The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q. Compute Marginal cost and average cost
Step-by-step explanation:
There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7 correct? (b) What is the probability that the student gets exactly 8 correct? (c) What is the probability that the student gets exactly 9 correct? (d) What is the probability that the student gets exactly 10 correct? (e) What is the probability that the student gets more than 6 correct?
Answer:
Probability getting 7 correct :- 1/10Probability getting 8 correct :- 1/10 Probability getting 9 correct :- 1/10Probability getting 10 correct :- 1/10 → Probability getting more than 6 :- 4/10Help help help help math math
Answer:
No Solution
Step-by-step explanation:
-y = -2x + 8
y = 2x - 8
2x + 8 = 2x - 8
2x - 2x = -8 - 8
0 = -16
No Solution
You can also graph y = 2x + 8 and y = 2x - 8. The slope are the same and so they are parallel
41. Henry stands on a platform and shoots a rocket in his 10th
grade science class. He found that the motion of the rocket can be
described by the equation y = 60 + 28x – x2, where y is the
vertical distance and x is the horizontal distance traveled. If this
trajectory equation were to be graphed, find the x-intercepts of the
equation. (Fun fact: The positive x-intercept is how far away from
the platform the rocket hits the ground!)
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
What are the x-intercepts of a quadratic equation?A quadratic equation is modeled by:
y = ax² + bx + c.
The x-intercepts are the values of x when y = 0, given by:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is:
y = 60 + 28x - x².
Hence the coefficients are a = -1, b = 28, c = 60.
Then:
[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]
[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]
[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
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give me list of letter arrangement and number arangement
Answer:
what the heck question is this
Help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
53
Step-by-step explanation:
[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]
Find the area of the parallelogram.
3 cm
5 cm
Answer:
Area = Base ×Height
Step-by-step explanation:
Area = Base × Height
Area = 3cm × 5cm
Area = 15cm
Area of the parrallelogram is 15cm
Martina is ordering an ice cream dessert. She must order a size and a flavor of ice cream. There are 4 sizes and 2 flavors to choose from. How many different
cream desserts could she order?
Answer: 8.
Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large. There are 2 flavors, so let's say that the flavors are chocolate and vanilla. The possible combinations are below:
Small chocolateMedium chocolateLarge chocolateExtra large chocolateSmall vanillaMedium vanillaLarge vanillaExtra large vanillaAs you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.
Have a great day! :)
Change 75m to decimeters
Answer:
750 decimeters
Step-by-step explanation:
1 meter is equal to 10 decimeters.
so 75 times 10 equals your answer: 750 decimeters
Hope that helps!
write balanced chemical equation for the process of photosynthesis giving the physical state of all the substances involved in the conditions of the reaction
Answer:
The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.
Step-by-step explanation:
Rewrite in simplest radical form
X^5/6 / X^1/6
Answer:
[tex]\sqrt[3]{x^2}[/tex]
Step-by-step explanation:
The rule of exponents says that we must use subtraction for [tex]\frac{5}{6}[/tex] and [tex]\frac{1}{6}[/tex] since we are dividing.
Thus, we have [tex]\frac{x^\frac{5}{6} }{x^\frac{1}{6} }\\\\\frac{5}{6}-\frac{1}{6}=x^\frac{4}{6}=x^\frac{2}{3}[/tex]
When dealing with fractions and radicals, we can find the simplest radical form by using the saying [tex]\frac{exponent}{index}[/tex]
Thus we have [tex]\sqrt[3]{x^2}[/tex]
5/6 of a number is 65.
Find the number.
Answer:
78 is the number
Step-by-step explanation:
(65*6)÷5 = 78.
5/6 of a number is 65.
And the number is 78.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A phrase: 5/6 of a number is 65.
To find the number:
Let the number be n.
Applying multiplication operation,
5/6 of n is 65.
(5/6)n = 65.
Applying cross multiplication,
n = 65 x 6/5
n = 390/5
n = 78.
Therefore, the number is 78.
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What is the factorization of the trinomial below?
3x^3 + 6x^2 - 24x
A. 3x(x - 2)(x + 4)
B. 3x(x - 2)(x - 4)
C. 3(x - 2)(x + 4)
D. 3(x^2 - 2)(x + 4)
Mrs. Williams' desk is located at (-5,2). The wireless internet box is halfway between her desk and the door. If the box is located at the coordinates (8, -8), what are the coordinates of the door?
Topic : Midpoint between points
desk = (-5,2)box = (8, -8)door = (x, y)formula:
[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]
=====================================
[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]
separate taking coefficients:
[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]
[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]
[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]
[tex]\rightarrow \sf x =21, \ y= -18[/tex]
coordinates of door: (21, -18)
Let that be (x,y)
So
[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]
(x,y)=(21,-18)
I need help with this question please
Answer:
Step-by-step explanation:
As ABCD is a rectangle, ∠A = 90°.
Diagonal BD will be the hypotenuse.
[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]
Length = AB = 33.8 cm
[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]
Width = 25.5 cm
PLEASE HELP! Match the steps to find the equation of the parabola with focus (-1, -8) and directrix y = - 12.
Answer:
3,2,1,6,5,4
Step-by-step explanation:
Hope this helps!!!
All the correct steps to find the equation of the parabola with focus (-1, -8) and directrix y = - 12 are,
1. 2p + (- 8) = - 12 Find p
2. Since the focus is at - 1, Find the x - coordinates for the vertex.
then, vertex is at - 1
3. y = - 8 - 2 Find the x - coordinates for the vertex.
4. (- 1, - 10) Vertex coordinates
5. (x + 1)² = 4(-2) (y+10) Write the formula for the parabola.
6. (x + 1)² = -8 (y+10) Simplify the formula.
Given that,
In a parabola,
Focus = (-1 , - 8)
And, Directrix =; y = - 12
The standard equation of a parabola is,
[tex]y = - p (x - h)^2 + k[/tex]
Where, (h, k) is the vertex of the parabola.
Now, the Statement with reason to find the equation of a parabola is,
Statement Reason
1. 2p + (- 8) = - 12 Find p
p = - 2
2. Since the focus is at - 1, Find the x - coordinates for the vertex.
then, vertex is at - 1
3. y = - 8 - 2 Find the x - coordinates for the vertex.
y = - 10
4. (- 1, - 10) Vertex coordinates
5. (x + 1)² = 4(-2) (y+10) Write the formula for the parabola.
6. (x + 1)² = -8 (y+10) Simplify the formula.
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A laptop computer is purchased for $2350. After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]
Find the equation of a line that contains the points (2,1) and (8,7). Write the equation in slope-intercept form.
Answer:
y = x - 1
Step-by-step explanation:
First find the slope. Subtract the y's and put that on top of a fraction. Then subtract x's and put that on the bottom. Simplify if possible.
7-1 is 6 goes on top.
8-2 is 6 goes below.
6/6 is 1 when simplified.
Slope is 1.
Slope-intercept form is y = mx + b.
m is slope, so fill that in.
y = (1)x + b
Now we need to find b.
Use either one of the given points; they will give you the same answer no matter which one you choose. Let's use (2,1) because smaller numbers.
y is 1 and x is 2.
y= (1)x + b
1 = (1)2 + b
1 = 2 + b
-1 = b
Now fill in both m and b. Leave x and y as letters (variables)
y = (1)x + -1
Final answer:
y = x - 1
An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 837 new employees. If a new route is not granted, it will hire only 199 new employees. If the probability that a new route will be granted is 0.37, what is the expected number of new employees to be hired by the airline?
Considering a discrete distribution, it is found that the expected number of new employees to be hired by the airline is of 446.16.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, considering the situation described in the text, the distribution is given by:
P(X = 837) = 0.37.P(X = 199) = 0.63.Hence, the expected value is given by:
E(X) = 0.37(867) + 0.63(199) = 446.16.
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(a) A color page prints 20 pages in 7 minutes. How many pages does it print per minute?
(b) it takes 55 pounds of seed to completely plant a 7- acre field. How many acres can be planted per pound of seed?
If needed round to nearest hundredth.
Answer:
A. 20 / 7 = 3 (or 2.85)
B. 55 / 7 = 8 (or 7.85)
Brainliest is appreciated!
_ daintysword.mp4
Answer:
A.3
B.8
Step-by-step explanation:
this is the answer
What’s the difference between 4, 7/9 and 2 1/2
[tex]\huge \mathbb \orange{ANSWER} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]
[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]
[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]
[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]
The Length Of A Room is two time its breadth and breadth is two time its height If The volume of room is 512m2 what is the cost of plastering its wall at rs 5.50 per m2
Answer:
Rs 2464
Step-by-step explanation:
Given:
The length of a room is 2 times its breadth and breadth is 2 times its height. The volume of the room is 512 cubic metre.To find:
The cost of plastering it's wall at Rs 5.50 per square metre.Solution : A/C to given data;
[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (2)
A/C to given data let, structure of room is cuboidal.
Now, we have to find out the height of the room, so we use formula of volume of the cuboid.
[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]
[tex]512 = 2B * 2H * H[/tex]
[tex]512 = 2 * 2H * 2H * H[/tex]
[tex]512 = 4H * 2H^{2}[/tex]
[tex]512 = 8H^{3}[/tex]
[tex]H^{3} = \frac{512}{8}[/tex]
[tex]H^{3} = 64[/tex]
[tex]H = \sqrt[3]{64}[/tex]
[tex]H = 4 m[/tex]
[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]
[tex]B = 2 * H[/tex]
[tex]B = 2 * 4[/tex]
[tex]B = 8 m[/tex]
[tex]\\[/tex]Now, put value of B in eq. {1}
[tex]L = 2 * B[/tex]
[tex]L = 2 * 8[/tex]
[tex]L = 16 m[/tex]
Now, we have to find out area of the room, so we use formula of total surface area of cuboid.
[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]
[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]
[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]
[tex]Area of the room = 256 + 128 + 64[/tex]
[tex]Area of the room = 384 + 64[/tex]
[tex]Area of the room = 448 m^{2}[/tex]
Now, to find out room wall plastering cost
[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]
[tex]Room wall plastering cost = 448 * 5.50[/tex]
[tex]Room wall plastering cost = Rs 2464[/tex]
[tex]ence, the room wall plastering cost is Rs 2464.[/tex]
Find the LCM of 20, 35 & 50.
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
What is the equation of a circle with center (−5, −8) and radius 2?
(x − 5)2 + (y − 8)2 = 4
(x + 5)2 + (y + 8)2 = 4
(x + 5)2 + (y + 8)2 = 2
(x − 5)2 + (y − 8)2 = 2
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Standard equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of centre k = y - coordinate of centrer = radius of the circle
Now, let's plug in the values ~
[tex]\qquad \sf \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]
Therefore, the correct choice is B
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The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4
How to determine the circle equation?The center of the circle is given as:
Center (a,b) = (-5, -8)
The radius is given as:
Radius, r = 2
The equation of the circle is calculated using:
(x - a)² + (y - b)² = r²
Substitute values for r and (a,b)
(x + 5)² +(y + 8)² = 2²
Evaluate the square of 2
(x + 5)² +(y + 8)² = 4
Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4
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What is the value if X? and how to find exterior angles.
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
given that 10022bse 3 is equal to 155base n find the value of n show all workings
Step-by-step explanation:
log 3 (10022)
= 8.38561
log n (155)= 8.38561
n^8.38561=155
log 10 (n)= log 10 (155)
lpg 10 (155)= 2.190331698
8.38561 log10 (n)=2.190331698
log10 n = 2.190331698÷8.38561
lo^-1 (0.2612012)
=1.825
n=1.825
pls help me in this math problem
Answer:
cUse the following equation
Step-by-step explanation:
Because of the way these angles are positioned, they must be equal to 180 together
(2x + 5) + (0.5x + 150) = 180
2.5x + 155 = 180
- 155 - 155
2.5x = 25
2.5x/2.5 = 25/2.5
x = 10
Put x into the original equations and solve
Heather planted 4 times as many tulips as Sarah planted. If Heather planted 64 tulips, how many tulips (s) did Sarah plant?
Step-by-step explanation:
let, the tulips be 'x'
According to the question,
heather=4x
& sarah=x
but heather planted 64 so,
4x=64
or, x=64/4
x=16
hence, sarah planted 16 tulips
Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).
How to determine how many tulips (s) Sarah planted using algebraLet's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.
Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:
Heather's tulips = 4 * Sarah's tulips
64 = 4s
Presently, ready to fathom for s:
s = 64 / 4
s = 16
Sarah planted 16 tulips.
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what is 4 1/8 x 1/4 equal to?
Answer:1.03125
Step-by-step explanation:
Barry has two cubes of different sizes. The first cube has a volume of 1 cubic unit. The second cube has sides one-third as long as the first cube does. What is the volume of the second cube?
Answer:
1/27 units cubed or 0.037037... units cubed
Step-by-step explanation:
Volume of a cube = s*s*s : Where s is a side length.
The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)
The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.
Volume of second cube= (1/3s)(1/3s)(1/3)s
Volume of second cube= (1/3)(1/3)(1/3)
Volume of second cube= 1/27