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2 years ago

The average of eight numbers is 56. When one of the numbers was left out, the mean decreased to 54. What number was left out?

Mathematics

1 answer:

Alexandra [31]2 years ago

4 0

The number that was left out is 70.

<h3>What is the number that was left out?</h3>

Average is the sum of a set of numbers divided by the total numbers in the data set.

Average = sum of numbers / total numbers

Sum of numbers when there are 8 numbers = 56 x 8 = 448
Sum of numbers when there are 7 numbers = 54 x 7 = 378
Difference = 448 - 378 = 70

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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4 0

3 years ago

a landscaping company needs 160 gallons of 40% fertilize the shrubs in an office park. They have in stock 50% fertilizer and 30%

Novay_Z [31]

Let

x--------> volume of 50% fertilizer

y--------> volume of 30% fertilizer

we know that

x+y=160-----> x=160-y-----> equation 1

x*0.5+y*0.3=160*0.4-----> equation 2

substitute equation 1 in equation 2

[160-y]*0.5+0.3*y=63.8----> 77-0.35*y+0.25*y=63.8

0.10*y=13.2------> y=13.2/0.10----> y=132 gal

x=220-y----> x=220-132----> x=88 gal

the answer is

88 gal of 50% fertilizer

132 gal 30% fertilizer

5 0

3 years ago

Solve If QR = 6x + 1, PR = 14x - 13, and PQ = 5x - 2, find PR

solong [7]

Answer:

P____Q____R

PR= PQ+ QR

(14x-13) = (5x-2)+(6x+1)

14x-13= 11x – 1

14x – 11x = 13–1

3x = 12

x= 12/ 3

x= 4

PR= 14x – 13 = 14 (4) – 13 = 18 – 13= 5

If you want (PQ , QR ) this is the solution

PQ =5x-2=5(4)-2=20-2=18

QR =6x+1=6(4)+1=24+1=25

I hope I helped you^_^

7 0

3 years ago

14 ) Mark Achin sells 3,600 electric motors each year . The cost of these is $ 200 each , and demand is constant throughout the

ANTONII [103]

Mark Achin's economic order quantity in units is D. 120 units.

<h3>What is economic order quantity?</h3>

The economic order quantity (EOQ) is the optimal order quantity that minimizes the total costs (ordering, receiving, and holding inventory).

The formula for the economic order quantity is the square root of [2(setup costs)(demand rate)] / holding costs.

<h3>Data and Calculations:</h3>

Annual demand = 3,600

Cost price per unit = $200

Ordering cost = $40

Holding cost per unit = $20

Working days per year = 360

Lead time = 5 days

Economic order quantity (EOQ) = square root of: [2(setup costs)(demand rate)] / holding costs.

= square root of (2 x $40 x 3,600)/$20

= 120

Thus, Mark Achin's economic order quantity in units is D. 120 units.

Learn more about the economic order quantity at brainly.com/question/13386271

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3 0

2 years ago

The value of x is______

Naddik [55]

Answer:

x = 20 ................

4 0

3 years ago