Abdul is creating a cushion that is 1 foot by 2 feet by 3 feet. He wants to find the least amount of fabric he will need to cover the cushion. He starts by drawing the net shown here.
A net is formed by 2 rectangles. 1 rectangle has a base of 4 feet and height of 3 feet. The other rectangle has a base of 5 feet and height of 2 feet.
What is the least amount of fabric he will need to cover the cushion?

Answer:

-4

Step-by-step explanation:

Answer:

a. 40/250

b. 70/250

c. Preferring diet soda and preferring hamburgers are not independent events

d.  Preferring regular soda and preferring hot dogs are not independent events

Step-by-step explanation:

We are given:

                      Regular Soda    Diet Soda    Total

Hamburgers             90                 40            130

Hot Dogs                   70                 50           120

Total                          160                90          250

a. The probability that someone who prefers diet soda will also prefer hamburgers can be calculated as:

No. of people who prefer hamburgers and diet soda / Total no. of people

40/250

b. The probability that someone who prefers hot dogs will also prefer regular soda can be calculated as:

No. of people who prefer hot dogs and regular soda/Total no. of people

70/250

c. For two events to be independent, they must fulfill the condition:

P(A and B) = P(A) * P(B)

P(Diet Soda) = No. of people who prefer diet soda/total no. of people

                     = 90/250

P(Hamburgers) = No. of people who prefer hamburgers/total no. of people

                     = 130/250

P(Diet Soda and Hamburgers) = 40/250

Now, we need to check:

P(Diet Soda and Hamburgers) = P(Diet Soda) * P(Hamburgers)

40/250 = 90/250 * 130/250

40/250 ≠ 11700/62500

So, we can conclude that these two events are not independent events.

d. P(Regular Soda) = No. of people who prefer regular soda/total no. of people

                     = 160/250

   P(Hot dogs) = No. of people who prefer hot dogs/total no. of people

                     = 120/250

P(Regular Soda and Hot Dogs) = 70/250

Now, we need to check if:

P(Regular Soda and Hot Dogs) = P(Regular Soda) * P(Hot dogs)

70/250 ≠ 160/250 * 120/250

So, these two events are not independent.

The solutions obtained are Part (a): The probability is 0.444, Part (b): The probability is 0.583, Part (c): Preferring diet soda and preferring hamburgers are not independent and Part (d): Preferring regular soda and preferring hot dogs are not independent.

Probability and Independence Analysis

Let's analyze the data provided from Manuela and Stephen's survey:

Regular Soda Diet Soda Total

Hamburgers 90 40 130

Hot Dogs 70 50 120

Total         160 90 250

→ Part A: Probability that Someone Who Prefers Diet Soda Also Prefers Hamburgers

The number of people who prefer diet soda is 90, and among them, 40 prefer hamburgers. Therefore, the probability is calculated as follows:

P(Hamburgers|Diet Soda) = 40 / 90

                                          ≈ 0.444

→ Part B: Probability that Someone Who Prefers Hot Dogs Also Prefers Regular Soda

The number of people who prefer hot dogs is 120, and among them, 70 prefer regular soda. Therefore, the probability is:

P(Regular Soda|Hot Dogs) = 70 / 120

                                            ≈ 0.583

→ Part C: Independence of Preferring Diet Soda and Preferring Hamburgers

To determine if these events are independent, we check if:

P(Diet Soda AND Hamburgers) = P(Diet Soda) * P(Hamburgers)

Calculations:

→ P(Diet Soda AND Hamburgers) = 40 / 250

→ P(Diet Soda) = 90 / 250

→ P(Hamburgers) = 130 / 250

→ P(Diet Soda AND Hamburgers) ≠ P(Diet Soda) * P(Hamburgers)

Since the equality does not hold, these events are not independent.

Part D: Independence of Preferring Regular Soda and Preferring Hot Dogs

We test the same independence condition for regular soda and hot dogs:

→ P(Regular Soda AND Hot Dogs) = P(Regular Soda) * P(Hot Dogs)

Calculations:

→ P(Regular Soda AND Hot Dogs) = 70 / 250

→ P(Regular Soda) = 160 / 250

→ P(Hot Dogs) = 120 / 250

→ P(Regular Soda AND Hot Dogs) ≠ P(Regular Soda) * P(Hot Dogs)

Therefore, these events are also not independent.

Answer:

7

Step-by-step explanation:

Answer:

7kg

Step-by-step explanation:

Answer:

c = 9

Step-by-step explanation:

-2c = -18

/-2     /-2 (Divide both sides by -2)

_______

c = 9

Answer:

c=-9

Step-by-step explanation:

-2c=18

divide the whole thing by -2

c=-9

Answer:

[tex]C=10(g+5)[/tex]

Step-by-step explanation:

Given the cost of a customers smartphone bill,

C=10g+50

We are required to factor the polynomial.

First, determine the G.C.D of both terms

Next, we divide each of the term by 10 and balance it by multiplying the expression by 10.

[tex]C=10g+50\\=10(\frac{10g}{10}+\frac{50}{10})\\C=10(g+5)[/tex]

The cost polynomial factored is C=10(g+5).

Answer:

10g+60=10(g+6)

Step-by-step explanation:

thats the answer

Answer:

C, y = 1.2x

Step-by-step explanation:

Notice that x, representing time, is multiplied by 1.2 each time to get y, representing the number of problems. You can find this out by dividing y by x. 36/30 = 1.2.

48/40 = 1.2.

And so on...

P.S.: If you ever come across a problem like this, subtract one y value by another y value, then subtract the corresponding x values from eachother, then make both numbers into one fraction with y as the numerator and x as the denominator. In this problem, that would look like this:  

48 and 36 are both y values: 48 - 36 = 12

40 and 30 are the corresponding x values: 40 - 30 = 10

We get 12/10, which can be simplified to 1.2. The slope is 1.2.

This method will always work for a straight line and will be taught to you soon if you haven't learned it already.

Answer:

a) 19

b) 3

Step-by-step explanation:

They are adding 3 sticks each time so n=3

I hope this helps

Answer:

see below

Step-by-step explanation:

We need to find the diameter of the square

We can find this using the Pythagorean theorem

a^2+b^2 = c^2  where the legs are 7 and 7 and the diameter is c

7^2 +7^2 = c^2

49+49 = c^2

98 = c^2

Taking the square root of each side

sqrt(98) = sqrt(c^2)

9.899494937 = c

Since 9.9 is less than 11 which is the diameter of the circle it will never touch the circle.

Since the longest part of the square is less than the diameter of the circle, the square will fit  inside the circle without touching

Answer:

Diagonal < Diameter

Step-by-step explanation:

The square will fit inside without touching if the diagonal length is less than the diameter

Diagonal = sqrt(7² + 7²)

7sqrt(2)

Diameter = 11

7sqrt(2) < 11

Because

(7sqrt(2))² < 11²

98 < 121

Answer:

a

Step-by-step explanation:

Answer:

V =41.41³

A = 94.41²

----

V =225.16³

SA =283.25²

----

V = 64³

SA =113.32²

----

V =433.33³

SA = 378.57²

Step-by-step explanation:

Picture 2 = a = 1/2 base = 3.5 x 3.5 = 12.25  b= 5 x 5 = 25

c²= a² + b² = 3.5² + 5²

c ²= √12.25 + √25

c ²= √ 37.5 = 6.12372435696

c ² = 6.1237   missing side

Picture 1 + 2  formula SA = bh + (s1 + s2 + s3)H

V =  V= 1/2 b x h  h x SA

Picture 3 + 4  formula SA= a²+ 2a   a² / 4 + h²    V= a²  h/3

Answer:

The discriminant of the quadratic equation is -7.

Step-by-step explanation:

We are given the following quadratic equation in the question:

[tex]x^2+x+2 = 0[/tex]

Comparing to general quadratic equation:

[tex]ax^2+bx+c = 0\\a = 1\\b = 1\\c = 2[/tex]

We have to find the discriminant of the quadratic equation.

Formula:

[tex]d = b^2-4ac[/tex]

Putting values, we get,

[tex]d = (1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]

Thus, the discriminant of the quadratic equation is -7.

Answer:

Blank 1: -6

Step-by-step explanation:

Because if you subtract 11-17 you get: -6

Answer:

x-3>15

x>18

Step-by-step explanation:

usually its better to read it from right to left, more than 15 tells you its gonna be >. then you see 3 less than x, which is x-3. Then solve as if the > was an equal sign

x-3>15

+3  +3

x>18

The inequality representing 'Three less than a number x is more than 15' is x - 3 > 15. Solving this, we get x > 18. Hence, x should be greater than 18.

The word sentence given is: 'Three less than a number x is more than 15'. To write this as an inequality, we start by identifying the mathematical phrase for 'Three less than a number x', which is 'x - 3'.

The phrase 'is more than' translates to the inequality symbol '>'.

Therefore, we set up the inequality as follows:

x - 3 > 15

Next, we solve the inequality step-by-step:

So, the solution to the inequality is x > 18.

In summary, when converting word sentences to inequalities, ensure you accurately translate the phrases and solve them step-by-step to find the solution.

Answer:

216

Step-by-step explanation:

Answer:

$3.00/ gallon

Step-by-step explanation:

Take the amount paid  and divide by the number of gallons

We are estimating so round 14.5 gallons to 15

$45/15 gallons

$3.00/ gallon

Answer:

Option B

Step-by-step explanation:

Diameter= 16cm

radius= 8cm

height = 3cm

[tex]volume = \pi {r}^{2} h[/tex]

[tex] =3.14 {(8)}^{2} \times 3[/tex]

[tex] = 3.14 \times 64 \times 3[/tex]

[tex] = 602.88 {cm}^{3} [/tex]

[tex] = 602.9 {cm}^{3} [/tex]

Answer:

12 units²

Step-by-step explanation:

Area = ½ × base × height

= ½ × 4 × 6

= 12 units²

Answer:

d. 7.3

Step-by-step explanation:

-16-10.2g = -14.7g + 16.85

4.5g = 32.85

g = 7.3

The solution for the equation -16 - 10.2g = -14.7g + 16.85 is g = 7.3. You can verify it by substituting the solution back into the original equation.

To solve the given equation, -16 - 10.2g = -14.7g + 16.85, we must first isolate the variable, g, by moving all terms involving g to one side of the equation and constant terms to the other side. Add 10.2g to both sides of the equation, giving,  -16 = -4.5g + 16.85. To further isolate g, subtract 16.85 from both sides resulting in -32.85 = -4.5g. Finally, divide by -4.5 to solve for g. Thus, g = -32.85 / -4.5 = 7.3. We verify our solution by substituting 7.3 back into the original equation and confirming that the equality holds true.

https://brainly.com/question/18262581

#SPJ2

Answer: without parentheses it'll be : -2x square 2 2x square 2 9x-2!

Step-by-step explanation: well to start with,Nothing will change when you solve it just rember the PEMDAS and you'll be fine! Good luck :3

Answer: 13:65, 8:40, 18:90

Answer:

First of all that bear is adorable second 1:3, 10:30, and 15:45

Step-by-step explanation:

To do this you have to figure out if the ratios equal the fraction 1/3 which is the fraction for the ratio 5:15 all of those equal 1/3

I know I didn't explain that well but I still hope that this helps you :)

Answer:

12 to 27

a long dividing the box will go at 23.5

11 to 12

the right whisker will go from 27 to 33

Step-by-step explanation: ^^^

The given sections of the box plot will be located, at the following places:

The box will go from 12 to 27 (IQR).

A line dividing the box will go at 23.5 (median).

The left whisker will go from 11 to 12.

The right whisker will go from 27 to 33 (see box plot in the image attached below).

A boxplot shows the following values:

Therefore, the given sections of the box plot will be located, at the following places:

The box will go from 12 to 27 (IQR).

A line dividing the box will go at 23.5 (median).

The left whisker will go from 11 to 12.

The right whisker will go from 27 to 33 (see box plot in the image attached below).

Learn more about box plot on:

https://brainly.com/question/24335827

Answer:

  [tex]b>3\frac{2}{15}[/tex]

Step-by-step explanation:

You can multiply by 15, add 8, divide by 15. (Or, you could get there directly by adding 8/15 to both sides.)

  [tex]2\frac{3}{5}<b-\frac{8}{15}\\\\39<15b-8\\\\47<15b\\\\\boxed{3\frac{2}{15}<b}[/tex]

Answer:

D; b > 3 2/15

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{8 - 6}{j - k} = \frac{2}{2 - 3} = \frac{2}{ - 1} = - 2 \\ [/tex]

Answer:

139.26990817 m² is the exact answer.

10*10=100

5²*pi + 100= 139.26990817

Hope this helped!!  :)

Answer:

c=25.12

Step-by-step explanation:

C=πd

C=3.14*8

C=25.12

Answer:

25.12ft

Step-by-step explanation:

take 8 and times that by 3.14, and you get:

25.12

Answer:

1.85

Step-by-step explanation:hope this helps god bless

Answer:

≈ 3

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

My answer:

The median number is the middle value of the dot plots

=> the median number is: 28

=> the median number is: 18

=> The difference between the median number of hummingbirds spotted per day at each feeder is: 28 -18 =10 and it is = 10 / 3.168

≈ 3 times  the variability

Answer:

45.8

Step-by-step explanation:

We can use the Pythagorean theorem with legs 3x and 4x+7

a^2+ b^2 = c^2

(3x^2) +(4x+7)^2 = c^2

Let x = 8

(3*8)^2 + (4*8+7)^2 = c^2

24^2+ 39^2 = c^2

576+1521 = c^2

2097 = c^2

Take the square root of each side

sqrt(2097) = sqrt(c^2)

45.79301257 =c

Rounding to the nearest tenth

45.8 =c

Answer:

45.8

Step-by-step explanation:

First solve for the other two sides by replacing x with 8

4(8)+7 = 39

3(8) = 24

Then use the pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]) to solve for the hypotenuse, c being the hypotenuse

[tex]39^{2} + 24^{2} = c^{2}[/tex]

1521 + 576 = [tex]c^{2}[/tex]

2097 = [tex]c^{2}[/tex]

[tex]\sqrt{2097} = \sqrt{c^{2} }[/tex]

45.8