Based on all student records at Camford University, students spend an average of 5.30 hours per week playing organized sports. The population’s standard deviation is 3.20 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates. Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)

Answer:

25(4 + 3)

Step-by-step explanation:

100 = 2^2 + 5^2

75 = 3 * 5^2

GCF = 5^2 = 25

100 + 75 =

= 25 * 4 + 25 * 3

= 25(4 + 3)

Answer:

There are 80 10th graders in the school

Step-by-step explanation:

Let the number of 10th graders be x

There are 25% fewer 11th graders

That mean x - 25% of x

x -0.25x = 0.75x

There are 20% more 11th graders than 12th graders

So if number of 12th graders = y, then

0.75x = y + 20/100 * y = y + 0.2y = 1.2y

Since ;

0.75x = 1.2y

then y = 0.75x/1.2 = 0.625x

So let’s add all to give 190

x + 0.75x + 0.625x = 190

2.375x = 190

x = 190/2.375

x = 80

Answer:

common ratio = 2

Step-by-step explanation:

T6 = ar^5

T3 = ar²

T6 = 8 x T³

ar^5 = 8 x ar²

ar^5/ar² = 8

r³ = 8

r = ³√8

r = 2

Answer:

35%

Step-by-step explanation:

[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]

[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]

Answer:

35%

Step-by-step explanation:

I REALLY HOPE I HELPED

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

 ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                PEACE!

Answer:

13 units

Step-by-step explanation:

Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.

Plug in the values and solve for r:

(5 - 0)² + (12 - 0)² = r²

25 + 144 = r²

169 = r²

13 = r

Answer: 56.9 years to 63.1 years.

Step-by-step explanation:

Confidence interval for population mean (when population standard deviation is unknown):

[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]

, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].

Given: n= 24

degree of freedom = n- 1= 23

[tex]\overline{x}[/tex]= 60 years

s= 7.4 years

[tex]\alpha=0.05[/tex]

Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:

[tex]t_{\alpha/2}=2.0687[/tex]

A 95% confidence interval on the true mean age:

[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]

Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

Answer:

  -11/13

Step-by-step explanation:

The equation of the line through these points can be written using the 2-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (4 -(-3))/(-9-4)/(x -4) -3

  y = (-7/13)x +28/13 -3

For x=0, the value of y is ...

  y = 28/13 -39/13 = -11/13

The output for an input of 0 is -11/13.

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Answer:

B

Step-by-step explanation:

Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.

The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.

Answer:

Left angle = 60°

Top angle = 120°

Right angle = 60°

Step-by-step explanation:

Use what you know about angle relationships to set up equations you can solve for each variable.

The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.

You have two variables, so you need at least two equations (I made three but only used two).

The work is in my attachment, comment of you have questions.

let [tex] \gcd(a,b)= G[/tex] , $a\ge b$

$\therefore a=G\cdot m$ and $b=G\cdot n$

$a-b=Gm-Gn=G(m-n)$

Now, $\gcd(a-b,b)$ clearly is, $G$

Answer:

C≈31.42

Step-by-step explanation:

C=2πr

C=2xπx5

C≈31.42

pls mark as brainliest

Answer:

D. The z scores are numbers without units of measurement.

Step-by-step explanation:

Z-scores are without units, or are pure numbers.

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome of event/Total outcome.

If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.

If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;

Probability of selecting 2 comedies  = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).

Probability of selecting 1 action movie = 6/15 = 2/5

Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125

Note that the rented movies will have to be returned hence reason for the replacement.

Answer:

The answer and explanation are below

Step-by-step explanation:

i followed the data that was given in the question.

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

a.)  please refer to the attachment for the scatter diagram. Y was plotted against X.

b. The equation is given as:

Y = b₁ + b₀X

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²

b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)

= 1375-1309.5/275-225

= 65.5/50

= 1.31

b₀ = 87.3/5 - 1.31(15/5)

= 87.3/5 - 1.31x3

= 13.53

the regression line is

Y = 13.53 + 1.31X

please refer to the attachment for the diagram for the regression line.

c. we are required to find r.

r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

inserting these values:

r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29

= 65.5/106.69

= 0.6139

Coefficient of determination = r²

r = 0.6139

r² = 0.3769 = 37.69%

Therefore 37.69% variation in y is explained by variation in x and the least square model.

Answer:

4i.

Step-by-step explanation:

To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA

F(x,y) = hxy,x - yi

div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i

So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA

= ∫∫(hy - i).dxdy

= ∫∫hydxdy - ∫∫idxdy

Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then

∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy

= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx

= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx

= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx

= 0 - i∫₋₁¹2dx

= - 2i[x]₋₁¹

= 2i[1 - (-1)]

= 2i[1 + 1]

= 2i(2)

= 4i  

Answer: C. 400  in^2

Step-by-step explanation:

First find the surface area or the area of the base which is in the shape of  a square and has a side length of 10 in. So square 10 to find the area.

Area of base:  10 * 10 = 100

Next find the area of one of the triangles.

As we could see the triangle has a slant height of 15 in and a base of 10. To find the area of a triangle we multiply the base times the height and multiply it by half.

Area of one triangle.  15 * 10 = 150 * 1/2 = 75  

Since one side of the triangle has a surface area of 75 inches we will multiply it by 4 since there are four triangles to find the total surface area of the four faces.

75 * 4 = 300  

We now know that the the 4 triangles surface area dd up to 300 so we will add it to the area of the base which is 100 to find the whole surface area of the figure.

300 + 100 = 400

Answer:

1/2

Step-by-step explanation:

The possible outcomes are

1,2,3,4,5,6,7,8,9,10

Factors of 6 are 1,2,3,6

or a 4

1,2,3,4,6 are the outcomes we want

There are 5 "good" outcomes

P( 4 or a factor of 6) = "good" outcomes/ total

                                  = 5/10

                                   =1/2

Answer:

[tex]\boxed{\frac{1}{2} }[/tex]

Step-by-step explanation:

There are total 10 outcomes.

[tex]1,2,3,4,5,6,7,8,9,10[/tex]

The probability of selecting 4 is 1 outcome out of total 10 outcomes.

Factors of 6 are [tex]1,2,3,6[/tex].

These are 4 outcomes out of total 10 outcomes.

The probability of selecting 4 or a factor of 6 is:

[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]

Answer:

D. The plane needs to be about 27 meters higher to clear the tower.

Step-by-step explanation:

In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).

The hypothenus is the distance travelled by the plane which is 83 meters (h)

The height of the tower is 98 Meters

We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.

According to Pythagorean theorem

(x^2) + (y^2) = h^2

y = √ (h^2) - (x^2)

y = √ (83^2) - (42^2)

y= √(6889 - 1764)

y= 71.59 Meters

The height from the plane's position to the top of the tower will be

Height difference = 98 - 71.59 = 26.41 Meters

So the plane should go about 27 Meters higher to clear the tower

Answer:

[tex]Probability = \frac{3}{7}[/tex]

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

[tex]Total = n(Electrician) + n(Mechanic)[/tex]

[tex]Total = 6 + 8[/tex]

[tex]Total = 14[/tex]

Next, is to determine the required probability using the following formula;

[tex]Probability = \frac{n(Electrician)}{Total}[/tex]

[tex]Probability = \frac{6}{14}[/tex]

Divide numerator and denominator by 2

[tex]Probability = \frac{3}{7}[/tex]

Hence, the probability of selecting an electrician is 3/7

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:

The interval for 95% will be given as,

Pr(X) = μ ± 2σ

Pr(X) = 200 ± 2(40)

Pr(X) = 200 ± 80

Pr(X) = (200 - 80, 200 + 80)

Pr(X) = (120, 280)

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ5

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

Answer: The missing number is 5.

Step-by-step explanation:

In the table we can only have numbers between 1 and 9,

The pattern that i see is:

We have sets of 3 numbers.

"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"

Goin from right to left we have:

9 - 6 = 3

6 - 2 = 4

4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)

4 - 4 = 0 (we can not use zero, so we use the next number, 9)

3 - 3 = 0 (same as above)

? - 1 = 4

? = 4 + 1 =  5

The missing number is 5.

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

Answer:

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Step-by-step explanation:

We formulate our null and alternative hypotheses as

H0 u≤ 6 ug     Ha : u > 6 ug

The significance level ∝ = 0.05

The test statistic used is

t = X` - u / s/ √n

which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.

The critical region t > t (0.05,11) = 1.796

We compute the t value from the data

Xi               Xi²

8.92         79.5664

6.99          48.8601

5.54          30.6916

5.73           32.8329

6.38           40.7044

5.51            30.3601

6.45           41.6025

7.50           56.25

8.48           71.9104

5.56          30.9136

6.90          47.61

6.46          41.7316          

80.42         553.0336      

Now x` = ∑x/ n = 80.42/12 = 6.70

S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)

= 1/11 (553.034-538.948) = 1.2805

s= 1.1316

Putting the values in the test statistics

t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12

= 2.1698

The critical region t > t (0.05,11) = 1.796

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Answer:

Step-by-step explanation:

Hello, please consider the following.

Question 1.

[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]

Question2.

[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]

So, it gives (by adding the two equations) 2x = 3

[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]

Step-by-step explanation:

Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:

1) [tex]t = 2-x[/tex] Given

2) [tex]y = 5\cdot x +11[/tex] Given

3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties

4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property

5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property

6) [tex]y = -5\cdot (-x)+11[/tex]  [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]

7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property

8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse

9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties

10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property

11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]

12) [tex]y = (-5)\cdot t +21[/tex] By 1)

13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result

14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition

15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition

16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property

17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property

18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].

Answer:

The  number is  [tex]N =1147[/tex] students

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 281[/tex]

     The standard deviation is  [tex]\sigma = 34.4[/tex]

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      [tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]

Generally  

             [tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]

So  

         [tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]

       [tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]

From the z table  the value of  [tex]P( z_2 < 0.698) = 0.75741[/tex]

                                         and  [tex]P(z_1 < -0.9012) = 0.18374[/tex]

     [tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]

      [tex]P(250 < X < 305 ) = 0.57[/tex]

The  percentage is  [tex]P(250 < X < 305 ) = 57\%[/tex]

The  number of students that will get this score is

           [tex]N = 2000 * 0.57[/tex]

           [tex]N =1147[/tex]