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3 years ago

Evaluate 4a + 7b + 3a − 2b for a = 5 and b = −3.

Mathematics

1 answer:

blsea [12.9K]3 years ago

5 0

Answer:

Step-by-step explanation:

$4a+7b+3a-2b\qquad\text{combine like terms}\\\\=(4a+3a)+(7b-2b)\\\\=7a+5b\qquad\text{put a = 5 and b = -3 to the expression}\\\\7(5)+5(-3)=35-15=20$

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Paul deposited $95,000 in a savings account that pays 4% interest compounded daily. What is his balance at the end of six months

Arada [10]

Answer:

$\$96,919.02$

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

$t=6/12=0.5\ years\\ P=\$95,000\\ r=4\%=4/100=0.04\\n=365$

substitute in the formula above

$A=95,000(1+\frac{0.04}{365})^{365*0.5}$

$A=95,000(1+\frac{0.04}{365})^{182.5}=\$96,919.02$

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3 years ago

If y varies directly as x, and y is 400 when x is randy is r when x is 4, what is the numeric constant of variation in this rela

juin [17]

The numeric constant of variation is 100

Step-by-step explanation:

Direct proportion means that increase in one variable cause increase in other variable

Here,

It is given that

y varies directly as x

y∝x

when the proportionality symbol is removed a proportionality constant is introduced

$y = kx$

Given that

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Keywords: Proportion variation

Learn more about direct proportion at:

#LearnwithBrainly

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3 years ago

Castle spent half of his weekly allowance buying pizza. To earn more money his parents let him mow the lawn for $10. What is his

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2 years ago

Read 2 more answers

We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys

marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation

$\bar X=19.2$ represent the battery life sample mean

$\sigma=2.5$ represent the population standard deviation

$n=25$ sample size

$\mu_o =18$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:

Null hypothesis: $\mu = 18$

Alternative hypothesis: $\mu \neq 18$

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis: $\mu \leq 18$

Alternative hypothesis: $\mu > 18$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4$

4) P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=25-1=24$

Since is a two tailed test for parts I and II, the p value would be:

$p_v =2*P(t_{(24)}>2.4)=0.0245$

And for part III since we have a one right tailed test the p value is:

$p_v =P(t_{(24)}>2.4)=0.0122$

5) Conclusion

I. This finding is significant for a two-tailed test at .05.

Since the $p_v$ . We reject the null hypothesis so we don't have a significant result. FALSE

II. This finding is significant for a two-tailed test at .01.

Since the $p_v >\alpha$ . We FAIL to reject the null hypothesis so we have a significant result. TRUE.

III. This finding is significant for a one-tailed test at .01.

Since the $p_v >\alpha$ . We FAIL to reject the null hypothesis so we have a significant result. TRUE.

So then the correct options is:

d. II and III only

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3 years ago