To plan a budget, first prioritize expenditures. True False

2. Two angle measures are in the ratio 5:9. Write

iris [78.8K]

The two angles are x and 9x/5

Let the two angles we require be x and y.

<h3 /><h3>Ratio of both angles</h3>

We have that the ratio of both angles are x:y

Since both angles are in the ratio 5:9, we have that,

x:y = 5:9

⇒ x/y = 5/9

<h3 /><h3>Value of the other angle</h3>

So, we Make y subject of the formula

Multiplying both sides by y, we have

y × x/y = 5/9 × y

x = 5y/9

Multiplying both sides by 9, we have

9 × x = 5y/9 × 9

9x = 5y

Dividing both sides by 5, we have

9x/5 = 5y/5

y = 9x/5

So, the two angles are x and 9x/5

Learn more about angles here:

brainly.com/question/14362353

3 0

2 years ago

Jeff writes comic strips for local newspaper. The number of comic strips he created is represented by the function f(x)=3x, wher

grin007 [14]

If Jeff writes comic strips at a rate of 3 comics an hour then you must put 3,4,7&9 into the function and add up the products.
9+12+21+27=69

5 0

3 years ago

As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple

zhenek [66]

Answer:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

$P(A)=\frac{Possible outcomes}{Total outcomes}$

For this case if we replace we got:

$P(A) =\frac{23}{56}=0.411$

And using the complemnt rule we got:

$0.411 +P(A')=1$

And solving for P(A') we got:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

4 0

2 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$