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bazaltina [42]
3 years ago
5

Samantha reports that 60% of the first year students at her university think they should be able to bring a car to campus. She a

lso notes that she is 95% certain that between 50 and 70% of the first year students agree. Which of the following statements is FALSE?A) the range from 50-70% is a confidence intervalB) 95% refers to her confidence levelC) 60% is a statisticD) the standard error for her sample is 15
Mathematics
1 answer:
Nostrana [21]3 years ago
4 0

Answer:

D) the standard error for her sample is 15

Step-by-step explanation:

Samantha is 95% certain that between 50% and 70% of the first year students agree that they should be able to bring a car to campus.

Here

  • 95% is the confidence level.
  • The range between 50% and 70% indicates 95% confidence interval.
  • 60% is the average proportion of the first year students at her university think they should be able to bring a car to campus.
  • 10% (0.1) is the margin of error from the mean

Since standard error can be obtained by dividing margin of error by the z-statistic of the confidence level which is 1.96. The standard error for her sample \frac{0.1}{1.96} does not equal to 15.

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What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5
jeyben [28]

Answer:

\displaystyle c = \frac{20}{3}

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one <em>c</em> within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a <em>c</em> in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to <em>x: </em>

<em />\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right]<em />

Differentiate:

g'(x) = -21x^2+182x-280

Let g'(x) = 0:

0 = -21x^2+182x-280

Solve for <em>x</em>. First, divide everything by negative seven:

0=3x^2-26x+40

Factor:

<h3>0=(x-2)(3x-20)</h3>

Zero Product Property:

x-2=0 \text{ or } 3x-20=0

Solve for each case. Hence:

\displaystyle x=2 \text{ or } x = \frac{20}{3}

Since the first solution is not within our interval, we can ignore it.

Therefore:

\displaystyle c = \frac{20}{3}

3 0
3 years ago
What is the product of –12 and –4? –48 –16 16 48?
Stels [109]

Answer:

The answer is +48

Step-by-step explanation:

a negative times a negative is a positive. Heres a little tip!

Love= Positive

Hate = Negative

if you love to love youre a lover

if you hate to hate youre a lover

if you hate to love youre a hater

if you love to hate youre a hater

hater= negative number

lover= positive number

(this only applies to multiplication and division)

                           

I hope this was helpful. Make sure to rate or mark as brainliest! or to thank. or all. your choice :)

3 0
4 years ago
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Write an equation in point-slope form of the line that passes through (-1,-4) with slope -2.
andrew-mc [135]

Answer:

y+4=-2(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-2(x-(-1))

y+4=-2(x+1)

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3 years ago
Find the equation of the sphere in standard form centered at (−6,10,5) with radius 5.
Dovator [93]

Answer:

The equation of the sphere in standard form is

x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0

Step-by-step explanation:

<u>Step 1</u>:-

The equation of the sphere having center and radius is

(x-h)^{2} +(y-k)^{2} +(z-l)^{2} = r^{2}

Given centered of the sphere is (-6,10,5) and radius r=5

(x-(-6))^{2} +(y-10)^{2} +(z-5)^{2} = 5^{2}

on simplification,we get

using (a+b)^{2} =a^{2} +2 a b+b^{2}

using (a-b)^{2} =a^{2} -2 a b+b^{2}

simplify , we get

x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0

8 0
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SOVA2 [1]

Answer:

  lies in the shaded regions of both the top and bottom inequalities

Step-by-step explanation:

For a point to be a solution of two inequalities, it must lie in both solution sets. It ...

  lies in the shaded regions of both the top and bottom inequalities

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3 years ago
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