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) = 95 for 1 < x ≤ 2
B. C(t) = 95 for 2 < x ≤ 3
C. C(t) = 120 for 2 < x ≤ 3
D. C(t) = 120 for 4 < x ≤ 5

Answers

Answer 1
To answer this question, it is easier to make a list of the repair cost based on the hour of labor. The first hour is $45 then after that $25/hour. Then the list would look like 

0-1 h= $45
1-2h= $70     ($45 +1*$25)
2-3h= $95    ($45 +2*$25)
3-4h= $120   ($45 +3*$25)

Looking at the list, the answer should be
B. C(t) = 95 for 2 < x ≤ 3

Related Questions

We can use the right outside diagonal of the empty Lacsap's triangle as the coefficients of a polynomial: $$t^3 + 6t^2 + 12t + 8.$$ If we replace every $t$ with $t-1,$ we get $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8.$$Expand and simplify this polynomial. Enter the polynomial as your answer.

Answers

The given equation with t -1 is:
(t – 1)^3 + 6 (t – 1)^2 + 12 (t – 1) + 8

Expand each term before combining for easier visualization:
(t – 1)^3 = t^3 – 3 t^2 + 3t – 1
6 (t – 1)^2 = 6 t^2 – 12 t + 6
12 (t – 1) = 12 t - 12

Then substitute and combine:
-> t^3 – 3 t^2 + 3t – 1 + 6 t^2 – 12 t + 6 + 12 t – 12 + 8

t^3 + 3 t^2 + 3 t + 1 (ANSWER)
Final answer:

To expand the given polynomial $(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8$, we can apply the binomial theorem to each term and then combine like terms.

Explanation:

To expand the polynomial $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8,$$ we can start by applying the binomial theorem to each term:

$$(t-1)^3 = t^3 - 3t^2 + 3t - 1$$

$$6(t-1)^2 = 6(t^2 - 2t + 1) = 6t^2 - 12t + 6$$

$$12(t-1) = 12t - 12$$

$$8$$

Now, we can combine like terms:

$$t^3 - 3t^2 + 3t - 1 + 6t^2 - 12t + 6 + 12t - 12 + 8$$

Cancelling out terms that add up to zero, we are left with:

$$t^3 + 6t^2 + 12t + 8$$

how long would it take a ball dropped from a 100 ft building to hit the ground

Answers

now, if the ball is just free-falling, is simply dropped from 100ft, then the initial velocity is 0, and the initial height is 100, and it hits the ground when its height reaches 0.

[tex]\bf \qquad \textit{initial velocity}\\\\ \begin{array}{llll} \qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \\\\ \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ h_o=\textit{initial height of the object}\\ h=\textit{height of the object at "t" seconds} \end{cases} \\\\\\ \begin{cases} h_o=100\\ v_o=0\\ h(t)=0 \end{cases}\implies 0=-16t^2+0t+100\implies 16t^2=100[/tex]

[tex]\bf t^2=\cfrac{100}{16}\implies t^2=\cfrac{25}{4}\implies t=\sqrt{\cfrac{25}{4}}\implies t=\cfrac{\sqrt{25}}{\sqrt{4}}\implies t=\cfrac{5}{2}~secs[/tex]

Final answer:

To find the time it takes for a ball to fall from a 100 ft building, convert the height to meters and use the free fall motion formula. Solving s = (1/2)gt² for time, it takes approximately 2.5 seconds for the ball to hit the ground.

Explanation:

To determine how long it would take for a ball dropped from a 100 ft building to hit the ground, we can use the formula for the free fall motion under the influence of gravity, assuming air resistance is negligible. The formula is s = (1/2)gt², where s is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s², but we will need to convert it to feet per second squared for this problem), and t is the time in seconds.

First, convert 100 feet to meters because the standard unit of gravity is in meters per second squared. There are approximately 3.281 feet in a meter, so 100 feet is roughly 30.48 meters.

Now apply the formula and solve for t:

Convert acceleration due to gravity to feet: 9.8 m/s² is approximately 32.2 ft/s².

Use the formula: 100 = (1/2)(32.2)t².

Solve for t: t² = 100 / 16.1.

Find t: t = √(100 / 16.1).

Calculate t: t ≈ 2.49 seconds.

Therefore, it would take approximately 2.5 seconds for the ball to hit the ground.

Suppose m<3 = 105. find m<6

Answers

To find the measure of angle 6, we can use the fact that angles 3 and 6 are vertical angles (opposite angles formed by the intersection of two lines). Therefore, their measures are equal.

Given that[tex]\( m\angle 3 = 105^\circ \), we have \( m\angle 6 = m\angle 3 = 105^\circ \).So, the measure of angle 6 is \( \boxed{105^\circ} \).[/tex]

The measure of angle 6 is 105 degrees. This is because angles 3 and 6 are vertical angles, meaning they are formed by intersecting lines and are opposite each other. According to the Vertical Angles Theorem, vertical angles are congruent, meaning they have the same measure. Therefore, if angle 3 measures 105 degrees, angle 6, being its vertical angle, also measures 105 degrees. This principle holds true regardless of the specific configuration of lines or shapes, as long as the angles are formed by intersecting lines. Hence, in this case, the measure of angle 6 directly corresponds to the measure of angle 3 due to their relationship as vertical angles, resulting in both having a measure of 105 degrees.

A student is trying to remember some formulas from geometry. in what follows, assume a is area, v is volume, and all other variables are lengths. determine which formulas are dimensionally consistent.

Answers

Given that A is area, V is volume, and all other variables are lengths.

To get the dimensions of a quantity, it is easier to compare the unit of the quantity and represent each value in the unit by the dimension.

The formular that is dimensionally consistent is
[tex]V= \frac{\pi d^3}{6} [/tex]

Which sign makes this number sentence true? |78| __ |-222|

Answers

The absolute value of 78 is < the absolute value of -222
The absolute value of |78|=78
The absolute value of |-222|=222
Therefore, 78<222.
The sign that makes this sentence true is <.

A turtle walks 7/8 mile in 50 minutes. What is the unit rate in miles per hour? (Hint: 50 minutes=5/6 of an hour.)

Answers

50 minutes = 7/8 mile = 0.875 miles

60 minutes = 60/50 X 0.875 = 1.05 mph

Find all values of x in the interval [0, 2π] that satisfy the equation. (enter your answers as a comma-separated list.) 3|tan(x)| = 3 g study

Answers

The absolute value of Tan(x) means that, while x = multiples of 45 degrees or Pi/4, the values are: Pi/4, 3Pi/4, 5Pi/4, 7Pi/4.
Final answer:

The values of x in the interval [0, 2π] that satisfy the equation 3|tan(x)| = 3 are π/4, 3π/4, 5π/4, and 7π/4.

Explanation:

The given equation is 3|tan(x)| = 3. This means the absolute value of the tangent of x times 3 is equal to 3. We can remove the 3 from both sides to simplify to |tan(x)| = 1. The absolute value operator denotes the non-negative value of a number. So, we need to find the values of x such that tan(x) equals 1 or -1.

The solutions for tan(x) = 1 in the interval [0, 2π] are π/4 and 5π/4. The solutions for tan(x) = -1 in the same interval are 3π/4 and 7π/4.

Thus, the values of x that satisfy the equation are π/4, 3π/4, 5π/4, and 7π/4.

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Estimate the square root to the nearest integer. Square root of 48

Answers

the square root to the nearest integer is 7 because 7 times 7 is 49
Answer~
7
Problem~
7x7=49
The nearest integer is 7


A​ 1-ounce serving of cream cheese contains 7.8

grams of saturated fat. How much saturated fat is in 12

ounces of cream​ cheese?

Answers

Sent a picture of the solution to the problem (s). Proportions are a quick set up to find a part of two things being compared. You will use this method a lot in math and science.
Final answer:

To find the total grams of saturated fat in 12 ounces of cream cheese, multiply the grams per ounce (7.8) by the total ounces (12), which equals 93.6 grams.

Explanation:

To answer this question, we need to multiply the amount of saturated fat in one ounce of cream cheese by the total number of ounces you have. Since one ounce of cream cheese contains 7.8 grams of saturated fat, you would multiply 7.8 by 12 (the total number of ounces) to get the total amount of saturated fat.

7.8 grams of saturated fat per ounce × 12 ounces = 93.6 grams

So, 12 ounces of cream cheese contains 93.6 grams of saturated fat.

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Divide 300 in a ratio of 3:7

Answers

now, if we divide 300 by (3+7), we get 10 equal pieces, then we give 3 of those pieces to one side, and 7 of those pieces to the other side.

[tex]\bf \textit{300 at 3:7 ratio}\qquad \cfrac{3\left( \frac{300}{3+7} \right)}{7\left( \frac{300}{3+7} \right)}\implies \cfrac{3\left( \frac{300}{10} \right)}{7\left( \frac{300}{10} \right)}\implies \cfrac{3(30)}{7(30)}\implies \cfrac{90}{210}[/tex]

and of course, 90 + 210 = 300.
Final answer:

To divide 300 by a ratio of 3:7, calculate the value of each part by dividing 300 by the sum of the ratio parts (10) and then multiply by each part of the ratio to get 90 and 210, respectively.

Explanation:

To divide 300 in a ratio of 3:7, first add the parts of the ratio together to determine how many parts you will split 300 into.

In this case, 3 + 7 equals 10 parts.

Then, you divide 300 by 10 to find out how much one part is worth.

This gives 300 ÷ 10 = 30. Now, to find the amounts corresponding to the ratio, multiply the single part value by the numbers in the ratio. For the first part (ratio 3), multiply 30 by 3 to get 90.

For the second part (ratio 7), multiply 30 by 7 to get 210.

So, 300 divided in a ratio of 3:7 gives us 90 and 210, respectively.

6,000 is 10 time as much as

Answers

6000/10 = 600....so 6000 is 10 times as much as 600

The line contains the point (-7,0) and is parallel to the line defined by 4x=3y. What is the equation of the line

Answers

Parallel line have the same slope. Since the slope of the line is:

4x = 3y
4/3 = y

4/3, we need to set this up in an equation:

y = 4/3x + b

Now, lets add our point in:

y = 4/3x + b
0 = 4/3(-7) + b
0 = -28/3
28/3 = b

Now we know all our information. Form the equation:

y = 4/3x + 28/3

Hope this helped!

the vega family has a cell phone plan that costs $75 per month including taxes and fees. the plan lets the 5 members of the vega family share 1000 minutes of talk time per month and 400 text messages per month. any minutes over 1000 cost $1 per minutes and any text over 400 cost $2 per text. because of a family emergency the family uses 1050 minutes and 415 texts in march. write an expression you could use to find the amount of the vega cell phone bill for march. evaluate the expression show the work

Answers

Sent a picture of the solution to the problem (s).

URGENT!: Which property justifies this statement? 
 
If x + y = z and z = x + 4, then x + y = x + 4.



 
A.
symmetric


 
B.
distributive


 
C.
transitive


 
D.
associative

Answers

The answer to that question is
C. transitive

Find the coordinates of point p which divides the line segment from A=(0,4)to B=(6,8)in a ratio of 1:2

Answers

check the picture below.

[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(0,4)\qquad B(6,8)\qquad \qquad 1:2\quad \textit{ from A to B} \\\\\\ \cfrac{AP}{PB} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(0,4)=1(6,8) \\\\ -------------------------------\\\\ { P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------[/tex]

[tex]\bf P=\left(\cfrac{(2\cdot 0)+(1\cdot 6)}{1+2}\quad ,\quad \cfrac{(2\cdot 4)+(1\cdot 8)}{1+2}\right) \\\\\\ P=\left( \cfrac{0+6}{3}~,~\cfrac{8+8}{3} \right)[/tex]

What is the lateral area of a pyramid with base edges 5 ft and surface area 55 ft2?

Answers

The answer is  30 ft²

The surface area (SA) of a pyramid is the sum of lateral area (LA) of the pyramid and the area of its base (BA):
SA = LA + BA

The area of the pyramid base (which is a square) with base edge a is:
BA = a²

We have:
SA = 55 ft²
LA = ?
a = 5 ft

LA = SA - BA = SA - a²
LA = 55 - 5²
LA = 55 - 25
LA = 30 ft²

the second angel im a triangle is 2° less the 3 times the first angle the third Angle is 14° more than twice the first angle find the measure of all three angles I'm the triangle (plz show step by step)

Answers

let's say the angles are "a", "b" and "c"

[tex]\bf \begin{cases} \stackrel{first}{a}\\ \stackrel{second}{b}=\stackrel{\textit{2 less than 3 times \underline{a}}}{3a-2}\\ \stackrel{third}{c}=\stackrel{\textit{14 more than twice \underline{a}}}{2a+14} \end{cases} \\\\\\ \textit{now, the sum of all internal angles in a triangle is }180^o \\\\\\ a+b+c=\implies a+(3a-2)+(2a+14)=180 \\\\\\ 6a+12=180\implies 6a=180-12\implies 6a=168\implies a=\cfrac{168}{6} \\\\\\ a=28[/tex]


so a = 28°, plug that in "b" and "c", to see how much each is.

The equation y = 6.3x + 67.4 is the equation of a linear model in a scatter plot comparing the ages of boys between 2 and 10 years old open (x) and their average heights in centimeters open (y).

What is the average height of a 5-year-old boy?


98.9 cm


78.7 cm


67.4 cm


62.4 cm

Answers

Since the age of the boy is represented using x,
when the boy is 5 years old, x = 5.
y = 6.3x + 67.4
= 6.3(5) + 67.4
= 98.9

Since the average height of an age group is represented using y,
when y = 98.9, the average height of a 5-year-old boy is 98.9 cm.

The answer is 98.9 cm.

The average height of a 5 year old baby can be obtained by substituting the x and y values into the regression equation ; Hence, the average height of the baby is 98.9 cm

Given the linear regression equation :

y = 6.3x + 67.4

x = age of baby = 5 ; y = height of baby

The average height of a 5 year old baby is thus :

y = 6.3(5) + 67.4

y = 31.5 + 67.4

y = 98.9

Hence, the average height a 5 year old baby will be 98.9cm

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Which is 10^-5 written in standard form?

A. 0.00001
B. 0.0001
C. 10.000
D. 100.000

Answers

10^-5 = 0.00001

answer
A. 0.00001
the answer is A

negative -5 moves the decimal point to the right, making your scientific notation value smaller

The movement of the progress bar may be uneven because questions more on your answer. The price of a CD decreased from $15 to $12. What is the percent of decrease? 3% 20% 33% 75%

Answers

15 -12 = 3

3/15 = 0.2 = 20% decrease

Daniela finds the sum of two addenda. The sum is odd. Which statement is true about the addenda

Answers

write it with numbers please.

theses two questions are together

Answers

8 x 3 = 24

(x - 24) + 6 = change of water level

We cannot solve for the top question, because we need to know either the water level before the 8 days or the water level it had right when the problem was created (which is after the rain)

hope this helps
8(-3) + 6

8 x -3 is -24
-24 + 6 = -18 inches

How do I find slope?

Answers

To find the slope in the graph you need to find two perfect points on the line then count how many times you went up which is the y over how many times you go right which is the x its called the rise/run. To find the slope in the equation use the formula y2-y1/x2-x1.
The equation of any Straight line called a linear equation can be written as y=Mx+b where m is the slope is the slope of the line and b is the y-intercept

For what values of r does the function y = erx satisfy the differential equation y'' − 6y' + 2y = 0? (enter your answers as a comma-separated list.)

Answers

The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]

Further explanation:

Given:

The function is [tex]y = {e^{rx}}.[/tex]

The differential equation is [tex]y'' - 6y' + 2y = 0\,\,\,\,\,or\,\,\,\,\dfrac{{{d^2}y}}{{d{x^2}}} - 6\dfrac{{dy}}{{dx}} + 2y = 0[/tex]

Explanation:

The given function can be expressed as follows,

[tex]y = {e^{rx}}[/tex]

Differentiate the above equation with respect to [tex]x[/tex].

[tex]\begin{aligned}\frac{{dy}}{{dx}} &= \frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&= {e^{rx}} \times \frac{d}{{dx}}\left( {rx} \right)\\&= {e^{rx}} \times r\\&= r{e^{rx}}\\\end{aligned}[/tex]

Again differentiate with respect to [tex]x[/tex].

[tex]\begin{aligned}\frac{{{d^2}y}}{{d{x^2}}} &= \frac{d}{{dx}}\left( {r{e^{rx}}} \right)\\&= r\frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&=r\times {e^{rx}} \times\frac{d}{{dx}}\left( {rx} \right)\\&= {r^2}{e^{rx}}\\\end{aligned}[/tex]

Now solve the differential equation.

[tex]\begin{aligned}y'' - 6y' + 2y &= 0\\{r^2}{e^{rx}} - 6r{e^{rx}} + 2{e^{rx}} &= 0\\{e^{rx}}\left( {{r^2} - 6r + 2} \right) &= 0\\{r^2} - 6r + 2 &= 0\\\end{aligned}[/tex]

Solve the quadratic equation [tex]{r^2} - 6r + 2 = 0.[/tex]

[tex]\begin{aligned}D&= {b^2} - 4ac\\&={\left( { - 6} \right)^2} - 4\left( 1 \right)\left( 2 \right)\\&= 36 - 8\\&= 28\\\end{aligned}[/tex]

The value of [tex]r[/tex] can be obtained as follows,

[tex]\begin{aligned}r&= \frac{{ - b \pm \sqrt D }}{{2a}}\\r&=\frac{{ - \left( { - 6} \right) \pm \sqrt {28} }}{{2 \times 1}} \\ r &= \frac{{6 \pm 2\sqrt7 }}{2}\\r&= 3 \pm \sqrt7\\r&= 3 - \sqrt 7 \,\,\,\,\,\,\,or\,\,\,\,\,\,\,r = 3 + \sqrt7 \\\end{aligned}[/tex]

The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Derivatives

Keywords: Derivative, value of x, function, differentiate, minimum value, dy, compute, given value of [tex]x, y=6x, x=4, x=1[/tex]

In the solution to this system, what is the value of y?

x+y+z=1x+y+z=1

2x+y−z=82x+y-z=8

x−y+z=−5

Answers

If you have multiple equations with multiple variables, you can either do clever substitutions, or turn it into a matrix on which you can perform linear combinations or multiplications (Gauss elimination)

1  1   1  1
2  1  -1  8
1 -1   1  -5

(note how the above 3 rows represent the 3 equations, just got rid of the variables, plus sign and equals sign)

subtract row1 from row3, that eliminates x and z from row 3.

1  1   1  1
2  1  -1  8
0 -2   0  -6

divide row3 by -2, that will give y a factor of 1

1  1   1  1
2  1  -1  8
0 1   0  3

The last row now says y=3



Through any three noncollinear points, there is exactly one plane containing them. Points W, X, and Y are noncollinear.

Answers

Correct!

When thinking of what determines a plane we can make the following comparison.

If a plane was the top part of a table, 3 legs, whose tops are points W, X and Y may hold it, as shown in the first picture.

but if the legs are in a line, as in the second figure, they may not hold the top part, so 3 collinear points cannot determine a plane. 

Answer:

There is exactly one plane containing points W, X, and Y

Step-by-step explanation:

The distance between the two islands shown on the map is 210 miles. A ruler measures the distance on the map is three 1/2 inches how many miles would be represented by one 3/4 inches on the map?

Answers

210 miles equals 1 and 1/2 inches (3 1/2"s or 0.5"). 1 and 1/2" is equal to two 3/4" (3/4 + 3/4 = 1 and 1/2). 1.5" is equal to 210 miles, and 1.5" is equal to 2 * .75", you can divide 210 miles by two, which gives you 105 miles.

Simplify 13 + 2 - 5 - 15

Answers

you're answer is negative 5

13 +2 = 15 -5= 10 -15 = -5

Curly used a shovel to dig his own swimming pool. He figured he needed a pool because digging it was hard work, and he could use it to cool off after working on it all day. He also planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the deck?

Answers

check the picture below.

The area of the deck that is built around the pool is 1352 ft².

What is the area of the deck?

A rectangle is a 2-dimensional quadrilateral with four right angles.  

Area of a rectangle = length x width

Length = 14 + 6 + 6 = 26 Width = 40 + 6 + 6 = 52

Area = 26 x 52 = 1352 ft²

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What are the factors of the trinomial x^2+6x-7

Answers

x^2 + 6x - 7 =
(x + 7)(x - 1)
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