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3 years ago

11

Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc

e between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. I pick Erik won and they asked,Use your previous answers to write an algebraic statement that represents all the ways your player will win. Be sure to define your variable

2 answers:

DanielleElmas [232]3 years ago

8 0

So erik is x and nita is y
x-y<10 or y-x<10
because if erik picks 11 then 11-y has to be less than 10 so nita would pick any number greater than one and if nita picks12 then 12-x has to be less than 10 so erik would have to choose a number greater than two

Luda [366]3 years ago

5 0

Erik- |x-y|<10

Nita- |x-y|>10

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(2 − 4) − (3 + 5) + ( − 6) − (5 + 7)

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Answer:

It is - 28

Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t

svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 450, \sigma = 100$

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

$Z = \frac{550 - 450}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 350

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

$Z = \frac{350 - 450}{100}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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

$1.88 = \frac{X - 450}{100}$

$X - 450 = 1.88*100$

$X = 638$

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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

$0.253 = \frac{X - 450}{100}$

$X - 450 = 0.253*100$

$X = 475.3$

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

$-0.385 = \frac{X - 450}{100}$

$X - 450 = -0.385*100$

$X = 411.5$

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

$0.385 = \frac{X - 450}{100}$

$X - 450 = 0.385*100$

$X = 488.5$

The middle 30% of the test scores is between 411.5 and 488.5.

7 0

3 years ago

each of 4 family members uses 175 minutes or fewer of their combined family cell phone plan. at the end of the month, the family

Mamont248 [21]

Answer:

x = ± ∜175 = ± 3.6371

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^4-(175)=0

Step by step solution :

STEP

1

:

Trying to factor as a Difference of Squares:

1.1 Factoring: x4-175

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 175 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Polynomial Roots Calculator :

1.2 Find roots (zeroes) of : F(x) = x4-175

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers. The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -175.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,5 ,7 ,25 ,35 ,175

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 -174.00

-5 1 -5.00 450.00

-7 1 -7.00 2226.00

-25 1 -25.00 390450.00

-35 1 -35.00 1500450.00

-175 1 -175.00 937890450.00

1 1 1.00 -174.00

5 1 5.00 450.00

7 1 7.00 2226.00

25 1 25.00 390450.00

35 1 35.00 1500450.00

175 1 175.00 937890450.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step

1

:

x4 - 175 = 0

STEP

2

:

Solving a Single Variable Equation:

2.1 Solve : x4-175 = 0

Add 175 to both sides of the equation :

x4 = 175

x = ∜ 175

The equation has two real solutions

These solutions are x = ± ∜175 = ± 3.6371

Two solutions were found :

x = ± ∜175 = ± 3.6371

4 0

3 years ago

Read 2 more answers

Indicate whether the following analysis involves a statistical test. If it does involve a statistical test, state the population

Pie

Answer:

a

Yes it involves a statistical test

The population parameter(s) of interest is

The sample size is n = 100

The average reaction time of the right hands for the right-handed participants $\mu_R$

The average reaction time of the left hands for the left-handed participants $\mu_L$

The null hypothesis is $H_o : \mu_R = \mu_L$ ,

The alternative hypothesis is $H_a: \mu_R < \mu_L$

b

Yes it involves a statistical test

The population parameter(s) of interest is

The sample size is n = 100

The average reaction time of the right hands for the right-handed participants $\mu_R$

The average reaction time of the left hands for the left-handed participants $\mu_L$

The null hypothesis is $H_o : \mu_R = \mu_L$ ,

The alternative hypothesis is $H_a: \mu_R < \mu_L$

c

Yes it involves a statistical test

The population parameter(s) of interest is

The percentage of people in the community living in a mobile home is denoted with p

The sample size is n = 1000

The null hypothesis is $H_o : p =10\% = 0.01$ ,

The alternative hypothesis is $H_a: p >10\% = 0.01$

Step-by-step explanation:

Considering the first statement

Testing 100 right-handed participants on the reaction time of their left and right hands to determine if there is evidence for the claim that the right hand reacts faster than the left.

Yes, the analysis does involve a statistical test.

The null hypothesis is $H_o : \mu_R = \mu_L$ ,

The alternative hypothesis is $H_a: \mu_R < \mu_L$

Here $\mu_R$ is the average reaction time of the right hands for the right-handed participants

and $\mu_L$ is the average reaction time of the left hands for the left-handed participants

Considering third statement

Polling 1000 people in a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater then 10%.

The percentage of people in the community living in a mobile home is denoted with p

The sample size is n = 1000

The null hypothesis is $H_o : p =10\% = 0.01$ ,

The alternative hypothesis is $H_a: p >10\% = 0.01$

3 0

3 years ago