Answer:
a. The start-up cost for the teenagers company is $50
b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs
c. The number of mugs that will give maximum profit is 15 mugs
d. The profit if she sells 10 mugs is $30
Step-by-step explanation:
The given profit function for selling x number of mugs is presented as follows;
f(x) = -0.4·x² + 12·x - 50
a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;
Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50
The negative sign represents amount put in the business
The start-up cost = (The initial) $50 put into the business.
b. The break even point is the point where, the revenue and costs are equal
At break even point; Revenue = Cost
∴ Profit, at break even point, f(x) = Revenue - Cost = 0
From the profit function, we get;
At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50
Dividing by -0.4 gives;
0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125
0 = x² - 30 + 125
∴ (x - 25)·(x - 5) = 0
The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.
c. From the general form of a quadratic equation, which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)
Comparing the profit function to the general form of the quadratic equation we have at the maximum point;
x = -12/(2×(-0.4)) = 15
Therefore, the number of mugs that will give maximum profit, x = 15 mugs.
d. The profit from selling 10 mugs, f(10) is given as follows;
f(10) = -0.4 × 10² + 12 × 10 - 50 = 30
The profit from selling 10 mugs, f(10) = $30
Answer the question based on the data in the two-way table.
Gender Grades
Below
Average Above
Average Total
Boy 14 23 37
Girl 16 22 38
Total 30 45 75
Which statement is true?
A.
P(boy|above average grades) = P(boy)
B.
P(above average grades|boy) = P(above average grades)
C.
P(boy|above average grades) P(above average grades)
D.
P(above average grades|boy) = P(boy)
This is a graph of the function g(x) =-3x+2. Determine the domain value when th
range value is -4.
Range = -4= g(x)
Therefore, g(x) = -3x+2
or, -4=3x +2
or, 3x= -4-2
or, 3x= -6
or, x= -6/3 = -2
OPTION A is the correct answer.
When the range value is -4 for the function g(x) = -3x + 2, the corresponding domain value is x = 2.
To find the domain value when the range value is -4 for the function
g(x) = -3x + 2, we need to solve for x when g(x) = -4.
Given: g(x) = -3x + 2
When the range value is -4, we have:
-3x + 2 = -4
Now, isolate x:
-3x = -4 - 2
-3x = -6
Now, divide by -3 to solve for x:
x = -6 / -3
x = 2
So, when the range value is -4 for the function g(x) = -3x + 2, the corresponding domain value is x = 2.
To know more about range:
https://brainly.com/question/29204101
#SPJ2
the function y=-2(x-3)^2+4 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the 0's of this function.
Find the value of 3 √ 512
Answer:
48√2
Step-by-step explanation:
3√(512)
= 3√(256×2)
= 3√(256)×√(2)
→ we know that 16² = 256 then √(256) = 16
Then
3√(512)
= 3 × 16 ×√(2)
= 48√(2)
Brainly to fastest and correct answer,
Answer:
0.02625
2.1 tenths
2.1
Step-by-step explanation:
Are shape I and shape II similar? If so, give the dilation that proves they are similar. If not, explain why the shapes are not similar.
Answer:
The answer is "They are similar".
Step-by-step explanation:
They were comparable in this respect because both aspect ratios of the top triangle are one square more. The top triangle is equal to the base triangles if you remove one square away from the height and width.
Otherwise, we can say that it forms all different. The dilation factor which translates that bottom left point of shape I to form II is 2. But this does not map the other shape I vertices onto form II. There's, therefore, no dilation in form I of maps on form II.
How many pounds of water must be evaporated from 50 pounds of a 3% salt solution so that the the remaining solution will be 5 % salt
Answer:
Step-by-step explanation:
This is kinda tricky, but not nearly as bad as d = rt problems. Those are a nightmare!
We will make a table for this:
#lbs solution * % salt = lbs. salt
3% solution
- Water
New solution
And we will now fill in what we know. The 3% solution part is easy. The number of pounds of that is 50 and the percent salt in 3% salt is....well, 3%. As a decimal, it is .03:
#lbs solution * %salt = lbs salt
3% solution 50 * .03 = 1.5
- Water
New solution
The last column there with a 1.5 in it is the product of 50 times .03, since that is what the formula at the top of the table tells us we have to use. Now for the water. That's easy, too, since the amount of water we are evaporating (notice the subtraction sign out front of the word "water"; that indicates we are removing water) is our unknown, and we also know that water has 0% salt in it:
#lbs solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution
Now all we have left is the new solution row and the equation. Finding the equation from a mixture table is as easy as it can be! Super easy!
The new solution will be 50 - x since, going down column 1, we are subtracting the water from the 3% solution, the % salt is to be 5%:
#lbs. solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution 50 - x * .05 = 2.5 - .05x
Now we're ready for our equation. I got the 2.5 - .05x from multiplying
.05(50 - x), just so you know.
if we had to subtract the water from the salt solution and set it equal to the new solution in the first column, we also have to do it in the third column:
1.5 - 0 = 2.5 - .05x and solve for x:
-1 = -.05x so
x = 20 pounds of water
A model of the Pythagorean Theorem is shown below.
If a = 6 and c = 10 , which of the following could NOT be used to find the value of b?
A. 102 = 62 + b2
B. 102 + 62 = b2,
C. 100 = 36 + b2,
D. 100−36=b2
Answer:
D can others can't..............
Find question attached.
a.x=50°
b.x=22°
Answer:
Solution given:
a:
3x=2*75°[inscribed angle is half of central angle]
3x=150°
x=150°/3=50°
x=50°
b.
<BDC=34°+x[exterior angle is equal to the sum of two opposite interior angle of triangle]
again
<DCB=34°+x[base angle of isosceles triangle]
again
<ABC=90°[inscribed angle on a semi circle is 90°]
Now.
In triangle
ABC
<A+ <B+<C=180°[sum of interior angle of a triangle is 180°]
34°+90°+34°+x=180°
x=180°-90°-68°
x=90°-68°
x=22°
a) Solution
By using the inscribed angle is half of central angle,
→ 3x = 2 × 75
→ 3x = 150
→ x = 150/3
→ x = 50°
Thus, 50° is the value of x.
b) Solution
By using the exterior angle is equal to sum of two opposite interior angle of triangle,
→ <BDC = 34+x
→ <DCB = 34+x
(base angle of isosceles triangle)
→ <ABC = 90°
(inscribed angle on a semi circle is 90°)
Then in ∆ ABC,
By sum of interior angle of a triangle is 180°,
→ <A+<B+<C = 180°
→ 34+90+34+x=180°
→ x = 180°-90°-68°
→ x = 90°-68°
→ x = 22°
Thus, 22° is the value of x.
The population of a town is 24,000 and is
increasing at a rate of 6% per year for 3 years
Which digit is in the thousandths place?
98.327
A. 7
B. 2
C. 3
D. 9
Answer:
A.
Step-by-step explanation:
it is A.
Answer: A. 7
Step-by-step explanation:
Given the number 98.327, then we are going to title each digit with a name
9 = tens
8 = ones
3 = tenths
2 = hundredths
7 = thousandths
Therefore, 7 is in the thousandths place
Hope this helps!! :)
Please let me know if you have any questions
Select the true statement about triangle ABC.
A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C
Answer:
B
Step-by-step explanation:
We know that cosθ= adjacent/hypotenuse, sinθ=opposite/hypotenuse, and tanθ=opposite/adjacent.
Using this, we can first try between cos and sin for A-C. We know that two different angles will not have the same side adjacent to both of them. However, one angle might have an adjacent side that is opposite to another angle. Using this knowledge, we can say that A is incorrect, as two different angles in the same triangle cannot have the same cos value (unless the triangle is isosceles).
For B, we can say that cos A = adjacent/hypotenuse = 12/13, and sin C= opposite/hypotenuse = 12/13. These are equal, but we can double check by making sure the other answers are wrong.
For C, we can tell that B is a right angle, signified by the small square representing the angle. sin(90°) = 1, and cosA = 12/13. These are not equal.
Finally, for D, sin A = opposite/hypotenuse = 5/13, while tan C = opposite/adjacent = 12/5. These are not equal
Solve for y in terms of x. 2/3 y - 4 = x
Answer:
y = 3/2x + 6
Step-by-step explanation:
2/3 y - 4 = x
2/3y = x + 4
y = 3/2 * (x + 4)
y = 3/2x + 6
Answer:y=(3x/2)+6
Step-by-step explanation:
(2/3)y-4=x
2y-12=3x
2y=3x+12
y=(3x/2)+6
help please summer school sucks!!!
Answer:
X =30
Step-by-step explanation:
= 60+90
=150
angle sum property
x+150=180
x=180- 150
x= 30
Answer:
Step-by-step explanation:
90 + 60 = 150
(right angles = 90)
There is 180 degrees in a triangle, therefore,
180 - 150 = 30
Therefore, x = 30
p.s. Are you good at history?
p.p.s I dont like summer school either =)
Solve the equation 3(2x+9)=30
Answer:
x=1/2
Step-by-step explanation:
3(2x+9) = 30
Multiply out the 3
6x + 27 = 30
Subtract 27 on both sides
6x = 3
Divide by 6 on both sides
x = 1/2
Answer:
x=1/2
Step-by-step explanation
Find IG in the image below .
Step-by-step explanation:
[tex]ig =2 \times yx = 2 \times 11 = 22[/tex]
Please help ASAP!!!
What is m
Answer:
∡A =115°
as for your question ... m is asking for the "m" (measure) of angle A
Step-by-step explanation:
Answer:
∠ A = 118°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
3x + 13 + x - 8 + x = 180, that is
5x + 5 = 180 ( subtract 5 from both sides )
5x = 175 ( divide both sides by 5 )
x = 35
Then
∠ A = 3x + 13 = 3(35) + 13 = 105 + 13 = 118°
Which sentence can represent the inequality 2.4 (6.2 minus x) greater-than negative 4.5?
Two and four tenths times six and two tenths minus a number is larger than negative four and five tenths.
Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.
The difference of six and two tenths and a number multiplied by two and four tenths is not less than negative four and five tenths.
The product of six and two tenths minus a number and two and four tenths is at minimum negative four and five tenths.
Answer: Choice B
Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.
======================================================
Explanation:
2.4 = 2 + 0.4
2.4 = 2 and 4/10
2.4 = 2 and 4 tenths
2.4 = two and four tenths
-------------------
Through similar reasoning,
6.2 = six and two tenths
And also,
-4.5 = negative four and five tenths
---------------------
Notice how 6.2 - x translates into "difference of six and two tenths and a number"
We then multiply that by 2.4, aka two and four tenths.
So that's how we get the phrasing "Two and four tenths multiplied by the difference of six and two tenths and a number"
All of this is greater than -4.5 aka negative four and five tenths.
This points us to Choice B as the final answer.
Answer:
Answer: Choice B
Step-by-step explanation:
Edgunity
find the area of the shaded region,(π=3.14).
plx help me
Answer:
115.395 cm2Step-by-step explanation:
The radius of the whole figure: 14 : 2 = 7 (cm)
The area of the whole figure: 7 x 7 x 3.14 = 153.86 (cm2)
The area of the unshaded region: 3.5 x 3.5 x 3.14 = 38.465 (cm2)
The area of the shaded region: 153.86 - 38.465 = 115.395 (cm2)
Answer: 115.395 cm2.
Hope it helps!
What are the features of the quadratic function ƒ(x) = x2 + 10x + 21?
Answer:
B is the answer
Step-by-step explanation:
The intercept is at x = 0 then y = 21 or (0,21) so A and D drop out.
The vertex (-5, -4) satisfies the equation but (-4,-5) does not so C drops out leaving B.
Answer:
B.
Step-by-step explanation:
B.
The ancient Greeks were able to construct a perpendicular bisector for a
given line segment using only a straightedge and compass.
O A. True
B. False
Answer:
True
Step-by-step explanation:
The answer is "True". Let me explain.
Let's say that we have a line segment which we will call AB, construct a perpendicular bisector. The following steps will be taken;
1) Draw a semi circle with its centre at point A and passing through point B.
2) Draw a semi circle with its centre at point B and passing through point A.
3) The two semicircles will intersect at two points with one being above and the other being below the straight line segment AB. Now, a line will have to be drawn that passes through those two intersecting points. This drawn line is called the perpendicular bisector for line segment AB.
Answer:
True
Step-by-step explanation:
Make sure you’re paying attention to if your question says “were able to” or “were not able to”.
The following are the dimensions of a triangle, 6 cm, 8 cm, and 12 cm.
Is this a right triangle?? Use the Pythagorean theorem and the basic law of exponents to prove whether this is a RIGHT triangle.
Show your work and POST your answer.
Answer:
Perimeter of original triangle: 6+8+10=24 cm
Perimeter of new triangle: 3+4+5=12 cm (You get 3, 4, and 5 from dividing 6, 8. and 10 by 2.)
Ratio of original to new is 24 to 12, simplified to 2 to 1.
The ratio of the perimeter is the ratio of the corresponding sides, as the original measurements are two times the length of the new measurements.
Area of original triangle: (6x8)/2=24 cm^2
Area of new triangle: (3x4)/2=6 cm^2
Ratio of original to new is 24 to 6, simplified to 4 to 1.
nolan uses 7 inches of string to make each bracelet. if nolan makes 3 bracelets, how many inches of string will he use?
Answer:
21 inches
Step-by-step explanation:
We can write a ratio to solve
7 inches x inches
------------- = -------------------
1 bracelet 3 bracelets
Using cross products
7*3 = 1x
21 = x
21 inches
Answer:
21 inches
Step-by-step
This can be solved two ways: addition or multiplication.
Addition: Since there are three bracelets you could add 7 three times
7+7+7
= 14+7
= 21
Multiplication: Simply multiply 7 x 3= 21
Find the measure of the indicated angle.
Answer:
∠? = 76°
Step-by-step explanation:
The two lines on the sides of the triangle indicate that this is an isosceles triangle. An isosceles triangle has 2 congruent sides and one side that is different. The same goes for its angles. The angle opposite to these same sides are also the same. So if one angle = 76°, then ∠? = 76° as well.
Hope this helps! Best of luck <3
HELP ME PLEASEEEEE!!!!!!!
Answer:
sas
Step-by-step explanation:
dide angle side is correct
express as a trinomial (3x-10)(3x-1)
Answer:
3x (3x-1)-10 (3x-1)
9x2-3x-30x+10 (the 2 in 9x2 is the square ok)
9x2-33x+10 Ans..
I hope this will help you
If this is incorrect forgive meplz
Can someone help me pls
Answer:
Step-by-step explanation:
Look at the photo
Sue read 12 more than twice as many pages is tom did last week if sue read 90 pages how many did tom read
Answer: 39 pages
Step-by-step explanation:
x = the amount of pages Tom read
[tex]2x+12=90\\2x=78\\\frac{2x}{2}=\frac{78}{2}\\x=39[/tex]
If Sue read 90 pages, which is 12 more than twice the amount, subtract 12 from 90, then divide the result by 2, boom, you got your answer. Which should be 39
What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)
Answer:
[tex]\displaystyle c = \frac{20}{3}[/tex]
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to x:
[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]
Differentiate:
[tex]g'(x) = -21x^2+182x-280[/tex]
Let g'(x) = 0:
[tex]0 = -21x^2+182x-280[/tex]
Solve for x. First, divide everything by negative seven:
[tex]0=3x^2-26x+40[/tex]
Factor:
[tex]0=(x-2)(3x-20)[/tex]Zero Product Property:
[tex]x-2=0 \text{ or } 3x-20=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]
Since the first solution is not within our interval, we can ignore it.
Therefore:
[tex]\displaystyle c = \frac{20}{3}[/tex]
Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cuantos metros bojo en 4 horas
Answer:
X = 32 meters.
Step-by-step explanation:
Let the unknown distance be X.Given the following data;
Distance = 8 meters per hourTime = 4 hoursTo find how many meters he would cover in four hours;
1 hour = 8 meters
4 hours = X meters
Cross-multiplying, we have;
X = 8 * 4
X = 32 meters.
