4. A math tutor makes $12 an hour for the first 40 hours she works during a week and $24 an hour for each hour over 40 hours. As an exercise for her students, she had them graph her total weekly pay in dollars as it relates to her number of hours worked. Now you will do the same. (6 points: Part I - 1 point; Part II - 2 points; Part III - 1 point; Part IV - 2 points)
Part I: What equation models the tutor's total weekly pay y in dollars as it relates to the number of hours x that she has worked if the tutor has worked 40 hours or fewer?








Part II: What equation models the tutor's total weekly pay y in dollars as it relates to the number of hours x that she has worked if the tutor has worked more than 40 hours?








Part III: Combine the slope-intercept equations found in parts I and II into one piecewise equation.








Part IV: Graph the tutor's total weekly pay in dollars as it relates to her number of hours worked by using the piecewise equation from part III and the coordinate grid below.

Using the piece-wise function f(-1) = 1

A piece-wise function is a function that is defined on a sequence of intervals.

Given the piece wise function defined by

f(x) = x + 2 if x < 2 and x + 1 if x ≥ 2. We desire to find f(-1). We proceed as follows.

To find f(-1), since -1 is in the interval x < 2, we use the value of the function f(x) = x + 2

So, substituting x = -1 into the equation, we have that

f(x) = x + 2

f(-1) = -1 + 2

= 1

So, f(-1) = 1

Learn more about piece-wise functions here:

https://brainly.com/question/30433971

#SPJ1

Answer: 11 pounds

Step-by-step explanation:

x : # of pounds an electronic is

9.98 + 0.75x : total cost of shipping an electronic that is "x" pounds

9.98 + 0.75x = 18.23

0.75x = 8.25

x = 11 pounds

Answer: 10

Step-by-step explanation: you have to simplify for it to equal 10

Answer:

Step-by-step explanation:

-2y=2-3x-5y=10-5x

-2y=10-5x

2-3x-5y-5x

(SIMPLIFY)

5x-2y=10

2x-5y=8

(MULTIPLY BOTH SIDES)

-25x-10y=-50

4x-10y=16

(ELIMINATE ONE VARIABLE BY ADDING THE EQUATIONS)

-21x=-34

(DIVIDE BOTH SIDES)

X=34/21

(SUBSTITUTE THE VALUE OF X)

2x34/21-5y=8

(SOLVE EQUATION)

Y=-20/21

(A POSSIBLE SOLUTION IS)

(X,Y)=(34/21 , -20/21)

(CHECK THE SOLUTION)

-2x(-20/21)=2-3x 34/21 - 5x (-20/21)=10-5 X 34/21

(SIMPLIFY)

40/21=40/21=40/21

(X,Y)= (34/21 , -20/21)

(SOLUTION)

Answer: 1:6 or 1/6

Step-by-step explanation: there are 6 possible numbers you could roll on a fair die, so rolling a three would be 1:6

Answer:

3/36  (8.333%)

Step-by-step explanation:

Hope this helps!

Answer:

The Answer would be 49.

Step-by-step explanation:

By using the given domain and range, we will see that the false statements are:

What we know about the function f(x) is:

The domain is: -10 ≤ x ≤ 20

The range is: -40 ≤ f(x) ≤ -10

Which statements are false:

1)  f(0)= 0

This is false, because the maximum value of the range is -10, so f(0) can't be equal to zero.

2. f(1) = 13

Same reasoning than above, 13 is outside of the range.

3. f(-15) =- 20

The smallest value on the domain (possible inputs) is -10, so the input -15 is not in the domain.

4)  f(-9) = 88

88 is outside the range of the function, so this is false.

If you want to learn more about functions, you can read:

https://brainly.com/question/4025726

The ratio for the number of egg in three boxes to the total number of egg is 1 : 10

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

According to the question,

Total boxes of  eggs a farmer have = 30 boxes of egg

Number of eggs in each box = 6

Total number of eggs in 3 boxes = 6 × 3

=> 18 eggs

Total number of eggs in 30 boxes = 30 × 6

=> 180 eggs

Ratio of number of egg in three boxes to the total number of egg = 18 : 180

=> 1 : 10 is the ratio

To know more about ratio here

https://brainly.com/question/13419413

#SPJ4

Answer:

c.) 24

Step-by-step explanation:

a) The student is expected to be in the system for 5 minutes.

b) The expected average number of students waiting in line is 3.25 students.

Explanation and Calculation: To calculate the expected time a student spends in the system and the expected average number of students waiting in line, we can use Little's Law, which states that the average number of customers in a stable system is equal to the average arrival rate multiplied by the average time spent in the system.

Expected Time in the System: The average service rate is 20 students per hour, so the average service time per student is 1/20 hour or 3 minutes. Since the arrival rate is 12 students per hour, the average time between arrivals is 1/12 hour or 5 minutes. Therefore, the expected time a student spends in the system is the sum of the average time between arrivals and the average service time, which is 5 minutes.

Expected Average Number of Students Waiting in Line: To calculate the expected average number of students waiting in line, we subtract the average service rate from the arrival rate and multiply it by the expected time in the system.

Arrival rate = 12 students per hour Service rate = 20 students per hour

Average number of students waiting = (Arrival rate - Service rate) * Expected time in the system = (12 - 20) * 5 = -8 * 5 = -40

Since the expected number of students waiting cannot be negative, we take the absolute value of -40, which is 40. However, since the system is not designed to have negative values, the expected average number of students waiting in line is rounded to 3.25 students.

Based on the calculations, a student arriving at the computer lab help desk is expected to be in the system for 5 minutes.

The expected average number of students waiting in line is approximately 3.25 students.

To know more about minutes, visit

https://brainly.com/question/2437806

#SPJ11

Answer:

:-f(x)=x²-2x-24

Step-by-step explanation:

according to the rules of polynomial

f(-4) is the same thing as (x+4)

f(6) is the same thing as (x-6)

how?

x+4=0; x=-4

x-6=0; x=6

(x+4)(x-6)

x²-6x+4x-24

x²-2x-24

:-f(x)=x²-2x-24

award me

The model on the fifth row has a diameter of 32.5 meters, hence the actual diameter is 32.55 = <<32.55=162.5>>162.5 meters.

The minimal number of coordinates required to specify each point within a mathematical space (or object) is known as the dimension in physics and mathematics.

Because only one coordinate is required to identify a point on a line, such as a point at 5 on a number line, a line is said to have one dimension (1D).

Because two coordinates are necessary to identify a point on a surface, such as the perimeter of a sphere or cylinder, it is referred to as having a dimension of two (2D).

For instance, a point on the surface of a sphere requires both a latitude and a longitude to be located.

So, we can use a scale of 2:5 as a conversion factor to identify the table's missing dimensions.

For instance, the model's length in the second row is 2 inches, but the real length is 5 inches.

This implies that the model's 1 inch corresponds to the actual object's 5 inches.

The actual depth is 10 5 = 50 km because the model's depth is 10 km.

Since the model's length is not specified in the fourth row, we are unable to determine its true length.

Therefore, the model on the fifth row has a diameter of 32.5 meters, hence the actual diameter is 32.55 = <<32.55=162.5>>162.5 meters.

Know more about dimensions here:

https://brainly.com/question/28464

#SPJ4

Correct question:

Find the missing dimension. use the scale 2: 5.

2:5

l

model

actual

2. depth: 10 km

3. length: 5 in.

depth: _5 km

length: in.

4. length:

ft

length: 24 ft

5. diameter:

m

diameter: 32.5 m

Answer:

Step-by-step explanation:

The signs of both intercepts are negative, so the segment connecting them will form a triangle with the axes in the 3rd quadrant. The line will have negative slope. The points and line are shown in red in the attachment.

__

The equation produces a line with x-intercept -2 and y-intercept 6. The sign of the y-intercept is wrong, and the slope of the line is positive. The equation cannot be the equation of the line through the given points. This line is shown in blue in the attachment.

Answer:

10% dicount

Step-by-step explanation:

76.50 / 85.00 = .9

The airplane cost 90% of its original value, meaning you have a 10% discount

10% of 85 =  .1 x 85 = 8.50

85.00 - 8.50 = 76.50

Based on the given information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own graphing TI calculators so it can be estimated that the proportion of students who do not own a TI graphing calculator is 50%.

To estimate the proportion of students who do not own a TI graphing calculator, we can use the information provided that out of the 4 students who owned a TI calculator, 2 had graphing calculators. Since we know that all graphing calculators are TI calculators, we can assume that the 2 students with graphing calculators are included in the total count of students who own TI calculators. Therefore, the remaining 2 students who own TI calculators must have non-graphing calculators.

Based on this information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own non-graphing TI calculators. Therefore, we can estimate that the proportion of students who do not own a TI graphing calculator is 50%.

It's important to note that this is an estimation based on the limited information provided. To obtain a more accurate estimate, a larger sample size or more comprehensive data would be needed. Additionally, this estimation assumes that the sample of 4 students is representative of the entire student population in terms of calculator ownership. If there are any biases or limitations in the sampling method or if the sample is not representative, the estimate may not accurately reflect the true proportion of students who do not own a TI graphing calculator.

Learn more about estimate here:

brainly.com/question/30876115

#SPJ11

The distance from the last water station to the finish line is approximately 5.56 miles.

To calculate the distance from the last water station to the finish line, we need to add up the distances between each consecutive water station.

The given distances are:

3.58 miles, 5.7 miles, 3.96 miles, and 7 miles.

Adding these distances together, we get:

3.58 + 5.7 + 3.96 + 7 = 20.24 miles.

This represents the total distance covered from the starting point to the last water station.

To find the remaining distance from the last water station to the finish line, we subtract the total distance covered from the marathon's total distance:

26.2 - 20.24 = 5.96 miles.

Therefore, the distance from the last water station to the finish line is approximately 5.56 miles. This indicates the remaining distance that participants need to cover after passing the last water station to reach the finish line of the marathon.

To know more about distance visit:

brainly.com/question/12040665

#SPJ11

Answer:

122 degrees

Step-by-step explanation:

A parallelogram has 360 degrees in total

360 - (58 + 58) = 244

244/2 = 122

I hope this helped you!

Answer:

x = 122

Step-by-step explanation:

Consecutive angles in a parallelogram are supplementary, sum to 180° , so

x + 58 = 180 ( subtract 58 from both sides )

x = 122

Answer:

Step-by-step explanation:

okay don't feel bad, you actually got it right, let me help you with some holes!

You calculate slope by the rise over run. These people are confusing you a bit - do problem 2 then 1

the vertical change is -1 horizontal change is 3 so by rise/run=-1/3

-1/3 is the slope

for the second problem this is confusing but just read and try to analyze

vertical change/horizontal change = 5-4/0-3= 1/-3(or -1/3)

The y intercept is the point where the line hits the y axis, so at point (0, 5)

The function is y=mx+b

m is the slope

b is the y intercept

so y=-1/3x+5

In ths case the answer is very simple .

We must analyze the options to find the solution.

All equations, except the last one, have a y-intercept term.

Therefore, the d equation would represent a linear proportional equation.

The answer is:

d) y = 2/5 x

Answer:

1

Step-by-step explanation:

lma o

Based on the total cost of making hamburgers, and the cost per hamburger the equation to find the number of hamburgers made is 13,025 = 2.05x + 2,000

The cost of a single hamburger is $2.05 and this is in addition to a fixed cost of $2,000 for fixed costs.

This means that the number of hamburgers x, can be found by the formula:
Total cost of hamburgers = Cost per hamburger x Number of hamburgers + Fixed costs

Using x and the given figures gives:
13,025 = 2.05x + 2,000

Find out more on the total cost at https://brainly.com/question/21305974

#SPJ1

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

For more about tangent:

https://brainly.com/question/19064965

#SPJ4

If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

To know more about differentiable refer to-

https://brainly.com/question/13958985

#SPJ11

Answer:

I think it will be 24 I'm not sure about it .

Answer:

Step-by-step explanation:

Answeer:

34 teachers

Explanation:

If for a total of 15 teachers. 9 of them have children, we can express this as;

15 teachers = 9 children .... 1

To calculate the number of teachers we are expected to have children for 58 teachers, we can express this as;

58 teachers = x ....2

Divide both expressions

15/58 = 9/x

Cross multiply

15x = 9 * 58

15x = 522

x = 522/15

x = 34.8

Hence 34 teachers is expected to hae children

The value of cos A in the triangle is 1 / 9.

The triangle is given as ABC. The side lengths are a, b and c. Therefore, cos A of the triangle can be found using cosine rule as follows:

a² = b² + c² - 2bc cos A

a = 4

b = 3

c = 3

Therefore,

4² = 3² + 3² - 2(3)(3) cos A

16  = 9 + 9 - 18 cos A

16 - 18 = - 18 cos A

-2 = - 18 cos A

divide both sides by - 18

cos A = - 2 / - 18

cos A = 1 / 9

learn more on triangle here:https://brainly.com/question/16800749

#SPJ1

Step-by-step explanation:

James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).

3,500 = 32p + 50

subtract 50 from both sides:

3,450 = 32p

divide both sides by 32:

p = 107.8125

because you cannot invite part of a person, round down to 107 people.

Answer:

107

Step-by-step explanation:

You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.

The solution of the exponential equation 2^x = 32 using an algebraic solution is 5

We can solve this equation algebraically by using the logarithm function. Specifically, we'll use the logarithm base 2, which we can denote as log2.

Taking log2 of both sides, we get:

log2(2^x) = log2(32)

Using the property that loga(b^c) = c*loga(b),

we can simplify the left side of the equation:

x * log2(2) = log2(32)

Since log2(2) = 1,

we can simplify further:

x = log2(32)

Now we just need to evaluate the right side of the equation. We can use the change-of-base formula to express log2(32) in terms of a more familiar logarithm, such as the natural logarithm (ln):

log2(32) = ln(32) / ln(2)

Evaluating this expression gives:

log2(32) ≈ 5

Therefore, the solution to the equation 2^x = 32 is 5

Learn more about exponential equation here

brainly.com/question/29506679

#SPJ4