Find the zeros of polynomial function and solve polynomials equations.<br> f(x)=81x^4-16

In 2009 the number of vehicle sales in the United States was 10,002 thousand and in 2013 it was 17,884 thousand.a. [3 pts] Deter

anygoal [31]

Answer:

1970.5 thousand

Step-by-step explanation:

Given

Vehicle sales in 2009 = 10,002 thousand

Vehicle sales in 2013 = 17,884 thousand

Required

Determine the average rate of change;

From the given parameters, it can be seen that the number of vehicles is a function of year

Let x represent the years and y represent the number of vehicles;

Such that;

$x_1 = 2009;\ y_1 = 10,002$

$x_2 = 2013;\ y_2 = 17,884$

The rate of change is calculate as follows;

$m = \frac{y_1 - y_2}{x_1 - x_2}$

$m = \frac{10002 - 17884}{2009 - 2013}$

$m = \frac{-7882}{-4}$

$m = 1970.5$

Hence, the average rate of change is 1970.5 thousand

6 0

3 years ago

What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12? an = 4(−3)n

nadya68 [22]

The geometric sequence is given by:
an=ar^(n-1)
where:
a=first term
r=common ratio
n is the nth term
given that a=4, and second term is -12, then
r=-12/4=-3
hence the formula for this case will be:
an=4(-3)^(n-1)
where n≥1

5 0

2 years ago

Read 2 more answers

Use the t-distribution and the sample results to complete the test of the hypotheses. Use a significance level. Assume the resul

Ksenya-84 [330]

Answer:

Test statistic = 1.3471

P-value = 0.1993

Accept the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 4

Sample mean, $\bar{x}$ = 4.8

Sample size, n = 15

Alpha, α = 0.05

Sample standard deviation, s = 2.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 4\\H_A: \mu \neq 4$

We use two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{4.8 - 4}{\frac{2.3}{\sqrt{15}} } = 1.3471$

Now, we calculate the p-value.

P-value = 0.1993

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept it.

3 0

3 years ago

What is another way to write the expression t. (14--5) ?

melomori [17]

Answer: Second option.

Step-by-step explanation:

It is important to remember the Distributive Property in order to solve this exercise.

The Distributive property states that:

$a(b+c)=ab+ac\\\\\\a(b-c)=ab-ac$

In this case you have the following expression provided in the exercise:

$t(14-5)$

Then, in order to write this expression in another way, you can apply the Distributive property. Multiply each number inside the parentheses by "t".

Applying this procedure, you get:

$t(14-5)=(t14)-(t5)$

Notice that this expression matches with the one shown in the the second option.

8 0

3 years ago

HELP ASAP TIMED !!!! What is the exact value of cos(c + d), given Sine c = StartFraction 24 Over 25 EndFraction for c in Quadran

Keith_Richards [23]

9514 1404 393

Answer:

D

Step-by-step explanation:

In the second quadrant, ...

c = 180° -arcsin(24/25) ≈ 106.26°

In the third quadrant, ...

d = 360° -arccos(-3/4) ≈ 221.41°

Then cos(c+d) = cos(327.67°) ≈ 0.84498

This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:

$\dfrac{21+24\sqrt{7}}{100}\approx 0.84498$

_____

Perhaps you want to work this out using the trig identities.

cos(c) = -√(1 -sin(c)²) = -7/25

sin(d) = -√(1 -cos(d)²) = -(√7)/4

Then the desired cosine is ...

cos(c+d) = cos(c)cos(d) -sin(c)sin(d)

cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)

cos(c+d) = (21 +24√7)/100 . . . . matches choice D

8 0

2 years ago

Find the zeros of polynomial function and solve polynomials equations. f(x)=81x^4-16