Answer:
[tex]a.\ P(x) = - 0.002x^2+3.8x-40[/tex]
b. 320
[tex]c.\ P'(x) = -0.004 x + 3.8[/tex]
d. 3.76
Step-by-step explanation:
Given that:
Revenue function:
[tex]R(x) = 6x[/tex]
Cost Function:
[tex]C(x) = 0.002x^2+2.2x+40[/tex]
We know that,
Answer a: Profit = Revenue - Cost
[tex]\Rightarrow P(x) = R(x) - C(x)\\\Rightarrow P(x) = 6x - (0.002x^2+2.2x+40)\\\Rightarrow P(x) = - 0.002x^2+3.8x-40[/tex]
Answer b:
P(100) = ?
Putting value of x as 100 in above equation:
[tex]P(100) = - 0.002\times 100^2+3.8 \times 100-40\\\Rightarrow P(100) = -20+380 -40\\\Rightarrow P(100) = 320[/tex]
Answer c:
P'(x) = ?
Differentiating the equation [tex]P(x) = - 0.002x^2+3.8x-40[/tex]
[tex]P'(x) = -2 \times 0.002 x^{2-1} + 3.8 + 0\\P'(x) = -0.004 x + 3.8[/tex]
Answer d:
P'(100) = ?
Putting x = 100 in equation [tex]P'(x) = -0.004 x + 3.8[/tex]
[tex]P'(100) = -0.004 \times 100 + 3.8\\P'(100) = -0.4 + 3.8\\P'(100) = 3.76[/tex]
Which best describes her prediction?
Could you please help me with this problem.
Answer:
x=6√2please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
in a bag there are 2 red, 3 yellow, 4 green, 6 blue marbles.
what is the probability of p (blue)?
Answer:
2/5
Step-by-step explanation:
2 red, 3 yellow, 4 green, 6 blue marbles. = 15 marbles
P( blue) = blue / total
=6/15
=2/5
could you help me with this problem
Answer:
For x
We use cosine
cos 45° = 2/x
After solving
x = 2√2
Since we have the value of x we use it to get the value of y
we use cosine
cos 60° = 2√2/y
y =2√2/cos 60
y = 4√2
We use Pythagoras theorem to find z
(4√2)² = (2√2)² + z²
z² = 32 - 8
z² = 24
z = √24
z = 2√6
Therefore x = 2√2
y = 4√2
z = 2√6
Hope this helps.
A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them. If four of the homes are new and six have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new
Answer:
0.48% probability that all four are new
Step-by-step explanation:
The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Total of 10 homes, so N = 10.
We want 4 new, so x = 4.
In total, there are 4 new, so k = 4.
Sample of four homes, so n = 4.
Then
[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]
0.48% probability that all four are new
The calculated probability is "0.0048".
Probability calculation:From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.
Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.
X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.
[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]
[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]
[tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]
Using the excel function:
[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex] for calculating the [tex]P_{X} (4)[/tex]:
[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]
[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]
Find out more information about the probability here:
brainly.com/question/2321387
Please answer this correctly
Answer:
0| 2
1| 2
2| 0 0 3 9
3| 2 4 4 4 8 8
4| 2 2 4 5 5 6 7
Step-by-step explanation:
Same as the other similar questions
hope this helps!
Let's list the elements of these sets and write whether thoy are empty
(null), singleton, finite or Infinito sots.
a) A = {prime number between 6 and 7)
b) B = {multiples of 2 less than 20}
Answer:
a. They are empty set.
b. they are finite set.
Solution,
a. A={ prime number between 6 and 7}
There are not any number between 6 and 7.
So there will be no Elements.
A={ }
It is empty set.
Empty set are those set which doesn't contain any Element.
b.B={multiples of 2 less than 20}
B={2,4,6,8,10,12,14,16,18}
It is a finite set.
Finite set are those set which we can count easily.
Hope this helps...
Good luck on your assignment...
How can knowing how to represent proportional relationships in different ways be useful to solving problems
Answer:
appropriately writing the proportion can reduce or eliminate steps required to solve it
Step-by-step explanation:
The proportion ...
[tex]\dfrac{A}{B}=\dfrac{C}{D}[/tex]
is equivalent to the equation obtained by "cross-multiplying:"
AD = BC
This equation can be written as proportions in 3 other ways:
[tex]\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}[/tex]
Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.
I find this most useful to ...
a) put the unknown quantity in the numerator
b) give that unknown quantity a denominator of 1, if possible.
__
The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.
Example:
x/4 = 3/2
Usual method:
2x = 4·3
x = 12/2 = 6
Multiplying by the denominator:
x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step
__
Example 2:
x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...
x/1 = 4/2 . . . . . . written with 1 in the denominator
x = 2 . . . . simplify
Of course, this is the same answer you would get by multiplying by the denominator, 4.
The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.
What is the slope of the line represented by the equation y = 4/5x - 3?
in
Answer:
[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]
Step-by-step explanation:
when the equation is like y = ax + b
the slope is a
in this case we have
[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]
so the slope is
[tex]\dfrac{4}{5}[/tex]
Use reduction of order (NOT the integral formula we developed) to find the general solution of the nonhomogeneous linear DE, showing all work. Also clearly state the particular solution yp that you obtain using the reduction of order process and show a clear check that your particular solution yp satisfies the original nonhomogeneous DE. [Do NOT use the Method of Undetermined Coefficients here!]
''y + 6y' + 9y + 4e^x
Note: Use the characteristic polynomial to find a first solution yi of the associated homogencous DE.)
Answer:
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.
Step-by-step explanation:
Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation
[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]
which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.
To use the order reduction method, assume
[tex] y = v(x)y_h(x)[/tex]
where v(x) is an appropiate function. Using this, we get
[tex]y'= v'y+y'v[/tex]
[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]
Plugging this in the original equation we get
[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]
re arranging the left side we get
[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]
Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation
[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]
We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is
[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]
Or equivalently
[tex]w' = 4e^{4x}[/tex]
By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.
So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.
Then, the final solution is
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants
Rectangle is 5ft in length and 3 ft in height. What is the area of the rectangle
Answer: 15
Step-by-step explanation:
to find the area multiply the length by height
in this case it’s 5ft and 3ft
5 • 3 = 15
A=15
Heidi looks at the donkeys and
tourists. She counts 50 heads
and 114 legs.
How many donkeys are there?
o
ANSWER:
O The retired question
Answer:
7 donkeys
Step-by-step explanation:
Given
A system consisting of donkeys and tourists
Heads = 50
Legs = 114
Required
Calculate number of donkeys.
Represent donkeys with D and tourists with T.
By means of identification; donkeys and tourists (human) both have 1 head.
This implies that
Number of Heads = D + T
50 = D + T ----- Equation 1
While each donkey have 4 legs, each tourists have 2 legs.
This implies that
Number of legs = 4D + 2T
114 = 4D + 2T ---- Multiply both sides by ½
114 * ½ = (4D + 2T) * ½
57 = 4D * ½ + 2T * ½
57 = 2D + T ----- Equation 2
Subtract equation 1 from 2
57 = 2D + T
- (50 = D + T)
---------------------
57 - 50 = 2D - D + T - T
7 = D
Recall that D represents the number of donkeys.
So, D = 7 implies that
The total number of donkeys are 7
To solve the system given below using substitution, it is best to start by
solving the second equation for y.
5x + 2y = 33
6y + x = 3
true or false
Answer:
False, it is easier to isolate x.
Step-by-step explanation:
6y+x=3
x=3-6y
Change 3.2t into kilograms please help me
Let's think:
1 ton ------------ 1000 kilograms
3.2 tons ----------- x kilograms
Multiply in cross
1 . x = 1000 . 3.2
x = 3200
So 3.2t = 3200 kilograms
Answer:
It is 2902.99 to be exact
Step-by-step explanation:
Please answer this correctly
Answer:
20-39 ⇒ 5
40-59 ⇒ 3
60-79 ⇒ 5
80-99 ⇒ 10
Answer:
20-39: 5
40-59: 3
60-79: 5
80-99: 10
Step-by-step explanation:
If you just added up, you can find all the values.
Carla earns $564 for 30 hours of work. Which represents the unit rate?
a) $30 per hour
b) $168 per hour
c) $18.80 per hour
d) $5.30 per hour
What is the remainder when the product of the 5 smallest prime numbers is divided by 42?
Answer:
21
Step-by-step explanation:
The 5 smallest prime numbers are 1, 2, 3, 5, and 7.
So when multiplied it equals 105.
Divide by 42 and you get 2 21/42
So you have a remainder of 21
The populations and areas of four states are shown.Which statement regarding these four states is true?
If the volume of a cube is
64 cubic feet, what is the
surface area of the cube in
square feet?
Answer:
96 ft^2
Step-by-step explanation:
volume=l^3
l=4
4x4x4=64
Surface area (4x4)=16
16x6=96
Answer:
SA =96 ft^2
Step-by-step explanation:
The volume of a cube is given by
V = s^3
64 = s^3
Take the cube root of each side
64 ^ 1/3 = s^3 ^ 1/3
4 =s
The side length si 4
The surface area of a cube is
SA = 6 s^2
SA = 6 * 4^2
SA = 6 * 16
SA =96 ft^2
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
What is -5/4 to the 2nd power?
Answer:
[tex]\frac{25}{16}[/tex]
Step-by-step explanation:
[tex](-\frac{5}{4})^2\\\\ \text {Apply power of a fraction rule: } (\frac{a}{b})^x=\frac{a^x}{b^x}\\\\(-\frac{5}{4})^2 = \frac{-5^2}{4^2}=\frac{25}{16}\\\\\boxed{(-\frac{5}{4})^2=\frac{25}{16}}[/tex]
Solve the equation.
5x + 8 - 3x = -10
x = -1
x=1
x=9
Answer:
x=-9solution,
[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]
hope this helps..
Good luck on your assignment
Answer:
x = -9
Step-by-step explanation:
5x + 8 - 3x = -10
Rearrange.
5x - 3x + 8 = -10
Subtract like terms.
2x + 8 = -10
Subtract 8 on both sides.
2x = -10 - 8
2x = -18
Divide 2 into both sides.
x = -18/2
x = -9
Choose the ratio that you would use to convert 1.5 feet to miles. Remember
that there are 5,280 feet in one mile.
Answer: B, 1 mile / 5280 ft.
Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).
A contractor is considering whether he should take on a project that promises a profit of $8800 with a probability of 0.83 or a loss (due to bad weather, strikes, etc.) of $2900 with a probability of 0.17. What is the expected profit for the contractor
Answer: 6811
Step-by-step explanation:
in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17
--
so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811
Nolan is using substitution to determine if 23 is a solution to the equation. Complete the statements.
j – 16 = 7 for j = 23
First, Nolan must substitute
for
.
To simplify, Nolan must subtract
from
.
23
a solution of the equation.
Answer:
Step-by-step explanation:
Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.
First, Nolan must substitute for the value of j in the equation.
To simplify, Nolan must subtract the value of 7 from both sides to have;
j – 16 - 7= 7 - 7
j – 23 = 0
Then Nolan must add 23 to both sides of the equation to get the value of j as shown;
j – 23 + 23 = 0+23
j = 23
23 is therefore a solution to the equation
Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.
Step-by-step explanation:
I got it right on Edge
The computer hardware company requires all of its chips purchased from its supplier of computer chips to meet specifications of 1.2 cm with the margins of error of plus and minus 0.1 cm. Based on the computer chip supplied last month, the mean length of a computer chip was 0.9 cm. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications
Answer:
Step-by-step explanation:
The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm
This means that the required length of computer chips is between 1.1cm - 1.3cm
Where 1.1cm = [1.2 - 0.1]
1.3cm = [1.2 + 0.1]
Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.
The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:
- The length of the chips.
The length of the chips his production team produces should be tailored to meet the length specification of his client.
Can someone please help me?
Answer:
''0 is neither a rational number nor an irrational number.''
Step-by-step explanation:
Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?
Answer:
[tex]j^4k[/tex]
Step-by-step explanation:
[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]
Answer:
4
Step-by-step explanation:
give me brainliest
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
A game require rolling a six sided die numbered fro 1 to 6. What is the probability of rolling a 1 or a 2?
Answer:
1/3
Step-by-step explanation:
hello,
probability of 1 = 1/6
probability of 2 = 1/6
probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0
so the answer is 2/6=1/3