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hodyreva [135]
3 years ago
11

A mechanic charges $60 to inspect your heater, plus $70 per hour to work on it. You owe the mechanic a total of $410. Write and

solve an equation to find the amount of time h (in hours) the mechanic works on your heater.
Mathematics
1 answer:
uranmaximum [27]3 years ago
5 0

Answer:

($410 - $60) / $70 = 5

After subtracting the $60 base fee, you can just divide the hours paid for by the hourly wage and find out how many hours were worked. Hope this helps!

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The sum of five times a number, and 1, is equal to four times the number
larisa86 [58]

Answer:

5x + 1 = 4x

You can really put any letter for "a number":

5n + 1 = 4n

7 0
3 years ago
A quiz-show contestant is presented with two questions, question 1 and question 2, and she can choose which question to answer f
Mrrafil [7]

Answer:

The contestant should try and answer question 2 first to maximize the expected reward.

Step-by-step explanation:

Let the probability of getting question 1 right = P(A) = 0.60

Probability of not getting question 1 = P(A') = 1 - P(A) = 1 - 0.60 = 0.40

Let the probability of getting question 2 right be = P(B) = 0.80

Probability of not getting question 2 = P(B') = 1 - P(B) = 1 - 0.80 = 0.20

To obtain the better option using the expected value method.

E(X) = Σ xᵢpᵢ

where pᵢ = each probability.

xᵢ = cash reward for each probability.

There are two ways to go about this.

Approach 1

If the contestant attempts question 1 first.

The possible probabilities include

1) The contestant misses the question 1 and cannot answer question 2 = P(A') = 0.40; cash reward associated = $0

2) The contestant gets the question 1 and misses question 2 = P(A n B') = P(A) × P(B') = 0.6 × 0.2 = 0.12; cash reward associated with this probability = $200

3) The contestant gets the question 1 and gets the question 2 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.4×0) + (0.12×200) + (0.48×300) = $168

Approach 2

If the contestant attempts question 2 first.

The possible probabilities include

1) The contestant misses the question 2 and cannot answer question 1 = P(B') = 0.20; cash reward associated = $0

2) The contestant gets the question 2 and misses question 1 = P(A' n B) = P(A') × P(B) = 0.4 × 0.8 = 0.32; cash reward associated with this probability = $100

3) The contestant gets the question 2 and gets the question 1 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.2×0) + (0.32×100) + (0.48×300) = $176

Approach 2 is the better approach to follow as it has a higher expected reward.

The contestant should try and answer question 2 first to maximize the expected reward.

Hope this helps!!!

3 0
3 years ago
What is the answer to this following question 11(a+6)
Ipatiy [6.2K]
11a+66 hope this helped
7 0
3 years ago
Read 2 more answers
In the diagram below, ΔABC is inscribed in circle P. The distances from the center of circle P to each side of the triangle are
4vir4ik [10]
Supposing the sides with 6 and 8 is a right angle, you can create a new line from C and P, and find the length using the equation of a²+b²=c² or 6²+8²=c², with c equaling the radius of the circle.

After finding c, you will have to find the length from C to the midpoint of AC, using the same equation a²+b²=c². If both the lengths of C to the midpoint of AC, and A to the midpoint of AC are equal, you can do b+b to find the length of AC.

Using the same approach, you can find AB. Hope this makes sense, if not, I can clarify more.
5 0
3 years ago
How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have m
Nadya [2.5K]

Answer with Step-by-step explanation:

Permutation : It is an arrangement of r elements out of n elements.

Combination : it is a selection of r element out of n elements .

Suppose we have a set

S={1,2,3}

If two elements are taken at a time then

Using permutation formula

Total number of outcomes=3P_2

Total number of outcomes=\frac{3!}{(3-2)!}

Total number of outcomes=3!=3\times 2\times1=6

Using combination formula

\binom{n}{r}=\frac{n!}{r!(n-r)!}

Total number of outcomes=\binom{3}{2}=\frac{3!}{2!1!}

Total number of outcomes=\frac{3\times2!}{2!}

Hence, total number of outcomes=3

Total number of outcomes determined by permutation have more outcomes.

Because permutation is an arrangement of elements  therefore, it consider order of arrangement of element   but combination is a selection of elements it does no consider order of elements

Arrangements of two elements out of 3 elements

{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}

By using combination if two elements taken at a time then combination

{1,2},{2,3},{1,3}

4 0
3 years ago
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