Please help this is a big test

1. When 15 is subtracted from the measure of an angle, the result is the measure of a right angle. What is the measure of the or

shutvik [7]

Answer:

It is 105 degrees. Since 105-15=90 degrees.

4 0

3 years ago

A pet store has 8 puppies, including 3 poodles, 2 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pe

Debora [2.8K]

Answer:

9 / 64

Step-by-step explanation:

- In this task you have 2 events and you are looking for a joint probability. The first event is "Rebecca chooses a poodle". The probability of this event is:

P ( Rebecca chooses a poodle ) = 3 / 8

- because among 8 dogs there are 3 poodles.

- The second event is "Aaron selects a poodle".

This event has a probability of that is equivalent to previous selection:

P ( Aaron chooses a poodle ) = 3 / 8

- Because after Rebecca's choice the chosen poodle is replaced with the poodle; hence, there are 8 pets in total and among them there are 3 poodles.

- To calculate probability of both events ("Rebeca selects a poodle and Aaron selects a poodle") with replacement you have to multiply both calculated probabilities - condition of independent events :

P ( Aaron and Rebecca both select poodle ) = 3 / 8 * 3 / 8

= 9 / 64

6 0

3 years ago

PLEASE HELP. I need DE AND EF!!!

AlekseyPX

Answer:

DE = about 41.843 (rounded to nearest thousandth)

EF= 34.276 (rounded)

Step-by-step explanation:

For DE, we know that the shorter side (the opposite side) is 24, while the angle across form it is 35°. We can use trigonometry to figure this out. SinФ equals the opposite side (in this case, 24) divided by the hypotenuse. Set sinФ equal to a ratio of the sides like this:

sin(35) = $\frac{24}{x}$

x represents the hypotenuse length, which we don't know; 35 is the angle measure. Next, isolate x so that the equation looks like this:

$\frac{24}{sin(35)}$ = x

You will need a calculator for the next part. (and make sure you're in degree mode!). evaluate sin(35) and divide 24 by that value. That is DE's length. DE = about 41.843 (rounded to nearest thousandth)

For EF, we can just use Pythagorean theorem now that we know the other sides' values.

EF^2 + 24^2 = DE^2

*a calculator might also be useful for this part.

EF= 34.276 (rounded)

8 0

3 years ago

The city purchased 24 new buses that each hold 32 passengers. It also purchased 18 new smaller buses that each hold 27 passenger

FrozenT [24]

You would multiply 24 and 32. Then multiply 18 and 27. Would add both answers together. That should 768+486= 1254 people. The total people is 1254.

4 0

3 years ago

Young people may feel they are carrying the weight of the world on their shoulders when in reality they are too often carrying a

Travka [436]

Answer:

A. [12.92;14.97]lb

B. [13.25;16.26]%

C. check explanation

Step-by-step explanation:

Hello!

To properly resolve any statistical problem you need to first identify your study variables and summarize the given data.

A.

Study variable:

X: "backpack weight of a sixth-grader" (lb)

sample n= 131

sample mean: x[bar]= 13.83 lb

sample standard deviation: S= 5.05 lb

Now you need to calculate a CI for the population mean of the backpack weight of sixth graders (μ) with a confidence level of 99%

Since you need to estimate the population mean, and you have a sample large enough (n≥30), although you don't know the distribution of this population, you can approximate the distribution of the sample mean to normal (applying CLT) and use the statistic Z= (x[bar] - μ)/(S/√n) ≈ N(0;1)

The formula for the CI is

x[bar] ± $Z_{\alpha/2}$ * (S/√n)

The confidence level to use is 1-α = 0.99

α = 0.01 ⇒ α/2 = 0.005

$Z_{\alpha/2}$ ⇒ $Z_{\0.005}$ = -2.58

Now you calculate the interval

13.83 ± 2.58 * 5.05/√131 ⇒ [12.92;14.97]lb

So with a confidence level of 99%, you'll expect that the real mean for the backpack weight of sixth graders is contained by the interval [12.92;14.97]lb

B.

It seems that for this item the information was measured from the same sample taken in item A.

Study variable

X: "Backpack weight as percentage of body weight" (lb)

Assuming is the same sample: n= 131

It was calculated the 95% CI [13.62;15.89]lb

And you need to calculate a 99% CI

For this item, you use the same statistic as before

x[bar] ± $Z_{\alpha/2}$ * (S/√n)

To calculate the asked interval you need to know the confidence level, the sample mean, sample standard deviation and sample size.

To know the sample mean and standard deviation for the backpack weight as percentage of body weight, you'll need to deduce it from the given interval.

Since this interval is for the population mean, it is constructed arround the sample mean. That means, that the sample mean is at the center of the interval.

x[bar] = (Li+Ls)/2 ⇒ x[bar] = (13.62+15.89)/2 = 14.76%

The standard deviation needs a little more calculation,

amplitude a= Ls - Li ⇒ a= 15.89-13.62= 2.27

semiamplitude d= a/2 ⇒ d=2.27/2= 1.135lb ≅ 1.14

$Z_{\1-alpha/2}$ ⇒ $Z_{\0.975}$ = 1.96

d= $Z_{\alpha/2}$ * (S/√n) ⇒ 1.14= 1.96 * (S/√131)

⇒ S= 6.657% ≅ 6.66%

Now the new CI has a confidence level of 99%

The Z value you need to use is $Z_{\0.995}$ = 2.58

x[bar] ± $Z_{\alpha/2}$ * (S/√n) ⇒ 14.76 ± 2.58 * (6.66/√131)

⇒ [13.25;16.26]%

With a confidence level of 99% you can expect that the interval [13.25;16.26]% contains the population mean of the backpack weight as percentage of body weight of sixth graders.

C.

"The American Academy of Orthopedic Surgeons recommends that backpack weight is at most 10% of body weight." As you can see in the calculated interval [13.25;16.26]%, the weight carried by the sixth graders is above the recommended backpack weight as percentage of body weight. This means that the sixth graders carry more weight than recommended.

I hope you have a SUPER day!

4 0

3 years ago