Which of the following is equivalent to

Answer:

C. 23%

Step-by-step explanation:

C. The probability that the student takes Spanish or French is 23%

If two events can not occur together at same time, then the events are called mutually exclusive.

If two events are mutually exclusive, then,

P(A∪B) = P(A)+P(B)

And If two events are not mutually exclusive, then,

P(A∪B) = P(A)+P(B)-P(A∩B)

In central high school,

15% of the students take Spanish language = P(A) (say)

12% of the students take French language = P(B) (say)

& 4% of the students take both the languages = P(A∩B)

Since some of students take both languages, so this is not mutually exclusive.

The probability that the student takes Spanish or French is P(A∪B).

∴ P(A∪B) = P(A)+P(B)-P(A∩B)

               = 15%+12%-4%

               = [tex]\frac{15}{100}+\frac{12}{100}-\frac{4}{100}[/tex]

               = [tex]\frac{15+12-4}{100}[/tex]

               = [tex]\frac{23}{100}[/tex] = 23%

Hence, Required probability is 23%

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The answer is -1

look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

m = - 1. (Slope)

Step-by-step explanation:

To find the slope of a line, you will need to use the slope formula: [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Plug in the 'x' and 'y' value of each coordinate into the equation:

[tex]m = \frac{0-6}{2-(-4)}[/tex]

Simplify this:

[tex]m = \frac{-6}{6}[/tex]

m = -1.

Therefore, the slope of the line is m = -1.

Answer:

13) x=4, y=0

15) x= -3, y=1

Step-by-step explanation:

13. Label the 2 equations.

y= x-4 -----(1)

-4x -6y= -16 -----(2)

From (2): -2x -3y= -8 -----(3)

(divide by 2 throughout)

Subst. (1) into (3):

-2x -3(x-4)= -8

-2x -3x +12= -8 (expand)

-5x= -8 -12 (simplify, constant to 1 side)

-5x= -20 (simplify)

x= 4 (divide by -5 throughout)

subst. x=4 into (1):

y= 4 -4

y= 0

15. x= y -4 -----(1)

-2x +3y= 6 -----(2)

subst. (1) into (2):

-2(y-4) +3y= 6

-2(y) -2(-4)= 6 (expand)

-2y +8= 6

-2y= 6 -8 (bring constant to 1 side)

-2y= -2

y= 1 (divide by -2 throughout)

subst. y=1 into (1):

x= 1 -4

x= -3

Answer:

Addition

Step-by-step explanation:

The first step in solving 4x-3=5 is to add 3 to both sides. This demonstrates the addition property of equality, since adding a number to both sides of an equation balances it.

Answer:

50%

Step-by-step explanation:

since talks is one side and heads is one side both together equal 100% so half aka heads would be 50%

Answer:

He started the day with 7.65

Step-by-step explanation:

Assuming at the beginning of yesterday he had a balance of x

He will be charged 34 dollars since he went negative

x- 3.75 -12.07 - 34 =-42.17

Combine like terms

x -49.82 = -42.17

Add 49.82 to each side

x -49.82+49.82 = -42.17+49.82

x = 7.65

Answer:

20%

Step-by-step explanation:

25x.20=5

25-5=20

Answer:

1/4 cup of sugar

Step-by-step explanation:

Answer:1/4

Step-by-step explanation:

1/2 divided by 2 = 1/4

Answer:

1. x ∈ (-∞, - 23/5)

2. x ≤ 17/3

Step-by-step explanation:

Answer:

Option (b)

Step-by-step explanation:

Let the points represented by the given table lie on a line.

And the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Let the points lying on the line are (0, -2) and (3, -3)

Slope of the line 'm' = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{-2-(-3)}{0-3}[/tex]

m = [tex]\frac{-2+3}{0-3}[/tex]

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

y-intercept 'b' = (-2)

Equation of the line is,

y = [tex]-\frac{1}{3}x-2[/tex]

This equation matches with equation given in option (b).

Option (b) will be the answer.

Answer:

[tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

Step-by-step explanation:

Given

[tex]16b^2c^{12} - 0.25[/tex]

Required

Factor Completely

Follow the steps below;

Rewrite 0.25 as a fraction

[tex]16b^2c^{12} - \frac{25}{100}[/tex]

Simplify fraction to lowest term

[tex]16b^2c^{12} - \frac{1}{4}[/tex]

Expand [tex]16b^2c^{12}[/tex]

[tex]4^2b^2c^{6*2} - \frac{1}{4}[/tex]

[tex](4bc^{6})^2 - \frac{1}{4}[/tex]

Expand [tex]\frac{1}{4}[/tex]

[tex](4bc^{6})^2 - \frac{1}{2}*\frac{1}{2}[/tex]

[tex](4bc^{6})^2 -( \frac{1}{2})^2[/tex]

From laws of product of two squares

[tex]a^2 - b^2 = (a+b)(a-b)[/tex]

So,

[tex](4bc^{6})^2 -( \frac{1}{2})^2[/tex] is equivalent to

[tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

The expression cannot be factorized any further;

Hence, the factor of [tex]16b^2c^{12} - 0.25[/tex] is [tex](4bc^{6} - \frac{1}{2})(4bc^{6} + \frac{1}{2})[/tex]

Answer:

4sqrt(3) inches

Step-by-step explanation:

The ratio of the lengths of the legs of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

The long leg is sqrt(3) times the length of the short leg.

Here, the short leg measures 4 inches.

long leg = sqrt(3) * short leg

long leg = 4sqrt(3) inches

Answer:

Solution,

Area=3.14 m^2

Radius=?

Now,

[tex]area \: of \: circle = \pi \: {r}^{2} \\ \: \: \: \: or \: 3.14 = 3.14 \times {r}^{2} \\ or \: 3.14 = 3.14 {r}^{2} \\ or \: {r}^{2} = \frac{3.14}{3.14} \\ or \: {r}^{2} = 1 \\ or \: r = \sqrt{1} \\ r = 1 m[/tex]

hope this helps..

good luck on your assignment

A circle is a curve sketched out by a point moving in a plane. The radius of the circle whose area is  3.14 m² is 1 m.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The area of a circle is the product of the square of the radius and pi. Therefore, the radius of the circle with an area of 3.14 m² can be written as,

[tex]\text{Area of circle}=\pi r^2[/tex]

[tex]3.14 = \pi r^2\\\\3.14 \times 3.14 \times r^2\\\\r = 1\rm\ m[/tex]

Thus, the radius of the circle whose area is  3.14 m² is 1 m.

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Answer:

A = 35 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 10)(7)

A = 35 cm^2

Answer:

(x-6)^(2)=y+7

Step-by-step explanation:

Answer:

The quantity of cardboard that is needed  to make the top of the box is:

Step-by-step explanation:

When the exercise asks you about the "inches squared," it's asking you about the area, the area of a rectangle (a rectangle because a cardboard box regularly is rectangular) is:

Now, you must replace the length and the width by the values in the exercise (doesn't matter what is width or length, remember the commutative property of the multiply):

Answer:

h(u)=-7/6u

Step-by-step explanation:

To write a formula for v in terms of u, you need to first isolate v.

4u+8v=-3u+2v

Add 3u to both sides:

7u+8v=2v

Subtract 8v from both sides:

7u=-6v

Divide both sides by -6:

v=-7/6u

Hope this helps!

Answer:

u= - 6v

      7

Step-by-step explanation

Answer: 63.36 in

Step-by-step explanation: To find the area of the base its just 4.8x4.8= 23.04 and the area of the triangle is (4.8x4.2)/2= 10.08 multiply that by 4 since there are 4 sides thats 40.32 and add the area of the base making it 63.36

Answer:

B.

Step-by-step explanation:

12.25 for n CD's

5.75 for u CD's

the total is 765

22 are more sold for more used than new

Answer: B) 12.23n + 5.75u = 765: u = n + 22

Step-by-step explanation: took the quiz.

Answer:

x = 20

KPL =  64

JPL =  116

Step-by-step explanation:

A linear pair adds to 180 degrees

2x+24  + 4x+ 36 = 180

Combine like terms

6x+60 = 180

Subtract 60 from each side

6x = 120

Divide by 6

6x/6 = 120/6

x = 20

KPL = 2x+24 = 2*20+24 = 40+24 = 64

JPL = 4x+36 = 4*20 +36 = 80+36 = 116

KPL = 64

x = 20

JPL =  116

Step-by-step explanation:

Linear = 180

2x+24  + 4x+ 36 = 180

Must combine like terms ( 2x and 4x)

6x+60 = 180

Isolate x by subtracting 60

6x = 120

Divide by 6 to simplify

6x/6 = 120/6

x = 20

KPL = 2x+24 = 2*20+24 = 40+24 = 64

JPL = 4x+36 = 4*20 +36 = 80+36 = 116

Answer:

P=1440

Step-by-step explanation:

"P is 90 more than Q."

P=Q+90

"20% of P is equal to 1/3 of Q."

1/5(P)=(1/3)Q

From the first equation, we have that P=Q+90.

Thus, we can substitute any P's for Q+90's!

The second equation becomes 1/5(Q+90)=(1/3)Q

Distribute the 1/5 and 1/3 to get (1/5)Q+180=(1/3)Q

Subtract 1/5 Q from both sides.

You should get 180= (2/15)Q

Multiply both sides by 15/2 to get 1350=Q.

Given Q, we can easily solve for P.

Remember the first equation- P=Q+90

Then substitute in 1350 for Q.

So we have P=1350+90

Finally, we have P=1440

Answer:

12 nickels, 9 quarters, 15 dimes

Step-by-step explanation:

Let's call the number of nickels n, the number of dimes d, and the number of quarters q. Now, we can set up the following equations:

n+d+q=36

q=n-3

d=q+6

Now, we can do some substitution:

d=(n-3)+6=n+3

Plugging this into the first equation, you get:

n+(n+3)+(n-3)=36

3n=36

n=12

There are twelve nickels, meaning that there are 9 quarters and 15 dimes. Hope this helps!

Answer: 1 cm = 25 meters or 1:25

Step-by-step explanation:

Divide the real distance by the measured distance and find the ratio from the simplified fraction.

Answer:

Step-by-step explanation:

y - 3 = -2(x - 1)

y - 3 = -2x + 2

y = -2x + 5

Answer: See below

Note: If the length and width does not match the picture, then just flip the numbers. I cannot guarantee the area is 100% correct because you did not provide a picture. If the top/bottom of the trapezoid is 27, 62, and the left/right of the trapezoid is 30, then the area below is correct. If the picture shows the opposite then but 30 into a and b.

Step-by-step explanation:

Though you did not attach a picture as described in the problem, we will have to try our best to work with what you gave us.

I am assuming the lengths are the lines on the left and right of the trapezoing and the widths are the lines on the top and bottom of the trapezoid.

A.

To find the perimeter, you add the lengths and widths.

P=30+30+27+63=150 ft

To find the area, you use the formula [tex]A=\frac{a+b}{2} h[/tex]. The a and b represent the bases or in this case, the widths.

[tex]A=\frac{27+63}{2} (24)[/tex]

[tex]A=1080 ft^2[/tex]

B.

The frame has to do with the area of the glass because the frame surrounds the outside of the glass. The surrounding of the glass would be the perimeter.

The glass would be the area because the area covers everything inside the frame.

Answer:

A: When you add all of the sides, you get 150 as the perimeter.

B: The frame has to do with the area of the glass. The frames surround the outside of the glass. This would be the perimeter. The glass would be the area.

Answer:

20 - 17

Step-by-step explanation:

Decreased means subtract

20 - 17

The correct translation of the expression "20 decreased by 17" is "20 - 17."

Given is a verbal expression we need to convert it into algebraic form,

To reach this conclusion, we need to understand the phrase "decreased by" means subtraction.

When we say "20 decreased by 17," it implies that we are subtracting 17 from 20. In mathematical terms, this can be represented as 20 - 17.

Let's analyze the other options:

17 - 20: This option represents 17 subtracted by 20, which is the opposite of the original expression and doesn't match the given phrase.

20 + 17: This option represents the addition of 20 and 17, which doesn't align with the original expression. We are looking for subtraction, not addition.

17 + 20: This option also represents addition, and as mentioned before, the original expression involves subtraction, not addition.

Therefore, the correct answer is 20 - 17.

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Answer:

6

Step-by-step exp

Answer:

6

Step-by-step explanation: