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Tcecarenko [31]
2 years ago
11

Solve the following multiplication and division problems. a. 8 T. 1,398 lb. 14 oz. × 6 b. 349 lb. 6 oz. ÷ 130 c. 6 T. 294 lb. ÷

3,071
Mathematics
2 answers:
tester [92]2 years ago
6 0

Answer:  a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

1\ ton=32000\ oz\\\\1\ lb=16\ oz

so, it becomes,

8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz

8 T. 1,398 lb. 14 oz. × 6 becomes

278382\times 6\\\\=1670292\ oz

b) 349 lb. 6 oz. ÷ 130

It becomes,

349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

6\times 32000+294\times 16\ oz\\\\=196704\ oz

At last it becomes,

\frac{196704}{3071}\\\\=64.1\ oz

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

vaieri [72.5K]2 years ago
5 0

Answer:

A. 278382 ounces

B. 43 ounces

C. 64.1 ounces

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The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat
Oliga [24]

A geometric series is written as ar^n, where a is the first term of the series and r is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by r.

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots.

Let's use the other information, since the last term is 4374 > 6, we know that r>1, otherwise the terms would be bigger and bigger.

The information about the sum tells us that

\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558

We have a formula to compute the sum of the powers of a certain variable, namely

\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}

So, the equation becomes

6\cfrac{r^{n+1}-1}{r-1} = 6558

The only integer solution to this expression is n=6, r=3.

If you want to check the result, we have

6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558

and the last term is

6*3^6 = 4374

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2 years ago
At a local fitness center, members pay a $14 membership fee and $5 for each aerobics class. Nonmembers pay $6 for each aerobics
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4. The data shows the number of siblings each student in a 9th-grade class has.
antiseptic1488 [7]

Answer:

The correct option is Mean and standard deviation.

Step-by-step explanation:

The data set provided, arranged in ascending order is:

S = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 4}

Now, it is provided that Macy was absent when the data was collected and the class guessed she had 4 siblings. When  she returned, they found out she actually has 9 siblings.

So, the new data set is:

X = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 9}

The mean of a data set is the average value representing the entire data.

\bar X=\frac{1}{n}\sum X_{i}

The median is the middle value of the data set.

The inter-quartile range is the difference between the first and the third quartile.

The standard deviation is the value that represents how dispersed the data values are.

SD=\sqrt{\frac{1}{n}\sum (X_{i}-\bar X)^{2}}

From all the above statistic, the mean and standard deviation are the only ones that uses all the observations in the data set to compute their value.

So, on changing one of the 4s by a 9, the set of measures that will be affected are the mean and standard deviation.

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2 years ago
A 3-gallon tub of ice cream yields about 90 scoops of ice cream. There are roughly 3785 cubic centimeters in 1 gallon. Determine
ASHA 777 [7]

Answer:

The radius of the scoop is r = 3.1 cm

Step-by-step explanation:

Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.

3 gallons = 3 × 3785 cm³ =  11355 cm³

So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.

Since 90 scoops = 11355 cm³, then

1 scoop = 11355 cm³/90 = 126.2 cm³

Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have

r = ∛(3V/4π)

Substituting V = 126.2 cm³, we have

r = ∛(3× 126.2 cm³/4π)

= ∛(378.6 cm³/12.57)

= ∛30.13 cm³

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So, the radius of the scoop is r = 3.1 cm

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If a 10-pound turkey costs $20.42.how much does a 21-pound turkey cost
sergij07 [2.7K]

Answer:

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Step-by-step explanation:

Let's create a proportion using the following setup:

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Round to the nearest cent, or hundredth.

42.88=x

x= $42.88

A 21 pound turkey costs $42.88

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2 years ago
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