Answer:
15. 80 benches
16. 45 cost units
Step-by-step explanation:
The two problems together are asking you to find the coordinates of the vertex of the cost function. To do this you can use the procedure for writing a quadratic in vertex form.
C(x) = 0.1x^2 -16x +685
= 0.1(x^2 -160x) +685 . . . . . . factor out the leading coefficient
= 0.1(x^2 -160x +6400) +685 -(0.1)(6400) . . . add and subtract 0.1(6400)
C(x) = 0.1(x -80)² +45 . . . cost function in vertex form
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15.The number of benches that minimizes the cost function is the x-coordinate of the vertex. That is the value that makes the square equal to zero.
x = 80 . . . benches
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16.The minimum value of the cost function is the value obtained when the squared term is zero:
C(80) = 0.1(80 -80)² +45
C(80) = 45
The minimum cost per bench is 45. (The problem statement gives no units for cost. It could be pesos, or millions of rubles. We can't tell.)
_____
Additional comment
The square of a binomial is ...
(x +a)² = x² +2ax +a²
You will notice that the constant (a²) is the square of half the x-coefficient. To "complete the square", we put the equation in a form where we have (x² +2ax) in parentheses. Then we divide the x-coefficient by 2, and add its square inside parentheses: (x² +2ax +a²) and rewrite to the form of a square: (x +a)².
In order to keep the expression the same, we must subtract the same quantity elsewhere in the equation. Outside parentheses, it must be multiplied by the coefficient in front of the parentheses. In the above, we added (0.1)(6400) and subtracted (0.1)(6400) so that we could rearrange the cost function to vertex form: a(x -h)² +k has vertex (h, k).
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We find a graphing calculator to be an extremely handy tool for dealing with polynomial functions. The attached shows the graph of the cost function. The calculator marks the vertex for us. Since it is a plot of cost versus number of benches, the units of the vertex are (benches, cost units).
the sum of two numbers is ten one number is five times the other
Answer:
let the other number be x.
then,X+5=10
X =10-5
X=5
Step-by-step explanation:
Math Questions about graph
Answer:
(i) gradient: 2/3
(ii) equation: y -1 = 2/3(x +1)
(iii) area: 10 square units
(iv) length: 4.12 units
Step-by-step explanation:
The gradient of a line is found by using the slope formula with two points on the line. The length between points is found using the distance formula, which is based on the Pythagorean theorem. The equation of a line can be written in several forms. One is the point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
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(i)The points A and B can be used in the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (5 -1)/(5 -(-1)) = 4/6 = 2/3
The gradient of the line is 2/3.
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(ii)Using the found slope in the point-slope equation with point A, we find the equation of the line to be ...
y -1 = 2/3(x +1)
__
(iii)The area of a triangle is found from the formula ...
A = 1/2bh . . . . . triangle with base b and height h
The base length will be the difference in x-coordinates of the horizontal segment AC: 4 -(-1) = 5.
The height will be the difference in y-coordinates from that horizontal segment and point B: 5 -1 = 4
Then the area of ABC is ...
A = 1/2(5)(4) = 10 . . . . square units
The area of ΔABC is 10 square units.
__
(iv)The length of BC is found from the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((5 -4)² +(5 -1)²) = √(1 +16) = √17
d ≈ 4.12 . . . . units
The length of BC is about 4.12 units.
Sarah wants to swim across a 193 m river. Due to the current she is swept 67 m downriver from where she wanted to be. What is the length that she actually swam from start to where she ended? Round to the nearest tenth
Answer:
Step-by-step explanation:
Sarah swam the diagonal length of a right-angled triangle with sides of river width, 193m and how far she was swept downstream, 67m.
By Pythagorean Theorem, distance swam = sqrt(193^2+67^2)
= 204.3 m
Apply Pythagorean theorem
[tex]\\ \rm\rightarrowtail H^2=P^2+B^2[/tex]
[tex]\\ \rm\rightarrowtail H^2=193^2+67^2[/tex]
[tex]\\ \rm\rightarrowtail H^2=41738[/tex]
[tex]\\ \rm\rightarrowtail H=204ft[/tex](Approx)
A teacher administers a standardized math test to his class of 75 students. The mean score (out of 300 possible points) is 235. From previous studies, you know the population standard deviation is 28.
a) Using the sample data given, calculate a 95% confidence interval for the population mean.
b) Based on this confidence interval would you agree that the true population mean is under 239? Explain. x=235
Answer: (228.7, 241.3)
Step-by-step explanation:
Two car rental companies have the following payment plans: Cart: $90 per week and 15c per kilometre Renta: $110 per week and 10c per kilometre What is the maximum whole number of kilometres that can be travelled in one week with Carz if it is to cost less than it would with Renta?
Using linear function concepts, it is found that the maximum whole number of kilometres that can be travelled in one week with Carz if it is to cost less than it would with Renta is of 399.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.For each car, Cart and Renta, the linear functions are given by:
C(k) = 90 + 0.15k
R(k) = 110 + 0.1k
Cart will cost less than Renta if:
C(k) < R(k)
Hence:
90 + 0.15k < 110 + 0.5k
0.05k < 20
k < 400
Hence, the maximum whole number of kilometres that can be travelled in one week with Carz if it is to cost less than it would with Renta is of 399.
More can be learned about linear function concepts at https://brainly.com/question/24808124
Solve for x please!
No links or trolls.
Answer:
help me
Step-by-step explanation:
Determine the area and perimeter and show your work please??
Find the geometric mean between 20 and 5
The answer is 10.
Step-by-step explanation:
I have the same question on some tests of mine
600x + 200y = 500x solve for x
yes thats all i need.
Answer:
x = -2y
Step-by-step explanation:
Simplifying
600x + 200y = 500x
Solving
600x + 200y = 500x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-500x' to each side of the equation.
600x + -500x + 200y = 500x + -500x
Combine like terms: 600x + -500x = 100x
100x + 200y = 500x + -500x
Combine like terms: 500x + -500x = 0
100x + 200y = 0
Add '-200y' to each side of the equation.
100x + 200y + -200y = 0 + -200y
Combine like terms: 200y + -200y = 0
100x + 0 = 0 + -200y
100x = 0 + -200y
Remove the zero:
100x = -200y
Divide each side by '100'.
x = -2y
Simplifying
x = -2y
hope this helps!
ibrahim
Please solve this in subtraction method
Will give brainliest!!
Answer:
x= 0 and y=1
Step-by-step explanation:
1st multiply the first equation by 3
3 (3x-2y=2)
9x-6y=6
multiply the next equation by 2
2 (5x-3y=3)
10x-6y=6
subtract equation 1 from 2
(10x-6y)-(9x-6y)=6-6
10x-9x-6y+6y=0
x=0
put X in equation 1
3 (0)-2y=2
-2y=2
y=-1
so X and y are 0 and -1 respectively
Dan pays £714. 73 a year on his car insurance. The insurance company reduces the price by 4. 1%. How much does the insurance cost now?Give your answer rounded to 2 DP
Answer:
[tex] \frac{4.1}{100} \times 714.73 = 29.30 \\ 714.73 - 29.30 = 685.43[/tex]
divide 4.1 with 100percent because per5 is always over 100 them multiply by the amount given
Step-by-step explanation:
subtract 29.30 from 714.30
subtract calculated amount from amount given
get yr final answer
Please help, I’ll mark your answer as brainliest.
Already answered here: https://brainly.com/question/26919792
Expand: (7m2 + 2m)2.
Answer:
[tex]49m^{4} +28m^{3} +4m^{2}[/tex]
Last Answer
Step-by-step explanation:
Answer:
[tex]49m {}^{4} + 28m {}^{3} + 4m {}^{2} [/tex]
explanation:
[tex]7m {}^{2} (7m {}^{2} + 2m) + 2m(7m {}^{2} + 2m) \\ \\ 49m {}^{4} + 14m {}^{3} + 14m {}^{3} + 4m {}^{2} \\ \\ 49m {}^{4} + 28m {}^{3} + 4m {}^{2} [/tex]l
]
Area of a circle. Please help!
Answer:
[tex]A = 50.24[/tex] Sq. M.
Step-by-step explanation:
Formula: [tex]A = \pi r^{2}[/tex]
[tex]A = \pi (4)^{2}[/tex]
[tex]A = 16\pi[/tex]
[tex]A = 16 (3.14)[/tex]
[tex]A = 50.24[/tex] Square Meters
Write a function rule for the table. (b is incorrect so please choose one of the other 3 answers.)
Answer: D
Step-by-step explanation: payment equals to money earned per hour (p=6.25h).
For the following system a) What is the value of x? b ) What is the value of y ?
Answer:
x = 12
y = -23
Step-by-step explanation:
to solve for this i think we have to do:
y = -3x + 13
-
y = -2x + 1
-----------------------
0 = -x + 12
-x = -12
x = 12
then i think.... i think you have to substitute to one of the equations
y = -3(12) + 13
y = -36 + 13
y = -23
then to check we substitute to the second equation
-23 = -2(12) + 1 ?
-23 = -24 + 1?
-23 = -23
A cylinder has a height of 20 centimeters and a radius of 11 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
7598.8 [tex]cm^{2}[/tex]
Step-by-step explanation:
v (volume) = π[tex]r^{2}[/tex]h
v = 3.14 x [tex]11^{2}[/tex] x 20
v = 3.14 x 121 x 20
v = 7598.8
Answer:
7598.8 cm³
Step-by-step explanation:
Given :-
height = 20 cm
radius = 11 cm
value of π = 3.14
Formula to be used :-
Volume of cylinder = πr²h
Inputting the values :-
V = 3.14 x 11 x 11 x 20
= 3.14 x 121 x 20
= 3.14 x 2420
= 7598.8 cm³
The sum of 4/5 and 1/10 is closer to 1/2 than to 1
What is the value
of 9 2/3 - 4 1/5
What is the sum of 547+31321? Enter your answer in the box as a mixed number in simplest form.
35+34
HE HE HE
STOP HERE AND ANSWER
I TOLD YOU TO STOP
FINE, YOUR FUNERAL!
69
69 (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x) (x_x)
London has a collection of 260 coins. How many coins represent 25% of her collection?
Answer:
65 coins
Step-by-step explanation:
Set this problem up with a porportion.
[tex]\frac{?}{260} \frac{25}{100}[/tex]
After that, cross multiple and divide.
25 times 260. Then divide by 100. That is then your answer.
Will give Brainliest!!!!!
Determine the solution to the system of equations below. Explain your reasoning.
The solution(s) for the provided graph are (0, 6) and (6, 0)
What is a solution of a graph?The solution of the system of equations is the intersection of the two equations.
Reasoning.In the image provided, we can see two solutions (intersection points) that are intersected by a line and a circle.
Those two solutions are:
(0, 6) and (6, 0)which choices are equivalent to the expression below √16 • √9
Answer:
12
Step-by-step explanation:
=> √16 • √9
=> Take square roots
=> 4 • 3
=> 12
Find P(C|Y) from the information in the table. A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 32, 6, 18, 56. The third column is labeled Y with entries 10, 5, 15, 30. The fourth column is labeled Z with entries 28, 25, 7, 60. The fifth column is labeled Total with entries 70, 36, 40, 146. To the nearest tenth, what is the value of P(C|Y)? 0. 4 0. 5 0. 7 0. 8.
The probability is the ratio of the favorable event to the total number of events. The P(C|Y) is 0.5. Then the correct option is B.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
According to the problem, the table is made
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Then the probability of will be
[tex]\rm P(C|Y) = \dfrac{15}{30}\\\\P(C|Y) = 0.5[/tex]
The P(C|Y) is 0.5. Then the correct option is B.
More about the probability link is given below.
https://brainly.com/question/795909
Tara has 4/5 kg of beads. She shares the beads evenly between 3 friends.
How many kilograms does each friend receive?
Answer:
[tex]\frac{4}{15}[/tex] kilograms
Step-by-step explanation:
We will take the total amount of beads and divide it by 3, since there are 3 friends.
[tex]\frac{4}{5}[/tex] kg / 3
[tex]\frac{4}{5}[/tex] kg * [tex]\frac{1}{3}[/tex]
[tex]\frac{4*1}{5*3}[/tex]
[tex]\frac{4}{15}[/tex] kg
Each friend recieves [tex]\frac{4}{15}[/tex] kilograms of the beads.
Student Guide (continued)
1) Using the regression calculator in your tool bar, create a scatterplot using your data set from step
1. Insert a screenshot of your scatterplot, or recreate it below.
The photo shows the 10 students I chose please Help!
so the scatterplot will more or less look like the one in the picture below.
The sum of twice a number and 5 is 21. What is the number?
Hello.
First, "twice a number" means we multiply 2 times that number.
Let the number be s.
Now, the sum of 2 times s and 5 is 21.
The product of 2 and s can be written like so:
[tex]\sf{2s[/tex]
Now, the sum of 2s and 5 is 21:
[tex]\sf{2s+5=21[/tex]
Subtract 5 from both sides:
[tex]\sf{2s=21-5[/tex]
[tex]\sf{2s=16}[/tex]
Now, divide both sides by 2:
[tex]\Large\boxed{\sf{s=8}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
x = 8
Step-by-step explanation:
Let the required number be x.
According to the given question,
=> 2x + 5 = 21
=> 2x = 21 - 5
=> 2x = 16
=> x = 16/2
=> x = 8
Hope it helps you!!Mila built a wooden toy bin with a lid to sell in her store. The bin is shaped like a rectangular prism and measures 2 feet long,1 foot wide,and 2 feet deep. To make the wood darker,she stained the outside of the toy bin including the top of the lid and the bottom of the bin. What is the area that mila stained?
The rectangular prism having a length of 1 feet, width of 2 feet and that
is 1 feet deep, gives the area Mila stained as 8 square feet.
How can the area that Mila stained be found?The given dimensions of the rectangular prism bin are;
Length of the bin = 2 foot
Width of the bin = 1 feet
Depth of the bin = 2 feet
Required:
The surface area of the rectangular prism bin.
Solution:
The surface area, S. A., of the rectangular prism bin is given as follows;
S. A. = Length × Width + Depth × Width + Length × Depth
Which gives;
S. A. = 2 × 1 + 2 × 1 + 2 × 2 = 8
The surface of area Mila stained, S. A. = 8 ft.²Learn more about surface area of a rectangular prism here:
https://brainly.com/question/987829
given that x=6 and y= -4
3x + x over y - y^2
Step-by-step explanation:
x=6
y=-4
3x+x / y-y^2
3(6)+6/-4-(-4)^2
24/-20
= -1.2