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erma4kov [3.2K]

3 years ago

14

In some? country's Congress, the number of Representatives is 20 less than five times the number of Senators. There are a total

of 520 members. Find the number of Senators and the number of Representatives.

1 answer:

cestrela7 [59]3 years ago

7 0

Answer:

Senators: 90
Representatives: 430

Step-by-step explanation:

Let s represent the number of Senators in the Congress. Then the number of Representatives is (5s-20) and the total number of members is ...

s + (5s -20) = 520

6s = 540 . . . . . . . . . add 20, simplify

s = 90 . . . . . . . . . . . divide by 6

The number of Senators is 90; the number of Representatives is 430.

_____

You can find the number of Representatives either as 520 -90 = 430 or as 5·90 -20 = 430.

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Plot the two decimals on the number line below 0.43, 0.39. Write an inequality comparing the two decimals. Explain your answer u

Ilya [14]

Answer:

See the image below.

Step-by-step explanation:

The decimals 0.43 and 0.39 are equivalent to 43/100 and 39/100. These decimals lie between 0 and 1.

Draw a number line, mark off and label the multiples of 0.10(e.g 0.10, 0.20) in the interval 0-1.

Mark 0.43 between 0.4 and 0.5, a little closer to 0.4.

Mark 0.39 between 0.3 and 0.4, just behind 0.4.

Since 0.39 is smaller than 0.43( 0.39 lies on the left to 0.43), the inequality is:

0.39<0.43

5 0

4 years ago

The function f(x)=501170(0.98)x gives the population of a Texas City x years after 1995. What was the population in 1995?

galina1969 [7]

Answer:

The population of a Texas City in 1,995 was $501,170\ people$

Step-by-step explanation:

we have

$f(x)=501,170(0.98^{x})$

we know that

The population in 1,995 is for $x=0$

so

substitute the value of $x=0$ in the function f(x)

$f(0)=501,170(0.98^{0})=501,170\ people$

4 0

4 years ago

7300 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest tenth of a year, how long will it tak

Ivenika [448]

Answer:17.4

Step-by-step explanation:

8 0

3 years ago

Psychology students at Wittenberg University completed the Dental Anxiety Scale questionnaire (Psychological Reports, August 199

fredd [130]

Answer:

a) $Z = 1.43$

b) There is a 48.696% probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale is

Step-by-step explanation:

Normal model problems can be solved by the zscore formula.

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

Each z-score value has an equivalent p-value, that represents the percentile that the value X is.

In our problem, the mean score was 11 and the standard deviation was 3.5.

So, $\mu = 11$ , $\sigma = 3.5$ .

(a) Suppose you score a 16 on the Dental Anxiety Scale. Find the z-value for this score.

What is the value of Z when $X = 16$ ?

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16 - 11}{3.5} = 1.43$

(b) Find the probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale.

We have to find the percentiles of both of these scores. This means that we have to find Z when $X = 10$ and $X = 15$ . The probability that someone scores between a 10 and a 15 is the difference between the pvalues of the z-value of X = 10 and X = 15.

When $X = 10$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 11}{3.5} = -0.29$

Looking at the z score table, we find that the pvlaue of $Z = -0.29$ is 0.3859.

When $X = 15$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{15 - 11}{3.5} = 1.14$

Looking at the z score table, we find that the pvlaue of $Z = 1.14$ is 0.87286.

So, the probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale is

0.87286 - 0.3859 = 0.48696 = 48.696%

(c) Find the probability that someone scores above a 17 on the Dental Anxiety Scale

This probability is 100% minus the pvalue of the zvalue when $X = 17$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17 - 11}{3.5} = 1.71$

When $Z = 1.71$ , the pvalue is 0.95637. This means that there is a 95.637% probability that someone scores BELOW 17 on the dental anxiente scale.

100 - 95.637 = 4.363%

There is 4.363% probability that someone scores above a 17 on the Dental Anxiety Scale

4 0

4 years ago

What is the slope of y=2+3.5x pls answer

Lady bird [3.3K]

The slope of this equation is 3.5

3 0

3 years ago

Read 2 more answers