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Rufina [12.5K]
2 years ago
9

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

Mathematics
1 answer:
dusya [7]2 years ago
3 0
The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190

Answer: first number is 190
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You would multiply the radius by 2 which would make the diameter 4
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2 years ago
Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout
Keith_Richards [23]

Answer:

The correct answer to the question is

C) The mean and range of the fingerling catfish are both greater than those of the large catfish.

Step-by-step explanation:

From the attached chart and table, it is seen that the mean = (∑ f×m)/n

Where Mean x = Mean estimate of frequency distribution

f = Class frequency

m = midpoint of each class

∑ f×m = the sum of the product of each midpoint value and its respective frequency

n = The sum of the frequencies

Therefore from the tables we have

For the Fingerling catfish  

(∑ f×m)/n = 11037.5/1.375 = 8027.3

and the range = (Maximum value) - (minimum value) in the data set

= 10500 - 3500 = 7000

For the Large catfish we have

(∑ f×m)/n = 2931.25/2.1 = 1395.83

and the range = (Maximum value) - (minimum value) in the data set

= 2125 - 375 = 1750

As seen above, the mean and range of the fingerling catfish are both greater than those of the large catfish

8 0
2 years ago
Marcia has a balance of $1700 on her credit card, which she plans to pay off by making a payment of the same amount each month.
I am Lyosha [343]

Amount that is left on Marcia credit card = $ 1700

Marcia thought that ,she will pay off her balance,by making a payment of the same amount each month.

As, there are four payment methods are given , we have to find the way in which balance can be paid fastly.

A.→ 55 × Number of months = 1700

Number of months = \frac{1700}{55}=31 months (approx)

B. → 45 × Number of months = 1700

Number of months = \frac{1700}{45}=38 months (approx)

C.→ 75 × Number of months = 1700

Number of months = \frac{1700}{75}=23 months (approx)

D.→ 90 × Number of months = 1700

Number of months = \frac{1700}{90}=19 months (approx)

The monthly amount of $ 90,will allow Marcia to pay off her balance fastest.

8 0
2 years ago
Read 2 more answers
What is the value of h in the figure below? In this diagram BAD~CBD
liberstina [14]

Answer:

The correct option is E. 8

The value of h is 8 unit.

Step-by-step explanation:

Given:

Δ BAD ~ Δ CBD

AC = 20

DC = 4

∴ AD = AC - DC=20-4=16

To Find:

h = ?

Solution:

Δ BAD ~ Δ CBD      ................Given

If two triangles are similar then their sides are in proportion.

\frac{BD}{CD} =\frac{AD}{BD} =\frac{BA}{CB}\ \textrm{corresponding sides of similar triangles are in proportion}\\  

On substituting the given values we get

\dfrac{BD}{CD} =\dfrac{AD}{BD}

\dfrac{h}{4} =\dfrac{16}{h}\\\therefore h^{2}=64\\\therefore h=8\ unit

The value of h is 8 unit.

8 0
2 years ago
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Gabi is working on another backyard project. She is building a fence to keep deer out of her garden. One side of her garden is a
nydimaria [60]

Answer:

  • length: 14 feet , width: 43 feet, or
  • length: 86 feet, width: 7 feet

Both solutions are valid.

Explanation:

1. First assumption is that the shape of the fence is <u>rectangular</u>.

2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet

  • 2x + y = 100

3. The, the area of the fence will be:

  • length × width = xy = 600

4. Now you have two equation with two variables which you can solveL

  • Solve for y in the first equation: y = 100 - 2x
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5. Solve the last equation by completing squares:

  • Distributive property: 100x - 2x² = 600
  • Divide both sides by - 1: 2x² - 100x = - 600
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  • Square root both sides: x - 25 = ± 18.028
  • Clear x: x = 25 ± 18.028
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Both values are valid,

If x = 43 , then y = 600/43 = 14

If x = 7, then y = 600/7 = 86

Thus, the lenght and width of the fence may be:

  • 43 feet (width) and 14 feet (length), or
  • 7  feet (width) and 86 feet (length).
3 0
2 years ago
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