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Pavlova-9 [17]
3 years ago
7

A recipe calls for 3 1/2 cups of sugar. If you want to make only 1/3 of the recipe, how much sugar should you use?

Mathematics
1 answer:
Sav [38]3 years ago
3 0

Answer: 1 1/6 cups of sugar

Step-by-step explanation:

First let’s convert 3 1/2 into an improper fraction: 7/2

Then we multiply 7/2 by 1/3: 7/2*1/3=7/6

Then finally we convert 7/6 into a mixed number, so your answer will be 1 1/6

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A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and
Papessa [141]

Answer:

1 : 1

Step-by-step explanation:

When a circle is inscribed in a cylinder, the height of the cylinder is equal to the diameter of the sphere and the radius of the cylinder is same as that of the sphere.

Let the radius of sphere is r.

height of cylinder, h = 2r

radius of cylinder = r

Surface area of sphere, A = 4πr²

lateral surface area of cylinder, A' = 2 πrh

A' = 2πr x 2r = 4πr²

The ratio of surface area of sphere to the lateral surface area of cylinder is 1 : 1.

5 0
3 years ago
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test.
Bess [88]

Answer:

4c+6a\leq120\\\\4c+4a\leq100

Step-by-step explanation:

Let c represents child bikes and a represents adult bikes.

Given :  Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test.

With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week.

Then, the required system of inequality :-

4c+6a\leq120----(1)\\\\4c+4a\leq100-----(2)

If company make 10 child bikes and 12 adult bikes in the week.

Then Put c=10 and a=12 bikes in (1) and (2).

4(10)+6(12)=40+72=112\leq120⇒Bike order meets the restrictions

4(10)+4(12)=40+48=88\leq100⇒Bike order meets the restrictions

Hence, the system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week.

4c+6a\leq120\\\\4c+4a\leq100

3 0
3 years ago
If r(X)=2-x^2 and w(X)=X-2, what is the range of (w*r)(X)
slega [8]
The given function are
r(x) = 2 - x²    and     w(x) = x - 2
<span>(w*r)(x) can be obtained by multiplying the both function together
</span>
So, <span>(w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)</span>
<span>(w*r)(x) = x (2-x²) - 2(2-x²)</span>
            = 2x - x³ - 4 + 2x²

∴ <span>(w*r)(x) = -x³ + 2x² + 2x - 4
</span>

<span>It is a polynomial function with a domain equal to R
</span>
The range of <span>(w*r)(x) can be obtained by graphing the function
</span>
To graph (w*r)(x), we need to make a table between x and (w*r)(x)

See the attached figure which represents the table and the graph of <span>(w*r)(x)
</span>

As shown in the graph the range of <span>(w*r)(x) is (-∞,∞)
</span>

8 0
3 years ago
Read 2 more answers
The city of Raleigh has 10400 registered voters. There are two candidates for city council in an upcoming election: Brown and Fe
iVinArrow [24]

Answer:

Step-by-step explanation:

Hello!

a) The population of interest is the registered voters of the city of Raleigh.

b) This population is finite and its size is 10400 voters.

c) The sample was taken by making a telephone poll, calling 400 registered voters.

d) The sample size is n= 400 voters

The number of people that answered they'd vote for Brown are 151, so the sample proportion of voters that would vote for bron is:

p= 151/400= 0.3775 ≅ 0.38

e) To know how many people is expected to vote for Brown based on the results of the telephone poll you can do the following calculation:

10400*0.38= 3952

Based on the information obtained from the sample, it is expected that only 3952 voters will vote for Brown.

4 0
3 years ago
Solve for j.<br> J + 22/8 =8
Monica [59]

Answer:

j=5.25

Step-by-step explanation:

j+22/8=8

j=8/1-22/8

j=64-22/8

j=5.25

Proof:

5.25+22/8=8

525/100+22/8=8

4200+2200/800=8

6400/800=8

8=8

7 0
3 years ago
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