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3 years ago

7

A board 125 centimeters long is cut into 12 pieces of equal length . What is the length of each piece , to the nearest tenth of

a centimeter

1 answer:

alexgriva [62]3 years ago

3 0

Each board is cut to 10.4 cm

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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

Read the following excerpts from the New York Times (December 17, 1996) article Chance of Heart Attack Increases for Those Who S

nataly862011 [7]

Answer:

1. B

2. A

3. A

4. A

Step-by-step explanation:

Hello!

The study claimed that subjects who suffer depression are more likely to have a heart attack than those who are not depressed.

1551 persons were interviewed as part of the experiment and classified according to their answers in two groups "suffered depression" and "didn't suffer depression"

Afterward, the researchers looked up the medical history of all 1551 subjects and recorded how many of them had heard issues.

1.

An observational study is one where the researcher only determines the variables he wants to study without controlling or influencing any factor of the population of interest. Because there is no interference from the researchers, there is a high risk that confounding factors may affect the conclusions of it. These studies are usually precursors to experimental tests, it allows the researcher to have an idea of the association between the two variables but you cannot establish causal relationships from them.

This is an example of an observational study, the researcher merely recorded the variables of interest without interfering with any aspects that may influence them. (For example diet or exercise habits of the subjects)

2. and 3.

The objective of the study is to determine if "depression" causes "disposition to heart attacks"

The explanatory variable is "depression status of the subject" since it is what is suspected to influence over the heart condition of said subject and "heart attack status" is the response variable.

4.

Of the 1551 subjects originally studied, 444 were classified as depressed, of these 27 had heard attacks. You can calculate the "proportion of subjects that suffered depression and had heart attacks" as:

p': 27/444= 0.06 ⇒ 6%

Since this value was obtained from the sample, it is an estimation of the population parameter, also called statistic.

I hope it helps!

4 0

2 years ago

1. A pond has 85 frogs, 20% of the frogs are green the rest are orange, brown, and yellow. How many frogs are green?

alexandr402 [8]

Answer:

17 green frogs

Step-by-step explanation:

You need to multiply the decimal form of 20% by 85.

To find the decimal form of a percent you take the decimal (20.00) and move it twice to the left (20.00 ---> .2000)

Now, multiply by .2 by 85

(.2)(85) = 17

Therefore, 17 frogs in the pond of 85 frogs are green

<em>Hope this helps!!</em>

<em>- Kay :)</em>

4 0

2 years ago

Divide £945 in the ratio 2:5

dybincka [34]

The answer is 675. 2270. 657

5 0

3 years ago

Person 1 writes internal operating procedures 3 times faster than Person 2. Most of the procedures took 30 minutes each to creat

ad-work [718]

Person 1 takes 3 hour 10 minutes to complete 9 procedures

<em><u>Solution:</u></em>

From given question,

Person 2 takes 30 minutes per procedure

Person 1 writes internal operating procedures 3 times faster than Person 2

So we get, Person 1 takes 3 times faster than Person 2

Person 1 takes 10 minutes per procedure

But two of the procedures for Person 1 took an hour each

So person 1 takes 60 minutes each for two of procedures ( since 1 hour = 60 minutes )

<em><u>Calculate how long it took Person 1 to complete 9 procedures:</u></em>

So for first 7 procedures person 1 would take 10 minutes per procedure and for last two procedures person 1 would take 60 minutes per procedure

$time $=7$ procedures $\times \frac{10 \text { minutes }}{1 \text { procedure }}+2$ procedure $\times \frac{60 \text { minutes }}{1 \text { procedure }}$$

$time=70 minutes +120minutes\\\\time=190minutes$

We know that,

1 hour = 60 minutes

Therefore,

190 minutes = 60 minutes + 60 minutes + 60 minutes + 10 minutes

190 minutes = 1 hour + 1 hour + 1 hour + 10 minutes = 3 hour 10 minutes

Therefore Person 1 takes 3 hour 10 minutes to complete 9 procedures

7 0

3 years ago