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3 years ago

8

You have $1,900 in savings for retirement. If your investments earn 8% annually, how much will you have in your retirement accou

nt in 6 years?

1 answer:

natima [27]3 years ago

6 0

Answer:

$3,015

Step-by-step explanation:

To determine the amount that you will have in 6 years, you have to use the formula to calculate the future value:

FV=PV*(1+i)^n

FV= future value

PV= present value= $1,900

i= interest rate= 8%

n= number of periods of time= 6 years

FV=1,900*(1+0.08)^6

FV=1,900*(1.08)^6

FV=3,015

According to this, the answer is that in 6 years you will have $3,015 in your retirement account.

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a national survey conducted among a simple random sample of 1,507 adults shows that 56% of americans think the civil war is stil

soldier1979 [14.2K]

a)

$z=4.658\\p_v=P(z > 4.65)=1-P(z < 4.65)=1.581x*10^{-6}$

b) By assuming a significance level of α = 0.05 and observing that $p_v$ > α, we can reject the null hypothesis at this level of significance. And in this instance, it makes sense that more than 50% of Americans believe that the Civil War still has an impact on American politics and political life.

c) The confidence interval at 90% would be shown (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

<h3>What is a survey?</h3>

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

a)

1) The presented data and the notation "n=1507" refer to the random sample of Americans, "X" denoting the proportion of those Americans in the sample who believe that the Civil War is still significant to American politics and political life, and "p cap" denoting the estimated number of those Americans.

Since the problem specifies that majority α=0.05 represents the significance threshold, $p_0$ is the number that we wish to test (no given, but is assumed)

Z would stand for the statistic (interesting variable), and $p_v$ for the p value (variable of interest)

P is the percentage of the public that believes that the Civil War still has an impact on American politics and political life.

2) Useful concepts and formulas

The allegation that more Americans than 50% believe the Civil War is still significant to American politics and political life needs to be tested through a hypothesis (Majority). :

Alternative Hypothesis: p $\geq$ 0.5

Null Hypothesis: p $\leq$ 0.5

The proportion is thought to have a normal distribution.

This test for the percentage of union membership has one tail higher.

Verify whether the sample conforms to the presumptions required for the test to be applied.

a) The random sample must be representative; in this situation, there is no mention of this issue, but it is safe to presume that it exists.

b) The sample size must be sufficient.

$np_0=1507*0.5=753.5 > 10\\n(1-p_0)=1507*(1-0.5)=753.5 > 10$

3. Determine the statistic.

The formula used to calculate the statistic is as follows:

$z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }= \frac{0.56-0.5}{\sqrt{\frac{0.5(1-0.5)}{1507} } }=4.658$

P value= $p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}$

According to the alternative hypothesis, the following would be the p value:

P value= $p_v=P(z > 4.65)=1-P(z < 4.65)=1.581*x*10^{-6}$

Using this formula, the confidence interval would be determined.

p ± $z_{\frac{\alpha }{2}}\sqrt{\frac{p(1-p)}{n} }$

With the value of $\alpha$ and $\alpha _2$ , we can get the quantile necessary for the interval in the normal standard distribution for the 90% confidence interval.

$z_{\frac{\alpha }{2} }=2.58$

adding the following to the formula for the confidence interval:

$0.56-2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.527\\0.56+2.58\sqrt{\frac{0.56(1-0.56)}{1507} } = 0.593$

Also provided would be the 90% confidence interval (0.527;0.593).

About 54% to 59% of all Americans, in our opinion, believe that the Civil War is still significant today.

And because the interval does not contain the value of 0.5, we can conclude that, at a 90% level of confidence, the percentage of Americans who believe that the Civil War is still relevant to American politics and political life is higher than 0.5. This result is consistent with the result of part b.

To know more about survey, visit:

brainly.com/question/13192080

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6 0

2 years ago

Apples are 94 cents a pound, and pears are $1.22 a pound. write an expression for the total cost, in dollars, of a pounds of app

sineoko [7]

1 apple: 94 cents = 0.94 dollars
a apples: 0.94 ×a= 0.94a
p pears: 1.22× p= 1.22p
total: 1.22p + 0.94a
hope it helps!

4 0

3 years ago

Read 2 more answers

Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value.

Blizzard [7]

First,

We are dealing with parabola since the equation has a form of,

$y=ax^2+bx+c$

Here the vertex of an up - down facing parabola has a form of,

$x_v=-\dfrac{b}{2a}$

The parameters we have are,

$a=-5,b=-10, c=6$

Plug them in vertex formula,

$x_v=-\dfrac{-10}{2(-5)}=-1$

Plug in the $x_v$ into the equation,

$y_v=-5(-1)^2-10(-1)+6=11$

We now got a point parabola vertex with coordinates,

$(x_v, y_v)\Longrightarrow(-1,11)$

From here we emerge two rules:

If $a$ then vertex is max value
If $a>0$ then vertex is min value

So our vertex is minimum value since,

$a=-5\Longleftrightarrow a$

Hope this helps.

r3t40

7 0

3 years ago

A manufacturer of pickup trucks is required to recall all the trucks manufactured in a given year for the repair of possible def

Crank

Answer: 2%

Step-by-step explanation:

Let A be the event of having defective steering and B be the vent of having defective brake linings.

Given: P(A) = 0.03 P(B) = 0.05

P(neither A nor B ) = 0.94

Using formula: P(either A nor B) = 1- P(neither A nor B )

= 1-0.94

i.e. P(either A nor B) =0.06

Using formula:P(A and B) = P(A)+P(B)-P(either A or B)

P(A and B) =0.03+0.05-0.06

= 0.02

Hence, the percentage of the trucks have both defects = 2%

8 0

3 years ago

Solve the following problem and show the work. (x - 6)^2 + (y + 1)^2 = 40

Taya2010 [7]

Answer:

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 6)² + (y + 1)² = 40 ← is the equation of a circle in standard form

centre = (6, - 1) and r = $\sqrt{40}$ = 2 $\sqrt{10}$

3 0

3 years ago