X A) altemate interior B) altemate exterior C) corresponding D) same-side interior

Question 3 of 10

miss Akunina [59]

Answer:

c. 5:6

Step-by-step explanation:

4 0

3 years ago

Every evening jenna empties her pockets and puts her change in a jar .at the end of the week she counts her money . one week she

Bad White [126]

There are 35 quarters and 15 dimes.
Systems of Equations:
q+d=50
.25q+.10d=10.25

6 0

3 years ago

Complete the statement to describe the expression ab+cd+ef+gh.

BigorU [14]

Answer with explanation:

The given expression is

=ab+cd+ef+gh

The meaning of expression is equal to terms which contains variables and constants and operation between them is Addition, Subtraction, Multiplication and Division.

→The expression consists of four terms which are, ab, cd, ef, and gh.

→Each term contains

Two factors.

8 0

4 years ago

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Let X denote the length of human pregnancies from conception to birth, where X has a normal distribution with mean of 264 days a

Kaylis [27]

Answer:

Step-by-step explanation:

Hello!

X: length of human pregnancies from conception to birth.

X~N(μ;σ²)

μ= 264 day

σ= 16 day

If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:

X[bar] ~N(μ;σ²/n)

When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ

When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)

a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.

P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602

b. P(X[bar]>b)= 0.05

You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.

P(X[bar]≤b)= 0.95

P(Z≤(b-μ)/(σ/√n))= 0.95

The value of Z that accumulates 0.95 of probability is Z= 1.648

Now we reverse the standardization to reach the value of pregnancy length:

1.648= (b-264)/(16/√15)

1.648*(16/√15)= b-264

b= [1.648*(16/√15)]+264

b= 270.81 days

c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.

Symbolically:

P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)

P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))

P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0

d. P(X[bar]>270)= 0.1151

P(Z>(270-264)/(16/√n))= 0.1151

P(Z≤(270-264)/(16/√n))= 1 - 0.1151

P(Z≤6/(16/√n))= 0.8849

With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:

P(Z≤1.200)= 0.8849

$Z= \frac{X[bar]-Mu}{Sigma/\sqrt{n} }$

$Z*(Sigma/\sqrt{n} )= (X[bar]-Mu)$

$(Sigma/\sqrt{n} )= \frac{(X[bar]-Mu)}{Z}$

$Sigma= \frac{(X[bar]-Mu)}{Z}*\sqrt{n}$

$Sigma*(\frac{Z}{(X[bar]-Mu)})= \sqrt{n}$

$n = (Sigma*(\frac{Z}{(X[bar]-Mu)}))^2$

$n = (16*(\frac{1.2}{(270-264)}))^2$

n= 10.24 ≅ 11 pregnant women.

I hope it helps!

6 0

3 years ago

Kendra dives off of a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation

il63 [147K]

Answer:

1) How high is the diving board?:  6 feet above the water surface

2) How deep does the diver dive into the water?: 6.5feet into the water

3) At what horizontal distance from the board does the diver enter the water? 1 feet from the board

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive? 6 feet from the board

Explanation:

The dive is modeled by the equation h(x) = x² - 7x + 6.

Two important features that you must notice quickly are:

That is a quadratic function, which is a parabola.

Since the leading term, x², is positive, the parabola open upwards, and the vertex is a minimum.

As for the questions:

1) How high is the diving board?

The diving board is the place from which Kendra dives off. At this point, the horizontal distance, x, from the diving board is 0.

Then, the height will be given by h(x) with x = 0. Substitute into the equation and compute:

h(0) = 0² - 7(0) + 6

h(0) = 0 - 0 + 6

h(0) = 6

Therefore, the diving board is 6 feet above the water surface.

2) How deep does the diver dive into the water?

This is the minimum heigth given by the function h(x).

As explained above, this is the vertex of the parabola.

You can find the x-coordinate of the vertex with the equation:

x-coordinate of the vertex = -b/(2a)

Where b and a are the coefficients of the linear term and the quadratic terms in the equation for h(x), respetively:

a = 1
b = -7

x-coordinate = - (-7) / (2 × 1) = 7/2 = 3.5

Now you can find h(x) for x = 3.5

h(3.5) = (3.5)² - 7(3.5) + 6 = 12.25 - 24.5 + 6 = - 6.25

That is 6.25 feet below the water surface.

3) At what horizontal distance from the board does the diver enter the water?

That is the x-intercept of the function. This is, the value of x when h(x) = 0.

Thus, solve the equation 0 = x² - 7x + 6.

You can factor the equation:

Find two numbers that add up -7 and their product is +6. Those are - 6 and -1:

0 = (x - 1) (x - 6)

Using the zero product property:

(x - 1) = 0 or (x - 6) = 0

x = 1 or x = 6

Thus, you have two solutions, which are the two x-intercepts of the funtion.

x = 1 represents the horizontal distance from the board where the diver enters the water.

The other solution is the answer to the next question.

4) At what horizontal distance from the board does the diver come to the surface of the water after the dive?

As explained above, the equation has two x-intercepts. They both are the points where the parabola crosses the x-axis, which is when the height, h(x) is 0. That height is the surface of the water level.

The first x-intercept is the point (horizontal distant from the board) where the diver enters the water, such as asserted above.

The other x-intercept is where the diver comes to the surface of water after the dive and after being submerged in the water: the diver enters the water, dives 6.5feet into the water, and returns to the surface.

Thus, this is the solution x = 6 for h(x) = 0.

Hence, Kendra comes to the surface of water at 6 feet from the board.

7 0

3 years ago

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