Mathematics, 03.04.2020 23:10 raquelqueengucci25

A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches. a study participant is randomly sleected. what height cuts off the top 5%

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Answer from: Acemirisa

The height that cuts off the top 5% is 74.83 inches.

Step-by-step explanation:

We are given that in the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches.

Let X = heights of respondents

So, X ~ N( $\mu=69.9,\sigma^{2} =3^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean height = 69.9 inches

$\sigma$ = standard deviation = 3.0 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, we have to find the height that cuts off the top 5%, that means;

P(X > ) = 0.05 {where is the height that cuts off top 5%}

P( $\frac{ X -\mu}{\sigma}$ > $\frac{ x -69.9}{3}$ ) = 0.05

P(Z > $\frac{ x -69.9}{3}$ ) = 0.05

Now, in the z table the critical value of X that gives the area of top 5% is given as 1.6449.

So, $\frac{ x -69.9}{3} = 1.6449$

$x -69.9= 1.6449 \times 3$

= 69.9 + 4.9347 = 74.83

Hence, the height that cuts off the top 5% is 74.83 inches.

Answer from: Quest

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get $6x^{2} -3x$

and solving the given expression :

3x(2x-1)

$6x^{2} -3x$

since solving the expression using tiles and solving the expression algebraically we get the same answer

thus we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

Which is true regarding armando’s use of algebra tiles? he used the algebra tiles correctly. he did

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$

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