A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the​ 90% confidence interval for the mean​ score, muμ​, of all students taking the​ test?

Answer:

c

Step-by-step explanation:

plato

Answer:

See bolded below.

Step-by-step explanation:

Take a look at the attachment below. It represents circle x and y, with respect to each of their radii. In each of the options we are given, we would have to translate and dilate the circles, by a fixed scale factor -

Now the first thing one would do is translate the circles so that they share a common center point, or in other words the center of one circle rests on the edge of the other circle. That way when dilating circle y, it may fit into circle x as it expands.

The second point is how much this smaller circle ( circle y ) has to expand. The radius of circle y being 2, has to increase by 3 times the value to equal the radius of circle x, and hence has to dilate by a scale factor of 3 as to match circle x,

Solution = " Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3 " / Option D

Complete Question is;

Write a polar equation of a conic with the focus at the origin and the given data. hyperbola, eccentricity 3.5, directrix y =2

Answer:

r = 14/(2 + 7(sinθ))

Step-by-step explanation:

We are given;

Eccentricity;e = 3.5

Directrix; y = 2

This means that d = 2

We are told that the focus is at the origin, so since the directrix is at y = 2,then the part of the hyperbola that is closest to this focus will open downwards and the equation is given by;

r = ed/(1 + e•sinθ)

Plugging in the relevant values, we have;

r = (3.5 × 2)/(1 + 3.5(sinθ))

r = 7/(1 + 3.5(sinθ))

To make every figure a whole number, let's multiply numerator and denominator by 2 to give;

r = 14/(2 + 7(sinθ))

Answer: the last one

Step-by-step explanation: because 7 times 24 equals 168 and x would be 21 so 21 times 8 equals 168.

Answer: The answer is D

Step-by-step explanation:

Answer:

9

i got it right on my test

The equivalent expressions to 243 Superscript two-fifths will be 9.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple, we simplify it.

Simplification usually involves making the expression simple and easy to use later,

The given expression is;

[tex]243^{2/5}[/tex]

We know that 2/3 = 0.4

So, the equivalent expressions to the given function;

[tex]243^{0.4}\\\\= 9[/tex]

Thus, The equivalent expressions to 243 Superscript two-fifths will be 9.

Learn more about expression here;

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Answer:

The answer is C (j' 1,4). It is not B J'(4, 1) because the new coordinate is moving 90 degrees clockwise not 180 degrees.

Step-by-step explanation:

J' will have coordinates (1, 4) after  90° clockwise rotation

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Rectangle JKLM is rotated 90° clockwise about the origin.

On a coordinate plane, rectangle J K L M has points (-4, 1), (-1, 1), (- 1, - 1), (- 4, - 1).

After rotating the rectangle 90° clockwise about the origin, the point J(-4, 1) will be transformed to a new point J' with coordinates (y, -x).

Thus, J' will have coordinates (1, 4).

Therefore,  J' will have coordinates (1, 4) after  90° clockwise rotation

To learn more on Graph click:

https://brainly.com/question/17267403

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▹ Answer

r = 4

▹ Step-by-Step Explanation

15r - 6r = 36

Collect like terms

9r = 36

Divide

r = 4

Final Answer

r = 4

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer: The answer would be 4, which is B, hopefully this helps.

Answer:

2x-y=4

Step-by-step explanation:

Standard form of a line: Ax+by=c

Use slope intercept form: y=mx+b

slope= 2

y=2x-4

Add 4 to both sides.

y+4=2x

subtract y from both sides.

4=2x-y

Rotate the equation

2x-y=4

Answer:

2x-y=4

Step-by-step explanation:

y=2x-4 is the slope intercept.

y-2x=-4

-2x+y=-4

2x-y=4

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▹ Answer

Exponential

▹ Step-by-Step Explanation

Every time 1 is added to x, y multiples by 2.

0 + 1 = 1

1 + 1 = 2

2 + 1 = 3

3 + 1 = 4

-2 * 2 = -4

-4 * 2 = -8

-8 * 2 = -16

-16 * 2 = -32

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

Well I took it"s Reflect the intermediate image.  and Multiply the vertices of polygon ABCD by One-half.

Step-by-step explanation:

Answer:

2 and 5 or B and E

Step-by-step explanation:

i did it on edge! ; )

Answer:

a. Country Z's GDP will double in 23 years' time, given the experts prediction of 5% growth for 3 and 3% thereafter.

b. Z's GDP 's growth rate would be 39%.

This growth rate is calculated by determining Z's GDP from the end of 2025 as 292,000.  So, (292,000 - 210,000)/210,000 x 100 = 39% from the 2019 base year.

Step-by-step explanation:

a) 2019 Country Z's GDP = 210,000

2019 Growth rate = 5%

Future growth rate:

2019 - 2022 = 5%

2022- 2025 = 3%

2025 - so on = 1%

Let Country Z's GDP in 2019 = G₀ = 210,000

n = number of years from 2019

g = growth rate = 5%

(1 + g)ⁿ = increase in GDP as a result of the growth rate and number of years

Gⁿ = GDP in n years

Therefore, Gⁿ = G₀(1 + g)ⁿ

b) With GDP growth of 5% from 2019 to 2022, the GDP will be

= 210,000 (1 + 5%)³

= 210,000 x 1.158

= 243,000 approx.

c) From 2022 to 2025 at 3%, the GDP will be

= 243,000 (1 + 3%)∧20

= 243,000 x 1.817

= 441,531

d) Z's GDP from 2025 with 1% growth and so on, will become double at:

Gⁿ = 265,600(1 + 1%)∧48

= 265,600 x 1.61

= 428,000

48 + 6 = 54 years.

Answer:

1st Graph

Step-by-step explanation:

Step 1: Find the inverse

y = 2x - 2

x = 2y - 2

x + 2 = 2y

y = (x + 2)/2

Step 2: Graph the inverse

Simply use a graphing calculator and we should see our answer is the top left graph.

Answer:

Net sales is $ 504285.71

Step-by-step explanation:

We have the following:

Let net sales be x.

Net sales - Cost of goods sold = Gross profit

We replace and we are left with:

x - $ 353000 = x * 30%

x - $ 353000 = 0.30 * x

x - 0.30 * x = $ 353000

0.7 * x = $ 353000

x = $ 353000 / 0.7

x = $ 504285.71

Therefore, net sales is $ 504285.71

Answer:

[tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex]

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

[tex]y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\[/tex]

[tex]\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}[/tex]

Therefore;

[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }[/tex]

Since x = cos y from the above substitute;

[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }[/tex]

Hence, [tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex] gives the required proof

Answer:

the probability that 7 out 10 Internet users will order something online is 0.78 or 78%

Step-by-step explanation:

Given that:

Internet users who order something online = 85%

To find:

Probability that 7 out of 10 Internet users will order something online ?

Solution:

This problem is of binomial distribution of probability.

where, p = 0.85

q = 1-p = 0.15

r = 7 and

n = 10

Formula is given as:

[tex]P(x = r) = _nC_r q^{n-r}p^r[/tex]

Putting all the values:

[tex]P(x = 7) = _{10}C_7 0.15^{10-7}\times 0.85^7\\P(x = 7) = _{10}C_3 0.15^{3}\times 0.85^7\\P(x = 7) = 10\times 9 \times 8 \times 0.15^{3}\times0.85^7\\P(x = 7) = 720 \times .0034 \times0.32\\P(x = 7) = 0.78[/tex]

So, the probability that 7 out 10 Internet users will order something online is 0.78 or 78%.

Answer:

Step-by-step explanation:

1. Given the integral function [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex], using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as [tex]asin \theta[/tex] i.e [tex]x = a sin\theta[/tex].

All integrals in the form [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex] are always evaluated using the substitute given where 'a' is any constant.

From the given integral, [tex]\int\limits {7\sqrt{49-x^{2} } } \, dx = \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx[/tex] where a = 7 in this case.

The substitute will therefore be   [tex]x = 7 sin\theta[/tex]

2.) Given [tex]x = 7 sin\theta[/tex]

[tex]\frac{dx}{d \theta} = 7cos \theta[/tex]

cross multiplying

[tex]dx = 7cos\theta d\theta[/tex]

3.) Rewriting the given integral using the substiution will result into;

[tex]\int\limits {7\sqrt{49-x^{2} } } \, dx \\= \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -(7sin\theta)^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -49sin^{2}\theta } } \, dx\\= \int\limits {7\sqrt{49(1-sin^{2}\theta)} } } \, dx\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, dx\\since\ dx = 7cos\theta d\theta\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, 7cos\theta d\theta\\= \int\limits {7\{7(cos\theta)} }}} \, 7cos\theta d\theta\\[/tex]

[tex]= \int\limits343 cos^{2} \theta \, d\theta[/tex]

Answer:

[tex] P(38.6 <X <57.8)[/tex]

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

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

And replacing we got:

[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]

[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]

We can find the probability of interest using the normal standard table and with the following difference:

[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]

Step-by-step explanation:

Let X the random variable who represent the expense and we assume the following parameters:

[tex]\mu = 45, \sigma 16[/tex]

And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:

[tex] P(38.6 <X <57.8)[/tex]

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

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

And replacing we got:

[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]

[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]

We can find the probability of interest using the normal standard table and with the following difference:

[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]

Answer:

AB/AD=1/2       AC/AE=1/2

Step-by-step explanation:

The distance between 2 points A(x1; y1)     and  B(x2;  y2) can be calculated as:

AB= sqrt((x1-x2)²+(y1-y2)²)

So in our case AB= sqrt ((1-3)²+(4-1)²)= sqrt(2²+3²)=sqrt(13)

AD=sqrt ((-1-3)²+(7-1)²)= sqrt(4²+6²)=sqrt(52)

AB/AD=sqrt(13)/sqrt(52)= sqrt(13/52)=sqrt(1/4) =1/2

AB/AD =1/2

AC= sqrt ((5-3)²+(3-1)²)= sqrt(2²+2²)=sqrt(8)

AE=sqrt ((7-3)²+(5-1)²)= sqrt(4²+4²)=sqrt(32)

AC/AE=sqrt(8)/sqrt(32)= sqrt(8/32)=sqrt(1/4)=1/2

AC/AE=1/2

Answer:

first one is 1/2

second one is 1/2

Step-by-step explanation:

got it right on edge 2020

Answer:

A) 360

B) 360

Step-by-step explanation:

Part A)

Given that there are a total of 6 people and 4 person subcommittee is to be selected.

Number of ways to select 1st person = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select 2nd person = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select 3rd person = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select 4th person = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Part B)

Given that there are a total of 6 people in the committee

Number of ways to select president  = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select vice president = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select secretary = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select treasurer = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Answer:

  270

Step-by-step explanation:

  f(5) = 7 +4·5 = 27

  g(5) = 1/(2·5) = 1/10

The ratio of functions is the ratio of their individual values:

  (f/g)(5) = f(5)/g(5) = 27/(1/10)

  (f/g)(5) = 270

Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

Answer:

m∠1 = 99°

Step-by-step explanation:

∠2 and ∠81° are Corresponding Angles, so they are equal to each other:

∠2 = 81°

∠1 and ∠2 are Supplementary Angles, so they add up to 180°:

180 - m∠2 = m∠1

180 - 81 = 99°

Answer:

[tex]f^{-1} = \frac{x-1}{2}[/tex]

Step-by-step explanation:

[tex]f(x) = 2x+1[/tex]

Replace it with y

[tex]y = 2x+1[/tex]

Exchange the values of  x and y

[tex]x = 2y+1[/tex]

Solve for y

[tex]x = 2y+1[/tex]

Subtracting 1 from both sides

[tex]2y = x-1[/tex]

Dividing both sides by 2

[tex]y = \frac{x-1}{2}[/tex]

Replace it by [tex]f^{-1}[/tex]

So,

[tex]f^{-1} = \frac{x-1}{2}[/tex]

Answer:

[tex]\displaystyle f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]

Step-by-step explanation:

f(x) = 2x + 1

f(x) = y (output)

y = 2x + 1

Solve for x.

y - 1 = 2x

Divide 2 on both sides.

y/2 - 1/2 = x

1/2y - 1/2 = x

Switch variables.

1/2x - 1/2 = y

[tex]f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]

Answer:

A)

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is  significant difference between in drug resistance between the two states

B)

The calculated value Z =  2.7261 > 2.054 at 0.02 level of significance

Rejected H₀

There is a significant difference in drug resistance between the two states.

C)

P - value = 0.0066

P - value = 0.0066 < 0.02

D)

1) Reject H₀  

There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 174

Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.

First sample proportion

                    [tex]p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632[/tex]

Given second sample size n₂ = 375

Given data  Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant

Second sample proportion

                 [tex]p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186[/tex]

Step(ii):-

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is  significant difference between in drug resistance between the two states

Test statistic

          [tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

       Where

        [tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }[/tex]

       [tex]P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } = \frac{17.9718}{549} = 0.0327[/tex]

      Q = 1 - P = 1 - 0.0327 = 0.9673

Step(iii):-

 Test statistic

          [tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

         [tex]Z = \frac{0.0632-0.0186 }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }[/tex]

      Z  =   2.7261

Level of significance = 0.02 or 0.98

The z-value = 2.054

The calculated value Z =  2.7261 > 2.054 at 0.02 level of significance

   Reject H₀  

There is a significant difference in drug resistance between the two states.

 P- value

P( Z > 2.7261) = 1 - P( Z < 2.726)

                        = 1 - ( 0.5 + A (2.72))

                        = 0.5 - 0.4967

                         = 0.0033

we will use two tailed test

2 P( Z > 2.7261)  = 2 × 0.0033

                           = 0.0066

P - value = 0.0066 < 0.02

 Reject H₀  

There is a significant difference in drug resistance between the two states.

Answer:

D. 17 11/20 tubs

Step-by-step explanation:

Convert the cones into scoops.

234 regular cones = 468 scoops; 156 large cones = 468

So in total, Richard scooped 936 scoops. Since each scoop is 3 oz:

936 scoops * 3 oz = 2808 oz

Because a tub is 10 pounds or 160 oz:

2808 / 160 = 17.55 tubs

The answer is D. Here is how I found the answer:

Hope this helps!

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Answer:

The new salary of that person (for the period of a year) would be [tex]\$ 16,\!275[/tex].

Step-by-step explanation:

Start by considering: what is the exact value (in dollars) of that "[tex]5\%[/tex] raise in salary"?

[tex]5\%[/tex] (five percent) is equal to [tex]\displaystyle \frac{5}{100}[/tex].

To find the value of [tex]5\%[/tex] of [tex]\$15,\!500[/tex], simply multiply [tex]\$15,\!500[/tex] by [tex]5\%[/tex]:

[tex]\begin{aligned}&5\% \times \$15,\!500\\ &= \frac{5}{100} \times \$15,\!500 \\ &= 5\times \$155 = \$775 \end{aligned}[/tex].

Add that to the original (one-year) salary of this person to find the new one-year salary:

[tex]\$15,\!500 + \$775 = \$16,\!275[/tex].

Answer:

The new salary is $16,725

Step-by-step explanation:

To find the new salary, multiply 5% and $15,500

5% * $15,500

First, convert 5% to a decimal. Divide 5 by 100 or move the decimal place 2 spaces to the left.

5/100=0.05

5.0 --> 0.5--> 0.05

0.05 * $15,500

Multiply

$775

The raise is equal to $775.

Next, add the raise to the salary.

raise + salary

The raise is $775 and the salary is $15,500

$775 + $15,500

Add

$16,275

The new salary is $16,275

Explanation:

Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)

r = radius

h = height of cone

In this case,

r = 8 is the radius

h = 41

So,

SA = surface area

SA = pi*r^2 + pi*r*sqrt(r^2+h^2)

SA = pi*8^2 + pi*8*sqrt(8^2+41^2)

SA = 1250.936884057 use a calculator for this step

SA = 1251 square meters approximately

Answer:B.

Step-by-step explanation: it is better to have empty seats than toforce people to give up their seats.