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Novosadov [1.4K]
3 years ago
12

Describe the strength and sign of the relationship you expect for each pair of variables. Explain your reasoning.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
4 0

Answer:

i dont get it

Step-by-step explanation:

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What is the total cost of a $95.00 item with a sales tax of 6%
MaRussiya [10]

Answer: $100.70

Step-by-step explanation: 6% is equal to 0.06, so you can add multiply the price of the item by 1.06 because that is the base cost plus the tax. Then you get $100.70.

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2 years ago
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I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur
Butoxors [25]
\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx

Setting x=5\sin\theta, you have \mathrm dx=5\cos\theta\,\mathrm d\theta. Then the integral becomes

\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta
\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta
\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta
\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta

Now, \sqrt{x^2}=|x| in general. But since we want our substitution x=5\sin\theta to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means \theta=\sin^{-1}\dfrac x5, which implies that \left|\dfrac x5\right|\le1, or equivalently that |\theta|\le\dfrac\pi2. Over this domain, \cos\theta\ge0, so \sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta.

Long story short, this allows us to go from

\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta

to

\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta
\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta

Then integrate term-by-term to get

\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)
=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C

Now undo the substitution to get the antiderivative back in terms of x.

=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C
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Find the total cost of a 36 month car lease, if: monthly payment = $175 down payment = $1,500 residual value = $10,000
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17,800 is correct answer or the third one
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Men and women (ages 22–40) were surveyed to choose a favorite free-time activity: playing sports, dancing, or watching movies/TV
Gnesinka [82]

The correct two-way frequency table for the data is <u>Men </u><u>and </u><u>Women </u><u>Leisure Time Activity Preferences.</u>

<h3>What is a correct two-way frequency table?</h3>

A correct two-way frequency table displays frequencies for two categories (rows and columns) collected from categorical variables (men and women).

Men and Women Leisure Time Activity Preferences;

                Playing Sports     Dancing     Watching movies/TV   Row totals

Men                  11                         3                          6                          20

Women             5                       16                          9                          30

Column totals 16                       19                         15                          50

Hence, the correct two-way frequency table for the data is Men and Women Leisure Time Activity Preferences.

To learn more about two-way frequency tables click the link given below.

brainly.com/question/4555163

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