2) John made $55,000 in 2007, but his income decreased by 17% in 2008 due to the recession. What was his 2008
income?

Answer:

0.0043957 ; 0.105498 ; 2nd option is better

Step-by-step explanation:

Option 1:

First card :P(club) = 13/52

Second card: P(diamond) = 13/51

Third card : P(heart) = 13 / 50

Fourth card: P(spade) = 13/49

Hence,

P(club, diamond, heart, spade) = (13/52) * (13/51) * (13/50) * (13/49) = 0.0043957

Probability of winning $10 = 0.0043957

2nd option:

P(card of different suit) [order of arrangement does not matter]

(13C1 * 13C1 * 13C1 * 13C1) / 52C4

= 28561 / 270725

= 0.105498

Probability of winning $10 = 0.105498

Because the probability of winning for the second option is higher than for the first option, then the second option is better.

Answer:

Step-by-step explanation:

6x + 120 = 168

6x = 48

x = 8

Answer:

8

Step-by-step explanation:

6(x+20)=168. Substitute the x variable for 8

Then do your PEMDAS, which parenthesis come first, so 8+20= 28

Now multiply 28 by 6 and you get 168.

So your answer is 8.

Answer:

Step-by-step explanation:

2x×1=(√3)²

2x=3

x=3/2

The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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Answer:

5/12

Step-by-step explanation:

3/4 - 1/3

We need to use the common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 = 4/12

9/12 - 4/12 = 5/12

Answer:

-$35.00

Step-by-step explanation: I think

The final ratio of weight 195.5 pounds and is 69.3 inches tall in grams per millimeter is 88677.414: 1760.22.

To expres this in the  final ratio of grams per millimeter, then we need to make some conversion of the given figures,

the weight =195.5 pounds , this can be converted to gram by using the conversion rate of ;

1gram = 0.00220462 pounds

X= 195.5 pounds

where X = the weight in gram

then X = 195.5 pounds/0.00220462 pounds

then  the weight in gram=88677.414 gram.

We can as well express  69.3 inches to millimeter using the conversion rate ;

1inch = 25.4millimeter

then  69.3 inches = 1760.22millimeter

Then the final ratio in grams per millimeter is 88677.414: 1760.22

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Answer:

5.)Dogs were the type of pet chosen most often by the students at the elementary school.

Step-by-step explanation:

Dogs have the most out of every pet at 110

From the two-way table, the correct option is:

5.) Dogs were the type of pet chosen most often by the students at the elementary school.

Statement 1:

\(P = \frac{60}{105} \times 100\% = 57\%\)

Statement 2:

\(P = \frac{60}{215} \times 100\% = 29\%\)

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Answer:

Step-by-step explanation:

Its is

6CM wide. as to find the area we have to times the length x height :)

Answer:

wide = 6 cm

Step-by-step explanation:

\(t=tall=10\)

\(w=wide=?\)

\(P=perimeter=32\)

The equation:

\(P=2t+2w\)

\(32=2(10)+2w\\32=20+2w\)

\(32-20=2w\\12=2w\)

\(\frac{12}{2} =w\)

\(6=w\)

Hope this helps.

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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Answer:

C = 36°, 57°, 87°

Step-by-step explanation:

scalene = all angles are different.

acute = all angles are under 90°.

triangle = all angles add up to 180°.

The only option that works for this is C) 36°, 57°, 87°

The first number = x

The second number = 5 + 2x

80 = x + 5 + 2x

Let's combine like terms.

80 = 3x + 5

Subtract 5 from both sides.

75 = 3x

Divide both sides by 3

25 = x

The first number = 25

Let's plug 25 into x for our second number's equation.

The second number = 5 + 2(25) = 55

Answer:

x = first number

y = second number

1. y = 2x +5

2. x = x

3.  x + 2x + 5 = 80

4. 3x +5 = 80

5. 3x = 75  

x = 25

sub back in to steps 1 and 2:

x = 25

y = 2(25) + 5

y = 55

the first number is 25, and the second number is 55.

CHECK:

80 - 25 = 55

Step-by-step explanation:

1. define your variables

2. use the question to find what each number equals

3. set them equal to 80

4. combine like terms, divide, etc. (SOLVE)

5. sub back into defined variables.

6. check it by subtracting and adding

Answer:

33

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

The answer is x³ - x² - 13x + 4.

Step-by-step explanation:

I have this was helpful <3

Answer:

\(x^3-x^2-13x+4\)

Step-by-step explanation:

Distribute

\((x-4)(x^2+3x-1)\)

\(x(x^2+3x-1)-4(x^2+3x-1)\)

Distribute

\(x(x^2+3x-1)-4(x^2+3x-1)\)

\(x^3+3x^2-x-4(x^2+3x-1)\)

Distribute

\(x^3+3x^2-x-4(x^2+3x-1)\)

\(x^3+3x^2-x-4x^2-12x+4\)

Combine like term

\(x^3+3x^2-x-4^2-12x+4\)

\(x^3-1x^2-x-12x+4\)

Combine like term

\(x^3-x^2-x-12x+4\)

\(x^3-x^2-13x+4\)

Solution

\(x^3-x^2-13x+4\)

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

110,033 ways :)

Step-by-step explanation:

Alright, so, there can be between 2 and 6 people in the team.

For a team of 2, there are C(22, 2) = 231 ways to form a team.

For a team of 3, there are C(22, 3) = 1540 ways

For a team of 4, there are C(22, 4) = 7315 ways

For a team of 5, there are C(22, 5) = 26334 ways

For a team of 6, there are C(22, 6) = 74613 ways, mind boggling! :)

So, the total is 231 + 1540 + 7315 + 26334 + 74613 = 110,033 ways!

Answer:

#4

Step-by-step explanation:

Answer:

The last one

Step-by-step explanation:

A positive is ALWAYS more than a negative unless the negative is multiplied by another negative or an abstract value such as |-4|. Also, the "gator" will eat the bigger number

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

Two polygons are similar if the ratio of their corresponding sides are in the same proportion. Hence:

Similarity ratio of STUV to GFIH = TU / GH = 5 / 1

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

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The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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The graphs of the functions f(x) and g(x) are attached with the answer.

       \(${\displaystyle G=\{(x,f(x))\mid x\in X\}.}\)

Given are the functions f(x) and g(x).

The given functions are -

f(x) = \($100(\frac{3}{5})^{x}\)

g(x) = \($100(\frac{2}{5})^{x}\)

Refer to the graphs of the function f(x) and g(x).

Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.

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The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.