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Hatshy [7]
2 years ago
11

37. The sum of first three terms in an arithmetic progression is 24 and the sum of their squares is 224. Find the first three te

rms of this arithmetic progression.
​
Mathematics
1 answer:
Airida [17]2 years ago
8 0

Answer:

12, 8, and 4

Step-by-step explanation:

  • Given

a + d + a + a - d = 24

3a = 24   ⇒  [ a = 8 ]  

and (a + d)² + a² + (a - d)² = 224

3a² + 2d² = 224

2d² = 224 - 192 = 32

d² = 16

[ d = ±4 ]

∴ The first three terms to A.P are

a + d = 8 + 4 = 12

a  -  = 8

a - d = 8 - 4 = 4

∴ Three terms are 12 , 8, and 4

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Which the following is a linear algebraic expression<br><br>pleaseee...help me in math​
Serga [27]

Answer:

C 9s-8t

Step-by-step explanation:

A linear expression is an algebraic expression in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear expression can have one or more variables.

3 0
3 years ago
Jack popped some popcorn, but 3 of the 150 kernels did not pop
frutty [35]
That sucks for jack. But uhm what is your question. Also Jack can just put the popcorn in for a longer amount of time
5 0
3 years ago
If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate cos 2 θ . -7/25 -1/5 7/25
Grace [21]

Answer:

-7/25.

Step-by-step explanation:

From the given point P we see that the hypotenuse =  √(3*2 + 4^2) = 5.

So cos  θ = 3/5

cos 2 θ =  2 cos^2 θ - 1

= 2 * (3/5)^2 -1

= -7/25.

6 0
3 years ago
A business school has a goal that the average number of years of work experience of its MBA applicants is more than three years.
gizmo_the_mogwai [7]

Answer:

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

p_v =P(z>0.280)=0.390  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=3.1 represent the sample mean

\sigma=\sqrt{6} represent the sample standard deviation for the sample

n=47 sample size  

\mu_o =3 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 is higher than 3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3  

Alternative hypothesis:\mu > 3  

If we analyze the size for the sample is > 30 and we know the population deviation so 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".  

Calculate the statistic

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

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

P-value

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

p_v =P(z>0.280)=0.390  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

3 0
3 years ago
What is the value of x in trapezoid ABCD?<br>x=15<br>x=20<br>x=45<br>x=60<br>​
Zepler [3.9K]

Answer:

I think its x=15

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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