331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Include a let statement in your answer.

Answer:

-4a + b

Step-by-step explanation:

Take away the parentheses (brackets) and solve.

-a + 2b - 3a - b

-a - 3a + 2b - b

-4a + b

Answer:

It's -[tex]4a + b[/tex]

Step-by-step explanation:

Simplify the expression.

The correct expression with the correct statement has matched below.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.

The price of a game that’s been discounted by 18% of its list price

It will be (x - 0.18x)  =  0.82x

The price of a toy that sells for 18% more than the amount needed to build the toy

It will be (x + 0.18x) = 1.18x

The volume of water remaining in a tank after 3/10 of its original volume is drained out.

It will be [ x - (3/10)x ] = 7/10x

The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.

It will be [ x + (3/10)x ] =  13/10x

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Answer:

4

Step-by-step explanation:

I'm guessing that each number represents the number of rectangles that overlap. Where you see 1, there is only one rectangle, 2 shows where two rectangles overlap, and so on.

At the question mark, it appears as though four rectangles overlap. So a 4 would go there.

Answer:  1. [tex]\dfrac{9}{8}[/tex] .

Step-by-step explanation:

The given expression  [tex]2x^2-3x+1[/tex]

Using completing the square method.

First, we divide the entire expression by 2 and write in the form of [tex]x^2+bx=c[/tex] , we get

[tex]x^2-\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

Such that [tex]b=\dfrac{3}{2}\ \ \ , c=\dfrac{1}{2}[/tex]

Now add and subtract [tex](\dfrac{b}{2})^2[/tex] on both sides.

[tex](\dfrac{b}{2})^2=(\dfrac{\dfrac{3}{2}}{2})^2\\\\=(\dfrac{3}{2\times2})^2\\\\=(\dfrac{3^2}{4^2})\\\\=\dfrac{9}{8}[/tex]

Here, we add and subtract [tex]\dfrac{9}{8}[/tex] .

Hence, the correct answer is  1. [tex]\dfrac{9}{8}[/tex] .

Answer:

A. m∠2 + m∠3

Step-by-step explanation:

The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles.

So m∠4's non-adjacent angles are 2 and 3 NOT 1. Therefore, the measure of ∠4 = m∠2 + m∠3.

Hope this helps!

Answer:

A) m∠2 + m∠3

Step-by-step explanation:

Triangle Exterior Angle Theorem: The Sum of the outside angle is found using by adding the two opposite interior angles.

In the case of ∠4, the opposite interior angles are ∠2 & ∠3.

~

Answer:

Your correct answer is option C. Equilateral triangles

Step-by-step explanation:

In similar polygons, it is all the corresponding angles that are congruent.

Answer:

40/46+x=30/46-x

Step-by-step explanation:

Speed=distance/time

s=d/t

x=speed of the boat

Downstream speed=x+46

Upstream speed=x-46

Downstream

s=d/t

x+46=40/t

t=40/(x+46)

Upstream

s=d/t

x-46=30/t

t=30/(x-46)

Equate upstream and downstream

30/x-46=40/x+46

30(x+46)=40(x-46)

30x+1380=40x-1840

30x+1380-40x+1840=0

-10x+3220=0

-10x=-3220

Divide both sides by -10

x=322

x=322 miles/hour

The function that models the inverse variation is y=96/x. Thus, the correct option is A.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Given that x and y vary inversely. Therefore, the relation can be written as,

y  ∝ 1/x

y = k × 1/x

y = k/x

Also, when y =8, the value of x is 12, therefore, if we substitute the points in the above-formed equation,

y = k/x

8 = k /12

k = 96

Hence, the function that models the inverse variation is y=96/x. Thus, the correct option is A.

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Answer:

see below

Step-by-step explanation:

1.the equations have different slopes?  They will intersect at one point so one solution

2.the equations have the same slope and different y-intercepts.  They are parallel lines with a different y intercept so they will never intersect - no solutions

3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions

Answer:

1. One solution

2. no solution

3. infinite number of solutions.

Step-by-step explanation:

How many solutions a system of linear equations have if: Questions.

(assuming a system of two equations)

1.the equations have different slopes?

One unique solution, which is at the intersection point.

2.the equations have the same slope and different y-intercepts.

The equations/lines are then parallel but NOT coincident.  They will never meet, therefore NO solution.

3.the equations have the same slope and same y-intercepts.

The two lines/equations are in effect coincident.  Therefore there is an infinite number of solutions.

Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution

Answer:

15

Step-by-step explanation:

you need to get to 35. if one bag is 5 pounds what else plus 5 is 35. so each bag is 15 pounds

Answer: 15

Step-by-step explanation:

35 - 5 = 30

30 ÷ 2 = 15

Hope this helped.

(15 each)

Answer:

I'm confused what's the question ?

Answer:

27. 4x + 44  (D)

28. 17.5 in (A)

29. 189 cm² (C)

Step-by-step explanation:

27. 4 (2x + 11 - x) → 4 (x + 11) → 4x + 44

28. 369.25 ÷ 42.2 = 8.75 → 8.75 × 2 = 17.5 in

29. 21 × 9 = 189 cm²

Hope this helps! :)

Answer:

27.D

28.A

29.C

Step-by-step explanation:

27.   8x+44-4x= 4x+44         D

28. (369.25*2)/42.2=17.5      A

29.     9*21=189 cm^2           C

Answer:

? = 56.

Step-by-step explanation:

In the problem, the side 20 corresponds to side 32 and side 20 + 35 corresponds to side 32 + ?.

[tex]\frac{20}{32} =\frac{20 + 35}{? + 32}[/tex]

[tex]\frac{5}{8} =\frac{55}{? + 32}[/tex]

[tex]\frac{1}{8}=\frac{11}{? + 32}[/tex]

? + 32 = 8 * 11

? + 32 = 88

? = 56.

Hope this helps!

Answer:

56

Step-by-step explanation:

We can find the missing side length through ratios.

20/35 = 32/x

Cross multiply.

20x = 35(32)

20x = 1120

x = 1120/20

x = 56

Answer:

A. 10/(3x^2+3x)

Step-by-step explanation:

2x5=10

3x(x+1) = 3x^2+3x

Answer:

logarithmic I think

Step-by-step explanation:

Use process of elimination

Answer:

C). linear

Step-by-step explanation:

test

Answer:

-2

Step-by-step explanation:

The product of the slope of perpendicular lines= -1.

Slope of given line= ½,

since the equation is in the form of y=mx +c, where m is the slope of the line.

½(slope of line)= -1

slope of line

= -1 ÷½

= -1 ×2

= -2

Answer:

Step-by-step explanation:

Slope of perpendicular line = -1

y = (1/2)x + 5

Slope [tex]m_{1}\\[/tex] = 1/2

[tex]m_{1}*m_{2}=-1\\\\\frac{1}{2}*m_{2}=-1\\\\m_{2} = -1*\frac{2}{1}\\\\ m_{2}= -2[/tex]

y = -2x + 7

Answer:

y-intercept: (0, 2.5)

x-intercept: (1.67, 0)

Step-by-step explanation:

Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.

2y = -3x + 5

y = -3/2x + 5/2

From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).

To get the x-intercept, substitute 0 for y.

0 = -3/2x + 5/2

3/2x = 5/2

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).

Hope this helps!

Answer:

Step-by-step explanation:

To find the x-intercept, let y = 0.  Then 3x = 5 and x = 5/3, or x = 1.667, and the x-intercept is (1.667, 0).

To find the y-intercept, let x = 0.  Then 2y = 5 and y = 5/2 or 2.5.  Then the y-intercept is (0, 2.5).

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

Explanation:

Label the friends A,B,C,D,E

There are 5 choices for the first ticket, then 4 for the second, and 3 for the third. We have 5*4*3 = 20*3 = 60 permutations. One permutation is ABC and another permutation is CBA if order mattered. However, order does not matter. All that counts is the group overall rather than the individual. This is because there is no ranking and all the friends are effectively treated equally.

With a set like {A,B,C} there are 3! = 3*2*1 = 6 ways to arrange this set of three items. This means we have overcounted by a factor of 6. Divide the previous result (60) by 6 to get 60/6 = 10

So there are exactly 10 different groups possible.

-------------

You can use the combination formula

[tex]_n C _r = \frac{n!}{r!(n-r)!}[/tex]

with n = 5 and r = 3 to get the same result.

Or you could use Pascal's triangle to find "10" located in the row that has 1,5,10,10,5,1. Notice how 10 is located in slot 3. You start counting at slot 0.

There are 55 two-bedroom units  in the apartment.

Let x represent the number of one bedroom units and y represent the number of two bedroom units.

Since the apartment building contains 100 units, hence:

x + y = 100      (1)

The total monthly rent paid by the tenants is $55,275, hence:

495x + 600y = 55275   (2)

Solving equation 1 and 2 simultaneously gives:

x = 45, y = 55

Hence, there are 55 two-bedroom units  in the apartment.

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Answer:

A domain of a parabola is all real numbers because you can input any x-value into the equation.

Step-by-step explanation:

Since there are no restrictions of numbers you can put in x², we can plug anything in. Therefore, our domain is infinite numbers.

Answer:

Step-by-step explanation:

Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.

We now only need to find a fraction that simplifies to 3/4.

8/12 = 2/3 [tex]\neq[/tex] 3/4

12/16 = 3/4 ✅

4/6 = 2/3 [tex]\neq[/tex] 3/4

6/9 = 2/3 [tex]\neq[/tex] 3/4

This means that the correct answer is B. 12 and 16.

Answer:

B. 12 and 16

Step-by-step explanation:

Answer:

1 10/17

I answered it in the pervious question

Answer:

v = -52

Step-by-step explanation:

Divide both sides by -5

v + 65 = 13

v = 13 - 65

v = -52

Answer:

v= -52

Step-by-step explanation:

-5(v+65)=-65

-5v-325=-65

-5v=260

v=-52

Answer:

A, C and D

Step-by-step explanation:

The missing inequality is:

y > 2x -4

To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.

Option A: (-2,-5)

2(-2) -4 = -8

y = -5 > -8

then, the point is solution

Option B: (0,-4)

2(0) -4 = -4

y = -4 = -4

then, the point is not solution

Option C: (1,1)

2(1) -4 = -2

y = 1 > -2

then, the point is solution

Option D: (3,5)

2(3) -4 = 2

y = 5 > 2

then, the point is solution

Option E: (5,5)​

2(5) -4 = 6

y = 5 < 6

then, the point is not solution

Answer:

x=pm-rm

Step-by-step explanation:

[tex]\frac{x}{m}+r=p\\\\ \frac{x}{m}+r-r=p-r\\\\\frac{x}{m}=p-r\\\\\frac{x}{m}*m=(p-r)*m\\\\\boxed{x=pm-rm; m\neq 0}[/tex]

Answer:

45

Step-by-step explanation:

g(4) = 3 * 4 - 7 = 5

f[g(4)] = f(5) = 2 * 5² - 5 = 45

Answer:

45

Step-by-step explanation:

Answer:

24 Combinations Total

Step-by-step explanation:

METHOD 1 (no advanced math skills needed)

i. Number the friends: a, b, c, and d

ii. List all possible combinations...

To speed up the process instead of sitting here and listing 24 combinations, after two sections you can see that with friend "a" sitting all the way at the left there are six combinations and the same goes for friend "b". You can then multiply 6 (number of combinations with that friend first) and 4 (friends) to get 24.

METHOD 2

n! means the total number for permutations calculation (1 x 2 x ... until you reach n ) = 24

Answer:

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.

Step-by-step explanation:

We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.

(a) The probability that a male is selected, then two females is given by;

Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]

Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(b) The probability that a female is selected, then two males is given by;

Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]

Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{770}{2300}[/tex]  =  0.3348

(c) The probability that two females is selected, then one male is given by;

Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]

Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]

                                           =  [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{1001}{2300}[/tex]  =  0.4352

(d) The probability that three males are selected is given by;

Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{165}{2300}[/tex]  =  0.0717

(e) The probability that three females are selected is given by;

Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]

Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]

So, the required probability =  [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]

                                           =  [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex]     {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

                                           =  [tex]\frac{364}{2300}[/tex]  =  0.1583

(a) The probability that a male is selected, then two females is 0.4352.

(b) The probability that a female is selected, then two males is 0.3348.

(c) The probability that two females are selected, then one male is 0.4352.

(d) The probability that three males are selected is 0.0717.

(e) The probability that three females are selected is 0.1583.