1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced.
zzz [600]

Answer:

CI=(66.54,78.46)                                  

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , \bar{X}=72.5\% , s=5.8%

Since the size of the sample is small.

We will use the student's t statistic to construct a 995 confidence interval.

\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}

From the t-table with 9 degree of freedom for \frac{\alpha}{2}=0.005

t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}

t_{n-1,\frac{\alpha}{2}}=3.250

The 99% confidence interval is given by,

CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}

CI=72.5 \pm 5.96

CI=(72.5+5.96),(72.5-5.96)

CI=(66.54,78.46)

8 0
3 years ago
20 - (-3) + 15 help a girl outt :(
Kryger [21]

Answer is 38

20 -(-3) + 15

20 + 3 + 15

38

6 0
3 years ago
Read 2 more answers
Which table values can be defined by the function y=2x+3
lbvjy [14]

Answer:

beggining poit:3   second point (potentially):  1,5

Step-by-step explanation:

in the y intercept 3 is it so which ever has a 3 as the starting point there could be an option

for the 2x part that is the slope otherwise known as rise over run so what you do is that you turn it to a fraction over or under 1 meaning you rise for 2 and go to the right 1

rise 2

      _

run  1

in order to rise 2 you go up 2 from the y intercept(3) and in order to run you go right since its a positive

once you plot those two dots then you draw a line across

4 0
3 years ago
Read 2 more answers
The sum of two integers is 33. The larger is 6 more than twice the smaller. Find the two
grandymaker [24]

Answer:

24 and 9

Step-by-step explanation:

Hi there!

Let x be equal to the larger integer.

Let y be equal to the smaller integer.

<u>1) Construct equations</u>

  1. x+y=33 (The sum of two integers is 33)
  2. x=6+2y (The larger is 6 more than twice the smaller)

<u>2) Solve for one of the integer</u>

Isolate x in the first equation

x+y=33\\x=33-y

Plug the first equation into the second

33-y=6+2y

Combine like terms

33-6=2y+y\\27=3y\\9=y

Therefore, the smaller integer is 9.

<u />

<u>3) Solve for the other integer</u>

x+y=33

Plug in y (9)

x+9=33\\x=33-9\\x=24

Therefore, the larger integer is 24.

I hope this helps!

4 0
3 years ago
Read 2 more answers
Complete the rational operation <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7Bx%20-%205%7D%20%20-%20%20%5Cfrac%7Bx%7
prisoha [69]
We have
                             3 / (x-5) - x/5
We make the GCF and we have
                                    15/[ 5(x-5) ] - x(x-5)/[ 5(x-5)]
                                  = [ 15 - x(x-5) ]  [5(x-5)]
                                  = [ 15 - x^2 + 5x] / [ 5 (x-5) ]
                                  = [15 - x^2 + 5x]/[5x - 25]
An answer to your question is (15-x^2+5x)/(5x-25)
6 0
3 years ago
Other questions:
  • Steve bought 2 plain pizzas and 1/4 of a pepperoni pizza.in all how much pizza did he buy
    10·2 answers
  • What is 14 52/60 simplified to
    12·2 answers
  • A tour bus travels 2160 miles in 36 hours. What is the average distance the bus travels in one hour?
    15·2 answers
  • Which is greater ratio than 2:7
    15·1 answer
  • What is 1 1/4 + ( 3 2/3 + 5 3/4)?
    8·1 answer
  • Jasmine had a pizza party with 3 of her friends to celebrate the Last Day of school. They order two pizzas. Each pizza had 8 sli
    12·1 answer
  • What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
    15·2 answers
  • Fill in the blank: Set up a ratio using _________. To get the right answers, you cannot skip this step
    12·1 answer
  • An experiment consists of spinning the spinners shown and adding the numbers together. Complete the array.
    14·1 answer
  • Tastee-Freeze Ice Cream
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!