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3 years ago

7

When the angle of elevation to the sun is 42 a flagpole casts a shadow that is 21 ft long. What is the height of the flagpole to

the nearest foot?

1 answer:

trapecia [35]3 years ago

7 0

Answer:

18.91 cm

Step-by-step explanation:

Let x represent the height of the flag pole

Tan= opposite/ adjacent

Tan 42°= x/21

x= Tan 42° × 21

= 0.9004 × 21

= 18.91 cm

Hence the height is 18.91 cm

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William invested $2,300 in an account paying an interest rate of 2 1/8% compounded quarterly. Nolan invested $2,300 in an accoun

shusha [124]

Answer:

$478

Step-by-step explanation:

After 20 years, William will have a total of $3,513.94

After 20 years, Nolan will have a total of $3,991.93

Difference = $478

William:

2300[1 + (.02125 ÷ 4)]^4 · 20

2300 · (1 + .0053125)^80

2300(1.5278)

$3,513.94

Nolan:

2300[1 + (.0275 ÷ 12)]^12 · 20

2300 · (1 + .0023)^240

2300(1.7356)

$3,991.93

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3 years ago

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Which scale factors produce a contraction under a dilation of the original image?

Svetlanka [38]

-1/2 and 1/2 i checked its right

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3 years ago

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There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

3 years ago

Help i want to know what is 5m and 10m in feet and explain if you can

tatyana61 [14]

Well, to start with, 1 meter = 3 feet.
5 meters = 15 feet.
10 meters = 30 feet.
so 5 meters is 15 feet, and 10 meters is 30 feet. Hope this helps:)

7 0

3 years ago

1. Mark is drawing the outside lines on

storchak [24]

232 ft.

Add each side twice:

74 + 74 + 42 + 42

or

(74 x 2) + (42 x 2)

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