Answer: 56%
Step-by-step explanation:
given data:
married women between 25 and 35 = 53%
working full time = 45%
married and working full time = 21%
Solution:
= 53% - 21%
= 32%
= 45% - 21%
= 24%
probability that she is working full time or married but not both
= 32% + 24%
= 56%
Solve for x.
0 ≤ 3x – 6 ≤ 18
Answer:
Inequality form: 2 [tex]\leq[/tex] x [tex]\leq[/tex] 8
Interval Notation: [2,8]
Step-by-step explanation:
Help mehhhhhh please!!!!!!!!!!!!
A family wants to build a rectangular garden on one side of a barn. If 600 feet of fencing is available to use, then what is the area of the largest garden that could be built?
(A) Define a function that relates the area enclosed by the fence (in 〖ft.〗^2) in terms of its length (in ft.)
(B) What is the practical domain of this function?
(C) What is the largest area that the fence could enclose?
Answer: (A) [tex]A=300l-l^{2}[/tex]
(B) Length varies between 1 and 150
(C) Largest area is 22500ft²
Step-by-step explanation: Suppose length is l and width is w.
The rectangular garden has perimeter of 600ft, which is mathematically represented as
[tex]2l+2w=600[/tex]
Area of a rectangle is calculated as
[tex]A=lw[/tex]
Now, we have a system of equations:
[tex]2l+2w=600[/tex]
[tex]A=lw[/tex]
Isolate w, so we have l:
[tex]2w=600-2l[/tex]
w = 300 - l
Substitute in the area equation:
A = l(300 - l)
A = 300l - l²
(A) Function of area in terms of length is given by A = 300l - l²
(B) The practical domain for this function is values between 1 and 150.
(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:
A' = 300 - 2l
Find the values of l when A'=0:
300 - 2l = 0
2l = 300
l = 150
Replace l in the equation:
w = 300 - 150
w = 150
Now, calculate the largest area:
A = 150*150
A = 22500
The largest area the fence can enclose is 22500ft².
1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
3. If the profit function for a product is P(x) = 3600x + 60x2 ? x3 ? 72,000 dollars, selling how many items, x, will produce a maximum profit?.
Answer:
a. The number of units which will minimize average cost is approximately 5,130 units.
b. The firm should produce 12,500 items, x, for maximum profit.
c. The number of items, x, that will produce a maximum profit is 60 items.
Step-by-step explanation:
Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:
1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?
The explanation to the answer is now given as follows:
1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
Given;
C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)
We first simplify (0.02x + 6)^3 as follows:
(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)
First, we have:
(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36
Second, we have:
(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)
(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216
(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216
(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216
Therefore, we have:
C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)
C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200
Therefore, the average cost (AC) can be calculated as follows:
AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x
AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)
AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)
Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:
0.032x + 10.08 - (43,300 / x^2) = 0
0.032x + 10.08 = 43,300 / x^2
X^2 * 0.32x = 43,300 – 10.08
0.32x^3 = 43,189.92
x^3 = 43,189.92 / 0.32
x^3 = 134,968.50
x = 134,968.50^(1/3)
x = 51.30
Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:
x = 51.30 * 100 = 5,130
Therefore, the number of units which will minimize average cost is approximately 5,130 units.
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
P(x) = R(x) - C(x) ……………. (3)
Where;
P(x) = Profit = ?
R(x) = 450x-1/100x^2
C(x) = 500 + 200x
Substituting the equations into equation (3), we have:
P(x) = 450x - 1/100x^2 - (500 + 200x)
P(x) = 450x - 0.01x^2 - 500 - 200x
P(x) = 450x - 200x - 0.01x^2 - 500
P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)
Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:
250 - 0.02x = 0
250 = 0.02x
x = 250 / 0.02
x = 12,500 items
Therefore, the firm should produce 12,500 items, x, for maximum profit.
3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?
Given;
P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)
Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:
3600 + 120x - 3x^2 = 0
Divide through by 3, we have:
1200 + 40x – x^2 = 0
1200 + 60x – 20x – x^2 = 0
60(20 + x) – x(20 + x) = 0
(60 – x)(20 + x) = 0
Therefore,
x = 60, or x = - 20
The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.
8(7q+6p+11) please help me
Answer:
56p + 48q + 88
Step-by-step explanation:
When you see parentheses in math, it usually means that you are distributing (multiplying).
So here you would multiply everything inside the parentheses by 8.
7q x 8 = 56q
6p x 8 = 48p
8 x 11 = 88
56q + 48p + 88
There are no like terms here so the answer cannot be simplified any further.
Can someone answer all of them please ;-;
[tex]\LARGE\leadsto\sf m \angle E=41°[/tex]
[tex]\LARGE\leadsto\sf m \angle F=41°[/tex]
No-9:-[tex]\LARGE\leadsto\sf m \angle T=60°[/tex]
[tex]\LARGE\leadsto\sf m \angle V=30°[/tex]
No-10:-[tex]\LARGE\leadsto\sf m\angle G =75°[/tex]
[tex]\LARGE\leadsto\sf m \angle H=60°[/tex]
[tex]\LARGE\leadsto\sf m \angle J=45°[/tex]
6.203x4.5
Help pls asap
Answer:
27.9135
Step-by-step explanation:
If f(x)= 3^x+ 10x and g(x) = 4x-2 find (f-g)(x)
Answer:
u may need a calculator
Step-by-step explanation:
7, 12, 10, 18, 13, 23, 29, 15, 16, 18, 15, 12, 20
find the outlier. explain your answer.
Answer:
29
Step-by-step explanation:
the rest of the numbers are closer to each other but if you plot these you see that 29 doesnt belong
Triangle JKL, shown below, is translated 7 units to the right
then reflected across the x-axis.
у
+6
K
+51
4
J
VL
*3
*2
1
-6 -5 -4 -3 -2 -1 0
*1 2 3 4 5 6
1
2.
3
5 6
What will be the new coordinates of point J, after the
triangle has been transformed?
Answer:
dont known sorry
Step-by-step explanation:
PLEASE ANSWER QUICK 20 POINTS!!!!!
what is the LCD of 1/3 and 1/4
log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)
I assume you're referring to the product,
[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]
Recall the change-of-base identity:
[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
where c > 0 and c ≠ 1. This means the product is equivalent to
[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]
and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to
[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]
What are the coordinates of the red dot?
O (2,5)
10
(5,2)
O (-5,2)
-5
0 (-5,-2)
Explain your thinking.
K
-10
-5
0
6
10
✓
Share with Class
- 10
Answer:
(5, 2)
Step-by-step explanation:
Coordinates of a point in a coordinate plane is usually written as (x, y). This point contains the value of x and its corresponding y value.
The red dot on the plane given, if you trace it down to the x-axis, it is at x = 5, while if you trace it horizontally against the y-axis, you'd have y = 2.
Therefore, the coordinates of the red dot is (5, 2).
The perimeter of a rectangle,p, is given by p =2L + 2W , where L is its length and w is its width what is the perimeter of a rectangle of length 15ft and width 15ft ?
Answer:
60ft
Step-by-step explanation:
multiple the length by 2
15 times two equals 30
multiple the width by two
15 times two equals 30
add the total lengths and widths
30 plus 30 equals 60
ans=60
Solve each proportion.
2/8=5/r+8
Answer:
r=-20/31
Step-by-step explanation:
1)divide the numbers
2) subtract 8 from both sides of the equation
1) Given: H is the midpoint of EG
mZE = mZG
G
D
Prove: ADEH - AFGH
H.
E
F
It is E
Duhhhhhhhhhhhhh
Perform the following food service calculation.
No of diners = 240 Meat served = meat with little bone
Amount of meat required?
A. 840
B. 600
C. 69
D. 96
Answer:C
Step-by-step explanation:
69 is the CORRECT answer
OWare
BD = ED, CD = FD, Prove BC = EF
HL postulate is the answer
Cliff's Rentals rents out jet skis. The hourly charge is $50. Marcus rented a jet ski for 3 hours and paid $165.
Which equation can be used to determine the price, P, for h hours? Pls help me
Answer:
50h + 3 = 165P
Step-by-step explanation:
the length of a rectangle is three times its width ,if the width is x cm. write down an expression of length in term of x
Answer:
L = 3x cm
Step-by-step explanation:
For this problem, let's consider the relation that is stated:
Length is 3 times as much as the width. The width is x cm.
Mathematically we can say the following:
L = 3W
W = x cm
So we can say the following about the length:
L = 3W
L = 3(x cm)
L = 3x cm
Cheers.
Points A and B are 200 mi apart.
Answer:
17*200/17+83
Step-by-step explanation:
Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other. The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?
The distance under the question is 17*200/17+83= 17*2 = 34 miles.
17+83 = 100 mph in the denominator is the relative speed of the participants, the rate of decreasing the distance between them.
200/17+83=200/100= 2 hours is the time before they meet.
therefore 17*200/17+83 is the time before they meet
Help! Write the equation of the line fully simplified slope-intercept form.
Answer:
the equation is y=-x+8
A science fair poster is a rectangle 4 feet long and 3 feet wide. What is the area of the poster in square inches?
Be sure to include the correct unit in your answer.
in
in?
in?
G
Х
?
In last Quiz, Ahmed answered 24 out of 30 questions correctly. In this quiz he answered 20 out of 24 questions correctly. On which quiz did Ahmed have better results?
Answer:
He scored better on the second test by a margin of 3%.
Step-by-step explanation:
Find the percentage of each one by dividing Ahmed's score / Total possible score
24/30 = 0.8 > move the decimal place over twice for % > 80%
20/24 = 0.83333 > move the decimal place over twice for % > 83%
He scored 3% better on the second test.
What subfield of mathematics requires the most spatial reasoning?
No answer needed, just need to get rid of all my points.
Answer:
brainlest?
Step-by-step explanation:
......
Answer: I looked it up and got a couple of answers of spatial reasoning. Don’t know if that helps but yeah thats what I got lol
Step-by-step explanation:
for algebra 2 please help <3
Answer:
A. 1
Step-by-step explanation:
✔️To find f(g(1)), first find g(1).
From the mapping given for g(x), the corresponding value of x = 1, is 0.
That is,
g(1) = 0
✔️Next is to find f(g(1)) by replacing x with 0 in f(x) = 3√x + 1
Thus:
f(g(1)) = 3√0 + 1
f(g(1)) = 0 + 1
f(g(1)) = 1
A trade-in is most closely related to which of the following?
a.
A down payment, because it reduces the amount financed.
b.
An interest payment, because it represents value given to the dealer.
c.
The list price, because it is derived from the price of a car.
d.
Amortization, because it is a way of paying for car financing.
Answer:c.
The list price, because it is derived from the price of a car.
Step-by-step explanation:
Tess is going to purchase a new car that has a list price of $29,190. She is planning on trading in her good-condition 2006 Dodge Dakota and financing the rest of the cost over four years, paying monthly. Her finance plan has an interest rate of 10.73%, compounded monthly. Tess will also be responsible for 7.14% sales tax, a $1,235 vehicle registration fee, and a $97 documentation fee. If the dealer gives Tess 75% of the listed trade-in price on her car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid.) ANSWER C
Answer: A. A down payment, because it reduces the amount financed.
Step-by-step explanation: I just took the quiz and got a 100%. Edge 2021
What is 0.76 as a fraction ?
76/100
76/10
76/1000
7/6
The percentage 0.76 when convert to fraction is: 76/100.
Conversion of percentage into quotient0.76 is a percentage which represent 76% when multiply by 100 calculated as:
0.76×100
=76%
Now 0.76 as a fraction or quotient will be 76/100 in which the numerator is 76 and the denominator is 100 and when you divide 76 by 100 we would arrive at 0.76.
Inconclusion 0.76 as a fraction is: 76/100.
Learn more about fraction here:https://brainly.com/question/1713644
in a company, 40% of the workers are women. If 1380 woman work for the company, how many total workers are there?
Answer:
Step-by-step explanation:
The total number of workers is our unknown. If 40% of this unknown number are women and the number of women is 1380, then the equation looks like this:
(remember that the word "of" generally means to multiply)
(also remember that we have to use the decimal form of a percent in an equation)
.40(x) = 1380 then divide to get the number of total workers:
x = 3450