5 times the sum of 40 and 80. what is the numerical expression that would represent the phrase?

Answer:

option B

28

Step-by-step explanation:

Given in the question,

C(8,2)

Formula to use

here n = 8

        r  = 2

We have to calculate combinations of 8 object taken 2 at a time, then

C(8,2)  

8C2

8! / 2! * (8 - 2)!

[tex]\frac{8*7*6*5*4*3*2*1}{2*1(6!)}[/tex]

[tex]\frac{8*7*6*5*4*3*2*1}{2*1(6*5*4*3*2*1)}[/tex]

[tex]\frac{8*7}2[/tex]

56/2

28

So, 8C2 = 28

The combination C(8, 2) in the given problem equals 28.

Mathematically, a combination refers to a selection of items from a larger set without regard to the order of selection. It is a way to count the number of different subsets or groups that can be formed from a given set.

In other words, a combination is a selection of r objects from a set of n distinct objects, where the order of selection is not considered. The number of combinations represented as C(n, r), represents the count of possible combinations.

It is known that C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex],

So,

C(8, 2) = [tex]\frac{8!}{2!(8- 2)!}[/tex],

           = [tex]\frac{8!}{2!6!}[/tex]

           = [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(2\times 1) (6\times 5\times 4\times 3\times 2\times 1)}[/tex]

           = 28.

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Answer:

1725

Step-by-step explanation:

50+65=115 divided by 2 =57.5     57.5*30H= 1725

Answer:

x=1

Step-by-step explanation:

8x+4y=12y

-4y         -4y

8x=8y

x=1

The equation doesn't provide enough context to definitively solve for 'r'. Given the original equation r16 ≥ 8, r shouldn't be less than 1 if only integer values are accepted.

In Mathematics, the original equation provided here, 'r16 ≥ 8', seems to indicate that a value 'r' is being multiplied by 16 and the product should be greater than or equal to 8. To solve for 'r', you would normally divide both sides of the equation by 16. However, each sub-question provided 'r ≥ 2', 'r ≤ 2', 'r ≥ 128', and 'r ≤ 128', indicates different potential solutions for 'r'. Without the proper context or further information it is difficult to properly solve for 'r'. Given the original equation, if only integer values are allowed, 'r' should not be less than 1 to maintain the inequality. Further clarification on the nature of 'r' and the context of the question is highly recommended.

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f(x)= 9x^3+ 2x^2 -5x+ 4

g(x)= 5x^3 -7x+ 4

f(x) - g(x)

= (9x^3+ 2x^2 -5x+ 4) - (5x^3 -7x+ 4)

= 9x^3+ 2x^2 -5x+ 4 -5x^3+ 7x -4

= (9x^3 -5x^3)+ 2x^2+ (7x -5x)+ (4-4) (combine like terms)

= 4x^3+ 2x^2+ 2x

= 2x* (2x^2+ x+ 1)

The final answer is 2x* (2x^2+ x+ 1).

The final answer in factored form is 2x(x² + x + 1).

f(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³ - 7x + 4

To find f(x) - g(x) ,, we subtract g(x) from f(x) term by term.

f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) = 4x³ + 2x² + 2x

The final answer in factored form is 2x(x² + x + 1).

Answer:

x = 2

Step-by-step explanation:

expand the brackets firstly,

so 12x-4 = 20

then add the -4 onto the other side

so 12x = 24

then divide 24 by 12 to get x

so x = 2

Answer:

Step-by-step explanation:

a1 = 3(1) - 7 = - 4

a2 = 3(2) - 7 = -1

d = a2 - a1

d = -1 - (-4)

d = -1 + 4

d = 3

a60 = 3(60) - 7

a60 = 180 - 7

a60 = 173

n = 60

Sum = (a1 + a60) * n / 2

Sum = (-4 + 173) * 60/2

Sum = (169)*30

Sum = 5070

==================

Just to check, we'll use the second summation formula

d = 3

n = 60

a1 = -4

Sum = (2*a1 + (n - 1)*d )*n / 2

Sum = (2*(-4) + (60 -1)*3)* 60/2

Sum = (-8 + 59*3) * 30

Sum = (177 - 8)*30

Sum = 169 * 30

Sum = 5070

Same answer.

Answer:   c) 286.5 in²

Step-by-step explanation:

S.A.= 2π r · h

      = 2π (7.3/2) · 12.5

      = 2π (3.65) (12.5)

      = 286.5

Answer: There are 180 dogs in the shelter.

Step-by-step explanation:

Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.

You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:

[tex]d+c=275[/tex]

If the number of cats is 5 more than one half of the number of dogs, you can express it with:

[tex]c=\frac{d}{2}+5[/tex]

Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:

[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]

d=4n

315=5n+10d

315=5n+40n

315=45n

315/45=n

7=n

d=4n

d=4(7)

d=28

28 dimes and 7 nickels

Answer:

x = 14

Step-by-step explanation:

3x+2x-7=2x+35

then solve for x

Answer:

x = 14

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is [tex] 3 x [/tex], length from B to C is [tex] 2x - 7 [/tex] and AC is [tex] 2 x + 35 [/tex].

We are to find the value of x.

[tex] A B + B C = A C [/tex]

[tex] 3 x + 2 x - 7 = 2 x + 3 5 [/tex]

[tex] 3 x + 2 x - 2 x = 3 5 + 7 [/tex]

[tex] 3 x = 4 2 [/tex]

[tex] x = \frac { 4 2 } { 3 } [/tex]

x = 14

Answer:

See below.

Step-by-step explanation:

Part A: A system will have no solution when the graphs are parallel and do not intersect.

Part B: A system will have no solution when the equations have the exact same slope. The same slope means they are parallel and do not intersect. This is done easiest in slope-intercept form.

Answer:

Step-by-step explanation:

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Answer: The answer without estimation is 1,519.76 but with estimation it’s 1,520 m.

Step-by-step explanation:

The formula for this situation is A = pi(or in this case 3.14) times the radius squared. If you know the formula then the rest is just to plug in and estimate if you have too.

Answer:

-36

Step-by-step explanation:

We don't need one, do we? It's just simple math.

An equation is formed of two equal expressions. The number which when divided by -3 gives 12 as the result is -36. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number be represented by x.

Given that the number when divided by -3 gives 12 as the result. The given situation can be written in the form of an equation as,

x/-3 = 12

Solving the equation to get the value of x,

x/-3 = 12

x = 12 × -3

x = -36

Hence, the number which when divided by -3 gives 12 as the result is -36.

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Answer: 20

Step-by-step explanation:

6/30 = 0.2

0.2 times 100 = 20

Final answer:

After setting up a proportion and solving the equation 0.30x = 6, we find that there are 20 students in Mrs. Rutherford's class.

Explanation:

To determine how many students are in Mrs. Rutherford's class when 30% like chocolate ice cream and we know that 6 students like chocolate ice cream, we can set up a proportion where 30% (or 0.30) of the total number of students (which we will call x) is equal to 6. Therefore, the equation to find x is 0.30x = 6.

To solve for x, we divide both sides of the equation by 0.30:

0.30x = 6

x = 6 / 0.30

x = 20

So, there are 20 students in Mrs. Rutherford's class.

Answer:

9/5 = 9 x  1/ 5

Answer:

9/5 = 9 * 1/5

Step-by-step explanation:

Formula of [tex]p hat = \frac{X}{n}[/tex] help us to calculate p hat , where X represents the number of occurrence of desired event and n represents the specified of sample space.

" p hat is defined as the probability of the occurrence of random event to the specified sample space."

According to the definition,

p hat can be calculated using formula

[tex]p hat = \frac{X}{n}[/tex]

'X' represents the number of occurrence of the desired event

'n' represents the specified sample space.

p hat is nothing but the probability of finding specified sample size.

Hence, formula of [tex]p hat = \frac{X}{n}[/tex] help us to calculate p hat.

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Answer:

[tex]\large\boxed{x=53^o}[/tex]

Step-by-step explanation:

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore e have the equation:

[tex]x+45^o+82^o=180^o[/tex]

[tex]x+127^o=180^o[/tex]        subtract 127° from both sides

[tex]x=53°[/tex]

Step-by-step explanation:

You would need how many square feet. Divide the amount of square feet of land by 3. That should be the answer if it divides evenly, if there is a decimal or a fraction after it then round up to the next whole number

Answer:

Paula needs to sod

3,855

square feet of land. Assuming that Paula can cut the sod into pieces, the number of 3-square-foot pieces of sod she needs is

1,285

.

Step-by-step explanation:

The diagram shows one way to decompose this shape into two rectangles. One rectangle is 75 feet × 50 feet, and the other is 7 feet × 15 feet.

Answer:

$3.38

Step-by-step explanation:

6.75/2= $3.375

Answer: $3.375

Step-by-step explanation:

Given : Sid needs 0.5 meters of canvas material to make a carry all bag for his wheelchair.

Also, the cost of one meter of canvas = $6.75

Then, the cost of 0.5 meters is given by :-

[tex]0.5\times\$6.75\\\\=\$3.375[/tex]

Therefore, Sid will spend $3.375 on buying canvas material to make a carry all bag for his wheelchair..

answer = 9.125

first i changed the mixed number to a percentage 73/8 and did 73 divided by 8 to get my decimal.

5/15 or 1/3 would be the correct answer

Answer: 11.6

Step-by-step explanation:

We know that a radius that is perpendicular to a chord divides the chord into two equal parts .

Then by Pythagoras theorem of right triangle ,we have

[tex](6.5)^2=3^2+(\dfrac{x}{2})^2\\\\\Rightarrow\ 42.25=9+\dfrac{x^2}{4}\\\\\Rightarrow\ \dfrac{x^2}{4}=33.25\\\\\Rightarrow\ x^2=134\\\\\Rightarrow\ x=\sqrt{134}=11.5758369028\approx11.6[/tex]

Hence,the value of x = 11.6

Answer:

[tex]\large\boxed{(x+1)^2+(y-7)^2=100}[/tex]

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (-1, 7) and the radius r = 10. Substitute:

[tex](x-(-1))^2+(y-7)^2=10^2\\\\(x+1)^2+(y-7)^2=100[/tex]

Answer:

91,125

Step-by-step explanation:

V=Bh

V=l*w*h

V=45*45*45

V=2,025 *45

V=91,125

Answer:

50,505 cm

Step-by-step explanation:

In order to calculate this you just have to calculate the length necessary to create a wooden box with the volume of 454545 cubic centimeters, and now you just have to calculate since you have the base of the area, measuring 3 cm by 3 cm, that would be 9 square centimeters, so you just have to divide the desired volume by 9 square centimeters:

454545/9=50,505 cm

So the length of the wooden box should be 50,505 cm in order to have a 454545 cubic centimeters wooden box.

Answer:

Step-by-step explanation:

You can represent Morgan's scenario with the expression, 25w + 615, and you can represent Kendall's scenario with the expression, 15w + 975.  To find out when they both have the same amount of money in their accounts, you set them equal to each other and solve for w:

25w + 615 = 15w + 975

25w = 15w + 360

10w = 360

w = 36

Morgan and Kendall will have the same amount of money after 36 weeks.

To find the week when Morgan and Kendall will have the same amount of money in the bank, we set up the equation 615 + 25x = 975 - 15x and solve for x.

To find the week when Morgan and Kendall will have the same amount of money in the bank, we need to set up an equation. Let x represent the number of weeks. The equation for Morgan's savings is 615 + 25x, and the equation for Kendall's savings is 975 - 15x. To find the week when they have the same amount of money, we set up the equation 615 + 25x = 975 - 15x. Solving this equation will give us the value of x, which represents the number of weeks.

615 + 25x = 975 - 15x
Combine like terms:
40x = 360
Divide both sides by 40:
x = 9

Therefore, Morgan and Kendall will have the same amount of money in the bank after 9 weeks.

Answer:

In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.

Step-by-step explanation:

(B)

The error in the step 1, she should have also distributed -3/8 over –16d, to get 3 + 6d + 2d = 24

An equation is an expression used to show the relationship between two or more numbers and variables.

Given the equation:

(-3/8)(-8-16d) + 2d = 24

Step 1: Distribute -3/8 over the expression in parentheses:

3 + 6d + 2d = 24

Step 2 Simplify like terms:

3 + 8d = 24

Step 3 Subtract 3 from both sides of the equation:

8d = 21

Step 4 Divide both sides of the equation by 8:

d = 21/8

The error in the step 1, she should have also distributed -3/8 over –16d, to get 3 + 6d + 2d = 24

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