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1 year ago

ben earned 45 dollars mowing lawns. he worked 3.2 hours on monday and 4.3 hours on tuesday. how much did he earn per hour?

Mathematics

1 answer:

dlinn [17]1 year ago

3 0

Answer:

6 dollars per hour

Step-by-step explanation:

We can set up and solve an equation to answer this question. For this problem, let x stand for the amount he earned per hour. The equation that represents this situation is 3.2x + 4.3x = 45. The first term represents monday and the second represents tuesday. When these add up they should equal 45 because that is the total amount he made. To find his pay per hour, solve for x.

First, combine the like terms

7.5x=45

Next, divide both sides by 7.5

x=6

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After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 lb. What was Lisa's original weight?

AlekseyPX

Answer:

175lb

Step-by-step explanation:

Let's say 100% - original weight

and 12% - 21lb

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2 years ago

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The student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretar

natima [27]

Answer:

P=1/42.

Step-by-step explanation:

We know that the student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretary and Treasurer. We calculate the probability that the President is a Senior:

We calculate the number of possible combinations:

$C_4^{10}=\frac{10!}{4!(10-4)!}=210$

Number of favorable combinations is 5.

Threfore, the probability is

P=5/210

P=1/42.

8 0

3 years ago

3. Two cars are parked, 150m apart, and on opposite sides of a building. A camera on the top of the building rotates and can vie

allsm [11]

Answer:

<em>The building is 61.5 m tall</em>

Step-by-step explanation:

The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:

h = height of the building

a, b = internal angles of each triangle

x = base of each triangle

The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:

a = 90° - 37° = 53°

b = 90° - 42° = 48°

Now we apply the tangent ratio on both triangles separately:

$\displaystyle \tan a=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 53^\circ=\frac{150-x}{h}$

$\displaystyle \tan 48^\circ=\frac{x}{h}$

From the last equation:

$x=h.\tan 48^\circ$

Substituting into the first equation:

$\displaystyle \tan 53^\circ=\frac{150-h.\tan 48^\circ}{h}$

Operating on the right side:

$\displaystyle \tan 53^\circ=\frac{150}{h}-\tan 48^\circ$

Rearranging:

$\displaystyle \tan 53^\circ+\tan 48^\circ=\frac{150}{h}$

Solving for h:

$\displaystyle h=\frac{150}{\tan 53^\circ+\tan 48^\circ}$

Calculating:

h = 61.5 m

The building is 61.5 m tall

5 0

2 years ago

Is multiplying 10 to the power of 3 the same as multiplying by 10 factors of 3

andrew-mc [135]

No because since multiplying by 10³ is multiplying by 10 times 10 times 10 which equals 1000 and multiplying by 10 factors of 3 is multiplying by 3 times 3 times 3 times 3…….for 10 times equals 59049

7 0

2 years ago

In ΔOPQ, o = 58 cm, q = 13 cm and ∠Q=52°. Find all possible values of ∠O, to the nearest degree.

PSYCHO15rus [73]

Answer:

There is no possible triangles

Step-by-step explanation:

\frac{\sin A}{a}=\frac{\sin B}{b}

sinA

sinB

From the reference sheet (reciprocal version).

\frac{\sin O}{58}=\frac{\sin 52}{13}

sinO

sin52

Plug in values.

\sin O=\frac{58\sin 52}{13}\approx 3.5157403

sinO=

58sin52

≈3.5157403O=\sin^{-1}(3.5157403)= \text{ERROR}

O=sin

−1

(3.5157403)=ERROR

Sine cannot be greater than 1.

{No Possible Triangles}

No Possible Triangles

{}

7 0

2 years ago