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oksano4ka [1.4K]
3 years ago
12

Consider the equation x^2 + 12x + c = 0. If c = -28, list the steps to solve the equation by completing the square, and give the

solution or solutions.
Mathematics
1 answer:
nlexa [21]3 years ago
8 0
X^2+12x-28
(x-2)(x+14)

Solve for x
x-2=0
x=2

x+14=0
x=-14
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You deposit $650 in a savings account. How long does it take an account with an annual interest rate of 5% to earn $178.25 in in
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Answer:

It takes an account 5.4 years  to earn $178.25 in interest with an annual interest rate of 5%.

Step-by-step explanation:

You can use the following formula to calculate the time it takes an account to earn a certain amount in interest:

t=(1/r)*((F/P)-1), where:

t= time

r= rate of interest= 5%

F= future value= 650+178.25=828.25

P= present value= 650

Now, you can replace the values on the formula:

t=(1/0.05)*((828.25/650)-1)

t=20*0.27

t=5.4

According to this, the answer is that it takes an account 5.4 years  to earn $178.25 in interest with an annual interest rate of 5%.

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3 years ago
I cant understand this hepl me help me
Aleonysh [2.5K]

Answer:

A

Step-by-step explanation:

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What is the inequality
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Problem: Square root of x<12


To solve that, we square both size, x<144

Choices that is less than 144 are the correct answers
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The mean annual premium for automobile insurance in the United States is $1503 (Insure website, March 6, 2014). Being from Penns
romanna [79]

Answer:

If we compare the p value and the significance level for example \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.

Step-by-step explanation:

1) Data given and notation  

\bar X=1440 represent the mean annual premium value for the sample  

s=165 represent the sample standard deviation for the sample  

n=25 sample size  

\mu_o =1503 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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean annual premium in Pennsylvania is lower than the national mean annual premium, the system of hypothesis would be:  

Null hypothesis:\mu \geq 1503  

Alternative hypothesis:\mu < 1503  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-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".  

Calculate the statistic

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

t=\frac{1440-1503}{\frac{165}{\sqrt{25}}}=-1.909    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=25-1=24  

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

p_v =P(t_{(24)}  

Conclusion  

If we compare the p value and the significance level for example \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.  

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Answer:

i would a say Microwave

Step-by-step explanation:


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