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Sergeeva-Olga [200]
3 years ago
7

Of 12000 applicants to Carver college, 1/3 were accepted and 3/8 of those decided to attend. How many of the original applicants

decided to attend the college
Mathematics
1 answer:
ladessa [460]3 years ago
8 0

Answer:

total  \: applicants \:  = 12000 \\ number \: of \: applicants \: who \: were \: accepted =  \frac{1}{3}  \times 12000 \\  = 4000 \\ number \: of \: applicants \: who \: decided \: to \: attend \: the \: college =  \frac{3}{8}  \times 4000 \\  = 1500

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Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at
Amiraneli [1.4K]

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

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3 years ago
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Drupady [299]

Answer:

0.125

Step-by-step explanation:

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3 years ago
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Ghella [55]

Answer:

The answer of the first on is 15 b because to find the perimeter of 2d shapes we have to add all the sides given ex: 5+5+5=15 so the answer of first question if 15.

Step-by-step explanation:

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Estimate 76.216+66.36 by first rounding each number to the nearest whole number.
xeze [42]

Answer:

142

Step-by-step explanation:

  • Round the numbers to their nearest WHOLE NUMBER.

76.216=76\\66.36=66

  • Then ADD

76+66=142

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2 years ago
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Svetlanka [38]

Answer:

\sqrt[]{\frac{x+8}{4}}-3

Step-by-step explanation:

g(x)=4(x+3)^2-8

First rewrite g(x) as y

y=4(x+3)^2-8

Now swap y and x

x=4(y+3)^2-8

Add 8 on both sides.

x+8=4(y+3)^2-8+8

x+8=4(y+3)^2

Divide by 4.

\frac{x+8}{4} =\frac{4(y+3)^2}{4}

\frac{x+8}{4}=(y+3)^2

Extract the square root on both sides.

\sqrt[]{\frac{x+8}{4}}=\sqrt[]{(y+3)^2}

\sqrt[]{\frac{x+8}{4}}=y+3

Subtract 3 on both sides.

\sqrt[]{\frac{x+8}{4}}-3=y+3-3

\sqrt[]{\frac{x+8}{4}}-3=y

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3 years ago
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