Which point represents the unit rate?

There are 12 different outfits that can be put together using the given 3 different pairs of pants, 2 shirts, and 2 pairs of shoes.

There are 12 different outfits that can be put together using 3 different pairs of pants, 2 shirts, and 2 pairs of shoes.

How to solve the problem:

To find out the number of different outfits that can be put together using the given 3 different pairs of pants, 2 shirts, and 2 pairs of shoes, we will simply multiply the number of options for each category together.

Number of options for pants = 3

Number of options for shirts = 2

Number of options for shoes = 2

Number of different outfits that can be put together

= 3 × 2 × 2

= 12

Therefore, there are 12 different outfits that can be put together using the given 3 different pairs of pants, 2 shirts, and 2 pairs of shoes.

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Answer:

1 - 8/9 + 4/9 = 9/9 -8/9 +4/9 = (9-8+4)/9 = 5/9

Step-by-step explanation:

Answer:

The answer is 5/9.

Step-by-step explanation:

First, you have to make all the denorminator of the fractions the same by multultiplying :

\(1 - \frac{8}{9} + \frac{4}{9} \)

\( = \frac{1}{ 1} - \frac{8}{9} + \frac{4}{9} \)

\( = \frac{1 \times 9}{1 \times 9} - \frac{8}{9} + \frac{4}{9} \)

\( = \frac{9}{9} - \frac{8}{9} + \frac{4}{9} \)

Next, you have to make it into 1 fraction and simplify :

\( \frac{9}{9} - \frac{8}{9} + \frac{4}{9} \)

\( = \frac{9 - 8 + 4}{9} \)

\( = \frac{5}{9} \)

Answer:

The simplified expression is given as

\(8x^2y^4(17x^2-2)\)

Step-by-step explanation:

step one:

Given the expression

\(x^2y^4(x^2 - 16) - 9y^4(x^4 - 16)\)

step two:

First, let us open the bracket we have

\(x^2y^4(x^2 - 16) - 9y^4(x^4 - 16)\\\\x^4y^4-16x^2y^4-9x^4y^4+144x^4y^4\\\\\)

step three:

collect like terms we have

\(x^4y^4-16x^2y^4-9x^4y^4+144x^4y^4\\\\x^4y^4-9x^4y^4+144x^4y^4-16x^2y^4\\\\-8x^4y^4+144x^4y^4-16x^2y^4\\\\136x^4y^4-16x^2y^4\\\\\\\)

step four:

we can now factor out \(8x^2y^4\)we have

\(8x^2y^4(17x^2-2)\)

Answer:

10

Step-by-step explanation:

answer 10 10x10= 100 100/10=10

Answer:

38 square feet

Step-by-step explanation:

How do we find the area of a circle?

  ❖ The area of a circle is πr², where r = radius. For this case, we're going

       to approximate pi as 3.14.

How do we find the radius given diameter?

  ❖ We are given the diameter of Claire's hot tub as 7 feet. The diameter

       is 2x the radius, so we divide 7 by 2 to get the radius, which is 3.5

       feet.

Solving

Therefore, the answer is 38 square feet. Have a lovely rest of your day/night, and good luck with your assignments! ♡

The Taylor Polynomial T3(x) for ex centered at 0 is 1 + x + x^2/2 + x^3/6. Using T3(x) to approximate the value of e results in e ≈ 2.333, with an error bound of |e - 2.333| ≤ 0.00875.

The Taylor Polynomial T3(x) for ex centered at 0 is found by substituting n = 0, 1, 2, and 3 into the formula for the Maclaurin Series of ex. This yields T3(x) = 1 + x + x^2/2 + x^3/6.

To use this polynomial to approximate the value of e, we substitute x = 1 into T3(x) and simplify to get T3(1) = 1 + 1 + 1/2 + 1/6 = 2 + 1/3. This gives an approximation for e of e ≈ 2.333.

To find the error bound for this approximation, we can use the Taylor Inequality with n = 3 and x = 1. This gives |e - 2.333| ≤ max|x| ≤ 1 |f^(4)(x)| / 4! where f(x) = ex and f^(4)(x) = ex. Substituting x = 1, we get |e - 2.333| ≤ e / 24 ≤ 0.00875. This means that the approximation e ≈ 2.333 is accurate to within 0.00875.

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The equation \(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0 is true

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

Using digits 0 to 9, no more than once each.

we want to place them in such a way that the division will be zero.

As we know that a quotient is equal to zero iff the numerator is equal to zero and the denominator other than zero.

So if we put some numbers on the numerator in such a way by adding them gives 0.

So, 5 - 3 - 2 = 0

Use all the other numbers in the denominator.

\(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0

which is true.

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The number of hours it will take until the drill reaches its final depth of y feet would be (y * 24) / x.

To find the number of hours it will take for the drill to reach its final depth, we need to determine the drilling rate per hour.

Let's assume the drill can drill to a depth of x feet in one day (24 hours). Therefore, the drilling rate per hour would be:

Drilling rate per hour = Depth drilled in one day (feet) / Number of hours in one day

Now, we can calculate the drilling rate per hour:

Drilling rate per hour = x feet / 24 hours

To find the number of hours it will take to reach the final depth of y feet, we can set up the following proportion:

Drilling rate per hour = Depth drilled (feet) / Number of hours

We can rearrange this proportion to solve for the number of hours:

Number of hours = Depth drilled (feet) / Drilling rate per hour

Substituting the values we have:

Number of hours = y feet / (x feet / 24 hours)

Simplifying this expression:

Number of hours = (y * 24) / x

Therefore, the number of hours it will take until the drill reaches its final depth of y feet would be (y * 24) / x.

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The difference in the amount paid by Cathy and Steven is $4000.

Simple interest is when the interest that is paid on the loan of a customer is a linear function of the loan amount, interest rate and the duration of the loan.

Simple interest = amount borrowed x interest rate x time

Simple interest of Cathy = $20,000 x 0.052 x 10 = $10,400

Simple interest of Steven = $20,000 x 0.048 x 15 = $14,400

Difference in interest = $14,400 - $10,400 = $4000

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Answer:

2797.5

Step-by-step explanation:

Answer:

i think its 12 hours

Step-by-step explanation:

use calculator

The factorization of x2 - 6x + 5 is (x - 1)(x -5)

From the graph, the zeros of the function are:

x = 1 and x = 5

Set the zeros to 0

x - 1 = 0 and x - 5 = 0

Multiply the zeros

(x - 1)(x -5) = 0

Hence, the factorization of x2 - 6x + 5 is (x - 1)(x -5)

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The annual growth rate between 1993 and 2006 was 2.23%. If the house value continues to grow at the same rate, it will be worth approximately $161,000 in 2010.

A) The annual growth rate between 1993 and 2006 is 0.0223 or 2.23%.
B) The correct answer to part A in percentage form is 2.23%.
C) The value of the house in the year 2010 will be approximately $161,000.
A) To calculate the annual growth rate, use the formula: (final value / initial value)^(1/years) - 1
Step 1: Calculate the number of years: 2006 - 1993 = 13 years
Step 2: Calculate the growth rate: (145000 / 110000)^(1/13) - 1 = 0.0223
B) Convert the growth rate to percentage: 0.0223 * 100 = 2.23%
C) To find the house value in 2010, use the formula: initial value * (1 + growth rate)^(years)
Step 1: Calculate the number of years: 2010 - 2006 = 4 years
Step 2: Calculate the house value: 145000 * (1 + 0.0223)^4 ≈ 161000

Summary:
The annual growth rate between 1993 and 2006 was 2.23%. If the house value continues to grow at the same rate, it will be worth approximately $161,000 in 2010.

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The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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Answer:

B. Radius

The line from the center of a circle to the edge is called a radius. The radius can be used in pi and a lot of other things

Answer:

It c

Step-by-step explanation:

The domain restriction in the left side of the equation is x = 12.

Here we have the equation:

8/(x - 12) = -8/x

The domain restrictions are the values of x such that we will have a zero in one of the denominators (this is because we can't divide by zero)

Then we need to remove these values.

We can see that in the left side of the equation, when x = 12 the denominator becomes zero, so that is the domain restriction.

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Answer:

22

Step-by-step explanation

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Therefore, function of x f(f(2)) = f(-3) = 9

To find  function of f f (2) we need to find the function f(2).

Given  f(3x - 1) = -6x + 3

Let  3x -1 = 2  we will get

3x =3

x =1

Therefore, let input x =1

f(3x - 1) = -6x + 3

f(3(1) - 1) = -(1) + 3

Therefore, we need to find function of f(-3) and get  f f (2).

f f (2). =f(-3) =9

f(3x - 1) = -6x + 3

f(-3) = -6(-1) + 3 =9

Therefore, if f(3x - 1) = -6x + 3, function of f(f(2)) = f(-3) = 9

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True. If the zero conditional mean assumption holds, the coefficients can be given a causal interpretation.

True. If the zero conditional mean assumption, also known as the exogeneity assumption or the assumption of no omitted variables bias, holds in a regression model, then the coefficients can be given a causal interpretation.

The zero conditional mean assumption states that the error term in the regression model has an expected value of zero given the values of the independent variables. This assumption is important for establishing causality because it implies that there is no systematic relationship between the error term and the independent variables.

When this assumption is satisfied, we can interpret the coefficients as representing the causal effect of the independent variables on the dependent variable, holding other factors constant. However, if the zero conditional mean assumption is violated, the coefficients may be biased and cannot be interpreted causally.

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The average rate of change of f(x) = 2x^2 + 8 over interval [1, 4] is:

R = 10

For a function f(x) we define the average rate of change on an interval [a, b] as:

r = ( f(b) - f(a))/(b - a)

In this case the function is:

f(x) = 2x^2 + 8

And the interval is [1, 4]

Evaluating the function in these values we will get:

f(4) = 2*4^2 + 8  = 2*16 + 8 = 40

f(1) = 2*1^2 + 8 = 10

Then the average rate of change will be:

R = (40 - 10)/(4 - 1) = 30/3 = 10

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The probability question you asked is incomplete, so I will make an assumption based on the information provided. If you are asking about the probability of selecting a clarinet or a French horn player from the school band,

we can calculate it as follows:

1. Calculate the total number of members in the band: 36.
2. Calculate the total number of clarinets: 5.
3. Calculate the total number of French horns: 2.
4. Add the number of clarinets and French horns together: 5 + 2 = 7.
5. Divide the total number of clarinets and French horns by the total number of band members: 7 / 36.
6. Simplify the fraction if needed.
  - In decimal form, the probability would be 0.1944 (rounded to four decimal places) or 19.44% (rounded to two decimal places).

The probability of selecting a clarinet or a French horn player from the school band is approximately 0.1944 or 19.44%.

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A. The measures of center shows that the mean is 41.3 and the median is 5.

B. The measure of variability shows that the range is 8 and IQR is 5.

C. Based on the given data, if you are interested in a smaller class size, Bay Side School would be a better choice for you.

Part A: For Bay Side School:

Mean: We sum up the class sizes and divide by the total number of classes.

Class sizes: 8, 6, 5, 8, 6, 5, 4, 2, 0, 5, 3, 2, 0, 0, 3

Sum = 8 + 6 + 5 + 8 + 6 + 5 + 4 + 2 + 0 + 5 + 3 + 2 + 0 + 0 + 3 = 62

Mean = 62 / 15 = 4.13

Class sizes in ascending order: 0, 0, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 8, 8, 8

Median = (5 + 5) / 2 = 5

For Seaside School:

Mean: We sum up the class sizes and divide by the total number of classes.

Class sizes: 5, 8, 1, 0, 2, 5, 6, 8, 5, 7, 7, 8, 0, 6, 4

Sum = 5 + 8 + 1 + 0 + 2 + 5 + 6 + 8 + 5 + 7 + 7 + 8 + 0 + 6 + 4 = 72

Mean = 72 / 15 = 4.8

Median: We need to arrange the class sizes in ascending order and find the middle value.

Class sizes in ascending order: 0, 0, 1, 2, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8

Median = 6

Part B: In order to calculate the measures of variability, we will find the range and interquartile range (IQR) for each school's class sizes.

For Bay Side School:

Range: The range is the difference between the largest and smallest values.

Range = 8 - 0 = 8

IQR: The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 = median of the lower half of the data = (2 + 2) / 2 = 2

Q3 = median of the upper half of the data = (6 + 8) / 2 = 7

IQR = Q3 - Q1 = 7 - 2 = 5

For Seaside School:

Range: The range is the difference between the largest and smallest values.

Range = 8 - 0 = 8

IQR: The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Q1 = median of the lower half of the data = (2 + 5) / 2 = 3.5

Q3 = median of the upper half of the data = (7 + 8) / 2 = 7.5

IQR = Q3 - Q1 = 7.5 - 3.5 = 4

C Based on the given data, if you are interested in a smaller class size, Bay Side School would be a better choice for you.

Considering both the measures of center and measures of variability, Bay Side School offers a smaller average class size (mean) and a smaller range of class sizes (IQR) compared to Seaside School. Therefore, if you prefer smaller class sizes, Bay Side School would be the better choice for you.

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Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Answer:

\(x=0, g(x) =-4\)

Step-by-step explanation:

Given that:

Graph of \(g(x)=3|x|-4\) represents the path of a person from their house to school and then from school to their friend's house.

First of all let us learn about the graph of an absolute function.

An absolute function first decreases and then starts increasing from one point.

At that point, value of \(x=0\).

As per the problem statement given, the location of the school can only be the point that we have discussed above.

Given that the equation is:

\(g(x)=3|x|-4\)

Let us put the value of \(x=0\)

\(g(x)=3|0|-4\\\Rightarrow g(x)=-4\)

Therefore, the location of the school is:

(0, -4)  or \(x=0, g(x) =-4\)

Answer: (If I'm right can I get marked brainiest?)

100

2

+

50

2

=

12500

;  

√

12500

=

111.80

yards

Step-by-step explanation:

A football field is a rectangle, so a diagonal line creates 2 right triangles. The formula for the length of the sides of a right triangle is  

a

2

+

b

2

=

c

2

For this problem, we know  

a

and  

b

, so we just have to find  

c

.

100

2

+

50

2

=

c

2

=

12500

The length of the diagonal is  

√

12500

, which is 111.80 yards.

The possible dimensions of the sports field are width 70 yards, length 7-3x yards.

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.

Given that, the width is at least 50 yards and area is (490-210x)

We can conclude the shape of the sports field is rectangular.

We need to find the Greatest Common factor between 490 and 210, this way:

490 = 2 × 5 × 7 × 7

210 = 2 × 5 × 3 × 7

Then the greatest common factor is 2 × 5 × 7 = 70

This GCF is also equal to 70 yards (given in option), therefore it's one of the dimensions of the sports field.

Now, we calculate the other side of the sports, this way:

Second dimension of the sports field = (490-210x)/70

= 7-3x

Hence, The possible dimensions of the sports field are width 70 yards, length 7-3x yards.

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b.

because if you use math it tells you b