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2 years ago

A manufacturer determines that the number of toys it can sell is given by the formula

Mathematics

1 answer:

otez555 [7]2 years ago

4 0

Answer:

The price where the manufacture sells the maximum number of toys is $20

Step-by-step explanation:

The given equation for that represents the number of toys the manufacturer can sell is given as follows;

T = -4·p² + 160·p - 305

Where;

p = The price of the toys in dollars

At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0

Therefore, at the maximum point;

The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160

∴ -8·p + 160 = 0

160 = 8·p

8·p = 160

p = 160/8 = 20

The price where the manufacture sells the maximum number of toys is = p = 20 dollars

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3 years ago

If E F = 7 , A C = 16 , and A F = 9

Vilka [71]

Answers:

CB = 14

GF = 8

FB = 9

EF is parallel to CB

====================================

Explanations:

Points E and F are midpoints of their respective sides. They form the midsegment EF. Because EF is a midsegment, A midsegment is half the length of its parallel counterpart, so CB is two times longer than EF. If EF is 7 units long, then CB = 2*EF = 2*7 = 14

For similar reasons, GF is parallel to AC. If AC = 16, then half of that is GF = (1/2)*AC = 0.5*16 = 8.

FB = FA = 9 as these segments have the same single tickmark to indicate they are the same length

EF is parallel to CB because EF is a midsegment, and this is one of the properties of being a midsegment. We can show that quadrilateral EGBF is a parallelogram to help prove this.

8 0

3 years ago

Express the first quantity as a percentage of the second. <br>1 h 3 min, 3 h 30min.

KatRina [158]

Answer:

30%

Step-by-step explanation:

first we require both quantities to have the same units

converting both to minutes

1 h 3 min = 60 + 3 = 63 min

3h 30 min = (3 × 60) + 30 = 180 + 30 = 210 min

then express as a fraction and multiply by 100% to express as a percentage

$\frac{63}{210}$ × 100%

= 0.3 × 100%

= 30%

8 0

1 year ago

The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (nk). True or false.

AVprozaik [17]

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk, False

The kth coefficient of the binomial expansion, (x + y)ⁿ is $\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)$

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion (x + y)ⁿ = $C(n,k)$ not nk

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2 years ago

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MatroZZZ [7]

Answer:

48-20x=21

Step-by-step explanation:

So, we basically have to clear the fractions (get rid of the denominators)

Multiply everything by the LCM of 6 and 8 (24)

24(2)-24(5/6x)=24(7/8)

48-20x=21

Hope this helps!

6 0

3 years ago