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3 years ago

What is the sum of the arithmetic sequence 6, 14, 22, if there are 26 terms

1 answer:

3 0

Sum of nth term of arithmetic sequence is given by Sn = n/2[2a + (n - 1)d]
Here, a = 6, n = 26 and d = 14 - 6 = 8
S26 = 26/2[2(6) + (26 - 1)8] = 13[12 + 25(8)] = 2,756

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2 years ago

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Each set of furniture costs $2,419. How much would it cost to buy 5 sets of furniture?

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Answer:

2419 times 5 equals 12095$

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2 years ago

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Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t

-Dominant- [34]

Let

x--------> the number of children

y------> the number of teenagers

z------> the number of adults

we know that

$2x+3y+5z=1,950$ ------> equation A

$x+y+z=570$ -----> equation B

$y=\frac{3}{4}x$

$x=\frac{4}{3}y$ -------> equation C

Substitute equation C in equation A and equation B

$2[\frac{4}{3}y]+3y+5z=1,950$

$\frac{17}{3}y+5z=1,950$ --------> equation D

$[\frac{4}{3}y]+y+z=570$

$\frac{7}{3}y+z=570$ --------> equation E

Multiply equation E by $-5$

$-\frac{35}{3}y-5z=-2,850$ --------> equation F

Adds equation D and equation F

$\frac{17}{3}y+5z=1,950\\\\-\frac{35}{3}y-5z=-2,850\\\\---------\\\\-\frac{18}{3}y=-900\\\\y=3*900/18\\\\y=150\ teenagers$

therefore

<u>the answer is the option</u>

$150\ teenagers$

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2 years ago

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According to a study, 68% of all males between the ages of 18 and 24 live at home. (Unmarried college students living in a d

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Answer:

a) P(X≥143)=0

b) This contradicts the study as getting a sample with this proportion is almost impossible (if the proportion of 68% is true).

Step-by-step explanation:

If we use the normal approximation to the binomial distribution we have the following parameters (mean and standard deviation):

$\mu=np=0.68*206=140.1\\\\ \sigma=\sqrt{np(1-p)}=\sqrt{206*0.68*0.32}=\sqrt{44.8256}=6.7$

Then, we can calculate the probability of X being equal or more than 143 using the z-score:

$z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{143-140.1}{6.7/\sqrt{206}}=\dfrac{2.9}{0.4668}=6.2124\\\\\\P(x\geq143)=P(z>6.2124)=0$

This contradicts the study as getting a sample with this proportion is almost impossible (if the proportion of 68% is true).

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3 years ago

the triangle and square shown below have the same perimeter . what is the length of one side of the square

qaws [65]

Answer:

If "x" = 1 then triangle perimeter = 12 and square perimeter = 12

So, one side of the square = (x +2) = (1 + 2) = 3

Step-by-step explanation:

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3 years ago