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pantera1 [17]
3 years ago
10

The volume of a cylindrical soup can is represented by the expression πr3 + 7πr2, where r is the radius of the cylinder. Which s

tatement best interprets the factor (r + 7) in this context
Mathematics
1 answer:
Ganezh [65]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²

From V = πr³ + 7πr²;

factor out the common variable

V = πr³ + 7πr²

V = πr²(r+7) ... 1

The original volume of a cylinder V =  πr²h .... 2 where;

r is the radius of the cylinder

h is the height of the cylinder

Equating equation 1 and 2, we will have;

πr²(r+7)  =  πr²h

Divide both sides by  πr²

πr²(r+7)/ πr² = πr²h/ πr²

r+7 = h

h = r+7

<em>Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r</em>.<em> The statement means that the height of the cylindrical soup is 7 more than its radius.</em>

<em></em>

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A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the differen
gavmur [86]

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 8 of each brand, assigned at random to the left and right rear wheels of 8 taxis. The tires are run until they wear out and the distances, in kilometers, are recorded in the accompanying data set. Find a 95% confidence interval for Hx - Hy. Assume that the differences of the distances are approximately normally distributed Data Set Let, Hx be the population mean for brand A and let Hy be the population mean for brand B. The confidence interval is -42- (Round to one decimal place as needed.) Taxi Brand A 37,700 46,800 36,500 40,600 43.600 31,300 37,600 43.800 Brand B 39,800 47,500 37.100 39,200 42,900 36,000 38,700 45,000

Solution:

For brand A,

Mean,x1 = (37700 + 46800 + 36500 + 40600 + 43600 + 31300 + 37600 + 43800)/8 = 39737.5

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (37700 - 39737.5)^2 + (46800 - 39737.5)^2 + (36500 - 39737.5)^2 + (40600 - 39737.5)^2 + (43600 - 39737.5)^2 + (31300 - 39737.5)^2 + (37600 - 39737.5)^2 + (43800 - 39737.5)^2 = 172438750

Standard deviation = √(172438750/8

s1 = 4642.72

For brand B,

Mean,x2 = (39800 + 47500 + 37100 + 39200 + 42900 + 36000 + 38700 + 45000)/8 = 40775

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (39800 - 40775)^2 + (47500 - 40775)^2 + (37100 - 40775)^2 + (39200 - 40775)^2 + (42900 - 40775)^2 + (36000 - 40775)^2 + (38700 - 40775)^2 + (45000 - 40775)^2 = 111635000

Standard deviation = √(111635000/8

s2 = 3735.56

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (8 - 1) + (8 - 1) = 14

z = 2.145

x1 - x2 = 39737.5 - 40775 = -1037.5

z√(s1²/n1 + s2²/n2) = 2.145√(4642.72²/8 + 3735.56²/8)

= 4519.1

95% Confidence interval = - 1037.5 ± 4519.1

3 0
3 years ago
A computer room has 12 computers. The room is open for 4 hours each day. 25 students sigh up for computer time. Each student get
GuDViN [60]

Answer:

155 minutes

Step-by-step explanation:

1. Find the total available "computer time": 4 hours * 12 computers= 48 hours

2. Split this among all of the students: 48 hours/25 students= 1.92 hours

3. Convert to minutes: 1.92 hr/student * 60 minutes ≈ 155 minutes/student

8 0
3 years ago
What function/equation is best for this
professor190 [17]
The answer is y= -2x !
5 0
3 years ago
Read 2 more answers
Please help me i need it right now please
12345 [234]

Given:

The rate of interest on three accounts are 7%, 8%, 9%.

She has twice as much money invested at 8% as she does in 7%.

She has three times as much at 9% as she has at 7%.

Total interest for the year is $150.

To find:

Amount invested on each rate.

Solution:

Let x be the amount invested at 7%. Then,

The amount invested at 8% = 2x

The amount invested at 9% = 3x

Total interest for the year is $150.

x\times \dfrac{7}{100}+2x\times \dfrac{8}{100}+3x\times \dfrac{9}{100}=150

Multiply both sides by 100.

7x+16x+27x=15000

50x=15000

Divide both sides by 50.

x=\dfrac{15000}{50}

x=300

The amount invested at 7% is 300.

The amount invested at 8% is

2(300)=600

The amount invested at 9% is

3(300)=900

Thus, the stockbroker invested $300 at 7%, $600 at 8%, and $900 at 9%.

4 0
3 years ago
8-2b=-2/3(12b+6) solve
Natalija [7]
We have to mutiply factor -2/3 times every agument from the parenthesis.
8-2b=- \frac{2*12b}{3}- \frac{2*6}{3}   \\ 8-2b= -8b-4 \\     /+8b
8+6b=-4         /-8
6b=-12         /:6
b=-2 - its the answer
7 0
2 years ago
Read 2 more answers
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