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3 years ago

Find the 50th term of the sequence 5, –2, –9, –16, ...

2 answers:

8 0

The sequence 5, -2, -9, -16... is a arithmetric sequence with the difference between a number and its succeding term is -7. The formua for getting the nth term of an arithmetric sequence is
$a_n = a_1 + (n-1)d$
where $a_n$ is the nth term
$a_1$ is the first term
n is the number of terms
d is the difference

The first term in the sequence is 5. You need to find the 50th term so n is 50. The difference (d) is -7. Substituting these values in the equation, we get the final answer
$a_{50} = 5 + (50-1)(-7) \\ a_{50} = -338$

The 50th term is -338.

Alecsey [184]3 years ago

5 0

The correct answer: -338

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A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. How

anyanavicka [17]

Answer: 60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of 20% solution that should be mixed.

Let y represent the number of gallons of 50% solution that should be mixed.

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that

0.2x + 0.5y = 0.4×180

0.2x + 0.5y = 72- - - - - - - - - - - -1

Since the total number of gallons is 180, it means that

x + y = 180

Substituting x = 180 - y into equation 1, it becomes

0.2(180 - y) + 0.5y = 72

36 - 0.2y + 0.5y = 72

- 0.2y + 0.5y = 72 - 36

0.3y = 36

y = 36/0.3

y = 120

x = 180 - y = 180 - 120

x = 60

4 0

3 years ago

K/4 - 5k + 1 = 1<br> please

irinina [24]

Answer:

-19k ≠ 0

No solutions

Step-by-step explanation:

k/4 - 5k + 1 = 1

4 (k/4 - 5k + 1 = 1)

k-20k + 4 = 4

-19k ≠ 0

4 0

2 years ago

Last month, 17 people showed up to help a local charity. This month, 55 people volunteered. What is the percentage increase?

astra-53 [7]

Step-by-step explanation:

The formula for percent change is

change/original.

So let's subtract 17 from 55 to find the change. 55-17=38

This is the change. Now we divide it by the original, 17.

38/17=2.235294

We're not done yet! We have to move the decimal point over to the right 2 spaces to make it a percentage. So, the percentage increase is

about 223.53 percent

6 0

3 years ago

A carnival ride is in the shape of a wheel with a radius of 15 feet. The wheel has 24 cars attached to the center of the wheel.

Anarel [89]

The radius the wheel (circle) is 15 ft a circle is equal to 360° so
1the central angle is: 5/360=24°
the circumference is: 2 π 24= 150.7ft
The arc is: 150.7/24= 6.28ft
The area of sector is: = 1/20 * Area of circle
<span>= 1/20 * pi * (25)^2 </span>
<span>= 98.17 feet^2
</span>I hope that this is helpful :)

3 0

2 years ago

7 copper spheres with radii of 4

Anit [1.1K]

We will see that the cube must be 10.23 inches tall.

The volume of the cube must be equal to the volume of the 4 spheres. Remember that the volume of a sphere of radius R is:

V = (4/3)*3.14*R^3

In this case, the radius is 4 inches, so we can write:

V = (4/3)*3.14*(4 in)^3 = 267.95 in^3

Then the volume of the 4 spheres is:

4*267.95 in^3 = 1,071.79 in^3

The volume of a cube of side length S is given by:

V = S^3

Then we must have:

S^3 = 1,071.79 in^3

S = ∛(1,071.79 in^3) = 10.23 in

We conclude that the cube is 10.23 inches tall.

If you want to learn more about spheres, you can read:

brainly.com/question/10171109

6 0

2 years ago