If the sum of the positive integer a and 5 is less than 12, what is the sum of all possible values of a?

Answers

Answer 1

Final answer:

To find the sum of all possible values of a, we subtract 5 from both sides of the inequality a + 5 < 12 and find the maximum value of a. The sum of all possible values of a is 21.

Explanation:

To find the sum of all possible values of a, we need to determine the range of possible values for a. We are given that the sum of a and 5 is less than 12. This can be expressed as a + 5 < 12. To find the maximum value of a, we subtract 5 from both sides of the inequality: a < 12 - 5 = 7. Therefore, the possible values of a are all the positive integers less than 7. To find the sum of all these values, we can use the formula for the sum of consecutive positive integers: S = (n/2)(n+1), where n is the largest integer. In this case, n = 6, so the sum of all possible values of a is (6/2)(6+1) = 21.

Answer 2

Final answer:

The sum of all possible values of a is 21.

Explanation:

The question states that the sum of the positive integer a and 5 is less than 12. To find the sum of all possible values of a, we need to determine the range of values that satisfy this inequality. Let's set up the inequality:

a + 5 < 12

Subtract 5 from both sides:

a < 7

So, the possible values of a are all positive integers less than 7. To find the sum of all these values, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

Here, the first term is 1 and the last term is 6 (since we want integers less than 7). The number of terms, n, is 6, since there are 6 possible values of a. Plugging in these values:

Sum = (6/2)(1 + 6) = 3 * 7 = 21

So, the sum of all possible values of a is 21.

Related Questions

HELP WILL MARK BRAINLIEST!!!!!!!!!!!Cindy has to write an 18-page report. If she has written 1/3 of a report so far, how many pages has she written?
A. 4 pages
B. 6 pages
C. 8 pages
D. 9 pages

Answers

18

1/3 of 18 = 6

Cindy has written 6 pages of her report so far.

Also: This means she has 12 pages left.

18/3=6
6 x 1= 6

The answer is 6 pages, or B.

in a first aid kit the ratio of large bandages to small bandages is 5 to 2. Based on this ratio, how many large bandages are in the kit if there are total of 60 bandages?

Answers

The best way to answer this question is to set up the first sentence as a ratio of large bandages to total bandages. You would write 5 large bandages to 7 total bandages to 7 total bandages. Then you would make this equivalent to x number of large bandages to 60 total. It would look like this 5:7 = x:60. You could use cross products to multiply 60 by 5 to get 300. 7 times x also should equal 300. Unfortunately, this example will not leave us with a whole number of bandages, but 300/7 is a repeating decimal or a mixed number (42 6/7 large bandages).

PLEASE HELP ME PLSSSSSSSSSSSSS

The scatter plot below shows the number of pizzas sold during weeks when different numbers of coupons were issued. The equation represents the linear model for this data. y = 3.4x + 43

According to the model, what is the average number of pizzas sold in one night if no coupons are issued?

Question 5 options:

A 43

B 0

C 11

D 21

Answers

the answer wolud be 43 good luck

Answer:

option: A is correct.

Step-by-step explanation:

We are asked to find the average number of pizzas sold in one night if no coupons are issued.

i.e. we have to find the value of y such that x=0 i.e. no coupon was issued.

We are given a equation which represents the linear model for this data:

y = 3.4x + 43

where y denotes the average number of pizza sold and x denotes the number of coupons issued.

Hence when x=0 we have value of y from the above linear equation as:

y=3.4×0+43=0+43=43

i.e. y=43.

Hence, average number of pizzas sold in one night if no coupons are issued are 43.

The equation b=540−30m gives the balance b (in dollars) that you owe on a drum set after m monthly payments. What is the balance after 9 monthly payments?

Answers

b=in dollars, m= months
b=540-30m
b=540-30(9)
b=540-270
b=270

So the answer is b=270

What is the length of the diagonal of a 10cm by 15com rectangle

Answers

a2 + b2 = c2

102 + 152 = c2

100 + 225 = c2

√325 = c

5√13 = c

The diagonal measures 5√13 cm.

The distance between Rosa’s house and her school is 3/4 mile. She ran 1/4 mile.What fraction of the way to school did she run?

Answers

She ran 1/4
.25
25%
She ran 1 forth of the distance.

I think it is 2/4 since 1/4+2/4=3/4

Prove it is rational by writing it as a quotient of two integers. Please answer these problems, I need to check my answers. Ignore the blank ones, I was able to check them. Thank you!
1. 2.4

2. 74

3. 17.3333333…

4. π

5.

6. –18

7.

8. 87.125

9. –30

10. –8.3

11. 58.25

12. 121

13. 4.5

14.

Answers

1. 2.4 = 24/10

2. 74 = 74/1

3. 17.3333333… = 52/3

4. π - not rational

6. –18 = -18/1

8. 87.125 = 87125/1000

9. –30 = -30/1

10. –8.3 = -83/10

11. 58.25 = 5825/100

12. 121 = 121/1

13. 4.5 = 45/10

Most of the decimals can be reduced to lower terms by removing at least one factor of 2 or 5. If all you want is a ratio of integers, that is irrelevant.

Expand the polynomial:
(5a+1/5 b)^2

Answers

Expand the following:
(5 a + b/5)^2

(5 a + b/5) (5 a + b/5) = (5 a) (5 a) + (5 a) (b/5) + (b/5) (5 a) + (b/5) (b/5):
5×5 a a + (5 a b)/5 + (5 b a)/5 + (b b)/(5×5)

(5 a b)/5 = 5/5×a b = a b:
5×5 a a + a b + (5 b a)/5 + (b b)/(5×5)

(b×5 a)/5 = 5/5×b a = b a:
5×5 a a + a b + b a + (b b)/(5×5)

Combine powers. (b b)/(5×5) = (b^(1 + 1))/(5×5):
5×5 a a + a b + b a + (b^(1 + 1))/(5×5)

1 + 1 = 2:
5×5 a a + a b + b a + (b^2/5)/5

5 a×5 a = 5×5 a^2:
5×5 a^2 + a b + b a + (b^2/5)/5

5×5 = 25:
Answer: 25 a^2 + a b + b a + (b^2/5)/5

Replaced A for X and B for Y

(25x^2)+(2xy)+(y^2/25)

(80z) to the 3/4 power

Answers

[tex] 80z^{3/4} [/tex] is also equal to 80[tex] \sqrt[4]{z^{3}} [/tex] then simplify

what is the circumference of a circle with a diameter of of 8.4 cm?

Answers

The answer would be 26.39 cm.

Hope this helps!

- Juju

C= d•pi(3.14).
3.14•8.4= 26.376. :)
C= 26.376

To write f(x) = 2x2 – 44x + 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x + 121) + 185 – 242 The function written in vertex form is f(x) = (x – )2 + .

Answers

Write f(x) = 2x2 – 44x + 185 in vertex form.

To write f(x) = 2x2 – 44x + 185, factor out
2
from the first two terms.

Next, form a perfect square trinomial keeping the value of the function equivalent:

f(x) = 2(x2 – 22x + 121) + 185 – 242

The function written in vertex form is f(x) =
2
(x –
11
)2 +
-57
.

Answer:

f(x) = 2(x-11)^2 - 57

Step-by-step explanation:

To write f(x) = 2x^2 – 44x + 185, factor out from the first two terms.

Next, form a perfect square tri nomial keeping the value of the function equivalent: f(x) = 2(x^2 – 22x + 121) + 185 – 242

To get vertex form we factor x^2 -22x+121

product is 121 and sum is -22

-11*-11= 121 and sum -11+(-11)= -22

x^2 -22x+121

(x-11)(x-11)

f(x) = 2(x^2 – 22x + 121) + 185 – 242

f(x) = 2(x-11)(x-11)+ 185 – 242

f(x) = 2(x-11)^2 - 57

Suppose the population of a town is 15,200 and is growing 2% each year. Write an equation to model the population growth. Predict the population after 10 years. y = 15,200 ∙ 2x; about 15,564,800 people y = 2 ∙ 15,200x; about 304,000 people y = 15,200 ∙ 1.02x; about 18,529 people y = 15,200 ∙ 2x; about 18,529 people

Answers

For this case, what you need to know is that to model this problem, you must use equations of the potential type:
y = A * (b) ^ t
Where:
A: initial population.
b: growth rate.
t: time.
Substituting values we have:
y = 15200 * (1.02) ^ t
After 10 years we have:
y = 15200 * (1.02) ^ 10
y = 18529
Answer:
An equation to model of the population growth is:
y = 15,200 ∙ 1.02 ^ x
the population after 10 years is:
about 18,529

Would (j^-13)(j^4)(j^6) equal to j^-312?

Answers

No.

[tex](j^{-13})(j^{4})(j^{6}) = j^{(-13+4+6)} = j^{-3}[/tex]

write y=(- 3/4)x+3 in standard form using intregers

Answers

y = (-3/4)x + 3
4y = 4 * [ (-3/4)x + 3 ] ... multiply both sides by 4
4y = 4*(-3/4)x + 4*3 ...... distribute
4y = -3x + 12
4y + 3x = -3x + 12 + 3x .... add 3x to both sides
3x + 4y = 12

Answer: 3x + 4y = 12

What value of k makes the equation true?

a.2
b.3
c.4
d.8

Answers

your answer would be c

Its C. 4

Correct on edge :D

o decorate his bedroom, Mike spent $41.64 on new bedding, $36.84 on paint, and $72.49 on accessories. About how much did he spend to decorate his bedroom?

Answers

He spent 150.97 hope this helps :) have a good day

Answer:

Mike spent $150 on his decorations.

Step-by-step explanation:

In order to find the amount of money Mike spent on his decorations you must add all the costs together.

$41.64 + $36.84= $78.48

$78.48 + $72.49= $150.97

Then you round 150.97 to 151, which is also close to 150.

Hope this helps :)

800 hm = _____ cm

8
0.08
8,000,000
80,000

Answers

To solve this conversion factor problem we are going to multiply our original quantity 800hm by conversion factors (expressed as fractions) in order to cancel units until we get centimeters:
We know that 1 hectometer= 100 meters, so our first conversion factor expressed as a fraction is [tex] \frac{100m}{1hm} [/tex]
We also now that 1 meter = 100 centimeters, so our second one is [tex] \frac{100cm}{1m} [/tex]

Now that we have our fractions, lets multiply our original quantity by them to get our answer in the required units:
[tex]800hm( \frac{100m}{1hm} )( \frac{100cm}{1m})=8000000cm [/tex]

We can conclude that 800hm are 8,000,000cm

Answer:

Exactly what they said (the answer is i bold at the bottom)

Step-by-step explanation:

Which is the ratio for sin A, written as a fraction in simplest form?

Answers

When you have a right triangle (A triangle which has a angle of 90°), you can find the "Sine". This is one of the basi trigonometric ratios. By definition, the Sine is:

Sin(α)=Opposite leg/Hypotenuse

You want to find Sin(A), so the opposite leg will be 8√3 and the hypotenuse will be 16.

When you substitue these values, you have:

Sin(α)=Opposite leg/Hypotenuse
Sin(A)=8√3/16

When you simplify, you obtain:

Sin(A)=4√3/8
Sin(A)=2√3/4
Sin(A)=√3/2

Which is the ratio for Sin(A)?

The answer is: The ratio for Sin(A) is √3/2

Answer:

√3/2

Step-by-step explanation:

Trent is fishing from a pier. ●The tip of his fishing rod is 53 ¾ feet above the surface of the water. ●The hook on the end of the fishing line is directly below the tip of the fishing rod 12 ⅔ feet below the surface of the water. Trent estimates that the distance between the tip of his fishing rod and the hook is less than 65 feet. Is Trent’s estimate reasonable? Explain your answer. HELP Please

Answers

I would say yes and no because estimations aren't exact, they're close to the correct value. Trent's estimation is correct since 53+12=65, if we were looking for the exact distance, Trent would be wrong because there are fractions too, so the exact value would be 66 (5/12) or 65 (17/12).

Hope this helped :)

find two consecutive odd integers such that 36 more than the lesser is three times the greater

Answers

Two consecutive odd integers means there's a difference of 2 between the numbers. More than the lesser is adding to the lower integer (x). The greater is the larger integer (x+2). "Is" means equals. Times means multiply.

x= first integer
x+2= second integer

x + 36= 3(x + 2)
multiply 3 by everything in parentheses
x + 36= 3x + 6
subtract x from both sides
36= 2x + 6
subtract 6 from both sides
30= 2x
divide both sides by 2
15= x

x= 15 first consecutive odd integer

x+2= second consecutive odd integer
15+2= 17

ANSWER: 15, 17

Hope this helps! :)

Final answer:

To find two consecutive odd integers such that 36 more than the lesser is three times the greater, set up an equation and solve for the variable x. The two consecutive odd integers are 15 and 17.

Explanation:

To find two consecutive odd integers such that 36 more than the lesser is three times the greater, we can set up an equation:

x + 36 = 3(x + 2)

Simplifying this equation, we get:

x + 36 = 3x + 6

Subtracting x from both sides, we get:

36 = 2x + 6

Subtracting 6 from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

Therefore, the two consecutive odd integers are 15 and 17.

a map is drawn with a centimeter representing 25 Miles. if the distance between two towns ia 3 centimeters on the map, what is the actual distance between the two towns?

Answers

25 miles * 3 cm= 75 miles

The answer is 75.
1cm=25miles
3cm=xmiles
Cross multiply to get x=75miles

Between which two consecutive integers does ???147 lie?

A.
146 and 148

B.
12 and 13

C.
11 and 12

D.
10 and 11

Answers

If those question marks are supposed to be a radical, then 12 and 13. The square root of 147= 12.12, which puts it between 12 and 13.

The consecutive numbers where the square root of 147 will lie are between 12 and 13.

Consecutive numbers simply mean the numbers that follow each other. Examples of consecutive numbers are 2,3, 4.

It should be noted that the square root of 147 is 12.12. Therefore, 12.12 can be found between 12 and 13. In conclusion, the numbers will be 12 and 13.

Answers

You can infer from this problem that the shape of the wooden plank is a rectangle based on the dimensions given. The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm. Therefore, the width is 8.5 cm.

The length of a rectangle is usually the longest side of the rectangle so you can conclude that the length of the rectangle is 12.5 cm the width is 8.5 cm.

I need help with my assignments on these two questions

Answers

a. Using properties of exponents, the value of the expression is 10⁰

b. The equation has no solution

What are properties of exponents?

a. Properties of exponents are mathematical rules that allow us to simplify and manipulate expressions involving exponents. These properties help us perform operations such as multiplication, division, and raising to a power more efficiently.

In the given problem, we have to solve and simplify using properties of exponents.

Given that; [tex]\frac{10^-^3}{10^-^3}[/tex];

we can apply quotient rule when dividing exponents here;

[tex]\frac{10^-^3}{10^-^3} = 10^-^3 ^+^3 = 10^0[/tex]

The answer is 10⁰

b. To simply the equation, we just need to use basic mathematical operation to find the value of x.

3x - 2x + 4 = 5x - 4x - 8

Simplify;

x + 4 = x - 8

Collect like terms

x - x = -8 - 4

0 = -12

No solution

Learn more on properties of exponents here;

https://brainly.com/question/3187898

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Samuel needs $29 to download some songs and movies on his MP3 player. His mother agrees to pay him $6 an hour for raking leaves in addition to his $5 weekly allowance. What is the minimum number of hours Samuel must work in one week?

Answers

29÷6=4.8
so just do 4 hours and just 1 week

29/6= 4.8.
So you’d do 4 hours, and get your weeks allowance :)

Write a real-world problem that can be represented by a rule and a table using division

Answers

A company makes different size square containers. How can you find the length of each side if you know the perimeter of each of the containers? Represent your answer in a table, and right and equation that shows the rule used. You would write the equation x/4=y. I would create an input/output table with the labels x and y. I would then write various lengths for the perimeters and use the rule of dividing by 4 to find the y values.

HELP THIS IS URGENT HELLPP

Answers

Ok, so the key says 1cm=10mm. So you do 25x10=250cm, then do 250(the fish)-25(the guinea pig)= 225cm

what is the mean median and mode

Answers

mean-the average of numbers
to calculate add all the numbers and divide by how many numbers there are
4,600,000+4,500,000+4,000,000+4,600,000+10,200,000 and since there are 5 numbers divide that by 5

median-find the middle number
put numbers in order from least to greater and find the number in the middle
4,000,000x 4,500,000x 4,600,000 4,600,000 10,200,000x so your answer should be 4,600,000

mode-if a number appears more than once
4,600,000

Make a conjecture about the position, size and shape of a figure if a composition of transformation included a dilation

Answers

If a dilation is included, then there should be a different size in the image as well as a reasonable scale factor.

What is 3 1/3 +(-2 1/4) + 1 5/6 as a mixed fraction

Answers

The answer is 2 11/12 because you do 3 1/3 + -2 1/4 which gets you 1 1/2. Then you need to add 1 5/6 to the 1 5/6 to get your answer. So when you add up your answer you get 2 11/12. Hope this helps.

By separating between whole numbers and fractions, we will see that the sum is equal to 2 + 11/12.

How to add mixed numbers?

Here we want to perform the sum:

(3 + 1/3) + (-2 - 1/4) + (1 + 5/6)

We separate between whole and fractions, so we get:

(3 - 2 + 1) + (1/3 - 1/4 + 5/6)

The left part is easy: 3 - 2 + 1 = 2

The right part needs to find a common denominator, we will use 12.

1/3 - 1/4 + 5/6 = 4/12 - 3/12 + 10/12 = 11/12

Then the sum is:

(3 + 1/3) + (-2 - 1/4) + (1 + 5/6) = 2 + 11/12

If you want to learn more about mixed numbers:

https://brainly.com/question/723406

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