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Lilit [14]
2 years ago
12

Justin is working two summer jobs, making $8 per hour babysitting and $14 per hour lifeguarding. Last week Justin earned a total

of $92 and worked 4 times as many hours babysitting as he worked hours lifeguarding. Determine the number of hours Justin worked babysitting last week and the number of hours he worked lifeguarding last week.
Mathematics
1 answer:
alexdok [17]2 years ago
6 0

Answer:

Justin worked as a babysitter  8 hours and worked as a lifeguard 2 hours last week

Step-by-step explanation:

Let

x ----> number of hours worked as a babysitter  last week

y ----> number of hours worked as a lifeguard last week

we know that

8x+14y=92 ----> equation A

x=4y ----> equation B

Solve the system by substitution

Substitute equation B in equation A

8(4y)+14y=92

solve for y

32y+14y=92

46y=92

y=2

Find the value of x

x=4(2)=8

therefore

Justin worked as a babysitter  8 hours and worked as a lifeguard 2 hours last week

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USPshnik [31]

Answer:

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Step-by-step explanation:

6 0
1 year ago
A jar contains 4 white and 4 black marbles. We randomly choose 4 marbles. If 2 of them are white and 2 are black, we stop. If no
Airida [17]

Answer:

<em>Find the probability of success in a single trial and then think about the nature of the problem (when do we stop).  </em>

Step-by-step explanation:

Observe that in the single trial, we have (8 4) possibilities of choosing our set of balls. If we have chosen two white balls and two black balls, the probability of doing that is simply  

p=(4 2)*(4 2)/(8 4)

This is well know Hyper geometric distribution. Now, define random variable X that marks the number of trials that have been needed to obtain the right combination (two white and two black balls). From the nature of the problem, observe that X has Geometric distribution with parameter p that has been calculated above. Hence  

P(X = n) = (1— p)^n-1 *( p )

<em>Find the probability of success in a single trial and then think about the nature of the problem (when do we stop).  </em>

3 0
2 years ago
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length o
kumpel [21]

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

<em>In the right triangle XYZ</em>

Find the tangent of angle X

tan(X)=\frac{YZ}{XZ} ---> opposite side angle X divided by adjacent side angle X

substitute the given values

tan(X)=\frac{9}{12}

Simplify

tan(X)=\frac{3}{4}

Remember that

∠Q≅∠X

so

tan(Q)=tan(X)

therefore

tan(Q)=\frac{3}{4} ---->Three-fourths

7 0
1 year ago
Read 2 more answers
A regular decagon has sides that are 8 cm long. What is the area of the figure? Round to the nearest whole number.
blsea [12.9K]

<u>Given</u>:

Given that the regular decagon has sides that are 8 cm long.

We need to determine the area of the regular decagon.

<u>Area of the regular decagon:</u>

The area of the regular decagon can be determined using the formula,

A=\frac{s^{2} n}{4 \tan \left(\frac{180}{n}\right)}

where s is the length of the side and n is the number of sides.

Substituting s = 8 and n = 10, we get;

A=\frac{8^{2} \times 10}{4 \tan \left(\frac{180}{10}\right)}

Simplifying, we get;

A=\frac{64 \times 10}{4 (\tan \ 18)}

A=\frac{640}{4 (0.325)}

A=\frac{640}{1.3}

A=642.3

Rounding off to the nearest whole number, we get;

A=642 \ cm^2

Thus, the area of the regular decagon is 642 cm²

Hence, Option B is the correct answer.

5 0
1 year ago
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Greeley [361]

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\displaystyle\int_C2xy\,\mathrm dx+xy^2\,\mathrm dy=\iint_Q\frac{\partial(xy^2)}{\partial x}-\frac{\partial(2xy)}{\partial y}\,\mathrm dA

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6 0
2 years ago
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