The system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop is
b + c = 68
b + c = 680.08b + 0.15c = 6
Given:
Total amount paid = $6.00
Total copies = 68
cost of black-and-white copy = $0.08
cost of color copy = $0.15
let
number of black-and-white copies = b
number of color copies = c
The equation:
b + c = 68
b + c = 680.08b + 0.15c = 6
Therefore, the system or equations can be used to find b, the number of black-and-white copies,
and c, the number of color copies that the customer paid for at the print shop is
b + c = 68
b + c = 680.08b + 0.15c = 6
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I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone explain how to solve this definite integral?
First, look for the zeroes of the integrand in the interval [0, 6] :
x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4
Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.
• For x in (0, 2), take x = 1. Then
x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
• For x in (2, 4), take x = 3. Then
x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0
so x² - 6x + 8 < 0 over this sub-interval.
• For x in (4, 6), take x = 5. Then
x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0
so x² - 6x + 8 > 0 over this sub-interval.
Next, recall the definition of absolute value:
[tex]|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}[/tex]
Then from our previous analysis, this definition tells us that
[tex]|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}[/tex]
So, in the integral, we have
[tex]\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx[/tex]
Then
[tex]\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3[/tex]
[tex]\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43[/tex]
[tex]\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3[/tex]
and the overall integral would be
20/3 - (-4/3) + 20/3 = 44/3
PLEASE HELP ME!!!!!
Laura earns an hourly rate of $14.50 for the first 40 hours that she works in a week. She earns one- and-a-half times her hourly rate for any hours over 10. If she earned $775.75 in one week, how many hours did she work?
a. 35.7
b. 53.5
c. 45
d. 49
Answer:
I'm not 100% sure but I believe the answer is A
The total hours of work done by Laura is 39 hours.
What are Mathematical operators?A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:
Operands: Operands are the numbers that an operator uses. The terms that are given to the operands vary according to the kind of operation.
Given the hourly income Laura = $14.50
total hours she works in a week = 40
increase in rate after working after 10 hours is 1.5 times
the hourly rate after 10 hours = 14.50 x 1.5 = $21.75
amount earned in 10 hours = 10 x 14.5 = $145
total earning = $775.75
the amount left after reducing the amount of 10 hours = 775.75 - 145 = $630.75
$630.75 is earned in = 630.75/21.75 hours = 29 hours
total hours Laura worked = 10 + 29 = 39 hours.
Hence Laura worked 39 hours in a week.
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The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges.
Private colleges: 52.8, 43.2, 45.0, 33.3, 44.0, 30.6, 45.8, 37.8, 50.5, 42.0.
Public colleges: 20.3, 22.0, 28.2, 15.6, 24.1, 28.5, 22.8, 25.8, 18.5, 25.6, 14.4, 21.8.
Required:
a. Based on your computation of the two sample means and the two sample standard deviations, find the degrees of freedom.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
3. Vocabulary Suppose △MNP ∼△RST. How can you identify corresponding parts?
4. Reasoning Suppose △ABC ∼△TUV. Determine whether each pair of measures is equal.
a. the measures of ∠A and ∠T
b. the perimeters of the two triangles
c. the ratios of the sides BC/UV and AC/TV
5. Reasoning e scale of a map is 1 in. : 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.
Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.
(3) Corresponding sides of △MNP and △RST
Given that △MNP ∼△RST.
This means that, the corresponding sides are:
MN and RSMP and RTNP and ST(4) The equal measures
Given that △ABC ∼△TUV
This means that, the corresponding angles are equal, but corresponding sides are not.
So, the equal measures are:
(a). the measures of ∠A and ∠T (c). the ratios of the sides BC/UV and AC/TVThe unequal measure is:
(b). the perimeters of the two triangles(c) Scale mapping
The scale mapping is given as:
[tex]Ratio = 1\ in : 100\ mi[/tex]
The above scale means that 1 inches on the scale represents 100 miles of the actual distance.
Take for instance, 5 inches would represent 500 miles.
500 is 5 times 100
Hence, the actual distance between two towns 100 times the map distance between the two towns
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Simplify:
(8)214+(8)(−12)
plz help :(
3.8×102+1.7×103 giving answer in standard form
Answer: 5.15 x 10^2
Step-by-step explanation:
3.8 x 103 + 1.7 x 103 = 5 x 103 = 515 = 5.15 x 10^2
The table shows the proof of the relationship between the slopes of two parallel lines. What is the missing reason for step 2?
A.
Pythagorean theorem
B.
application of the distance formula
C.
application of the slope formula
D.
transitive property
The missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As we know,
Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
From the graph of two parallel lines:
r ║ s
The slope is the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
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Help help help help
Answer:
-1
Step-by-step explanation:
a jar has 654 jelly beans emily says the jar has 710 jelly beans, Find the percent error of emily's estimate
Answer:0.07% because 710-654 is 56 and 56 divided by 710 is 0.07
Answer:
8.56%Step-by-step explanation:
Find the difference between the actual and estimate, this is the error:
710 - 654 = 56Find the percent error, which is the error over the actual:
56/654*100% = 8.56%4.A counterexample can be used to show that a conjecture is false. Below are three
conjectures students made after visiting a zoo. Write a counterexample that shows that each
conjecture is false.
a. There are always more elephants in a zoo than giraffes.
TS
b. The oldest leatherback sea turtle in captivity is 33 years old.
c. American bison are never over 6 feet tall.
Answer:
Step-by-step explanation:
1. In some zoos the are more elephants than giraffes, then this conjecture can be true sometimes, however, this can not always be true because some zoo could have more giraffes
2. This can be true unless that turtle ages, or another is found that is taken into captivi9ty and found to be older
3. While most American bison are usaually below 6 feet, that is no gureantee there is no occasaional taller American Bison.
I do not know if these meet your teacher's starndard, but I hope they do. Please thanks and rate!
You go to a restaurant and get a bill for $95. You need to tip the waitress. The service was good so you decide on tipping the waitress 20%. What is the tip that the waitress will receive
Answer:
19 dollars.
Step-by-step explanation:
0.20 x $95.00=$19.00.
1 1/2 - 1/2 pls helpppppppppp
Answer:
It would be 1 whole
Step-by-step explanation:
1/2 - 1/2 is 0 the only thing left is one whole
help with this please i dont understand?
a) Evaluate the given function at each value of x. We have f(x) = 2x + 3.
• If x = -2, then
f(-2) = 2 (-2) + 3 = -4 + 3 = -1
• If x = -1, then
f(-1) = 2 (-1) + 3 = -2 + 3 = 1
• If x = 0, then
f(0) = 2 (0) + 3 = 0 + 3 = 3
and so on.
b) Kind of a silly question. Of course f(x) is a function, the instructions for part (a) say so!
But the real reason f(x) is indeed a function is that no single value of x returns more than one value of f(x).
4e-4=e-4
help me plsssssssssssssssssssssss
Answer:
E= 0 Good luck answering the other questions :)
Step-by-step explanation:
A man buys an article for $600 and sells it for $710. what is his profit or loss
Answer:
Profit of $110
Step-by-step explanation:
$710-$600=$110
Find the difference. 2/5(d-10)-2/3(d+6)
[tex]\dfrac 25(d-10) - \dfrac 23(d+6)\\\\\\=2 \left(\dfrac{d-10}5 - \dfrac{d+6}3 \right)\\\\\\=2\left[\dfrac{3(d-10) - 5(d+6)}{15}\right]\\\\\\=2 \left( \dfrac{3d-30-5d-30}{15} \right)\\\\\\=2\left(\dfrac{-2d-60}{15} \right)\\\\\\=2(-2) \left(\dfrac{d+30}{15} \right)\\\\\\=-4 \left(\dfrac{d+30}{15} \right)\\\\\\=-4\left(\dfrac d{15} +2 \right)\\\\\\=-\dfrac{4d}{15}-8[/tex]
How do I subtract fractions? Please explain step by step to get marked as brainliest
Answer: Here I hope this helps!
Step-by-step explanation:
For example lets work with this fraction
[tex]\frac{6}{5} -\frac{3}{7}[/tex]
First you need to find a common denominator. (The number at the bottom of the fraction always.)
Multiply until you get a number both denominators go into.
For this it would be 35.
[tex]\frac{6}{5} -\frac{3}{7}[/tex]
5x7=35 7x5=35
You then have to do the same to the top as you did the bottom.
So multiply your numerators (number at the top) the same number as you did to the denominator below it.
[tex]\frac{6}{5} -\frac{3}{7}[/tex]
So 6x7=42.
And 3x5=15
You then subtract the numerators.
42-15=27
So now you have [tex]\frac{27}{35}[/tex]
[tex]\frac{6}{5} -\frac{3}{7}[/tex] =[tex]\frac{27}{35}[/tex]
Hope this helps! Have a great day!!
A company tests two new products to make sure they last for more than a year. Product 1 had 950 out of 1,000 test items last for more than a year. Product 2 had 150 out of 200 last for more than a year. If you had to choose one of these two products to use for more than a year, which one is more likely to last? Explain your reasoning
30 POINTS GIVE GOOD ANSWER
Answer:
product one; it has a higher success rate
Step-by-step explanation:
to find out which has a higher rate of success we can find out their percentage of success
we can divide their success amounts by test amounts
950 / 1000 = 95/100 = 95%
150/200 = 75/100 = 75%
product 1 has a higher success rate
The product is more likely to last is mathematically given as
Product 1
What product is more likely to last?
Question Parameter(s):
Product 1 had 950 out of 1,000 test
Product 2 had 150 out of 200 test
Generally, the equation for the percentage success is mathematically given as
Product 1 950 / 1000 = 95/100 x 100 = 95%
Product 2 150/200 = 75/100 x 100 = 75%
In conclusion, the product is more likely to last is
Product 1
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Find the value of a
I’m decided go between 40 and 6.4
Please help me solve this
Answer:
Solve what?
Step-by-step explanation:
You didn't put the question.
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
Answer:
x-intercept: 4
y-intercept: -4
Step-by-step explanation:
Hope this helps. Plz give brainliest! Also, plz sub to kgirl633 on yt!
x - y = -4
-5 + 6y = 22
The answer is (-2,2) but i just need to show the work for it so please help with that.
Answer:
(-2, 2).
Step-by-step explanation:
x - y = -4
-5x + 6y = 22 Multiply the first equation by 5:
5x - 5y = -20 Now Add the last 2 equations:
y = 2.
Substitute y = 2 in the first equation:
x - 2 = -4
x = -4 + 2
x = -2.
Answer:
x=1/2, y=9/2. (1/2, 9/2).
Step-by-step explanation:
x-y=-4
-5+6y=22
--------------
y=x-(-4)
y=x+4
-5+6(x+4)=22
-5+6x+24=22
6x+24-5=22
6x+19=22
6x=22-19
6x=3
x=3/6
x=1/2
y=1/2+4=1/2+8/2=9/2.
How would the model and answer in the example problem change if Felicia lives 7/10 miles from the soccer field???
Step-by-step explanation:
step 1: simplify both sides of the equation.
7x+8(x+
1
4
)=3(6x−9)−8
7x+(8)(x)+(8)(
1
4
)=(3)(6x)+(3)(−9)+−8(distribute)
7x+8x+2=18x+−27+−8
(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)
15x+2=18x+−35
15x+2=18x−35
tep 2: subtract 18x from both sides.
15x+2−18x=18x−35−18x
−3x+2=−35
step 3: subtract 2 from both sides.
−3x+2−2=−35−2
−3x=−37
step 4: divide both sides by -3.
−3x
−3
=
−37
−3
x=
37
3
Answer:
what the
Step-by-step explanation:
It took Erika 8 games to score 30 points. At that rate, how many games will it take her to score 45 points?
Answer : 12 games
Step - by - step explanation :
In - order to find out how many games it will take Erika to get 45 points we need to find out how many points she normally gets in 1 game . . .
What is 30 divided by 8 ? 3.75 ( So Erika gets 3.75 points per game ! )
What is 45 divided by 3.75 ? 12 ( So Erika had to play 12 games in - order to get 45 points ! )
An angle measures 157.2° more than the measure of its supplementary angle. What is the measure of each angle?
Two supplementary angles equal 180 degrees
Subtract the difference from 180:
180-157.2 = 22.8
Divide by 2:
22.8 /2 = 11.4
One angle is 11.4
Now add the difference to 11.4
11.4 + 157.2 = 168.6
The second angle is 168.6
Answer: 11.4 and 168.6
Can you simplify these two?
5 points for each.
Answer:
See attached files.
The answers are there.
I need help plz.....
Answer:
(c) y^2/16 -(x -7)^2/9 = 1
Step-by-step explanation:
The center, focus, and vertex are on a vertical line, so the hyperbola opens in the direction of the y-axis. The y-term will have the positive coefficient.
The vertex-center distance in the y-direction is 4, so the denominator of the y-term is 4^2 = 16. The denominator of the x-term is 5^2 -16 = 9, where 5 is the center-focus distance.
The equation is ...
y^2/16 -(x -7)^2/9 = 1
The price of a bicycle is $108.00 plus 7% sales tax. What is the sales tax on this bicycle in dollars and cents?
Answer:
$7.56
Step-by-step explanation:
7% = 0.07
108.00 x 7% = $7.56
67*25 helpppp pleaseeee
Answer:
1675
Step-by-step explanation:
do people not have calculators?
PLEASE HELP ME please please
Answer:
if its before bed time I think it is A
Step-by-step explanation: