Which of the following is equivalent to<br> ?<br> 36 37

The boundary lines for the system of inequalities is given in the graph.

diamong [38]

Answer:

C)

region C

Step-by-step explanation:

We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:

$\displaystyle y ≤ -x + 2$

0 ≤ 2 ☑ [We shade the portion of the graph that CONTAIN THE ORIGIN, which is the bottom portion.]

$\displaystyle y ≥ 2x - 3$

0 ≥ −3 ☑ [We shade the portion of the graph that CONTAINS THE ORIGIN, which is the left side.]

So, now that we got that all cleared up, we can tell that both graphs share a region where the ORIGIN IS VISIBLE. Therefore region C matches the above inequalities.

I am joyous to assist you anytime.

4 0

3 years ago

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The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

Statisticians use ______ scores to divide the ______ under a curve the way people use a knife to cut pizza. Just as the pizza is

solong [7]

Answer:

Statisticians use z-scores to divide the area under a curve the way people use a knife to cut pizza.

Step-by-step explanation:

Statisticians use z-scores to divide the area under a curve the way people use a knife to cut pizza.

z-score:

A z-score is a numerical measurement which is measured in terms of standard deviations from the mean.
Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

If a z-score is 0, it tells that the data point is same as the mean.
Area under the normal curve is 1.

6 0

3 years ago

Find the mean of the data in the dot plot below.

salantis [7]

The mean of the following dot plot:

Mean: 3

Step-by-step explanation:

0 x 1 = 0

3 x 1 = 3

6 x 1 = 6

(we only add the numbers that only has a dot on the number in the dot plot)

So:

Mean: 0 + 3 + 6 = 9/3 = 3

Read more on Brainly.com - brainly.com/question/16754217#readmore

this was my previous answer from your other question

7 0

3 years ago

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The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr

boyakko [2]

100,000 t-shirts were sold

3 0

3 years ago

Which of the following is equivalent to ? 36 37