Find the sum of the multiples of 3 from 3 to 99 inclusive

Answers

Answer 1

Answer: Multiples of 3 from 3 to 99 inclusive is a Aritmetic Progression where:

a1 = 3
an = 99
r = 3

Using the formula of general terms:

$a_n=a_1+(n-1).r\n \n 99=3+3(n-1)\n \n 99-3=3n-3\n \n 3n=99\n \n n=33$

Calculating sum:

$S_(33)=(33(a_1+a_(33)))/(2)\n \n S_(33)=(33(3+99))/(2)=(33*102)/(2)=1683$

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The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:Car A y = 45x + 20 Car B y = 35x + 60 WILL UPVOTE After how many hours will the two cars be at the same distance from their starting point and what will that distance be? 3 hours, 200 miles 3 hours, 180 miles 4 hours, 200 miles 4 hours, 180 miles
an expression is shown: 8^2/(-4)^2+(-1/2) x 2^3 group of answer choices 64/-8 + 6/-2 -11 64/16 +8/-2 0
An orbiting satellite has seven solar cells, which function independently of each other. During a mission, each cell fails with a probability of 0.3. What is the probability that there will be adequate power output for the mission if 7. All 7 cells must be active?
-5x-4=? a.1 b.-1 c.20 d.-20
What would you assume at the beginning of an indirect proof for the following?A number divisible by 2 is even. The number 13 is not even.A. Even numbers are not divisible by 2B. Even numbers are divisible by 2C. The number 13 is not evenD. The number 13 is even

I need help w this soon

Answers

Answer:

Step-by-step explanation:

Answer:

18 because it's asking for the tw

The list of multiples for 6 is infinite.
True or False?

Answers

Answer:

True

Step-by-step explanation:

As there are infinite numbers, the list of multiples are also infinite.

Multiples of 6 : 6, 12 , 18 , 24 ..............

Answer:

True; yes.

Step-by-step explanation:

Think about it, what does etc, etc mean? It means repetitive-a pattern, in a sort of way. So here are some multiples of 6:

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240,246,252,258,264,270,276,282,288,294, etc.

As you can see, all I'm doing is adding 6 to every step I go. So when you say there is an infinite number, then these multiples are going to be infinite.

What us the length of the altitude of the equilateral triangle below

Answers

Answer:

Height ( h) = 12 units.

Step-by-step explanation:

Given : An equilateral triangle with side = 8 √3.

To find : What us the length of the altitude of the equilateral triangle .

Solution : We have given equilateral triangle with side = 8 √3.

By taking the half triangle,

By the Pythagorean theorem :

(Hypotenuse)² = ( adjacent)² + (opposite)².

Plug the values Hypotenuse = 8√3 , adjacent = 4√3 , opposite = h.

(8√3)² = ( 4√3)² + (h)².

192 = 48 + (h)².

On subtracting by 48 both sides.

192 -48 = (h)².

144 = (h)².

On taking square root .

h = 12 .

Therefore, Height ( h) = 12 units.

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Ms. Howard wrote a test. Part A had true/false questions, each worth points. Part B had multiple choice questions, each worth points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible.

Answers

Full question attached

Answer and explanation:

Since x = number of true or false questions correct

And y = number of multiple choice questions correct

And each question for x =2 points

each question for y=3 points

since she then needs a total score of more than 93 to pass, we add up total correct questions and

Inequality equation = 2x +3y >93

Final answer:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find the least common multiple (LCM) of the values of points for true/false questions and multiple choice questions.

Explanation:

To find the least number of points for which the number of points for Part A is equal to the number of points for Part B, we need to find a common multiple of the values of points for true/false questions and multiple choice questions. Let's assume the number of points for true/false questions is x and the number of points for multiple choice questions is y. We need to find the least common multiple (LCM) of x and y. Once we find the LCM, that will be the minimum number of points for which the number of points in Part A is equal to the number of points in Part B.

For example, if the number of points for true/false questions is 4 and the number of points for multiple choice questions is 6, we can find the LCM as follows:

List the multiples of 4: 4, 8, 12, 16, 20, 24, ...
List the multiples of 6: 6, 12, 18, 24, 30, ...
Find the smallest number that appears in both lists: 12

Therefore, the least number of points for which the number of points in Part A is equal to the number of points in Part B is 12.

Learn more about Least Common Multiple (LCM) here:

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Bridget needs an actor. Actor A is offering her services for an initial $250 in additionto $50 per day. Actor B is offering her services for an initial $200 in addition to $60
per day. When will the two actors charge the same amount of money?

Answers

$250 + 50x = $200 + 60x

Get like terms on the same side using subtraction
250 -200 + 50x = 60x
50 + 50x - 50x = 60x -50x
50 = 10x now divide by 10 and get 5 days.

Let's check

Day 1 Actor A is $250 + 50 = $300 Actor B = $200 + 60 = $260
Day 2 Actor A is $250 + 100 = $350 Actor B = $200 + 120 = $320
Day 3 Actor A is $250 + 150 = $400 Actor B = $200 + 180 = $380
Day 4 Actor A is $250 + 200 = $450 Actor B = $200 + 240 = $440
Day 5 Actor A is $250 + 250 = $500 Actor B = $200 + 300 = $500

Answer:

The two actors will have the same amount of money in 5 days.

Step-by-step explanation:

Write 850 as the product of its prime factor

Answers

2*5*5*17=850

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