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4 years ago

10

Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. f(x) = 3^x-7 g(x) = 2 l

og(2x)

1 answer:

Gemiola [76]4 years ago

5 0

Answer:

(.5 , 0) (7.8 , 2.4)

Step-by-step explanation:

The solution to a system of equations is when they cross each other on a graph.

When this is graphed you case use the trace and zoom in tools to find where they are solutions at.

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how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% com

miskamm [114]

To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula: $A=P(1+rt)$
where
   $A$ is the final investment value
   $P$ is the initial investment
   $r$ is the interest rate in decimal form
   $t$ is the time in years
For our problem we know that $P=5000$ , $r= \frac{4}{100} =0.04$ , and $t=5$ , so lets replace those values in our simple interest formula to find $A$ :
$A=5000(1+(0.04)(5))$
$A=5000(1.2)$
$A=6000$

Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: $A=P(1+ \frac{r}{n})^{nt}$
where
   $A$ is the final investment value
   $P$ is the initial investment
   $r$ is the interest rate in decimal form
   $n$ is the number of times the interest is compounded per year
   $t$ is the time in years
For our problem we know that $P=5000$ , $r= \frac{4}{100} =0.04$ , and $t=5$ . Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded $\frac{12months}{4months} =3$ times per year, so $n=3$ . Now that we have all the vales, lets replace them in our formula:
$A=5000(1+ \frac{0.04}{3} )^{(3)(5)}$
$A=5000(1+ \frac{0.04}{3} )^{15}$
$A=6098.95$

now that we know the final amounts of our investments, lets find how much difference is between them:
$6098.95-6000=98.95$

We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.

5 0

4 years ago

Which sequence of transformations could have been used to transform triangle ABC to produce triangle A"B"C"?

Andreyy89

The sequence of transformations that could have been used to transform triangle ABC to produce triangle A"B"C" is B.Triangle ABC was reflected across the y-axis and then translated 7 units down.

6 0

4 years ago

Write the equation of the line that has a y-value that increaes by 4 for every 4 for every x that increases by 1. it also crosse

Nataly [62]

The answer is
<span>a. y=4x-2</span>

6 0

3 years ago

At a large midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

nasty-shy [4]

Answer:

B. Z=1.98

Step-by-step explanation:

1) Data given and notation

$X_{1}=20$ represent the number of sampled freshmen finished in the bottom third of their high school class in 1993

$X_{2}=10$ represent the number of sampled freshmen finished in the bottom third of their high school class in 1997

$n_{1}=100$ sample 1 selected

$n_{2}=100$ sample 2 selected

$p_{1}=\frac{20}{100}=0.20$ represent the proportion of sampled freshmen finished in the bottom third of their high school class in 1993

$p_{2}=\frac{10}{100}=0.0023$ represent the proportion ofsampled freshmen finished in the bottom third of their high school class in 1997

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion graduated in the bottom third of their high school class is higher for 1993 than 1997 , the system of hypothesis would be:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{20+10}{100+100}=0.15$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.20-0.10}{\sqrt{0.15(1-0.15)(\frac{1}{100}+\frac{1}{100})}}=1.98$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(Z>1.98)=0.024$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion graduated in the bottom third of their high school classes in 1993 is not significant higher than the proportion in 1997.

3 0

4 years ago

A grocer stacks oranges in a square pyramid. each orange sits on the 4 oranges below it. so, the top layer has 1 orange and the

scoundrel [369]

A. No. of oranges in layer no. i = i*i
b. No oranges reqired for 10 layers = ∑i² where i=0 and i-->10
= 385

6 0

3 years ago