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kvv77 [185]
2 years ago
9

The ice cream parlor serves spherical scoops of ice cream with a radius of 1 in. What is the approximate volume of 2 scoops of i

ce cream? (Use 3.14 as an approximation of pi.)
Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
6 0

Answer: 8.37 in³

Step-by-step explanation:

Given the following :

Shape of icre cream scoop = sphere

Radius (r) = 1 inch

Volume of a scoop of icecream = volume of sphere :

4/3πr³

(4/3) × 3.14 × 1³

1.333 × 3.14 × 1

= 4.1867 in³

Hence, the volume of 2 scoops of ice cream will be :

2 × ( volume of a scoop of ice cream)

(2 × 4.1867) in³

= 8.37 in³

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A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. If the interest received
marin [14]

Answer: $31000 was loaned at 13%.

Step-by-step explanation:

Let x represent the amount loaned out at 13% interest rate.

Let y represent the amount loaned out at 5% interest rate.

The bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. It means that

x + y = 68000

The interest received made from $x in one year is

13/100 × x = 0.13x

The interest received made from $y in one year is

5/100 × x = 0.05y

If the interest received was $5880, it means that

0.13x + 0.05y = 5880- - - - - - - - - 1

Substituting x = 68000 - y into equation 1, it becomes

0.13(68000 - y) + 0.05y = 5880

8840 - 0.13y + 0.05y = 5880

- 0.13y + 0.05y = 5880 - 8840

- 0.08y = - 2960

y = - 2960/- 0.08

y = 37000

x = 68000 - y = 68000 - 37000

x = $31000

5 0
3 years ago
For the problem, use the discriminant to determine the number of real solutions for the equation. Then, find the solutions and c
Ksivusya [100]

Answer:

Discriminant = 55.2 > 0 -> 2 real solutions

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

Step-by-step explanation:

To find the time when the ball will reach the height of 2 meters, we just need to use the value of h = 2 in the equation given. So, we have that:

−4.9t^2 − 4t + 4 = 2

−4.9t^2 − 4t + 2 = 0

For this equation, we have the constants a = -4.9, b = -4 and c = 2. So the discriminant Delta is:

Delta = b^2 - 4ac = 16 + 39.2 = 55.2

sqrt(Delta) = 7.4297

As Delta > 0, we have 2 real solutions

t1 = (-b + sqrt(Delta)) / 2a = (4 + 7.4297) / (-9.8)  = -1.1663 s

t2 = (-b - sqrt(Delta)) / 2a = (4 - 7.4297) / (-9.8)  = 0.35 s

Number of real solutions: 2

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

8 0
3 years ago
A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a c
IgorLugansk [536]

Answer:

  • Implied population is all listeners of the radio talk show
  • the variable is opinion of a listener
  • Yes, bias is voluntary response. Those with the strongest opinions are most likely to call in.

Step-by-step explanation:

Radio talk show host asked listeners to respond therefore the population is all listeners of the radio talk show.

The variable is the response "yes" or  "no"

There is voluntary response bias, because the respondents are volunteered to answer, therefore sample is consisted of self-selected listeners.

3 0
3 years ago
Carolyn paid a mechanic x dollars per hour for a 5-hour job plus $70 for parts. The total charge was less than $320. Which equat
snow_lady [41]

Answer: should be 70+50x is less than 320

Step-by-step explanation:$70 is only added once, and for 5 hours, she pays him a certain amount of $(x). I don't know if the multiple choices are valid

3 0
2 years ago
Solve for x.
andriy [413]

Answer:

5.7392839+381

Step-by-step explanation:

Because if you add and divide 0 you get 0

7 0
2 years ago
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