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3 years ago

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Two S-year old girls, Alyse and Jocelyn, have been training to run a mile racc Alyse's I mile A is approximately Normally distri

buted with a mean of 13.5 minutes and a standard deviation of 2.5 minutes. Jocelyn's I mile time approximately Normally distributed with a mean of 12 minutes and a standard deviation of 1.5 minutes. Assuming A and J are independent random variables, what is the probability that Alyse has a smaller time than Jocelyn in a 1 sile race on a randomly selected day?

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

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Step-by-step explanation:

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PLEASE HELPPP!!!!!!!!!!!!!

Leto [7]

For this case we have:

Question 1:

According to Heron's formula, the area of a triangle is given by:

$A=\sqrt{(s(s-a)(s-b)(s-c))}$

Where a, b and c are the sides of the triangle and s is the semi-perimeter of the triangle given by:

$s=\frac{(a+b+c)}{2}$

Let:

$a = 20mm\\b = 23mm\\c = 27mm$

We have s:

$s=\frac{(20+23+27)}{2}\\s=\frac{70}{2}\\s=35$

Substituting in the formula of the area:

$A=\sqrt{(35(35-20)(35-23)(35-27))}\\A=\sqrt{(35(15)(12)(8))}\\A=\sqrt{(50400)}\\A=224.5mm^2$

Thus, the area of the triangle is $A = 224.5mm ^ 2$

Answer:

$A = 224.5mm ^ 2$

Question 2:

The area of a traingule can be expressed as:

$A=\frac{(b*h)}{2}$

Where:

b: Base of the triangle

h: Triangle height

Let:

$b = 20m\\h = 18m$

Substituting the values in the expression we have:

$A=\frac{(20*18)}{2}\\A=\frac{360}{2}\\A=180m^2$

Thus, the area of the triangle is $A = 180m ^ 2$

Answer:

$A = 180m ^ 2$

Question 3:

It is known that the area of a rectangle is given by:

$A = l * w$

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

So:

$l = 9 feet\\w = 8 feet$

Substituting:

$A = (9 * 8) feet ^ 2\\A = 72 feet ^ 2$

Thus, the area of Laura's carpet is given by $A = 72 feet ^ 2$

Answer:

$A = 72 feet ^ 2$

Question 4:

We must take out the area of the outer wall, given by a rectangle, then:

$A = l * a$

Where:

l: It is the length of the rectangle

a: It is the height of the rectangle

We have:

$l = 48 feet\\a = 9 feet$

Substituting in the formula we have:

$A = (48 * 9) feet ^ 2\\A = 432ft ^ 2$

Thus, the area of the exterior wall is given by: $A = 432 feet ^ 2$

$432ft ^ 2> 400ft ^ 2$

So, a can of paint is not enough to cover the exterior wall.

Answer:

A can of paint is not enough to cover the exterior wall.

Question 5:

A regular hexagon is formed by 6 equal triangles. The area of the hexagon is given by:

$A=\frac{(perimeter* apothem)}{2}$

Where the perimeter is given by the sum of the sides, that is:

$perimeter = (10 + 10 + 10 + 10 + 10 + 10) cm\\perimeter = 60cm$

And the apothem is the height of each of the triangles that make up the hexagon, that is:

$apothem = 5cm$

Substituting in the formula:

$A=\frac{(60*5)}{2}\\A=\frac{300}{2}\\A=150cm^2$

Thus, the area of the hexagon is $A = 150cm ^ 2$

Answer:

$A = 150cm ^ 2$

7 0

3 years ago

Describe the types of transformation given by each parameter in g(x) = -4f(-x + 2) + 6

forsale [732]

Step-by-step explanation:

Starting with f(x)

f(x)

f(-x) ...... reflection in the y - axis

f(-x+2) ..... horizontal translation by 2 units in the negative x-direction

f(-x+2) + 6 ...... vertical translation by 6 units in the positive y-direction

4f(-x+2) + 6 ..... scaling (or dilation) by a factor of 4

-4f(-x+2) + 6 ..... reflection in the x-axis

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4 years ago

To increase the value of estimated Cohen's d, a researcher increases the sample size. Will this change the value of d?

tatyana61 [14]

Answer:

a. A) Yes; as sample size increases, effect size increases.

b. A) The critical value increases.

Step-by-step explanation:

a.

If all possible samples of size N are drawn from a ﬁnite population, Np, without replacement, and the standard deviation of the mean values of the sampling distribution of means is determined then:

σx =d √N

d = σx . √N

d ∞ N

from this, we can say d is directly proportional to √N

where σx is the standard deviation of the sampling distribution of means and d is the standard deviation of the population’. The standard deviation of a sampling distribution of mean values is called the standard error of the means,

therefore, we can conclude that:

A) Yes; as sample size increases, effect size increases.

b.

In this estimate, tc is called the conﬁdence coefﬁcient for small samples, d is the standard deviation of the sample, x is the mean value of the sample and N is the number of members in the sample.

When determining the t-value, given by

t =( (x−µ) /s) * $\sqrt{N-1}$

it is necessary to know the sample parameters x and s and the population parameter µ. x and s can be calculated for the sample, but usually an estimate has to be made of the population mean µ, based on the sample mean value.

from the above equation it can be deduced that t value is determined with the sample size, and as the sample size increases

A) The critical value increases.

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3 years ago

Anyone tryna help me

polet [3.4K]

Answer:

y < (3/2) |x - 3| +2

Step-by-step explanation:

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3 years ago

Can y’all help me.......

ira [324]

Yes is the correct answer

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3 years ago