Mathematics College

An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 145 for 5 < x ≤ 6
B. C(t) = 145 for 6 < x ≤ 7
C. C(t) = 170 for 5 < x ≤ 6
D. C(t) = 170 for 6 < x ≤ 7

Answers

Answer 1
The total cost is given by the equation:
C(t) = 45 + 25(h-1) where h is the number of hours worked.

We can check for each option in turn:

Option A:

Inequality 5 < x ≤ 6 means the hour is between 5 hours (not inclusive) to 6 hours (inclusive)
Let's take the number of hours = 5
C(5) = 45 + (5-1)×25 = 145
Let's take the number of hours = 6
Then substitute into C(6) = 45 + (6-1)×25 = 170
We can't take 145 because the value '5' was not inclusive.


Option B:
The inequality is 6 < x ≤ 7
We take number of hours = 6
C(6) = 25(6-1) + 45 = 170
We take number of hours = 7
Then C(7) = 25(7-1) + 45 = 195

Option C:
The inequality is 5 < x ≤ 6
Take the number of hours = 5
C(5) = 25(5-1) + 45 = 145
Take the number of hours = 6
C(6) = 25(6-1) + 45 = 170
We can't take the value 145 as '5' was not inclusive in the range, but we can take 170

Option D:
6 < x ≤ 7
25(6-1) + 45 < C(t) ≤ 25(7-1) + 45
170 < C(t) ≤ 195

Correct answer: C


Related Questions

In a certain town, 22% of voters favor a given ballot measure. for groups of 21 voters, find the variance for the number who favor the measure.
a. 1.9
b. 13
c. 4.6
d. 3.6

Answers

Final answer:

The variance for the number of voters who favor the ballot measure in groups of 21 is calculated using the formula for a binomial distribution, which yields an answer of 3.78. The closest option to this value is 3.6, answer option d.

Explanation:

In the question about a town where 22% of voters favor a given ballot measure, we are asked to find the variance for the number of voters who favor the measure in groups of 21 voters. To calculate the variance, we use the formula for the variance of a binomial distribution, which is np(1-p), where 'n' is the number of trials (voters in this case), 'p' is the probability of a voter favoring the measure, and '1-p' is the probability of a voter not favoring the measure.

Using the information provided:

n = 21 (the number of voters in a group)p = 0.22 (the probability of a voter favoring the measure)

Thus, the variance (Var) is:

Var = np(1-p) = 21 × 0.22 × (1 - 0.22) = 21 × 0.22 × 0.78 = 3.78

The closest answer to 3.78 is 3.6, which is option d.

Variance formula: [tex]\(npq\)[/tex]. Substitute [tex]\(n = 21\), \(p = 0.22\), \(q = 0.78\)[/tex]. Calculate to get variance. Answer: d. 3.6

To find the variance for the number who favor the measure in groups of 21 voters, we can use the binomial distribution formula.

The variance of a binomial distribution is given by [tex]\(npq\)[/tex], where:

- [tex]\(n\)[/tex] is the number of trials (number of voters in each group),

- [tex]\(p\)[/tex] is the probability of success (proportion of voters favoring the measure), and

- [tex]\(q\)[/tex] is the probability of failure (proportion of voters not favoring the measure).

Given:

- [tex]\(n = 21\)[/tex],

- [tex]\(p = 0.22\)[/tex] (22% favor the measure), and

- [tex]\(q = 1 - p = 1 - 0.22 = 0.78\)[/tex],

Let's calculate the variance:

[tex]\[ \text{Variance} = npq = 21 \times 0.22 \times 0.78 \][/tex]

[tex]\[ \text{Variance} = 21 \times 0.1716 \][/tex]

[tex]\[ \text{Variance} = 3.5976 \][/tex]

Rounded to one decimal place, the variance is approximately [tex]\(3.6\)[/tex].

So, the correct answer is d. 3.6.

Write the equation in standard form of the circle with radius 5 and center 0,3

Answers

The equation of a circle is (x-h)²+(y-k)²=r², with h being the x value in the center, k being the y value, and r being the radius. x and y can stay variables, so we can plug numbers in to get (x-0)²+(y-3)²=5²=25=x²+(y-3)²

Another tent has the perimeter of 7.2 metres. If the width is 1.3 metres, what is the length?

Answers

P = 2( L + W)
P = 7.2
W = 1.3

7.2 = 2(1.3 + L)
7.2 = 2.6 + 2L
7.2 - 2.6 = 2L
4.6 = 2L
4.6/2 = L
2.3 = L <== length is 2.3 m 

Answer:  Length of tent would be 2.3 meters.

Step-by-step explanation:

Since we have given that

Perimeter of tent = 7.2 meters

Width of tent = 1.3 meters

Since we have given that

Perimeter = 2( length + width)

[tex]7.2=2(Length+1.3)\\\\\dfrac{7.2}{2}=Length+1.3\\\\3.6=Length+1.3\\\\3.6-1.3=Length\\\\2.3\ m=Length[/tex]

Hence, Length of tent would be 2.3 meters.

In Christopher Marlowe's The Tragical History of Doctor Faustus, why did Faustus begin to believe that human salvation was impossible? Faustus first began to believe that human salvation was impossible because In addition, he had

Answers

In Christopher Marlowe's The Tragical History of Doctor Faustus, Faustus began to believe that human salvation was impossible because he read the scripture and saw that all human beings sin and are doomed. He thought that this meant that no matter how you lived your life, and how much you tried to be a good person, in the end you would still sin and thus God won't forgive you. This is why he consciously gave in to sin. 

In addition, he had been misled by Mephastophills, who caused him to misread the scriptures. Mephastophills is the Devil, and obviously the Devil won't tell the truth because he wants to collect more souls to torture in his realm. Faustus fell for his tricks and was mislead to misinterpret the scriptures, which lead to him losing his soul ultimately. 

Answer:

he read the scripture and saw that all human beings sin and are doomed

Step-by-step explanation:

14+3n=8n-3(n-4) this is really hard please help me

Answers

14+3n=8n-3(n-4)
distribute
14+3n=8n-3n+12
add like terms
14+3n=5n+12
subtract 3n from both sides
14=2n+12
subtract 12 from both sides
2=2n
divide both sides by 2
n=1
Hope this helps!!

What is the value of n?

9×27+2×31-28= n

Answers

Hey, there! 

[tex]9(27) + 2(31) = n \\ \\ 9(27) = 243 \\ \\ 2(31) = 62 \\ \\ 28 = -28 \\ \\ \\ 243 + 62 + (-28) = n \\ \\ n = 277 [/tex]

Good luck on your assignment and enjoy your day 

~[tex]MeIsKaitlyn:)[/tex]

n=277

Hope this will help!

5n=35 what is n equal to?

Answers

Salutations!

5n=35 what is n equal to?

5n = 35

Isolate the number 5, why? because all the variables should be aside, also, we are finding the "n".

n = 32/5

n = 5.

N equals to 5.

Hope I helped (:

Have a great day!

Determine the unit rate of a marathon runner who travels 5/2 miles in 1/4 hour.

Answers

The unit rate is 10mph 
[tex]\bf \cfrac{\frac{5}{2}~miles}{\frac{1}{4}~hr}\implies \cfrac{5~miles}{2}\cdot \cfrac{4}{1~hr}\implies \cfrac{5\cdot 4~miles}{2\cdot 1~hr}\implies \cfrac{20~miles}{2~hr}\\\\\\ 10\frac{miles}{hr}[/tex]

3) Linda started taking piano lessons. She had to practice 1 3/4 hours each day. If after only 8 days Linda decided she wanted to stop, how many hours did she take lessons?

Answers

since 1 3/4 hours is equal to 105 minutes and since she did that amount each day and she practiced for eight days. You would multiply 105 times 8 to get 840 minutes but converted to hours would be 14 hours.

​1/5 of the animals at a zoo are monkeys. 5/7 of the monkeys are male. What fraction of the animals at the zoo are male monkeys?

Answers

I think it is 1/7 I hope this helps

Answer : The fraction of the animals at the zoo are male monkeys, [tex]\frac{1}{7}[/tex]

Step-by-step explanation :

As we are given that:

Fraction of animals at a zoo are monkeys = [tex]\frac{1}{5}[/tex]

Fraction of monkeys are male = [tex]\frac{5}{7}[/tex]

So,

Fraction of the animals at the zoo are male monkeys = Fraction of animals at a zoo are monkeys × Fraction of monkeys are male

Fraction of the animals at the zoo are male monkeys = [tex]\frac{1}{5}\times \frac{5}{7}[/tex]

Fraction of the animals at the zoo are male monkeys = [tex]\frac{1}{7}[/tex]

Thus, the fraction of the animals at the zoo are male monkeys, [tex]\frac{1}{7}[/tex]

Ray
OC
divides ∠AOB into two angles. Find the measurement of ∠AOC, if m∠AOB = 155°, and m∠AOC is by 15° greater than m∠COB.

Answers

We are given that:

m∠AOB = m∠AOC + m∠COB

We are also given that:

m∠AOC = m∠COB + 15

m∠AOB = 155

Therefore:

155 = m∠COB + 15 + m∠COB

2 m∠COB = 140

m∠COB = 70°

and,

m∠AOC = m∠COB + 15 = 85°

 

Answers:

m∠COB = 70°

m∠AOC = 85°

What proportion of a normal distribution is located between z = 0 and z = +1.50?​ ​0.4332 ​0.8664 ​0.0668 ​0.9332?

Answers

0.4332 The problem is asking what proportion of a normal distribution is within 1.50 standard deviations on the positive half of the curve. So let's take a look. First thing is to figure out what would be a reasonable answer. Looking at the standard deviation, there will be 34.1% within 0 to +1 standard deviations. And there will be 47.7% within 2 standard deviations. So the correct answer will be something between 0.341 and 0.477. So let's look at the possible answers. ​0.4332 - This answer falls within the desired range. It's a candidate. ​0.8664 - This answer is way too large. Well over 50%, so it can't work. ​0.0668 - This answer is way too small. So once again, it can't work ​0.9332 - If the 0.8664 above was too large, imagine how unreasonable this answer is. Also wrong. So of the 4 available choices, only 0.4332 is possible. So that's the correct answer.

Let y be a random variable with p(y) given in the accompanying table. find e(y ), e(1/y ), e(y 2 − 1), and v(y ). y 1 2 3 4 p(y) .4 .3 .2 .1

Answers

Final answer:

This answer pertains to the computation of expected and variance values for a discrete random variable y using its given probability distribution function. Relevant principles include multiplying each value of y with its corresponding probability and then summing the products for the expected value, and further operations for other expected values and variance.

Explanation:

The subject pertains to finding the expected and variance values of a discrete random variable y, based on its probability distribution function (PDF). In this case, we have four values for y (i.e., 1, 2, 3, and 4) with corresponding probabilities given as .4, .3, .2, and .1 respectively.

E(y) or the expected value of y is obtained by multiplying each value of y with its corresponding probability and then summing the products, according to the formula E(y) = Σ y*P(y).

e(1/y) is the expected value of the reciprocal of y, obtained similarly by multiplying each 1/y with its corresponding P(y) and summing up the products.

e(y 2 − 1) represents the expected value of y-squared minus one, obtained by squaring each y, subtracting one, multiplying with the corresponding P(y), and then adding the results.

Finally, for v(y) or the variance of y, one would first need to find the expected value of y-squared [E(y^2)], and then use the identity v(y) = E(y^2) - {E(y)}^2 to compute the variance.

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A small piece of metal weighs 0.77 gram. What is the value of the digit in the tenths place

Answers

70 hundredths of a gram
0.7 is the value hope this helps

Find dy/dx
√(x+y) = x - 2y

Answers

[tex]\bf \sqrt{x+y}=x-2y\implies (x+y)^{\frac{1}{2}}=x-2y \\\\\\ \cfrac{1}{2}(x+y)^{-\frac{1}{2}}\left(1+\frac{dy}{dx} \right)=1-2\frac{dy}{dx} \implies \cfrac{1+\frac{dy}{dx} }{2(x+y)^{\frac{1}{2}}}=1-2\frac{dy}{dx} \\\\\\ 1+\frac{dy}{dx} =2(x+y)^{\frac{1}{2}}-2(x+y)^{\frac{1}{2}}\cdot 2\frac{dy}{dx} \\\\\\ 1+\frac{dy}{dx} =2(x+y)^{\frac{1}{2}}-4(x+y)^{\frac{1}{2}}\frac{dy}{dx} \\\\\\ \frac{dy}{dx}+4(x+y)^{\frac{1}{2}}\frac{dy}{dx} =2(x+y)^{\frac{1}{2}}-1[/tex]

[tex]\bf \cfrac{dy}{dx}\left[ 1+4(x+y)^{\frac{1}{2}} \right]=2(x+y)^{\frac{1}{2}}-1\implies \cfrac{dy}{dx}=\cfrac{2(x+y)^{\frac{1}{2}}-1}{1+4(x+y)^{\frac{1}{2}} } \\\\\\ \cfrac{dy}{dx}=\cfrac{2\sqrt{x+y}-1}{1+4\sqrt{x+y}}[/tex]

How many gallons of 20% antifreeze should be mixed with 10 gallons of 92% antifreeze to obtain a 65% antifreeze mixture?

Answers

Add G gallons.
10*92 + G*20 = (10+G)*65

A woman who is 64 inches tall has a shoulder width of 16 inches. Write an equation relating height to the width. Find the height of a woman who has a shoulder width of 18.5 inches.

Answers

64in/16in = x/18.5
64•18.5= 1184
1184/16x= 16x/16x
1184/16x
x= 74 in

The height of woman who has a shoulder width of 18.5 inches is 74 inches

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the height of a woman who has a shoulder width of 18.5 inches be = A

Now , the equation will be

The height of the woman be = 64 inches

The shoulder width of the woman be = 16 inches

So , the equation will be

Let the height of a woman who has a shoulder width of 18.5 inches be = 18.5 x ( height of the woman be / shoulder width of the woman )

Substituting the values in the equation , we get

The height of a woman who has a shoulder width of 18.5 inches be A =
18.5 x ( 64 / 4 )

The height of a woman who has a shoulder width of 18.5 inches be A =

18.5 x 4

The height of a woman who has a shoulder width of 18.5 inches be A =

74 inches

Therefore , the value of A is 74 inches

Hence ,

The height of woman who has a shoulder width of 18.5 inches is 74 inches

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What is the answer to 4+(-1 2/3)

Answers

4 - 1 2/3

12/3 - 5/3 = 7/3

7/3 is your answer

hope this helps

Solve the system by substitution . 2x+y=-11 3x-4y=11
(3,5)
(-5,-3)
(-3,-5)
(5,3)

Answers

2x + y = -11
y = -2x - 11

3x - 4y = 11
3x - 4(-2x - 11) = 11
3x + 8x + 44 = 11
11x = 11 - 44
11x = - 33
x = -33/11
x = -3

y = -2x - 11
y = -2(-3) - 11
y = 6 - 11
y = - 5

solution is (-3,-5) <==

Evaluate the expression for the given values.

mx−y when m=1, x=5x=5, and y=2

Enter your answer in the box.


Answers

Step 1) Start with the original expression

Step 2) Replace m with 1 (since m = 1)

Step 3) Replace x with 5 (since x = 5)

Step 4) Replace y with 2 (since y = 2). After this step we use PEMDAS to evaluate.

Step 5) Multiply (the M in PEMDAS)

Step 6) Subtract (the S in PEMDAS). Note how the S comes after the M. So subtraction is done after multiplication.

----------------------------------------------------------------

Step 1) m*x - y 

Step 2) 1*x - y

Step 3) 1*5 - y

Step 4) 1*5 - 2

Step 5) 5 - 2

Step 6) 3

----------------------------------------------------------------

So the final answer is 3

What is .0091 rounded to thousands?

Answers

.009 is the correct answer

a triangle with a base of 12 millimeters and height of 11 millimeters

Answers

Perimeter= 34
Area= 132

(b) we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above 100? (round your answer to one decimal place.)

Answers

Given that the iq scores for large populations are centered at 100.

To get what percent of these 78 students have scores above 100 we conduct a normal distribution probability of the data.

P(x > 100) = P(z > (100 - 100)/sd) = P(z > 0) = 1 - P(z < 0) = 1 - 0.5 = 0.5 = 50%

7x2+3[81-(4x6)]
Simplify

Answers

7x2+3[81-24]
7x2+3-57
14+3-57
17-57
-40

Give the derivative of f(x) = arctan(e^(5x)) at the point where x=0

Answers

[tex]f(x)=\arctan e^{5x}[/tex]
[tex]f'(x)=\dfrac{(e^{5x})'}{1+(e^{5x})^2}=\dfrac{5e^{5x}}{1+e^{10x}}[/tex]
[tex]f'(0)=\dfrac5{1+1}=\dfrac52[/tex]
Final answer:

The derivative of f(x) = arctan(e^(5x)) at x=0 is 2.5, using chain rule and the derivative of the arctan function.

Explanation:

The function given is f(x) = arctan(e^(5x)). To find its derivative at the point where x=0, we have to use the chain rule and the derivative of the arctan function.

Firstly, the derivative of arctan(u) is 1 / (1 + u^2). Therefore, if u = e^(5x), then the derivative of arctan(e^(5x)) is: 1 / (1 + (e^(5x))^2).

Secondly, because u = e^(5x), the derivative of u is 5e^(5x). We incorporate this using the chain rule to get the derivative: 5e^(5x) / (1 + (e^(5x))^2).

Finally, substitute x=0 into the derivative equation. We find that the derivative of the function at x=0 is: 5 / (1 + 1) = 2.5.

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Suppose a box contains 10 red balls, 10 green balls, and 10 orange balls. you will be choosing 3 balls from the box without replacement. 13. what is the probability of drawing an orange on the first draw and a red on the second draw?

Answers

.05


chance of getting orange on the first and red on the second

Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression.
(tan 45° + tan 60°)2

Answers

tan45° = 1
tan60° = √3

(tan45° + tan60°)²  
= (1+ √3)²
= 1 + 2√3 + 3
= 4 + 2√3   ←  answer

lynne took a taxicab from her office to the airport. she had to pay a flat fee of $2.05 plus $0.90 per mile. the total cost was $5.65. how many miles was the taxi trip?

Answers

2.05 + 0.90m = 5.65
0.90m = 5.65 - 2.05
0.90m = 3.60
m = 3.60 / 0.90
m = 4 <=== the taxi trip was 4 miles

The distance traveled by the taxi on trip is 4 miles.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Flat fee of a taxicab = $2.05

Fees per mile = $0.90

The total cost = $5.65

Distance traveled by the taxi on trip is

⇒ [tex]\frac{5.65-2.05}{0.90}[/tex]

⇒ [tex]\frac{3.60}{0.90}[/tex]

⇒ [tex]4[/tex]

Hence we can conclude that the distance traveled by the taxi on trip is   4 miles.

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Zach is 3 years older than twice his sister Michelle's age. Let m represent Michelle's age. Write an expression in terms of m to represent Zach's age.

Answers

zach is 3 yrs older then twice his sister (m)

zack is : 2m + 3
2m+3 is the answer to that

A​ country's people consume 6.6 billion pounds of candy​ (excluding chewing​ gum) per year. Express this quantity in terms of pounds per person per month. Note that the population of the country is 303 million.

Answers

A​ country's people consume 6.6 billion pounds of candy​ (excluding chewing​ gum) per year. Population of the country is 303 million. Specific consumption, = ((6.6*10^9 pounds)/( year* 303*10^6 persons))*(year/ 12 months) =1.8 pounds/(months*persons)

Final answer:

To find the candy consumption per person per month, divide the total consumption of candy by the population and then divide by 12 months. The calculation shows that each person consumes approximately 1.815 pounds of candy per month.

Explanation:

To calculate the amount of candy consumed per person per month, we first need to divide the total annual consumption by the population of the country. The total annual consumption is 6.6 billion pounds of candy, and the population is 303 million people. So, the annual consumption per person is:

(6.6 billion pounds) / (303 million people) = 21.78 pounds/person/year.

Now, to find the monthly consumption per person, we divide the annual consumption per person by 12 (months in a year):

(21.78 pounds/person/year) / (12 months/year) = 1.815 pounds/person/month.

Therefore, each person in the country consumes approximately 1.815 pounds of candy per month.

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