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3 years ago

A roofer requires 15 hours to shingle a roof, while an apprentice requires 21 hours. Write

Mathematics

1 answer:

AnnZ [28]3 years ago

7 0

The equation in terms of "t"

1/t = ¹/₂₁ + ¹/₁₅

On solving the equation "t"= 8 ³/₄ days

Step-by-step explanation:

Time taken by roofer to shingle a roof- 15 hours

Time taken by apprentice-21 hours

Time required to shingle if both worked together- “t” hours

If roofer shingles the roof in 15 hours

Part of the roof he would shingle in 1 hours= ¹/₁₅

Similarly, part of the roof shingled by apprentice in 1 hour- ¹/₂₁

Part of the roof shingles when they worked together for 1 hours- 1/t = ¹/₂₁ + ¹/₁₅

Total time taken= 1/t = ¹/₂₁ + ¹/₁₅

1/t= ⁽²¹⁺¹⁵⁾ /₃₁₅

t= 315/36 = 8 ³/₄ days

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27. If three more than one-fourth of a number is

ololo11 [35]

Answer:

Step-by-step explanation:

let the number be n , then

$\frac{1}{4}$ n + 3 = n - 3 ( multiply through by 4 to clear the fraction )

n + 12 = 4n - 12 ( subtract 4n from both sides )

- 3n + 12 = - 12 ( subtract 12 from both sides )

- 3n = - 24 ( divide both sides by - 3 )

n = 8

That is the number is 8

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3 years ago

In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H? 42°

Vinvika [58]

The complete question is shown in the attached image

Answer:
measure angle H = 42°

Explanation:
There is a theorem that states that:
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"

In the given, we have:
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H

Based on the above rule:
measure angle E = measure angle D + measure angle H

We are given that:
angle E = 87°
angle D = 45°

Substitute with the givens in the above rule and solve for the measure of angle H as follows:
angle E = angle D + angle H
87° = 45° + measure angle H
measure angle H = 87° - 45°
measure angle H = 42°

Hope this helps :)

3 0

3 years ago

The poster shows how many of its games of football team has won so far.Express this information as a fraction a,percent and as a

Harrizon [31]

12/15
Divide 12 by 15 and then you should get 0.8
0.8 is obviously equal to 8/10ths or 80%
Hope this helps :)

4 0

3 years ago

Since at t=0, n(t)=n0, and at t=∞, n(t)=0, there must be some time between zero and infinity at which exactly half of the origin

Airida [17]

Answer: t-half = ln(2) / λ ≈ 0.693 / λ

Explanation:

The question is incomplete, so I did some research and found the complete question in internet.

The complete question is:

Suppose a radioactive sample initially contains N0unstable nuclei. These nuclei will decay into stable nuclei, and as they do, the number of unstable nuclei that remain, N(t), will decrease with time. Although there is no way for us to predict exactly when any one nucleus will decay, we can write down an expression for the total number of unstable nuclei that remain after a time t:

N(t)=No e−λt,

where λ is known as the decay constant. Note that at t=0, N(t)=No, the original number of unstable nuclei. N(t) decreases exponentially with time, and as t approaches infinity, the number of unstable nuclei that remain approaches zero.

Part (A) Since at t=0, N(t)=No, and at t=∞, N(t)=0, there must be some time between zero and infinity at which exactly half of the original number of nuclei remain. Find an expression for this time, t half.

Express your answer in terms of N0 and/or λ.

Answer:

1) Equation given:

$N(t)=N _{0} e^{- \alpha t}$ ← I used α instead of λ just for editing facility..

Where No is the initial number of nuclei.

2) Half of the initial number of nuclei: N (t-half) = No / 2

So, replace in the given equation:

$N_{t-half} = N_{0} /2 = N_{0} e^{- \alpha t}$

3) Solving for α (remember α is λ)

$\frac{1}{2} = e^{- \alpha t} 

2 = e^{ \alpha t} 

 \alpha t = ln(2)$

αt ≈ 0.693

⇒ t = ln (2) / α ≈ 0.693 / α ← final answer when you change α for λ

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3 years ago

Felicia's pets eat thirty pounds of food in two weeks. How many pounds of food would they eat in 5 weeks?

Natali5045456 [20]

Answer:

Step-by-step explanation:150 libras de comida

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3 years ago