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Sophie [7]
3 years ago
5

What is the volume of this triangular prism? 6m 5m 10m

Mathematics
1 answer:
notsponge [240]3 years ago
6 0
Show the picture to answer this
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This month, Chun’s office produced 690 pounds of garbage. Chun wants to reduce the weight of garbage produced to 85% of the weig
Effectus [21]
Chun wants to <span>reduce the weight of garbage produced to 85% of the weight produced this month. 
This means that, Chun's garbage weight next month should be equal to 85% of his garbage weight this month.

Translating this into an equation, we will find that:
garbage weight next month = 85% of garbage weight this month
garbage weight next month = 0.85 * garbage weight this month
garbage weight next month = 0.85*690 
garbage weight next month = 586.5 pounds

Based on the above calculations, his target weight for the garbage next month is </span>586.5 pounds
8 0
3 years ago
Lowering powers write in terms of first power of cosine. Cos^6
yaroslaw [1]

The main identity you need is the double angle one for cosine:

\cos^2x=\dfrac{1+\cos2x}2

We get

\cos^6x=(\cos^2x)^3=\left(\dfrac{1+\cos2x}2\right)^3=\dfrac{(1+\cos2x)^3}8

Expand the numerator to apply the identity again:

\cos^6x=\dfrac{1+3\cos2x+3\cos^22x+\cos^32x}8

\cos^6x=\dfrac{1+3\cos2x+3\left(\frac{1+\cos2(2x)}2\right)+\cos2x\left(\frac{1+\cos2(2x)}2\right)}8

\cos^6x=\dfrac{1+3\cos2x+\frac32+\frac32\cos4x+\frac12\cos2x(1+\cos4x)}8

\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{16}\cos2x\cos4x

Finally, make use of the product identity for cosine:

\cos2x\cos4x=\dfrac{\cos6x+\cos2x}2

so that ultimately,

\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos2x+\dfrac1{32}\cos6x

\cos^6x=\dfrac5{16}+\dfrac{15}{32}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos6x

4 0
4 years ago
Type the correct answer in each box. Use numerals instead of words.
RSB [31]

Answer:

4

3

0

Step-by-step explanation:

3 0
3 years ago
Linda Roy received a $200,000 inheritance after taxes from her parents. She invested it at 4% interest compounded quarterly for
Kitty [74]

Answer:

Step-by-step explanation:

Matured amount of $200000 at 4% compounded quarterly after 3 years

= $200000 x ( FVIF , 1 , 12 )

= $200000 X 1. 1268

= $225360 .

Matured amount of $210000 at 3% compounded semiannually  after 2 years

= $210000 x ( FVIF , 1.5 , 4 )

= $210000 X 1. 1268

= $225360 x 1.0614

= $239197

Total amount after maturity

= $225360 + $239197

= $464557

Matured amount of $464557  at 2% compounded annually  after 7 years

= $464557  x ( FVIF , 2 , 7 )

= $464557 x 1.1487

= $533636.6

This amount is more than his target amount of 500000.00 So she meets the goal .

8 0
4 years ago
You draw one card from a standard 52-card deck. Make a table to show the probability distribution for each sample space.{the car
Ivahew [28]

Answer:

Step-by-step explanation:

What is the probability that when two cards are drawn from a deck of cards without

replacement that both of them will be 8’s?

(ℎ 8

′

) = ( 8) ∙ ( 8)

( 8) =

4

52

 There are three 8’s left in the deck if one is pulled and not replaced, and 51 total

cards remaining.

( 8) =

3

51

(ℎ 8

′

) =

4

52 ∙

3

51 =

12

2652 =

1

221 = .0045 .45%

4 0
3 years ago
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