An open box is made by cutting squares from the corners of a piece of
metal that is 16 inches by
20 inches, as shown in the figure. The edge of each cut-out square is x inches. Find V(x), the
volume of the box in terms of x.

Answer:

i) The probability that the number on the ticket is even is [tex]\mathbf{\frac{1}{2}}[/tex]

ii) the probability that the number on the ticket is a number less than 16 is [tex]\mathbf{\frac{6}{23}}[/tex]

iii) The probability that the number on the ticket is a perfect square is [tex]\mathbf{\frac{5}{46} }[/tex]

iv) the probability that the number on the ticket is a prime number less than 30 is [tex]\mathbf{\frac{4}{23} }[/tex]

Step-by-step explanation:

Tickets numbers are: 4, 5, 6......48, 49

So, total tickets in box = 46

We need to find probability that the number on the ticket is:

i) an even number.

Even number in tickets are: 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48

Total number of favourable outcomes = 23

So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]

Total number of outcomes = 46

Number of favourable outcomes = 23

Putting values and finding probability

[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{23}{46}\\Probability=\frac{1}{2}[/tex]

So, the probability that the number on the ticket is an even number is [tex]\mathbf{\frac{1}{2}}[/tex]

ii) A number less than 16

Even number in tickets are: 4,5,6,7,8,9,10,11,12,13,14,15

Total number of favourable outcomes = 12

So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]

Total number of outcomes = 46

Number of favourable outcomes = 12

Putting values and finding probability

[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{12}{46}\\Probability=\frac{6}{23}[/tex]

So, the probability that the number on the ticket is a number less than 16 is [tex]\mathbf{\frac{6}{23}}[/tex]

iii) a perfect square

Perfect squares are: 4,9,16,25,36

Total number of favourable outcomes = 5

So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]

Total number of outcomes = 46

Number of favourable outcomes = 5

Putting values and finding probability

[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{5}{46}[/tex]

So, the probability that the number on the ticket is a perfect square is [tex]\mathbf{\frac{5}{46} }[/tex]

iv)  a prime number less than 30.

Prime numbers less than 30 are: 5,7,11,13,17,19,23,29

Total number of favourable outcomes = 8

So, the formula used is: [tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}[/tex]

Total number of outcomes = 46

Number of favourable outcomes = 8

Putting values and finding probability

[tex]Probability=\frac{Number\:of\:favourable\:outcomes}{Total\:number\:of\:outcomes}\\Probability=\frac{8}{46}\\Probability=\frac{4}{23}[/tex]

So, the probability that the number on the ticket is a prime number less than 30 is [tex]\mathbf{\frac{4}{23} }[/tex]

Hello!

[tex]\large\boxed{C = 21.98in}[/tex]

Use the equation C = dπ to solve:

π ≈ 3.14

C = 7 × 3.14

C ≈ 21.98 in

oof whats that

Step-by-step explanation:

Answer:

The price of each CD before tax is $15.70

Step-by-step explanation:

Given that:

Number of CDs bought by Reuben = 5

Cost of five CDs = $81.50

Sales tax on each CD = $0.60

Sales tax on 5 CDs = 0.60*5 = $3.00

Price of CDs without tax = 81.50 - 3.00 = $78.50

Price of each CD = [tex]\frac{Cost\ of\ CDs}{No.\ of\ CDs}[/tex]

Price of each CD = [tex]\frac{78.50}{5}[/tex]

Price of each CD = $15.70

Hence,

The price of each CD before sales tax is $15.70

Answer:

a = 20 and b = 21

Step-by-step explanation:

Given:

2a-3b = -23

a and b are consecutive

Find:

a and b

Computation:

a = b - 1

So,

2a-3b = -23

2(b-1)-3b = -23

2b - 2 - 3b = -23

-b = -21

b = 21

So

a = b - 1

a = 21-1

a = 20

Answer:

n = 80

Step-by-step explanation:

Plug in 80 for n to check:

17 + 80/5 = ?

17 + 16 = 33

Answer:

B

Step-by-step explanation:

The required graph that represents the system of the equation and their solution is shown. Option D is correct.

Given that,

To determine the graph which shows the system of equation 8x-4y=-16 3x+15y=-6 and their solution,

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given system of equations is 8x-4y=-16 3x+15y=-6,
The solution of the above equation is given when applying methods like substitution, elimination and sublimation is (-2,0).

Plotting the graph of the system of equations it comes out to be as shown.

Thus, the required graph that represents the system of the equation and their solution is shown. Option D is correct.

Learn more about graphs here:

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Answer:

x>2

Step-by-step explanation:

Step 1: Subtract 60x from both sides.

100x−200−60x>60x−120−60x

40x−200>−120

Step 2: Add 200 to both sides.

40x−200+200>−120+200

40x>80

Step 3: Divide both sides by 40.

40x/40> 80/40

x>2

Hope this helped :)

Answer: B. 9(x + 9)

Step-by-step explanation:

Answer:

B. 9(z+9)

Step-by-step explanation:

Answer:c a b

Step-by-step explanation:because  √225 is = 15

36*[tex]\pi[/tex]=113.04

and 200=200 which is greater than both of those numbers.So the answer is c a b

Answer:

My guess would be

C. multiplicative identity property

Answer:

C.

multiplicative identity property

Answer:

A. None

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, we see that we have 2 parallel lines. Therefore, there will be no solution.

Answer:

Hmmm maybe d if it's not d I'm sorry at least I helped you

We can write the line's equation as y = 5.

To find the equation:

With the given conditions, we find the equation of the line.

We begin by recognizing that we can write the line's expression in the point-slope form, which is expressed as:

Where [tex]\left(x_0, y_0\right)[/tex] is the point through which the line passes and m is the slope We have already been given the point:

Which the line passes through.

We now write the line's equation:

[tex]\begin{gathered}y-y_0=m\left(x-x_0\right) \\y-5=(0)(x-4) \\y-5=0 \\y=5\end{gathered}[/tex]

Therefore, we can write the line's equation as y = 5.

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The complete question is given below:
Find an equation of the line that satisfies the given conditions. Through (4,5), parallel to the x-axis.

Answer:

13 m

Step-by-step explanation:

he starts at 0 then dive 8 m and another 5 m so

0-8-5= -13

A triangle's opposite side is split in half by an angle bisector into two segments that are proportional to the other two sides.

We can solve this problem by using the formula explained in the angle bisector theorem below.

Angle Bisector theorem :

            In the below image, PS is the angle bisector of ∠P in ΔPQR.

As a result, we can state that by using the angle bisector theorem as

PQ/PR = QS/SR

or

a/b = x/y.

By this, we can solve the angle bisector theorem.

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Answer:

5.5 yd

Step-by-step explanation:

To find the side length of the cube, the volume is a clue. We know that all sides of a square are equal, and the volume of a cube is length×width×height. Since the length, width and height are all the same, we know it is V=x³. Since we know the volume, we can plug in and solve for x.

166=x³

In order to get x alone, we have to cube root both sides.

x≈5.5 yd

Answer:

5x+3y+(-x)+6z

5x+(-x)+3y+6z

4x+3y+6z

The facts to apply is PEMDAS which is parenthesis,exponents, multiplication,division,addition and subtraction.

Then group like terms if there are any.

You finally get to a simplified answer if there are no like terms

Answer:

A, C, and D

Step-by-step explanation:

I just took the test.

Question isn't complete so we assume you wish to solve the equation above

`x-0.1x+2.70=56.70

Answer:

Step-by-step explanation:

To solve this equation

x-0.1x+2.70=56.70

We first find like terms and then subtract both sides of the equation

x-0.1x+2.70=56.70= 1x-0.1x+2.70=56.70

Add like terms

0.9x+2.70=56.70

Subtract both sides of equation

0.9x=56.70-2.70

Divide both sides

0.9x=54

x=54/0.9

x= 60

Answer:

$9.55

Step-by-step explanation:

152.80/8=19.10-what he makes per hour

19.10/2=9.55 what he makes for half an hour

Answer:

19.1 I think is the answer I am not sure

Step-by-step explanation:

An actual measurement represents a reading that is taken manually at the physical thickness measurement location on the equipment.

actual measurement = 8.6cm(bird's height), ? (beak)

photo measurement = 52.4(birds height), 1.1 (beak)

if 52.4 = 8.6

1.1 = 1.1 x 8.6

         52.4

= it is roughly 0.18cm

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Answer:

If I do not have power at my house I cannot charge my phone.

Step-by-step explanation:

This is a conditional statement so you can say anything you want as long as it makes sense. I don't know if you're a boy or girl so I'll put too statements. Boy: If I do not have power at my house I cannot play on my console with my friends. Girl: If I do not have power at my I cannot curl my hair for the dance tonight.

Hope this helps you!!!

Answer:

Takes her 2 hours

Step-by-step explanation:

Answer:

(x-2)-1=2

(x-2)-1 +1=2+1

(x-2)=3

x=3+2

x= 5

Answer:

(A) kailey paid $3.50 more per hour

Answer:

kailey paid $3.50 more per hour

Step-by-step explanation:

Answer:

35.6%

Step-by-step explanation:

31/87(100)

3100/87

35.6%

Answer:

35,6%

Step-by-step explanation:

31/87 = 0,35632184

As a percentage: 35,632184%

Rounded to one deciman place: 35,6%