Answer:
Sally earns graduated commission on her sales each month. She earns 6% commission on the first $45,000 in sales and 8% on anything over that. If Sally had $51,000 in sales this month, how much commission did she earn?
a. ) $4,080 b. ) $3,180 <<<CORRECT c. ) $3,060 d. ) $2,820
Step-by-step explanation:
Edge 2021
Is this table linear or not?
A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 lb/s. Find the work done in pulling the bucket to the top of the well. Show how to approximate the required work by a Riemann sum. (Let x be the height in feet above the bottom of the well. Enter xi* as xi.)
Answer:
Part A
The work done in pulling the bucket to the top of the well is 1,775 ft.·lb
Part B
By Reimann approximation, the work done is 2,130 ft.·lb
Step-by-step explanation:
Part A
The parameters of the filled bucket of water being pulled upwards are;
The mass of the bucket = 5 lb
The mass of the rope = Negligible
The mass of water that fills the bucket = 38 lb
The rate at which the bucket is pulled up = 1.5 ft./s
The rate at which the bucket leaks, l = 0.15 lb/s
The height in feet above the bottom of the well = x
Therefore, we have;
Height of the bucket, x = 1.5·t
The weight of the bucket after a given time, t, W = 38 - 0.15·t
The time it takes to pull the bucket to the top of the well, t = d/v = 50/1.5 = 100/3 s. = [tex]33.\overline3[/tex] s
We have;
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {F} \, dx[/tex]
x = 1.5·t, F = Weight of the bucket, W = 38 - 0.15·t
[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {(38-0.15\cdot t)} \, \cdot 1.5\cdot dt = \int\limits^{t = 33.\overline 3}_{t = 0} {(57-0.225\cdot t)} \, dt[/tex]
[tex]W = [57\cdot t - 0.225 \cdot t^2]_0^{33.\overline 3}[/tex]
Therefore, we have;
W = (57 × [tex]33.\overline3[/tex] - (0.225/2) × [tex]33.\overline3[/tex]²) - 0 = 1,775 ft.·lb
The work done in pulling the bucket to the top of the well, W = 1,775 ft.·lb
Part B
By summing the areas of the rectangular areas on the graph, we have
W = 10 × 38 + 10 × (38 - 0.1×10) + 10 × (38 - 0.1 × 20) + 10 × (38 - 0.1 × 30) + 10 × (38 - 0.1 × 40) + 10 × (38 - 0.1 × 50) = 2,130
Therefore, by left Reimann approximation, the work done, W = 2,130 ft.·lb
(More precisely, we have;
The weight at the bottom, F₁ = 38 lb.
The weight at the top of the well, F₂ = 38 - 0.15 × 100/3 = 33
∴ F₂ = 33 lb.
The average weight, [tex]F_{average}[/tex] = (F₁ + F₂)/2 = (38 lb. + 33 lb.)/2 = 35.5 lb.
Therefore, the work done, [tex]F_{average}[/tex] × d = 35.5 lb × 50 ft. = 1,775 ft.lb
The work done, W = 1,775 ft.lb)
please help me please help me please help
Answer:
a) September; b)October
Step-by-step explanation:
Just do the calculations, for example: 71+(-293). You will see September has a drop less 210 dollars and October has the biggest change of sales.
Can someone help me with the vertex of the parabola
Answer:
The vertex is (-1.5, 11.25)
Step-by-step explanation:
Find the unknown number 10% of what number is 300
Answer:3,000
Step-by-step explanation:
Answer:
3000
Step-by-step explanation:
300 x
10 100
300x100
30,000
30,000/10
3000
In a standard 52-card deck, half of the cards are red, and half are black. The 52 cards are evenly divided into 4 suits: spades, hearts, diamonds, and clubs. Each suit has three face cards (jack, queen, king), and an ace. Each suit also has 9 cards numbered 2 to 10.
Dawn removes two cards, without replacement.
What is the probability that Dawn removed two black cards?
What is the probability that Dawn removed a diamond and a spade?
What is the probability that Dawn removed two face cards?
Answer:
Byhrnegngrnhumhrnim jmmumtjmmtjmtj
Help
Which product are greater than 2 and 5\6? Select all that apply
Answer:
B, C, & E
Step-by-step explanation:
Find the volume of the cone.
Answer:
[tex]14.50[/tex]
...........
Pleaseeee help I'll give Brainliest urgent!!!!!!!!!!!!!!!!!
Answer:
The answer is
'The range of the data for girls is less than the range of the data for boys'
I'm don't know dfhgh fhfghfg hgf hgfh
Please help solve this!
how did you get 24/10?
Step-by-step explanation:
[tex] \tt{} \frac{24}{10} [/tex]
[tex] \tt{} \frac{24 \div 2}{10 \div 2} [/tex]
[tex]\tt{} \frac{12}{5} [/tex]
[tex]\tt{}2 \frac{2}{5} \: \: \: \: \: = 2.4[/tex]
Look at point w,x,y,and z on the number line
Answer:
u need toADD THE PITRUE
Step-by-step explanation:
Can someone please help meeeee
Answer:
45°
Step-by-step explanation:
The angle with measure of 9x and the angle with measure of 3x are supplementary
9x + 3x = 180°
12x = 180 divide both sides by 12
x = 15
The angle with measure of 9x and angle a are supplementary as well
9x + a = 180
9×15 + a = 180
135 + a = 180 subtract 135 ftom both sides
a = 45°
HELP SOON! Please!!!!
How does an outlier affect the mean of a population? The median? The range?
How can we adjust for the effects of outliers?
are z^3 and 3z equivalent expressions? explain.
Answer:
no, they are not.
Step-by-step explanation:
3z means a number multiplied by 3
so if z is 2, 3(2) = 6
but z^3 means z multiplied by z, and then multiplied by z again.
so if z is 2, it's 2x 2 = 4 x 2 = 8
let me know if you have questions
The two expressions are not equivalent to each other.
What are equivalent expressions?Equivalent expressions are expressions that are equal and synonyms to each other when used differently with various mathematical concepts.
From the expressions given:
z^33zThe first expression is a variable (z) raised to a power of 3. The power is also called an exponent.The second expression is a variable(z) that has a coefficient of 3Let us assume that:
z^3 = 3z
Now, let's replace 2 for the value of z on both sides, we have:
(2)^3 = 3(2)
8 ≠ 6
Learn more about equivalent expressions here:
https://brainly.com/question/2972832
if p and q are two different prime numbers then L.C.M is,
WILL MARK BRAINLIEST! Solve for x and each angles measure. Only asking for #5. Thank you!
Answer:
Step-by-step explanation:
2x + 3x + 135 = 180 Every triangle has 180 degrees
5x + 135 = 180 Subtract 135 from both sides.
5x = 45 Divide by 5
x = 9
2x = 18
3x = 27
Other angle 135
Total 280
‼️DIMENSIONAL ANALYSIS‼️
‼️ASAP!!! BRAINLIEST!!‼️
PLS HELP!!! SHOW ALL WORK +STEPS!! Thx!
Find the value of x. Pythagorean theorem and its converse
Function A and Function B are linear functions. Compare the two functions and choose all that are correct. Can someone help?
Answer:
(b) and (c) are true
Step-by-step explanation:
Given
Function A and B
First, calculate the slope of A
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{24 - -21}{8- -7}[/tex]
[tex]m = \frac{45}{15}[/tex]
[tex]m =3[/tex]
The equation of function A is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 3(x - 8) + 24[/tex]
[tex]y = 3x - 24 + 24[/tex]
[tex]y = 3x[/tex]
The general form of a function is:
[tex]y = mx + b[/tex]
Where [tex]m = slope[/tex] and [tex]b = y\ intercept.[/tex]
This implies that:
[tex]Slope = 3[/tex]
[tex]Y\ intercept = 0[/tex]
For function B:
[tex]y = 4x - 3[/tex]
[tex]Slope = 4[/tex]
[tex]Y\ intercept = -3[/tex]
By comparison:
(b) and (c) are true
builder is buying property where she can build new houses. The line plot shows the sizes of the lots for each house. What is the average size of the lots?
Answer:
I think she put it in the 2nd place because it has the smallest amount of x's , and 1 and 3 has more
On Monday, a local hamburger shop sold a combined total of 544 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the
number of hamburgers sold. How many hamburgers were sold on Monday?
Answer:
136 hamburgers
Step-by-step explanation:
Create an equation where x is the number of hamburgers sold.
The number of cheeseburgers sold can be represented by 3x, since it was 3 times the number of hamburgers.
3x + x = 544
Solve for x:
4x = 544
x = 136
So, 136 hamburgers were sold on Monday
Regina read his novel three nights in a row. Each night, he read for 3/4 of an hour. How many hours did regina read his novel altogether?
Answer:
Regina read for 2 1/4 hours or 2 hours and 15 minutes
Step-by-step explanation:
Select the correct answer.
Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y = 3:2 - 95 + 20
OA neither a relation nor a function
OB. both a relation and a function
OC function only
OD. relation only
Answer:
B. both function and relation
Step-by-step explanation:
Without performing the calculations, which expression equals the greatest value?
A)
2x (3-5)
B)
3x (
3-5)
)
5x (3-5)
D)
7x (3-5)
The 3rd term of an arithinetic progression is-9
and the 7th term is -29. Find the 10th term of the
progression.
Answer:
-64
Step-by-step explanation:
The computation of the 10th term of the progression is shown below:
The 3rd term is -9
A_n = a + (n - 1)d
-9 = a + (3 - 1)d
-9 = a + 2d
-9 - 2d = a
Now the 7th term is -29
A_n = a + (n - 1)d
-29 = a + (7 - 1)d
-29 = a + 6d
Put the a value to the above equation
-29 = -9 - 2d + 6d
-29 + 9 = 4d
-20 = 4d
d = -5
Now
-9 - 2d = a
-9 - 2(-5) = a
-9 - 10 = a
a = -19
Now finally the 10th term of the progression is
= a + (n - 1)d
= -19 + (10- 1)-5
= -19 -45
= -64
The function .... is symmetric with respect to what ?
Answer:
Reflection symmetry, lines of symmetry, mirror symmetry, mirror-image symmetry, are symmetry with respect to reflection. That is, a figure that does not change after undergoing reflection has re-symmetry
Please help me I wanna go to sleep :(
Answer:
a. -2
b. 48, -96, 192
Step-by-step explanation:
Which one is a unit rate?
sk
5 pounds in 2 bags
15 miles per gallon
$8.00 for 3 boxes of oranges
22gallons of water in 5 days
4. The teacher recommends that students read for 20
minutes each night. How many pages will the
student complete?
proportional relationships