Answer:
338.63 ounces
Step-by-step explanation:
1=35.274
35.274 times 9.6 is 338.6304
House of Mohammed sells packaged lunches, where their finance department has established a
weekly relationship between its Revenue R, in dollars and the number of lunches x, as R=x(82−x)
(a) Write the revenue R, in the form R=ax2+bx+c (b) What is the revenue when 35 lunches are sold? (c) Explain why the graph of R has a maximum.
(d) Write R in the form a(x−h)2+k
(e) How many lunches must be sold for them to achieve their maximum revenue?
(f) State the company's maximum revenue.
(2 marks) (2 marks) (2 marks)
(5 marks)
(2 marks) (2 marks)
(g) Complete the following table of values and graph the Revenue equation using the ordered pairs
(x , R). Label the coordinates of the vertex.
x
10
20
30
40
50
60
70
80
90
R
( 10 marks)
The revenue function is a quadratic equation and the graph of the function
has the shape of a parabola that is concave downwards.
The correct responses are;
(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d) R = -1·(x - 41)² + 1,681(e) 41(f) $1,681Reasons:
The given function that gives the weekly revenue is; R = x·(82 - x)
Where;
R = The revenue in dollars
x = The number of lunches
(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;
R = x·(82 - x) = 82·x - x²
Which gives;
R = -x² + 82·xWhere, the constant term, c = 0
(b) When 35 launches are sold, we have;
x = 35
Which by plugging in the value of x = 35, gives;
R = 35 × (82 - 35) = 1,645
The revenue when 35 lunches are sold, R = $1,645
(c) The given function for R is R = x·(82 - x) = -x² + 82·x
Given that the leading coefficient is negative, the shape of graph of the
function R is concave downward, and therefore, the graph has only a
maximum point.
(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;
(h, k) = The vertex of the equation
a = The leading coefficient
The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;
R = x·(82 - x) = -x² + 82·x
At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;
[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]
Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]
The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681
Which gives;
(h, k) = (41, 1,681)
a = -1 (The coefficient of x² in -x² + 82·x)
The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41
Therefore;
The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681
The maximum revenue of the company is $1,681Learn more about the quadratic function here:
https://brainly.com/question/2814100
A study of more than 3,000 toco toucans found that their weights were approximately Normally distributed, with a mean
of 20 ounces and a standard deviation of 2.3 ounces. Let Y be the weight of a randomly chosen toco toucan. Which of
the following correctly interprets the value of P(Y < 16)?
Find the Z-table here.
O P(Y< 16) = 0.50. About 50% of all toco toucans weigh less than 16 ounces.
OP(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ounces.
O P(Y < 16) = 0.959. About 95.9% of all toco toucans weigh less than 16 ounces.
P(Y < 16) = 0.041. About 4.1% of the toco toucans from this group weigh less than 16 ounces.
O P(Y< 16) = 0.959. About 95.9% of the toco toucans from this group weigh less than 16 ounces.
Using the normal distribution, it is found that the correct option is:
P(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ouncesIn a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 20 ounces, hence [tex]\mu = 20[/tex].Standard deviation of 2.3 ounces, hence [tex]\sigma = 2.3[/tex]P(Y < 16) is the p-value of Z when X = 16, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 20}{2.3}[/tex]
[tex]Z = -1.74[/tex]
[tex]Z = -1.74[/tex] has a p-value of 0.041.
This is valid for the entire population, hence, the correct interpretation is:
P(Y< 16) = 0.041. About 4.1% of all toco toucans weigh less than 16 ouncesA similar problem is given at https://brainly.com/question/24663213
Define
Rough calculating
Answer:
A rough calculation or guess is approximately correct, but not exact. roughly adverb.
Step-by-step explanation:
Explain in your own words the steps to dividing decimals by decimals.
Please Help - Suppose f(t)=6t−8−−−−√.
(a) Find the derivative of f.
f′(t) =
-3/(sqrt(t-8)(t-8))
(b) Find an equation for the tangent line to the graph of y=f(t) at the point (t,y)=(33,6/5).
Tangent line: y =
[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]
(b)
[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]
Using powers of 10, which would be the best choice for the first number to subtract in the division problem 14,941 ÷ 98?
Answer:
0.152
Step-by-step explanation:
What is the solution to this problem
A mechanic is paid $61,490 in salary for a year. Assuming there are 26 pays in a year, what is her biweekly (average) salary? $30,745 $3,074.50 $1,182.50 $2,365
Answer:
$2,365
Step-by-step explanation:
Divide $61,490 by 26...
Express sin U as a fraction in simplest terms.
S
12
13
5
U
Answer:
12/13
Sine is opposite over hypotenuse. The opposite side of U is 12 and the hypotenuse is 13, so the answer is 12/13
Betty had 1 1/4 hours to finish a test. She was nervous and it took her 1/2 an hour to calm down. How much time did she have left to finish the test? Express the answer as a mixed number.
Answer:
Betty had 45 minutes to take her test in mixed number form it is
Step-by-step explanation:
1 hour
1/4 an hour = 15 minutes
1/2 an hour is 30 minutes
1 hr 15- 30= 45
45= 3/4 of and hour remaining to test
Can I get the answers for all the questions and if you can explain how you got it that would help PLSSSSS!!!!
You are designing a new, larger coral reef habitat that will stun visitors with its size and vibrant colors. The tank requires special glass to protect this delicate environment. The glass costs $25,000 + a 10% engineering fee + a 5% shipping fee. The shipping fee is calculated on the cost of the glass plus engineering charges. What is the total cost of the glass, including fees?
Answer:
$28,875
Step-by-step explanation:
First, we would have to find 10% of $25,000
10% of $25,000 = $2,500
Now, we have to add the 2 values together
$25,000 + $2,500 = $27,500
Now, we can find the shipping fee, since it includes the engineering fee
5% of $27,500 = $1,375
Now, we can add the shipping fee to find the total
$27,500 + $1,375 = $28,875
please help me on this, thank you
45 - 4 =41 and x is 20.5 or 20 1/2
Astudent built a scale model of his house using a scale in which 3 inches represents 15 feet.The height of his real house is 45 feet.What is the height of the scale model in inches?
NEED HELP ASAP
Answer:
9 inches
Step-by-step explanation:
11,16,21,...
Find the 43rd term.
Find the 43rd term.
Answer:
You add 5 each time so we just need to multiple 5 by 40 since we alredy have the first three terms.
40*5=200
21+200=221
Hope This Helps!!!
You wish to buy a new skateboard. To earn money, you sell your baseball cards to
your friends for $2.50 each. If the new skateboard costs $98, what is the minimum number
of baseball cards you will have to sell?
What is the value of x and y?
Answer:
x = 90y = 43Step-by-step explanation:
The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.
x° = 90°
__
The acute angles in a right triangle are complementary.
y° = 90° -47°
y° = 43°
4x+4 =
What is the answer to this please help
Answer:4(x+1)
Step-by-step explanation:
4x+1
The polygons are similar. Find the value of each variable.
[tex]\\ \sf{:}\dashrightarrow \dfrac{4}{x}=\dfrac{6}{9}[/tex]
[tex]\\ \sf{:}\dashrightarrow 6x=36[/tex]
[tex]\\ \sf{:}\dashrightarrow x=6[/tex]
#y
[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{12}{18}[/tex]
[tex]\\ \sf{:}\dashrightarrow \dfrac{y}{12}=\dfrac{2}{3}[/tex]
[tex]\\ \sf{:}\dashrightarrow 3y=24[/tex]
[tex]\\ \sf{:}\dashrightarrow y=8[/tex]
Here we go
4/x=6/94/x=2/32/x=1/3x=6And
y/12=12/1818y=12²18y=144y=8can someone plssssssss help me
Answer:quizlet helps
Step-by-step explanation:
Consider the functions f(x) = 10^x and g(x)= f(x+4)
How will the graph of the function g differ from the graph of f ?
A) the graph of the function g is the graph of function f shifted 4 units down
B) the graph of the function g is the graph of function f shifted 4 units to the right
C) the graph of the function g is the graph of function f shifted 4 units to the left
D) the graph of the function g is the graph of function f shifted 4 units up
Help ASAP please. I really need the answer as soon as possible
Answer:
y intercept is 6 and the rate of change is Y=3x+6
Step-by-step explanation:
Answer:
y intercept = 6
rate of change = -4
Step-by-step explanation:
the line hits the y axis at 6 so that is the y intercept
The line falls 4 and goes over 1
I hope this helps!!
I need some help please
The answer is A.
A negative x a negative equals a positive so the square root of a negative value cannot be a negative value.
What is the value of the expression 2/5m−1/3 when m = 3?
1/15
13/15
23/15
I don't know.
Answer:
13/15
Step-by-step explanation:
i took the test :)
Identify the range of values for x.
Answer: Overall, the steps for algebraically finding the range of a function are:
Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
Find the domain of g(y), and this will be the range of f(x). ...
If you can't seem to solve for x, then try graphing the function to find the range.
Step-by-step explanation:
Consider continuous functions f, g, h, and k. Then complete the statements.
The function that has the least minimum value is function (options) F, H, G, K
The function that has the greatest minimum value is function (options) F, H, G, K
.
It wouldn't let me post the answer. See images for the answer and explanation
The function that has the least minimum value is function F & the function that has the greatest minimum value is function K.
What are the minimum values of the functions?Given:
Consider continuous functions f, g, h, and k.A graph is given in the attached image.Find:
The function that has the least minimum value is function.the function that has the greatest minimum value is function.Solution:
From the question, we get;
[tex]h(x) = 2(x-1)^{2}[/tex]
⇒ h(x)min = 0
⇒ g(x)min = -5
⇒ f(x)min = -7
⇒ k(x)min = 7
So, f(x)min < g(x)min < h(x)min < k(x)min
Therefore, The function that has the least minimum value is function F & the function that has the greatest minimum value is function K.
To learn more about the minimum of functions, refer to:
https://brainly.com/question/9180672
#SPJ2
Please help with this question
Answer:
D
Step-by-step explanation:
The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.
-hope it helps
Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.
Step-by-step explanation:
You are delt 1 card from a 52 card deck. Find the probability that you are not dealt a 10
Answer:
Step-by-step explanation:
There are 4 tens.
There are 48 cards that are not a 10. The probability of drawing 1 of the 48 is
P(~10) = 48/52 which is quite high as you might imagine.
you bought a bottle of water for $0.50 then you sold it for $1.00 tell whether this is an increase or decrease and give the percent value changed
Answer:
increase by 100%
Step-by-step explanation:
100% of 0.5 is 0.5 therefore 0.5+0.5=1
PLEASE HELP!!! Find the Least Common Multiple of these two monomials:
12a^4b^2c^5 and 40a^3b^7c^1
Answer:
The least common multiple of 12a^4b^2c^5 and 40a^3b^7c^1, is 1
Step-by-step explanation: