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3 years ago

6

Myra saved $15 a month for 18 months. She bought a book for $46.50 and a tennis racquet for $129.95. How much does she have left

? A. $93.55 B. $140.05 C. $186.55

1 answer:

Elis [28]3 years ago

7 0

Answer:

A

Step-by-step explanation:

15*18=270.

270-46.50=223.5

223.5-129.95=93.55.

A. $93.55

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As 9 hundreds is 9 thousand

s2008m [1.1K]

9 hundreds=900 9 thousands=9,000

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3 years ago

MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

The city of Omaha decided to build a new parking garage in hopes of luring more people to the Old Market district.The city will

dimulka [17.4K]

Answer:

Given:

Mean, u = 135

Sample size, n = 42

Sample mean, x' = 126

Standard deviation = 16

Significance level = 0.05

1) The null and alternative hypotheses:

H0 : u = 135 (the revenue per day is $135)

H1 : u < 135 (the revenue per day is less than $135)

2) In this case, we have a left tailed test.

Let's use the formula:

$= \frac{x' - u}{s/ \sqrt{n}} = \frac{126 - 135}{16 / \sqrt{42}} = -3.645$

t = - 3.645

Critical value: at a significance level of 0.05, left tailed test,

tcritical = -1.683

We reject null hypothesis, H0, since t calculated, -3.645 is less than tcritical, -1.683.

3) Given, a = 0.05, df = 41, left tailed test,

t-value = 2.02

For the corresponding confidence interval, we have:

$CI = (x' - \frac{t * \sigma}{\sqrt{n}}, x' + \frac{t * \sigma}{\sqrt{n}})$

$CI = (126 - \frac{2.02 * 16}{\sqrt{42}}, 126 + \frac{2.02 * 16}{\sqrt{42}})$

CI = (121.014, 130.986)

4) Conclusion:

We reject the estimated potential revenue advised by the consultant, H0, as it is too high, because the t-calculated falls in rejection region(i.e, less than critical value), also the upper limit of the confidence interval is less than $135.

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2 years ago

After each charging, a battery is able to hold only 97% of the charge from the previous charging. The battery was used for 18 ho

Cerrena [4.2K]

Answer:

The total nuber of hours that the battery can be used over its lifetime is 600.

Step-by-step explanation:

We use an infinite geometric series to solve this question.

The sum of all values of an infinite geometric series is given by the following equation:

$S = \frac{a_{1}}{1 - r}$

In which $a_{1}$ is the first term and r is the common ratio.

After each charging, a battery is able to hold only 97% of the charge from the previous charging.

This means that $r = 0.97$

The battery was used for 18 hours on its first charge before it had to be recharged.

This means that $a_{1} = 18$

What is the total number of hours the battery can be used over its lifetime?

$S = \frac{18}{1 - 0.97} = 600$

The total nuber of hours that the battery can be used over its lifetime is 600.

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3 years ago

1. Identify the vertex and the y-intercept of the graph of the function y=-2(x+ 2)+2.

KATRIN_1 [288]

Answer:

Please let me know if your quadratic is $y=-2(x+2)^2+2$ .

And if so your vertex is (-2,2) and your y-intercept is (0,-6)

Step-by-step explanation:

It says vertex so I'm thinking you meant $y=-2(x+2)^2+2$ . Please correct me if I'm wrong.

The vertex form of a quadratic is $y=a(x-h)^2+k$ . It is called that because it tells you the vertex (h,k).

So if you compare the two forms you should see -h=2 while k=2.

-h=2 implies h=-2.

So the vertex is (h,k)=(-2,2).

To find the y-intercept, set x=0 and find y.

$y=-2(0+2)^2+2$

$y=-2(2)^2+2$

$y=-2(4)+2$

$y=-8+2$

$y=-6$

So the y-intercept is (0,-6).

7 0

3 years ago