Answers
Step-by-step explanation:
the manufacturing costs are defined by
m(x) = 25x + 150
the selling revenue is defined by
s(x) = 50 + 30x = 30x + 50
clearly, the selling amount is bigger than the manufacturing amount (also supported by the fact that 30x > 25x). otherwise the company is going bankrupt in no time.
so,
a)
the profit is (as usual) revenue minus manufacturing :
p(x) = 30x + 50 - 25x - 150 = 5x - 100
b)
x = 150
p(150) = 5×150 - 100 = 750 - 100 = $650
since the result is positive, yes, they are making a profit. and it is $650.
Answer:
5.a) p = 5x - 100
b)p = $650
Step-by-step explanation:
5.a)
Revenue minus cost:p - Profit
p - Profitc - Cost
p - Profitc - Cost - revenue
p = r - c
p = (30x + 50) - (25x + 150)
p = 5x - 100
b) The company will make profit.
p = 5x - 100
p = 5(150) - 100
p = 750 - 100
p = $650
or
p = (30×150 + 50) - (25 × 150 + 150)
p = $650
Related Questions
If the diameter of the circle is 14 units, calculate its area: then calculate its circumference
Answers
Answer:
Area: 153.86
Circumference: 43.96
I can’t solve this problem
Answers
Answer:
f(-2) = -8f(-1) = -5f(0) = 0f(1) = 7Step-by-step explanation:
f(w) = [tex]w^{2}[/tex] + 6w
w = -2f(w) = f(-2) = [tex](-2)^{2}[/tex] + 6*(-2) = 4 - 12 = -8
w = -1f(w) = f(-1) = [tex](-1)^{2}[/tex] + 6*(-1) = 1 - 6 = -5
w = 0f(w) = f(0) = [tex]0^{2}[/tex] + 6*0 = 0 + 0 = 0
w = 1f(w) = f(1) = [tex]1^{2}[/tex] + 6*1 = 1 + 6 = 7
Find an equation of the plane passing through the points (1, 5, -3), (2, 5, -3) and (3, 5,2)
Answers
Answer:
[tex]y = 5[/tex].
Or, equivalently:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Step-by-step explanation:
Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:
[tex]\vec{n}[/tex] is a vector normal to the plane (a normal vector), and [tex]\vec{r}_{0}[/tex] is the position vector of a point in the plane.Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:
[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].
Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:
finding two distinct directions parallel to that plane, and taking the cross product between the two directions.Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:
[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].
[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].
The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:
[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].
(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)
Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Expand the dot product and simplify to obtain a scalar equation for this plane:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].
[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].
[tex](-3)\, (y - 5) = 0[/tex].
[tex]y = 5[/tex].
Find x. (x+10)+(3x-5)+x=180
For a triangle
Answers
Explanation: Remove the parentheses because they’re not important for this particular problem. Then combine all liked terms. Then you should be able to solve it like a normal algebraic problem.
Which polynomial function has a root of 1 with
multiplicity 2 and a root of 6 with multiplicity 1?
Of(x) = (x - 1)(x-6)
Of(x) = 2(x - 1)(x - 6)
Of(x) = (x - 1)(x - 1)(x-6)
O f(x) = (x - 1)(x-6)(x-6)
Answers
Answer:
C) f(x) = (x - 1)(x - 1)(x-6)
Explanation:
Multiplicity means number of times a factor appears in a particular equation.
For example, a root of 3 has multiplicity of 3 then = (x - 3)(x - 3)(x - 3)
Breakdown for this question:
If a polynomial where root of 1 has multiplicity of 2, then it means (x - 1)²
Where polynomial of root of 6 has multiplicity of 1, then it means (x - 6)
Joining them together:
(x - 1)²(x - 6) = (x -1)(x - 1)(x - 6) Hence option C is correct.
Choose ALL the numbers that round down when rounding to the nearest hundred! Is it!: 47,035, 3,140, 76,654, 1,298, 607,882, 8,560?
Answers
Answer:
The answer is:
the first one
second one
:D
Step-by-step explanation:
in this case, any number in the tens place less than five will make the number round down
A company rents storage sheds shaped like rectangular prisms. Each shed is 11 feet long, 7 feet wide, and 12 feat tall. The rental cost is $3 per cubic foot. How much does it cost to rent one shed?
Answers
Answer:
308
Step-by-step explanation:
so to find how much a rectangular prisim is by
length * with* height
11* 7 * 12
= 924 cubic feet
and then we just divid by 3
=308
Need help on this one please
Answers
You deposit $400 in an account earning 5% interest compounded annually. How much will you have in the account in 10 years?
Answers
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The amount that will be in the account after 10 years is $651.56.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
The principal amount is $400 which is invested for a period of 10 years at an interest rate of 5% annually. Therefore, the amount in the account after 10 years will be,
[tex]A = P(1+ \dfrac{r}{n})^{nt}\\\\A = \$400 (1+ \dfrac{0.05}{1})^{1 \times 10})\\\\A=\$651.56[/tex]
Hence, the amount that will be in the account after 10 years is $651.56.
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Help please?????????
Answers
You start by setting the top and bottom equal to each other to define x
5x-18=2x+12
X=10
Then apply this 10 wherever x is needed
Therefore
AB=32
BC=24
CD=32
And because every opposite side is equal, AD=24
So for perimeter add them up
Answer is 112
1. What is the volume of this composite figure?
i6m
16 m
10 m
4 m
5 m
Answers
Answer:
560
Step-by-step explanation:
16 times 5 times 4=320
6 times 16 divide 2 then multiple 5
amusement on a particularly boring transatlanfic fight one of the authors am used himseft by counting the heads of the people in the seats in front of him. He noticed that all 37 of them either had black hair or had a whole row to themselves or both. Of this total 33 had black hair and 6 were fortunate enough to have a whole row of seats to themselves. How many black haired people had whole rows to themselves?
Answers
53) Darryl wants to buy socks for $15.27. He
gives the cashier $20. What is his
change?
Answers
Answer:
$4.73
Step-by-step explanation:
just do 20 minus 15.27
Contagious diseases can spread quickly. Suppose 3 people are ill during the first week of an epidemic, and each person who is ill spreads the disease to five people by the end of the next week. By the end of the 8th week of the epidemic, how many people have become ill?
Answers
Answer:
1875
Step-by-step explanation:
3x5 = 15
15x 5 = 75
75x 5 = 375
375 x 5 = 1875
1875 because at the end of the next week, which basically turns 8 weeks into 4, and the number of contaminants multiply by 5 each other week.
Help -x/3 > 5
A. X<15
B. X > -15
C. X < -15
D. X > 15
Answers
Answer:
Steps
-x/3 >5
Multiply both sides by 3
3(-x/3)>5.3
Simplify
-X> 15
Multiply both sides by - 1 (reverse the inequality)
(-x)(-1)<15(-1)
Simplify
X< -15
so C is the answer
The area of a parallelogram is the product of the base b and the height h. Identify the formula.
Answers
Answer:
b x h
Step-by-step explanation:
product of the base (b) and the height (h) just means b x h.
What comes next in this pattern? 7/2, 6/3, 5/4, ... 4/9 4/7 4/5
Answers
Answer:4/3
4/3
Step-by-step explanation:
√343k please simplify this
Answers
Answer:
the answer of√343k is 18k
(x+3)^2+4=46
what is the solution of this equation
Answers
Answer:
x = -3 + √42
Step-by-step explanation:
1) Expand the square
2) Distribute
3) Distribute
4) Distribute
5) Combine like terms
6) Add the numbers
7) Move terms to the left side
8) Subtract the numbers
9) Use the quadratic formula
10) Simplify
11) Separate the equations
12) Solve
Therefore, the solution of this equation is x = -3 + √42
Step-by-step explanation:
(x + 3)² + 4 = 46
(x + 3)² = 42
x + 3 = ±sqrt(42)
x = ±sqrt(42) - 3
x1 = sqrt(42) - 3 = 3.480740698...
x2 = -sqrt(42) - 3 = -9.480740698...
Find the vertex of the parabola y=x^2 + 5x + 10
Answers
The coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
What is the vertex of a parabola?Vertex of the parabola is the point of intersection of symmetry axis of the parabola and the parabola itself.
The given equation of parabola is [tex]y=x^2 + 5x + 10[/tex].
To get the coordinates of vertex of this parabola, we have to write the equation of parabola in the standard form.
So, write the equation of parabola in its standard form as,
[tex]y=x^2 + 5x + 10\\y=x^2+2\times \dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\\y=(x-\dfrac{5}{2})^2+\dfrac{15}{4}\\(y-\dfrac{15}{4})=(x-\dfrac{5}{2})^2[/tex]
The standard form of parabola is,
[tex]y-b=(x-a)^2[/tex] where (a, b) is the coordinate of the vertex.
So, by comparing the equations, the vertex of the parabola will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
Therefore, the coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].
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Determine the exact value of sin 30° tan 45° + tan 30° sin 60⁰
Answers
Answer:
1.
Step-by-step explanation:
1) if sin30=0.5; tan45=1; tan30=1/√3; sin60=√3/2, then
2) 0.5+0.5=1.
Select the correct answer.
1
Which number is the additive inverse of –10 1/4
O A.
0
Ang
OB.
10 1/4
oc. 4/41
OD. -4 1/10
Reset
Answers
Answer:
The additive inverse of the number -10 1/4 is +41/4
The additive inverse of any number is such a number added to the given number to get zero.
Let the additive inverse of the given number be "x", hence:
-10 1/4 + x = 0
x = 0 - (-10 1/4)
x = 10 1/4
x = 41/4
Hence the additive inverse of the number -10 1/4 is +41/4
Enter the number that belongs in the green box.
Answers
Answer:
The answer is x = 10.
Step-by-step explanation:
Two options:
1. Looking at the image it looks like a parallelogram. So, most side lengths are equal to each other or are the same.
2. We can use the Pythagorean Theorem to solve for x.
a line passes through the point (-9,1) and has a slope of 4/3. Write an equation in slope-intercept form for this line.
Answers
Answer: y=4/3x+1
Step-by-step explanation:
The formula is Y=mx+b
b is the y-intercept and MX is slope
Which expression is not equivalent to −4x3+x2−6x+8?
Answers
The expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The expression given in the problem is
f(x)=-4x³+x²-6x+8
The option given as,
(1) x² (-4x+1)-2(3x-4)(2) x(-4x²- x + 6) + 8(3) -4x³ + (x - 2)(x - 4)(4) -4(x³ - 2) + x(x - 6)From the given expression, if we take out x from the first three terms, it looks like option 2.
f(x)=-4x³+x²-6x+8
f(x)=x(-4x²+x-6)+8
From the given expression, if the last three terms factored, it looks like option 3.
f(x)=-4x³+x²-6x+8
f(x)=-4x³+x^2-4x-2x+8
f(x)=-4x³+x(x-4)-2(x-4)
f(x)=-4x³+(x-4)(x-2)
Rearrange the given expression, and make it looks like option 4.
f(x)=-4x³+x²-6x+8
f(x)=-4x²+8+x²-6x
f(x)=-4(x³-2)+x(x-6)
Thus, the expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).
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Is AABC™ADEF? If so, identify the similarity postulate or theorem that
applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answers
Answer:
A. Similar - AA
Step-by-step explanation:
The AA similarity postulate states that two triangles are similar if they have two congruent corresponding angles.
The triangles in the picture have two corresponding congruent angles.
Similar triangles may or may not be congruent
The true statement is (a) Similar - AA
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
From the complete question, we have the following highlights about the triangles
The angles at points A and D are congruent (85 degrees)
The angles at points B and E are congruent (30 degrees)
This means that the triangles are similar.
The similarity theorem is the AA theorem i.e. Angle-Angle
Hence, the true statement is (a) Similar - AA
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7th grade math perimeter!!! Help
Answers
Answer:30.28 cm^2
Step-by-step explanation: area of the rectangle = 6x4 = 24
area of semicircle -> (πr^2)/2
radius of semcircle = 4/2 = 2
area of this question semicricle = (π2^2)/2
= 6.28 (3 s.f.)
total area = 24+6.28 =30.28 cm^2
remember put units ^^
demand for a certain product is random. It has been estimated that the monthly demand of the product has a normal distribution with a mend of 390units. The unit price of product is ETB 25. Ordering cost is ETB 40 per order and inventory carrying cost is estimated to be 35 percent per year. Calculate economic order quantity (EOQ)
Answers
The economic order quantity of the product with the demand of 390 units is 1392.86 units.
What is an economic order quantity?This refers to an inventory management technique that helps make efficient inventory management decisions.
The formula for economic order quantity is [tex]\sqrt{2 * D * S / H}[/tex]
Given data
Demand = 390 units.
Unit price of product is ETB 25.
Ordering cost is ETB 40 per order
inventory carrying cost is estimated to be 35 percent per yer
EOQ = [tex]\sqrt{2*390*25/40*0.35}}[/tex]
EOQ = 19,500 / 14
EOQ = 1392.85714286
EOQ = 1392.86 units
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Fred figured out the volume of the glass is 141.37cm. Show work
Answers
To solve this problem, we have to calculate the volume of a hemisphere and the volume of a cylinder and add them together. The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.
Volume of a HemisphereThe volume of a hemisphere is given as
[tex]v = \frac{2}{3} * \pi * r^3[/tex]
Data
r = 3cmLet's substitute the values into the equation and solve.
[tex]v = \frac{2}{3} * \pi * r^3\\v = 56.556cm^3\\[/tex]
Volume of a CylinderThe formula of volume of a cylinder is
[tex]v = \pi r^2 h[/tex]
data given
h = 3cmr = 3cmLet's substitute the values into the equation and solve
[tex]v = \pi r^2 h\\v = 3.142 * 3^2 * 3\\v = 84.834cm^3[/tex]
Let's add both volumes together so we have the volume of the glass cup
[tex]56.556 + 84.834 = 141.39cm^3[/tex]
The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.
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If you reflect point B(- 2, 5) over the y- axis, what is the reflected point ?
Answers
Answer:
(2,5)
Step-by-step explanation:
Since it is reflected across the y-axis only the x point will change and vise-versa
