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2 years ago

Solve for z -c + 6z = tz +83

Mathematics

2 answers:

Naya [18.7K]2 years ago

8 0

Answer:

the answer to this problem is

z= 83/-c+6-t

sladkih [1.3K]2 years ago

6 0

-c +6z = tz+83

add c to each side

6z = tz +83 +c

subtract tz from each side

6z-tz = c+83

factor out z

z(6-t) = c+83

divide by (6-t)

z = (c+83)/(6-t)

Answer:z = (c+83)/(6-t)

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If you set aside $9000 at the end of each year for the next 22 years in a Roth IRA, how much will you have at your retirement 22

madam [21]

Answer:

$501,049.37

Step-by-step explanation:

For computing the amount after 22 years we need to applied the future value which is shown in the attachment below:

Given that

PMT = $9,000

NPER = 22 years

Annual rate = 0.078

Quarterly= 0.078 ÷ 4 = 0.0195

Effective annual rate = (1.0195^4) - 1 = 0.0803113041

Now applied the formula which is given below

= -FV(RATE;NPER;PMT;PV)

After applying the above formula, the future value is $501,049.37

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2 years ago

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

zhuklara [117]

Answer:

The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is 5 units to the right and 23 units down.

Explanation:

1) Vertex form of the function that represents a parabola.

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression factor (in the case |A| < 1) factor.

2) Find the vertex of the first function, f(x) = x²

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

3) Find teh vertex of the second function, g(x) = x² -10x + 2

The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.

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2 years ago

Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp

yKpoI14uk [10]

Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

$H_0: \mu=2\\\\H_a:\mu< 2$

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803$

The degrees of freedom for this sample size are:

$df=n-1=52-1=51$

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0

2 years ago

A student wants to know how far above the ground the top of a leaning flagpole is. At high noon, when the sun is almost directl

MariettaO [177]

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem. Therefore, the distance of the top of the pole to the ground is:

$14 in = 1.1667 ft$

$1.1667x=6*3\\x = 15.43$

The distance of the top of the pole to the ground is 15.43 ft.

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2 years ago

HELP ASAP 40 POINTS REAL ANSWER

Jet001 [13]

Answer:

b) number of flowers.

c) 2830

Step-by-step explanation:

We are given the following in the question:

The number of flowers bloomed is given by the function:

where s is the s is the number of seeds she planted.

The number of seeds planted per week is given by

where w represents the number of weeks.

a) composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks.

The composite function can be written as:

where f(w) gives the number of flowers that bloomed in w weeks.

b) units of measurement for the composite function

The composite functions gives the number of flower that will bloom in w weeks. Thus, the unit of measurement is number of flowers.

c) Number of flowers in 35 weeks.

We put w = 35 in the composite function.

2830 flowers will bloom in 35 weeks.

Thanks

Step-by-step explanation:

8 0

2 years ago