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3 years ago

11

Together, Tim and Allen worked 22 hours on a project. Allen worked one more than twice the amount of hours Tim worked. How many

hours did each boy work?

1 answer:

erastova [34]3 years ago

3 0

Answer:

should be 43 hours

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Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. the

NeTakaya

$n_1=25, n_2=25\\ \bar{X_1}=35.5, \bar{X_2}=33\\ s_1=3, s_2=4$

Pooled Combined Variance $s_p=12.5$

Test Statistic:

$t=\frac{\left(\bar{X_1}-\bar{X_2}\right)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

$t=\frac{\left(35.5-33\right)}{12.5\sqrt{\frac{1}{25}+\frac{1}{25}}}$

$\left|t\right|=0.01414$

Degrees of freedom = $n_1+n_2-2=25+25-2=48$

$\alpha =0.05$

$t-Critical =t_{\alpha /2, n_1+n_2-2}=t_{0.025, 48}=-2.0206 \\Table value=|t|=2.0206\\|t|=2.0206$

The table value is greater than the calculated value.

Thus we accept H0.

8 0

3 years ago

Colossus Added to six flags st. Louis in 1986, the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a r

NemiM [27]

Given:

D=165 feet and the frequency of the motion is 1.6 revolutions per minute.

Solution:

The radius is half of the diameter.

The radius of the wheel is 82.5 feet.

$T=\frac{1}{1.6} \text{ minutes}$

As we know: $\omega=\frac{2\pi}{T}$

Substitute the value of T in the above formula.

$\omega=\frac{2\pi}{\frac{1}{1.6}}\\\omega=3.2\pi$

If the center of the wheel is at the origin then for $t=0$ the rest position is $-a$ .

This can be written as:

$h(t)=-a\cos(\omega t)\\h(t)=-82.5cos(32.\pi t)$

The actual height of the rider from the ground is:

$h(t)=\text{ Initial height from bottom}+\text{ radius}-82.5\cos(3.2\pi t)\\h(t)=15+82.5-82.5\cos(3.2\pi t)\\h(t)=97.5-82.5\cos(3.2\pi t)$

The required equation is $h(t)=97.5-82.5\cos(3.2\pi t)$ .

3 0

3 years ago

QUESTION IN SCREENSHOT

insens350 [35]

Get n to one side
-1/5=-2/5n
divide both sides by -2/5

n=1/2

5 0

3 years ago

A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off t

nexus9112 [7]

This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon.

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:

2.6s + 7.3

Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

1.5s + 12.4

To determine when both balloons are at the same height, we set the two equations equal to each other:

2.6s + 7.3 = 1.5s + 12.4

Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:

1.1s + 7.3 = 12.4

Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:

1.1s = 5.1

Last, we divide both sides by 1.1. So s = 4.63.

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:

2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33

1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33

After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.

6 0

3 years ago

Which graph best represents f(x)=|x|

jasenka [17]

The graph of f(x) = |x| would look like the image below.

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3 years ago