The ______ is the control center of the nervous system. It sends and receives signals to and from the entire body.

For f(x) =4x+1 g(x)=x²-5, find (f•g)(x)

Marta_Voda [28]

Step-by-step explanation:

The composite function (f o g)(x)

= f(x² - 5)

= 4(x² - 5) + 1

= 4x² - 19.

5 0

3 years ago

Read 2 more answers

How do I solve this with explanation?

kakasveta [241]

Answer:

x = 106°

Step-by-step explanation:

You must understand the picture to answer the question correctly.

The angle to the right has measure 68°.

The angle to the left has measure x, an unknown number.

Notice that 174° is written in gray, not black, and notice that the curve is also in gray. That means the entire angle made up of 68° and x measures 174°.

x + 68° = 174°

Subtract 68° from both sides.

x = 106°

7 0

2 years ago

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted t

LekaFEV [45]

Answer:

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Step-by-step explanation:

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:

At the null hypothesis, we test if the mean is the same, that is:

$H_0: \mu = 59.5$

At the alternate hypothesis, we test that it is different, that is:

$H_a: \mu \neq 59.5$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

59.5 is tested at the null hypothesis:

This means that $\mu = 59.5$

After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.

This means that $n = 250, X = 59.2, \sigma = 1.9$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}$

$z = -2.5$

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.

Looking at the z-table, Z = -2.5 has a pvalue of 0.0062

2*0.0062 = 0.0124

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

5 0

2 years ago

Surface Area of the pyramid

hichkok12 [17]

Answer:

C

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

1 bottom square (8×8)

4 side triangles

the area of a triangle is

baseline × height / 2

now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

8 0

1 year ago

Hello can you please help me posted picture of question

dsp73

The correct answer to your question is 6, option B.

The degree of a polynomial is the highest exponent or power of the variable that is involved in the expression. In the above question we have only one variable which is x, and from the given terms we can see that the highest power of x is 6. So the degree of polynomial is 6. The degree of polynomials helps us to know about the end behavior of the graph.

6 0

3 years ago