a child's toy train collection contains 5 engines, 5 red cars, 7 blue cars, and 2 cabooses. What is the probability of randomly selecting pieces to make a three-part train of engine, red car, caboose?

Answer:

Step-by-step explanation:

Perimeter of the figure = 6x - 4 + 6x - 4 + 12x +3 + 14x+ 13 + 12x + 3

Add like terms

                                    = 6x + 6x + 12x + 14x + 12x - 4 - 4 + 3 + 13 + 3

                                    = 50x  + 11

Answer:

Cory bought 6.47 gallons

rate of change is $2.78 per gallon

Step-by-step explanation:

cost of gas per gallon = $2.78

it means that if one buy 1 gallon he will have to pay $2.78 and similary for each increase in 1 gallon of gallon gas he will have to pay $2.78.

Thus, rate of change is cost of gas per gallon as cost to buy gas changes with the change in quantity of gallon.

Let the quantity of gas bought be x gallon.

Total cost for x gallons = cost of gas per gallon*x = 2.78x

Given that total money paid by him is $18

2.78x = 18

x = 18/2.78 = 6.47

Thus, Cory bought 6.47 gallons

rate of change is $2.78 per gallon

Left Side

if x = a number

five times a number means 5 · a number = 5 · x

add a negative sign; -5·x

simplify; you don't need the multiplication symbol; -5x

minus 2·x = -2x

plus 3 = +3

-5n-2x+3

Sign

less than or equal to = ≤

Right Side

triple of x = 3·x = 3x

4 minus triple of x = 4-3x

4-3x

The final inequality is -5x-2x+3 ≤ 4-3x

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

y = (-2/3)x + 490

Step-by-step explanation:

Our given equation is 2x + 3y = 1,470.

First subtract 2x from both sides of the equation:

3y = 1470 - 2x

Next divide both sides by 3:

y = 490 - (2/3)x

Move the terms on the right to fit the slope-intercept form (y = mx + b):

y = (-2/3)x + 490

Answer:

2x + 3y = 1470

=> 3y = 1470 -2x

=> y = 1470/3 - 2/3x

=> y = -2/3x + 490

First, I made the 3y alone by subtracting 2x to both sides.

Next, I divided 3 from both sides to make y alone.

Lastly, I got the slope-intercept form.

Slope = the number with which "x" is multiplied.

So, In this equation slope = -2/3

Y-intercept can be found my making the x as 0

=> y = -2/3(0) + 490

=> y = 490

So, the y-intercept is (0,490)

X-Intercept can be found by making y as 0

=> 0 = -2/3x + 490

=> -490 = -2/3x

=> -490 * 3 = -2x

=> -1470 = -2x

=> -1470/2 = -x

=> -735 = -x

=> x = 735

So, x-intercept = (735,0)

Answer:

Step-by-step explanation:

Answer:

(A) A translation one unit to the left followed by a 180-degree rotation.

Step-by-step explanation:

I figured this out by seeing that ABCD was one unit too far from the x=0 line than A’B’C’D. To get it the same distance, we move it left one, which is the same as transforming one unit to the left.

Now, we can see that the coordinates are opposite of each other - this signifies a 180° rotation around the origin.

So, it’s a transformation one unit to the left and a 180° rotation around the origin.

Hope this helped!

Answer: 5x2+3x -dx x3 2x2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Add real numbers and add imaginary numbers

(-7 + 3i)+(2 - 6i) = -7 + 2 + 3i - 6i

                        =  - 5 - 3i

[tex] &#128075 [/tex] Hello ! ☺️

Step-by-step explanation:

•What is the value of (-7+3i)+(2-6i)?

[tex] (- 7 + 3i) + (2 - 6i) = ( - 7 + 2 + 3i - 6i) = - 5 - 3i [/tex]

(-7+3i)+(2-6i) = [tex]\boxed{\color{gold}{ -5-3i}} [/tex]

[tex]<marquee direction="left" scrollamount="2" height="100" width="150">&#x1F498;Mynea04</marquee>[/tex]

Answer: 3 terms

Step-by-step explanation:

each term is separated by the plus or minus symbol

Answer:

3 terms

Step-by-step explanation:

5x + 3y - 6

We cannot combine any terms so there are 3 different terms

5x, 3y, -6

Answer:

see below the first three problems

Step-by-step explanation:

f(g(-2))

First, find g(-2) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(-2) = -2(-2) + 1

g(-2) = 5

f(x) = 5x

f(5) = 5(5)

f(5) = 25

f(g(-2)) = 25

g(h(3))

First, find h(3) using function h(x). Then use that value as input for function g(x).

h(x) = x^2 + 6x + 8

h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8

h(3) = 35

g(x) = -2x + 1

g(35) = -2(35) + 1 = -70 + 1

g(35) = -69

g(h(3)) = -69

f(g(3a))

First, find g(3a) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(3a) = -2(3a) + 1

g(3a) = -6a + 1

f(x) = 5x

f(-6a + 1) = 5(-6a + 1)

f(-6a + 1) = -30a + 5

f(g(3a)) = -30a + 5

Answer:

i

Step-by-step explanation:

√-1 is always going to be imaginary i

That is a math rule needed to memorize.

Answer:

i

Step-by-step explanation:

Answer:

property of zero.

Step-by-step explanation:

It is given that, (4y + 1) × 0 = 0 . We need to tell out of four given options, which property is used in this case.

The property of zero states that if any number is multiplied by 0, then the answer is equal to 0.

Here, the number is (4y+1). It is multiplied by 0. It means that the result is 0.

Hence, it shows "property of zero".

Answer:

14,641.

Step-by-step explanation:

214,358,881 ÷ 14,641 = 14,641.

Answer:

Step-by-step explanation:

Given the function  h(x) = (x – 1)³ + 10 so that h(x) = (g°f)(x). If f(x) = x + a and g(x) = x³ + b, then;

g(f(X)) = g(x+a).

To get g(x+a), we will have to replace the variable x with x+a in g(x) as shown;

g(x+a) =  (x+a)³ + b

g(f(x)) =  (x+a)³ + b

Since h(x)= g(f(x)) = (x – 1)³ + 10

g(f(x)) = (x+a)³ + b = (x – 1)³ + 10

Hence  (x+a)³ + b = (x – 1)³ + 10

On comparing the coefficients to get the value of a and b;

(x+a)³  = (x-1)³

Take the cube root of both sides

∛(x+a)³  = ∛(x-1)³

x+a = x-1

x+a-x = -1

a = -1

Also on comparing, b = 10

Hence the values of a and b would make the composition true are -1 and 10 respectively.

Answer:

a: -1

b: 10

edge 2020

Answer:

43.5 sq. units

Step-by-step explanation:

Area 1 = 1/2 * 3 * 2 =  3

Area 2 = 1/2 * 5 * 1 =  2.5

Area 3 = (8 + 11)/2 * 4 =  38

total area = 3 + 2.5 + 38 = 43.5 sq. units

Answer:

50%

Step-by-step explanation:

First, add up all the females that are Freshmen or Sophomores (296).

Now, we just divide 296 by the total (592) and get 50%

Answer: C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

100 000 000 = 10^8

So its square root = (10^8)^1/2

= 10^4

= 10,000.

  which is rational.

You can check out this answer on a calculator. It is correct.

Answer:

[tex] x^2 + x = 42[/tex]

Step-by-step explanation:

Let the required number be x

Therefore, it's square = [tex] x^2 [/tex]

[tex] \therefore \: x + {x}^{2} = 42 \\ \huge \red{ \boxed{{x}^{2} + x = 42}}[/tex]

Answer:

the answer is a

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

Expand the terms in the bracket

That's

Move - 2x to the left side of the inequality to make it positive

Add 4 to both sides

That's

Divide both sides by 8

We have the final answer as

Hope this helps you

Answer:

angle a + angle b + angle c = 180 (angle sum property)

a + 45+55= 180

a + 100 = 180

a = 180-100

a= 80

AD bisects angle a

i.e angle ADB= angle ADC

angle ADB + angle ADC = 80

angle ADB + angle ADB =80

2angleADB= 80

angle ADB = 80/2

angle ADB = 40

angle ADB = angle ADC

40 = angle ADC

plz mark as brainliest

Answer:

m = 3/2

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find 2 coordinates

(50, 20)

(70, 50)

Step 2: Find slope m by plugging into formula

m = (50 - 20)/(70 - 50)

m = 30/20

m = 3/2

Answer:

3/2

Step-by-step explanation:

To find the slope, pick two points on the line, and use the slope formula

( 50,20) and  (90,80)

m = ( y2-y1)/(x2-x1)

    = (80-20)/(90-50)

    =60/40

   = 3/2

Answer:

Proof given by contradiction.

Step-by-step explanation:

Given that:

[tex]n \geq 2[/tex]

To prove:

[tex]n[/tex] is prime if and only if no positive integer > 1 and [tex]\leq[/tex] [tex]\sqrt n[/tex] divides [tex]n[/tex].

Solution:

First of all, let [tex]n[/tex] is a composite number i.e. not a prime number such that:

[tex]n =a\times b[/tex]

and [tex]a[/tex] and [tex]b[/tex] are prime and [tex]a[/tex] divides [tex]n[/tex] and [tex]b[/tex] also divides [tex]n[/tex].

Let [tex]\sqrt n = p[/tex]

or [tex]n = p\times p[/tex]

1. [tex]\underline{a < p}[/tex]:

[tex]a[/tex] is prime and is a divisor of [tex]n[/tex].

2. [tex]\underline{a>p}[/tex]:

[tex]n = a\times b = p\times p[/tex]

We have assumed that [tex]a > p \Rightarrow b <p[/tex]

[tex]b[/tex] is a prime number and is a divisor of [tex]n[/tex].

But we are given that no prime number [tex]\leq \sqrt n[/tex] divides [tex]n[/tex] but we have proved that [tex]b < \sqrt n[/tex] divides [tex]n[/tex].

So, it is a contradiction to our assumption.

Therefore, our assumption is wrong that  [tex]n[/tex] is a composite number.

Hence, proved that [tex]n[/tex] is a prime number.

Answer:

[tex]\Huge \boxed{y=3x+6}[/tex]

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

The slope can be found from two points.

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The two points from the graph are (1, 9) and (2, 12).

Plugging in the values and evaluating.

[tex]\displaystyle m=\frac{12-9}{2-1}[/tex]

[tex]\displaystyle m=\frac{3}{1}[/tex]

[tex]m=3[/tex]

The slope of the line is 3.

The y-intercept of the line is where the line cross the y-axis.

The line crosses the y-axis at (0, 6).

[tex]b=6[/tex]

The slope-intercept form of the line is:

[tex]y=3x+6[/tex]

Answer:

Step-by-step explanation:

The commutative property lets you swap the order of operands. Here, the operands for addition, (8uv) and (9w), are interchanged. The Commutative Property of Addition lets you do that.

__

The associative property lets you group operands differently. Here, the operands in the product 8uv are changed from the grouping (8u)v to the grouping 8(uv). The Associative Property of Multiplication lets you do that.

Answers:

Step-by-step explanation:

Now let's see why these are the correct answers:

___________________________________________________________

Commutative Property of Addition states that changing the order of the addends will not affect the sum. For example 5 + 4 and 4 + 5 are both 9.

Here, this is a correct answer because 9w is moved from the end of the equation to the front.

___________________________________________________________

Commutative Property of Multiplication states that changing the order of multiplicands does not change the product. For example 5 x 2 and 2 x 5 both equal 10.

Here, this is not a correct answer because the multiplicands are associated differently in the parentheses.

___________________________________________________________

Associative Property of Addition states that the way in which addends are grouped within parentheses doesn't change the sum. For example (2 + 3) + 4 or 2 + (3 + 4) both equal 9.

Here, this is not a correct answer because the addends are not in parentheses, which is the only time this property applies.

___________________________________________________________

Associative Property of Multiplication states that the way in which multiplicands are grouped within parentheses does not affect the product. For example 2 x (2 x 2) and (2 x 2) x 2 both equal 8.

Here, this is a correct answer because the multiplicands are within parentheses and are regrouped in the second equation, the (8u)v having been regrouped as 8(uv).

___________________________________________________________

Answer: 36

Step-by-step explanation:

The 100% of the sweater is 45, we multiply 45 per 20 divided by 100, that will give you 9, you want to rest 45-20%

45-9=36

Answer: 36

Step-by-step explanation: The 100% of the sweater is 45, we multiply 45 per 20 divided by 100, that will give you 9, you want to rest 45-20%

45-9=36

Answer:

B.(x-3)(x+8)

Step-by-step explanation:

product of -3 and 8 is -24 and sum of -3+8 is +5

Answer:

(x+8) (x-3)

Step-by-step explanation:

x² + 5x – 24

What 2 numbers multiply to -24 and add to 5

8*-3 = -24

8+-3 = 5

(x+8) (x-3)