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2 years ago

7

Jacob spends 60 minutes in the gym every day doing freehand exercises and running on the treadmill. He runs on the treadmill 30

minutes more than he does freehand exercises. Part A: Write a pair of linear equations to show the relationship between the number of minutes Jacob does freehand exercises (y) and the number of minutes he runs on the treadmill (x). (5 points) Part B: How much time does Jacob spend on doing freehand exercises? (3 points) Part C: Is it possible for Jacob to have spent 40 minutes running on the treadmill? Explain your reasoning.

1 answer:

elixir [45]2 years ago

8 0

Answer:

a.

x + y = 60

x = y + 30

b.

substitution:

(y + 30) = y = 60

2y + 30 = 60

2y = 30

y = 15

15 minutes for freehand

c.

No, because if he spends 40 minutes on the treadmill, he would have spent 10 minutes for freehand exercises. His total time in the gym would be 50 minutes, not 60.

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We are given with the formula
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A wild animal generally stays at least x mi from the edge of a forest. For a rectangular forest preserve that is 2 mi

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Answer:

$Area = 4x^2 - 14x + 10$

Step-by-step explanation:

<em>See Attachment for Complete Question</em>

Given

$Width = 5mi$ --- For the forest

$Length = 2mi$ -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

$Width = 5 - (x + x)$

$Width = 5 - 2x$

$Height = 2 - (x +x)$

$Height = 2 - 2x$

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$Area = Width * Height$

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Expand

$Area = 5(2 - 2x) -2x(2 - 2x)$

Open Brackets

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Hence; the required polynomial for the habitat area is:

$Area = 4x^2 - 14x + 10$

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Answer:

a) $0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422$

$0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

b) $\hat p = \frac{25}{250}= 0.1$

$0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628$

$0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using mascara at 95% of confidence is between (0.0628 and 0.1372)

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Step-by-step explanation:

Part a

The estimated proportion of women with cosmetic dermatitis from using eye shadow is given by:

$\hat p =\frac{12}{131}= 0.0916$

The confidence interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the proportion is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

Replacing we got:

$0.0916 - 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.0422$

$0.0916 + 1.96\sqrt{\frac{0.0916(1-0.0916)}{131}}=0.1410$

So then we can conclude that the true proportion of women with cosmetic dermatitis from using eye shadow at 95% of confidence is between (0.0422 and 0.1410)

Part b: A 95% confidence interval for the women with cosmetic dermatitis from using mascara

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$0.1 - 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.0628$

$0.1 + 1.96\sqrt{\frac{0.1(1-0.1)}{250}}=0.1372$

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ki77a [65]

Answer:

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Step-by-step explanation:

It is given that area of the polygon WXYZ with its vertices at W(–3, –2), X(–3, 5), Y(2, 5), and Z(2, –2).

From the below graph it is noticed that the given polynomial is a rectangle with length 5 and width 7.

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Using the above formula we get,

$WX=7$

$XY=5$

$YZ=7$

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Using the Pythagoras theorem, the length of diagonal WY and XZ are

$WY=\sqrt{(WX)^2+(XY)^2}=\sqrt{7^2+5^2}=\sqrt{74}$

$XZ=\sqrt{(XY)^2+(YZ)^2}=\sqrt{5^2+7^2}=\sqrt{74}$

Since the length of the diagonal are same, therefore the given polygon is a rectangle.

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The area of given polynomial is

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