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3 years ago

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Abbot is paid weekly for every hour he works. He worked 6 hours each day for 5 days last week. He earned $408, before taxes. Wri

te an equation that represents Abbot’s total pay, p, if he works h hours each week?

1 answer:

Contact [7]3 years ago

3 0

Answer:

p=13.6h

Step-by-step explanation:

if he works 6 hours a day for five days that's 30 hours. $408 divided by 30 hours is $13.6 per hour.

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Find the sum of all natural numbers between 25 and 210 which are either divisible by 3 or divisible by 4? Please let me know I

Ray Of Light [21]

Let <em>S</em> be the sum of the integers 25-210:

<em>S</em> = 25 + 26 + 27 + … + 208 + 209 + 210

Let <em>S₃</em>, <em>S₄</em>, and <em>S₁₂</em> denote the sums of the integers in <em>S</em> that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

<em>S₃</em> = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (<u>62</u> terms)

<em>S₃</em> = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

<em>S₄</em> = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (<u>46</u> terms)

<em>S₄</em> = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

<em>S₁₂</em> = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (<u>15</u> terms)

<em>S₁₂</em> = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at <em>S₃ </em>:

<em>S₃</em> = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

<em>S₃</em>* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course <em>S₃</em> = <em>S₃</em>*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

<em>S₃</em> + <em>S₃</em>* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2<em>S₃</em> = 3 × <u>62</u> × 79 ==> <em>S₃</em> = 7,347

We can compute the other two sums in the same way.

<em>S₄</em> = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

<em>S₄</em>* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==> 2<em>S₄</em> = 4 × <u>46</u> × 59 ==> <em>S₄</em> = 5,428

<em>S₁₂</em> = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

<em>S₁₂</em>* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==> 2<em>S₁₂</em> = 12 × <u>15</u> × 20 ==> <em>S₁₂</em> = 1,800

Then the sum you want is

<em>S₃</em> + <em>S₄</em> - <em>S₁₂</em> = 10,975

We subtract <em>S₁₂</em> because each of its terms is counted twice (once in <em>S₃</em> and again in <em>S₄</em>).

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3 years ago

By the third day of a particular week, 2 accidents have already occurred in the intersection. What is the probability that there

Leona [35]

Answer:

The right answer is "0.70".

Step-by-step explanation:

The given query seems to be incomplete. Please find below the attachment of the full query.

By using the Bayes' theorem, we get

⇒ $P[(X$

By putting the values, we get

$=\frac{[P(2)+P(3)]}{[1-P(0)-P(1)]}$

$=\frac{(0.20+0.15)}{1-0.20-0.30}$

$=\frac{0.35}{0.5}$

$=0.70$

6 0

3 years ago

Which of these is a linear equation in<br> standard form for the graph shown?

vampirchik [111]

Answer:

B

Step-by-step explanation:

Because the slope is a positive slope (goes through the positive quandrants on the graph), we can eliminate answer choices c. Now, if we solve a, b, and d and we can see if the slope + y-intercept matches the graph.

For A.) (solve for y to get a y=mx + b equation)

3x-2y=4

-2y= -3x + 4

<u>y= 3/2 -2</u>

For B.)

3x-2y= -4

-2y= -4-3x

<u>y= 3/2 + 2</u>

For D.)

2x+3y= 4

3y= 4-2x

<u>y= -2/3x + 4/3</u>

Now, if we look at D, the slope is negative so it cannot be D. That leaves us with A and B. The b in the y=mx + b equation stands for the y-intercept, so we can see that the y-intercept is 2. So, since the graph intersects the y-axis at (0,2), the answer is B! y=3/2 + 2 has a positive slope and 2 for the y-intercept!

4 0

3 years ago

A lawn mower is pushed a distance of 100 ft. Along a horizontal path by a constant force of 60 lbs. Yhe handle of the lawn mower

stira [4]

For this case we have the following equation:
w = F • PQ
Where,
w: work done
F: is the force vector
PQ: is the vector of the direction of movement.
Rewriting the equation we have:
w = || F || • || PQ || costheta
Substituting values:
w = (60) * (100) * (cos (45))
w = (60) * (100) * (root (2) / 2)
w = 4242.640687 lb.ft
Answer:
The work done pushing the lawn mower is:
w = 4242.6 lb.ft

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3 years ago

Rania is playing with her friend Arun, and they are setting up dominoes across the room. Each domino is 2 inches long. They have

gogolik [260]

Answer:

no

Step-by-step explanation:

It should be less then or equal too, seeing as they want to reach all the way across the room.

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2 years ago