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3 years ago

When a number is decreased by 2.6%, the result is 83. What is the original number to the nearest tenth?

Mathematics

1 answer:

slavikrds [6]3 years ago

5 0

Answer:

The original number is 85.2

Step-by-step explanation:

we can represent this in an equation where the initial value is going to be and to this we will subtract 2.6% of it

x - x * 2.6/100 = 83

x - 0.026x = 83

0.974x = 83

x = 83 / 0.974

x = 85.2156

we round to the nearest tenth and finally we get that the result is 85.2

if we want to verify that it is ok we can replace the x with the value of 85.2156 and we should have the same number on each side of the equality

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The chorus has six sopranos and eight baritones. in how many ways can the director choose a quartet that contains at least one s

adell [148]

If you have six sopranos and eight baritones, you have fourteen musicians in total.
The number of possible quartets that you can get with 14 musician is:
$14C4= \frac{14!}{4!(14-4)!}$
$14C4= \frac{14!}{(4!)(10!)}$
$14C4=1001$

Now, the number of possible quartets without a soprano that you can have is:
$8C4= \frac{8!}{4!(8-4)!}$
$8C4= \frac{8!}{(4!)(4!)}$
$8C4=70$

Therefore, the number of quarters that contains at list one soprano will be the number of possible quarters minus the number of quarters without a soprano:
$1001-70=931$
We can conclude that the director can choose a quarter which contains at least one soprano in 931 ways.

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3 years ago

Given

arlik [135]

Answer:

a = 3, b = - 7

Step-by-step explanation:

Substitute x = 2 into the equation and equate to 5, that is

a(2)² + b = 5

4a + b = 5 → (1)

Substitute x = 3 into the equation and equate to 20

a(3)² + b = 20

9a + b = 20 → (2)

Subtract (1) from (2) term by term to eliminate b

(9a - 4a) + (b - b) = (20 - 5), that is

5a = 15 ( divide both sides by 5 )

a = 3

Substitute a = 3 into either of the 2 equations and solve for b

Substituting in (1)

4(3) + b = 5

12 + b = 5 ( subtract 12 from both sides )

b = - 7

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4 years ago

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Ilya [14]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Ab and ac are tangent to circle o. if ab measures 23 cm, what is the measure of ac?

topjm [15]

Answer:

AC = 23

Step-by-step explanation:

Discussion

AB and AC start from the same point -- A.

That means that when speaking of tangents to a circle that AB = AC

Answer

AB = 23 in Given

AC = 23 2 tangents to a circle starting from the same point are =

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2 years ago