Answer:
Step-by-step explanation:
The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:
[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and
[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.
x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.
Our variables for the quadratic are as follows:
a = -10
b = 600
c = -3588. Therefore,
[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:
[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:
[tex]k=-3588-(\frac{360000}{-40})[/tex] and
k = -3588 - (-9000) and
k = -3588 + 9000 so
k = 5412
That means that the profit made by selling the widgets at $30 apiece is $5412.
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
What is the maximum profit?
Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.
Here given that,
A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.
As the maximum profit found in the vertex of the parabola,
Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.
The number of items sold is [tex]x[/tex].
So, the quadratic equation is:-
[tex]a = -10b = 600c = -3588.[/tex]
Therefore, so the cost of each widget is $[tex]30[/tex].
For the profit:-
[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
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A train travelled 275 km in 2.5 hours how fast will the train go in an hour?
!!!!!!!!!
Answer: 110 mph
Step-by-step explanation: 275 / 2.5 = 110 mph
1.-Responde la pregunta: ¿para qué
me sirve el teorema de Pitágoras en la.
vida cotidiana?
Answer:
Respuesta. Respuesta: El Teorema de Pitágoras sirve para resolver una multitud de problemas; por ejemplo de, cálculo de distancias en el plano, en los mapas, en la realidad. ... En general, el Teorema de Pitágoras se puede utilizar para hallar longitudes en donde intervienen triángulos rectángulos.
The zeroes of the function are:
A) -2 and 0
B) 0 and 4
C) -2, 0, and 4
17. The hourly temperature at Portland, Oregon, on a particular day is recorded below.
1 A.M. 2 3 4 5 6 7 8 9 10 11 12 Noon
46° 44° 43° 41° 40° 40° 41° 43° 46° 52° 65° 69°
1 P.M. 2 3 4 5 6 7 8 9 10 11 12 Midnight
72° 74° 75° 75° 77° 75° 74° 70° 62° 55° 51° 48°
a. Find the amplitude of a sinusoidal function that models this temperature variation.
b. Find the vertical shift of a sinusoidal function that models this temperature variation.
c. What is the period of a sinusoidal function that models this temperature variation?
d. Use t = 0 at 5 P.M. to write a sinusoidal function that models this temp. variation.
e. What is the model’s temperature at 10 A.M.? Compare this to the actual value?
Answer:
a. Amplitude: 19.65446
b. Vertical Shift: 58.00713
c. Period: 2/0.22797 = 27.56146
d. 19.65446 * sin(0.22797x + 1.79552) + 58.00713
e. Model's Temperature at 10 A.M.: f(-7) = 61.91
This value is 9.91 degrees higher than the actual value.
Step-by-step explanation:
With 1 am being timed as t = 1, we fitted the temperature data collected at different points during the day in Portland, Oregon using sine regression. After receiving the sine function, we respond to the many questions connected to the sine function's properties.
What is sinusoidal Function?A smooth, repeating oscillation characterizes a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that may be described by sinusoidal functions.
Given, The hourly temperature at Portland, Oregon, on a particular day is recorded.
Using sine regression on the given data with t = 1 being the hour 1 am etc, we get the following sine regression formula using the TI-83 Graphing Calculator where T is the temperature:
T = a sin(bt + c) + d
Where a = 19.65, b = 0.28, c = -2.93, d = 58.01
From the sine regression function above:
a. The amplitude of the sinusoidal function is a = 19.65.
b. The vertical shift is d = 58.01.
c. The period is 2*pi /b = 2*pi/ 0.28 = 22.44
d. At 5 PM, the time value is t = 17. Hence the temperature distribution with 5 PM being t = 0 will be
t = asin[b(t - 17) + c] +d.
e. From the table, at 10 AM, the actual value of the temperature is 52 degrees.
Using the model in part a., at 10 AM, with t = 10, the temperature will be
T = a sin(10b + c) + d
T = 55.46 degrees
Learn more about sinusoidal functions here:c. The period is
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Complete question:
Find the Sum:
(20 - 6) + 3(c + 8)
Answer:
38 + 3c
Step-by-step explanation:
Apply the distributed property: (20 - 6) + 3c + 2420 - 6 = 14Plug 14 in: 14 + 3c + 24Combine like terms: 38 + 3cI hope this helps!
Perform the indicated operation.
Answer:
[tex] g(3) - h(3) = -16 [/tex]
Step-by-step explanation:
Given:
[tex] g(x) = 2x - 5 [/tex]
[tex] h(x) = 4x + 5 [/tex]
Required:
[tex] g(3) - h(3) [/tex]
SOLUTION:
Substitute x = 3 into [tex] g(x) = 2x - 5 [/tex]
[tex] g(3) = 2(3) - 5 [/tex]
[tex] g(3) = 6 - 5 [/tex]
[tex] g(3) = 1 [/tex]
Substitute x = 3 into [tex] h(x) = 4x + 5 [/tex]
[tex] h(3) = 4(3) + 5 [/tex]
[tex] h(3) = 12 + 5 [/tex]
[tex] h(3) = 17 [/tex]
Therefore:
[tex] g(3) - h(3) = 1 - 17 = -16 [/tex]
What is the measure of BDC
Answer:
105 degrees
Step-by-step explanation:
180 - 75 = 105
In the accompanying diagram, line a intersects line b.
Answer:
C. 10
Step-by-step explanation:
[tex] (x + 5) = (2x - 5) [/tex] (vertical angles are congruent)
[tex] x + 5 = 2x - 5 [/tex]
Add 5 to both sides
[tex] x + 5 + 5 = 2x [/tex]
[tex] x + 10 = 2x [/tex]
Subtract x from both sides
[tex] 10 = 2x - x [/tex]
[tex] 10 = x [/tex]
[tex] x = 10 [/tex]
Use the figure to find the measures of the numbered angles.
Answer: 5=49, 6= 131
Step-by-step explanation:
Last year, 450 people attended the Booster Club Breakfast. This year the number of people attending increased by 6%. Find the number of people who attended the breakfast this year.
Answer:
I'm pretty sure it's 477
Step-by-step explanation:
if you subtract 19 from my number and multiply the difference by -2, the result is -8
Answer:cool
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
let the number be 'a'
-2(a - 19)= -8
open the brackets
-2a + 38 = -8
collect like terms
38 + 8 = 2a
46 = 2a
a = 23
if caramel is put onto a sphere-shaped apple such that the surface area increase at a rate of 10 cm2/min, find the rate at which the diameter increases when the diameter is 15cm
Answer:
The diameter will increase at a rate of 1/30π cm/min
Step-by-step explanation:
Here we want to calculate the rate at which the diameter will increase
Mathematically, the area of a sphere is given as;
A = 4πr^2
But r = d/2
so A = 4 * π * d/2 * d/2 = πd^2
dA/d(d) = 2πd
Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π
Given dA/dt = 10
Mathematically;
d(d)/dt = d(d)/dA * dA/dt
dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min
I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?
Answer:
18
Step-by-step explanation:
The tens digit a is cubed (a³ ) still less than the biggest possible 1 -digit number . It can be only 0 or 1 , so even 2³ =8 ( in such case the unit digit is 15,- that's not possible) .
0 can not be the the first digit in 2 digit number. So the only possible tens digit is 1. So the unit number is 1+7=8.
Answer 18
Answer:
18
Step-by-step explanation:
Written as a rate, 96 miles in 12 hours would be ____ miles per hour.
Answer:
8 Miles per hour
Step-by-step explanation:
Answer:
8 miles per hour
Step-by-step explanation:
miles / hr = 96/12 = 8 miles per hr
hr / mile = 12/96 = 1/8 hr per mile <==
The price of a pack of steaks increased from $15 to $21. By what percentage did the price of the pack of steaks increase?
Step-by-step explanation:
21 - 15 = 6$
you have to find how many percent is 6$ in 15$
6 ÷ 15 = 0.4
15 × 0.4 (40/100)
= 6
40 percent
A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?
O $1.26
O $5.40
O $19.26
O $30.60
Answer:
1
Step-by-step explanation:
1.26
Factor out the coefficient of the variable term. The expression 1/7a + 1/7 factored is___
Answer:
17 and [a+1] is the factor
Step-by-step explanation:
Given:
1/7a + 1/7
Find:
Factor
Computation:
1/7a + 1/7
By taking 1/7 as a common
1/7[a+1]
So,
17 and [a+1] is the factor
The coefficient of the variable term in factored form is; 1
The given expression is;
(1/7)a + 1/7
Now, we want to factorize this and this means that we will bring out the common factor of both terms.
The common factor of both terms is 1/7. Thus, we have;
(1/7)(a + 1)
The variable term is a and as such we see that it's coefficient inside the bracket is 1.
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What do you think about raising the minimum wage? What do you think would be some negative outcomes of raising the minimum wage? What are some positive outcomes of raising the minimum wage
Find the next number in the pattern given below
-10, -2, 6, ____
please i’ll give you brainly thingy
Answer:
it would be 12
Step-by-step explanation:
divided 12.25 by 12 and it gives you 1.0 giving you the lowest out of all of them when doing the math
Answer:
D. 12
Step-by-step explanation:
8. The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving for a business trip to Boston and will cat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the meal cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. a) What is the probability that none of the meals will exceed the cost covered by your company
Answer:
0.2637
Step-by-step explanation:
Population size is top 15 ranking restaurants.
Number of draws = 3
Number of observed successes = 5
Probability formula : [r . x } { n -r] [n - x]
solving the equation we get 24 / 91 which is approximately 0.2637
PLEASE QUICK BRAINLISET
Answer: the answer is f
Answer:
F
Step-by-step explanation:
the measure of angle one must be equal to the measure of angle five and when doing the math I got x=34 plug that into the equation for angle five i got 48 and the same for plugging it into the equation for angle one.
HELP FAST. I NEED THIS ANSWER FAST
Answer:
abunda la caca
( its 10m*9y)
Step-by-step explanation:
Answer:
First find the cubes and squares of the 1st and 2nd expression.
1st expression ⇒ [tex](-\frac{2}{3} x^2y)^3 = -\frac{8}{27}x^6y^3[/tex]
2nd expression ⇒ [tex](-\frac{3}{4}xy^2)^2 = -\frac{9}{16}xy^4[/tex]
Now you all you need to do is multiply the 1st expression to 2nd expression.
[tex]-\frac{8}{27}x^6y^3*-\frac{9}{16}xy^4\\\\= \frac{72}{432} x^7y^7[/tex]
What is the y intercept of the line graphed on the grid? (-6, -8) (2,-2)
Did this today on a test lol.
(0,-7/2)
Pls help for Algebra 11b = 143
Answer:
b = 13
Step-by-step explanation:
Divide 143 by 11
Can you help me solve this
Answer:
A number that is 10x greater than 0.03 is 0.3.
Step-by-step explanation:
Answer:
The answer is c have a nice day
(01.02 MC)Which number line shows the solution to −6 − (−2)?
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 4 is shown.
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 8 is shown.
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to 6 is shown. Above this, another arrow pointing from 6 to 4 is shown.
Given:
The expression is
[tex]-6-(-2)[/tex]
To find:
The solution of given expression on the number line.
Solution:
We have,
[tex]-6-(-2)=-6+2[/tex]
[tex]-6-(-2)=-4[/tex]
So, the solution is -4.
Start from point 0, then use arrow to jump on -6 then use another arrow to jump 2 units right, as (-)(-)=(+) and positive sign means jump towards positive direction.
On the number line,
1. An arrow pointing from 0 to negative 6.
2. Another arrow pointing from negative 6 to negative 4.
Therefore, the correct option is A.
Answer:
what he say yeah
Step-by-step explanation:
Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones
Answer:
The value is [tex]n =271[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 5\% = 0.05[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally we will assume that the sample proportion is [tex]\^ p = 0.5[/tex] since we have no information on the proportion of of customers who click on ads on their smartphones
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.645 }}{0.05} ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n =271[/tex]
Using the z-distribution, as we are working with a proportion, it is found that 271 customers should be sampled.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
90% confidence level, hence the critical value is z = 1.645.No prior estimate, hence p = 0.5.Within five percentage points, hence M = 0.05.Then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 0.5 \times 1.645[/tex]
[tex]\sqrt{n} = [10(1.645)][/tex]
[tex](\sqrt{n})^2 = [10(1.645)]^2[/tex]
[tex]n = 270.6[/tex]
Rounding up, 271 customers should be sampled.
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0.079times what equals 7.9
Answer:
100
Step-by-step explanation:
A machine is used to fill 1-liter bottles of a type of soft drink. We can assume that the output of the machine approximately follows a normal distribution with a mean of 1.0 liter and a standard deviation of .01 liter. The firm uses means of samples of 25 observations to monitor the output, answer the following questions: Determine the upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control
Answer:
1.00434
Step-by-step explanation:
Given the following :
Given a normal distribution ;
Mean (m) = 1.0 liter
Standard deviation (σ) = 0.01 liter
Sample size (n) = 25
For 97% sample means (sm) = 0.97
Z = (m - sm) / s
Zcrit = 1 - (100% - 97%)/2
Zcrit = 1 - (0.03/2)
Zcrit = 1 - 0.015 = 0.985
The z score which corresponds to 0.985 = 2.17
Upper limit : m + z*(σ/√n)
Upper limit : 1.0 + 2.17*(0.01/√25)
Upper limit : 1. 0 + 2.17*(0.01/5)
= 1.0 + 2.17*0.002
= 1.0 + 0.00434
= 1.00434