-by-step explanation:

[tex]2+3x-10=0[/tex]

[tex]2-10=-8[/tex]

[tex]3x-8=0[/tex]

add 8 on both sides

[tex]3x-8+8=0+8[/tex]

[tex]3x=8[/tex]

divide 3 on both sides

[tex]x=\frac{8}{3}[/tex]

Answer:

8/3

Step-by-step explanation:

2 +3x + 10 = 0

2-10 +3x = 0

-8 + 3x = 0

3x = 8

x = 8/3

Answer:

18km

Step-by-step explanation:

1cm:4.5km/4cm then get the answer as 18km

1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.

Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]

Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.

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[tex]_nC_k=\dfrac{n!}{k!(n-k)!}\\\\\\_{34}C_{34}=\dfrac{34!}{34!0!}=1[/tex]

In general, [tex]_nC_n=1[/tex]

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find c using Law of Sines

[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]

[tex]c = sin13(\frac{6}{sin58})[/tex]

c = 1.59154

Step 2: Find a using Law of Sines

[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]

[tex]a = sin109(\frac{6}{sin58} )[/tex]

a = 6.68961

Answer:

Standard deviation= 4.46

B) 4.89 is the nearest answer

Step-by-step explanation:

Standard deviation √variance

Variance= (summation (x-mean)²)/n

Mean= summation of numbers/total

Mean =( 12+13+ 7+5+15 18)/6

Mean= 70/6

Mean= 11.67

Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6

Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6

Variance= 119.3334/6

Variance= 19.8889

Standard deviation= √variance

Standard deviation= √19.8889

Standard deviation= 4.46

Answer:

12/27

Step-by-step explanation:

Step 1

We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.

Where

R = Red

B = Blue

Y = Yellow

RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR

We have 27 Total outcomes for this 6 faced die

Step 2

The event that exactly one of the colors that appears face up is red.

RBY, RYB, YBR, YRB, RBB, RYY, BBR,

BRB, BRY, YRY, BYR, YYR

Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12

The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes

= 12/27

Answer:

solution below

Step-by-step explanation:

The question says 6 working mother's were selected so n = 6 not 0.6

We are expected to find

P(X = 0,1,2,3,4,4,6)

1. When x = 0

6C0*(0.34)⁰*(0.66)⁶

= 1 *1* 0.827

= 0.0827

2. When X = 1

6C1*(0.34)¹*(0.66)⁵

= 6 x 0.34 x 0.252

= 0.2555

3. When X = 2

6C2*(0.34)²*(0.66)⁴

= 15 x 0.1156 x 0.1897

= 0.3289

4. When x = 3

6C3*(0.34)³*(0.66)³

20 x 0.039304 x 0.2875

= 0.2599

5. When X = 4

6C4*(0.34)⁴*(0.66)²

= 15 x 0.01336 x 0.4356

= 0.8729

6. When x = 5

6C5*(0.34)⁵*(0.66)¹

= 6 x 0.0045 x 0.66

= 0.01782

7. When x = 6

6C6*(0.34)⁶*(0.66)⁰

1 x 0.0015 x 1

= 0.0015

THIS IS THE COMPLETE QUESTION BELOW;

In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

A. 0.10

B.0.50

C. 0.66

D. 0.06

Answer:

OPTION D is correct

d)0.06

the probability that a randomly selected team from Littletown goes to the city and state playoffs is [tex]0.06[/tex]

Step-by-step explanation:

The probability that a baseball team goes to city playoffs is 0.30.

P(baseball team goes to city playoffs)=0.30

The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.20.

P(team goes to state playoffs given that the team goes to the city playoffs)=0.20

From our knowledge of set, we know that

P(A | B)= P(A ∩ C)/P(C)

where A= city playoffs

B= state playoffs

P(State play off | city play off)=0.20

P(State play off ∩ city play off)/P(city play off,)=0.20

P(State play off ∩ city play off)/0.30 =0.20

P(State play off ∩ city play off)= 0.30 × 0.20

= 0.06

Hence,the probability that a randomly selected team from Littletown goes to the city and state playoffs is 0.06

Answer:

168

Step-by-step explanation:

first, split both 840 and 24 into there primes.

840=2×2×2×3×5×7

24=2×2×2×3

therefore any multiples of 24 must have those factor.

so, factors of 840 that are multiples of 24 are

2×2×2×3=24

2×2×2×3×5=120

2×2×2×3×7=168

2×2×2×3×5×7=840

there the answer is 168

Answer:

A

Step-by-step explanation:

f(x)→g(x)

(0, 0) → (3, -4)

Therefore it increases it x-axis from 0 to 3

And decreases in y-axis from 0 to -4

Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

Step-by-step explanation:

Using Sine Rule

[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]

[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]

[tex]a = 4.6[/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]

[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]

[tex]b = 7.4[/tex]

Answer:

a

  The point estimate of the population mean is  [tex]\= x = 56[/tex]

b

  The 80% confidence level is  [tex]50.57 < \mu < 61.43[/tex]

c

  There is  80% confidence that the true population mean lies within the confidence interval.

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  18

   The  standard deviation is  [tex]\sigma = 18 \ L[/tex]

   The  sample mean is  [tex]\= x = 56[/tex]

Generally the point estimate of the population mean is equivalent to the sample mean whose value is  [tex]\= x = 56[/tex]

Given that the confidence interval is 80% then the level of significance is mathematically represented as

      [tex]\alpha = 100 - 80[/tex]

      [tex]\alpha = 20 \%[/tex]

      [tex]\alpha = 0.20[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

 The  value is   [tex]Z_{\frac{ \alpha }{2} } = 1.28[/tex]

 Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>       [tex]E = 1.28 * \frac{18 }{\sqrt{18} }[/tex]

=>       [tex]E = 5.43[/tex]

     Generally the 80% confidence interval is mathematically represented as

    [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]56 - 5.43 < \mu < 56 + 5.43[/tex]

=>   [tex]50.57 < \mu < 61.43[/tex]

The  interpretation is that there is  80% confidence that the true population mean lies within the limit

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

Answer:

3 inches

Step-by-step explanation:

The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.

Answer: Jake is 9 and his dad is 33.

Step-by-step explanation: 9x3=27+6=33 9+33=42

Answer:

Jake is 9 and Jake's dad is 33

Step-by-step explanation:

To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake

J+D=42

3J+6=D

Solve by substitution

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

Answer:

you simply have to move one left. It thats decimal you can simply remove one zero

Answer:

You just have to move to the left once

Step-by-step explanation:

Answer: There is only 1 girl.

Step-by-step explanation:

As you can see the probability of choosing a girl is 4/11  out of the whole people which is 7 boys and 4 girls. And the same way the probability of choosing a boy  is 7/11 which is almost doubled the amount of girls. So to think about it, there will be more boys than girls if there is a random selection because the boys chances of getting picked is high.

Answer:

The area shaded is 95%

Step-by-step explanation:

The total area under the curve is 100 percent

1 standard deviation away from the mean is 68 percent

2 standard deviations away is 95 percent

The area shaded is 95%

The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.

Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.

This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

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Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Answer:

Graph (A)

Step-by-step explanation:

Given question is incomplete; find the question in the attachment.

Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]

Parent function of the given function is,

f(x) = [tex](0.5)^{x}[/tex]

When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,

h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]

When h(x) is shifted 4 units down, translated function will be,

g(x) = h(x) - 4

g(x) = [tex](0.5)^{x+3}-4[/tex]

g(x) has a y-intercept as (-4).

From the given graphs, Graph A shows the y-intercept as (-4).

Therefore, Graph A will be the answer.

Answer:

The Answer A is correct

Step-by-step explanation:

I took the edg2020 test

The perimeter is 21.66

The figure is something like the one that is in the image below:

We want to find the total perimeter of the polygon ABECD

This will be:

AB + BE + EC + CD + DA

Remember that for a triangle rectangle of catheti A and B, the area is given by:

A*B/2

We know that the sides of the triangle rectangle are:

BE, EC, BC.

Because BE = EC, these can not be the hypotenuse of the triangle, then the catheti are BE and EC

Knowing that the area of the triangle rectangle is 8, we can write:

EC*BE/2 = 8

and EC = BE = x

x^2/2 = 8

x^2 = 8*2 = 16

x = √16 = 4

Then the two catheti of the triangle rectangle are 4 units long.

EC = 4

BE = 4

and we know that:

AB = BE = EC

then:

AB = 4

and because this is a rectangle, we also have:

DC = AB = 4

now we want to find the last side of the figure, AD,

Which we already know is equal to the hypotenuse of the triangle.

Remember the Pythagorean's theorem, which says that the sum of the squares of the catheti is equal to the square of the hypotenuse.

Both catethus are equal to 4, then we have:

H^2 = 4^2 + 4^2 = 32

H = √32 = 5.66

then:

DA = 5.66

Now we have:

AB = BE = EC = DC = 4

DA = 5.66

Then the perimeter is:

AB + BE + EC + CD + DA

4 +  4 + 4 + 4+ 5.66 = 21.66

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