The triangles shown in the graph are congruent. Based on the graph, determine which congruency statement is correct.

Please Help! Algebra 2!

eduard

Answer:

The interest rate of the account is $3\%$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=14\ years\\ P=\$1,863\\ A=\$2,830.97\\n=4$

substitute in the formula above and solve for r

$\$2,830.97=\$1,863(1+\frac{r}{4})^{4*14}$

$(2,830.97/1,863)=(1+\frac{r}{4})^{56}$

$(2,830.97/1,863)^{1/56}=(1+\frac{r}{4})$

$[(2,830.97/1,863)^{1/56}-1]=\frac{r}{4}$

$r=4*[(2,830.97/1,863)^{1/56}-1]\\ \\r= 0.03$

Convert to percent

$r= 0.03*100=3\%$

8 0

3 years ago

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greate

spayn [35]

A + b s 30b2a yw

Why?
Because it is

4 0

3 years ago

Read 2 more answers

What is 87.252 dividend by 2.2 I am not sure how to do the work

WARRIOR [948]

Answer:

39.66

Step-by-step explanation:

If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

Divide like you usually do

Put decimal point directly above decimal point in the dividend.

Check your answer.

7 0

3 years ago

Read 2 more answers

HELP FAST NOW PLEASE IM HAVING TROUBLE!!

tia_tia [17]

First triangle=bxh/2
=3x4/2
=6in squared
rectangle=l x w
=3 x 10
=30in squared

trapezoid=3+5x2/2
=8in squared
6 + 30 + 8
=44 in squared

7 0

3 years ago

Read 2 more answers

In a study of red/green color blindness, 700 men and 2850 women are randomly selected and tested. Among the men, 66 have red/gre

olga55 [171]

Answer:

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

$p_v =P(Z>15.197) \approx 0$

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 of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

Step-by-step explanation:

Data given and notation

$X_{M}=66$ represent the number of men with red/green color blindness.

$X_{W}=8$ represent the number of women with red/green color blindness.

$n_{M}=700$ sample of male slected

$n_{W}=2850$ sample of female selected

$p_{M}=\frac{66}{700}=0.0943$ represent the proportion of male with red/green color blindness.

$p_{W}=\frac{8}{2850}=0.00281$ represent the proportion of female with red/green color blindness.

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion of men with red/green color blindness. is higher than the proportionof women with red/green color blindness. , the system of hypothesis would be:

Null hypothesis: $p_{M} \leq p_{W}$

Alternative hypothesis: $p_{M} > p_{W}$

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

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

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{66+8}{700+2850}=0.0208$

Calculate the statistic

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

$z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197$

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:

$p_v =P(Z>15.197) \approx 0$

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 of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

8 0

3 years ago