The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.
Explanation:The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, we have:
R(x) = 550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000
C(x) = 880[tex]x^3[/tex] - 21,000[tex]x^2[/tex] + 150,000x - 160,000
To find P(x), we subtract C(x) from R(x):
P(x) = R(x) - C(x)
Substituting the given functions, we get:
P(x) = (550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000) - (880x3 - 21,000[tex]x^2[/tex] + 150,000x - 160,000)
Simplifying, we combine like terms:
P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000
Therefore, the profit function, P(x), can be expressed as a polynomial in standard form as -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.
The profit function, P(x), is found by subtracting the cost function, C(x), from the revenue function, R(x). After performing the subtraction and simplifying, the profit function in standard form is P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000.[/tex]
To find the profit function, P(x), we must subtract the cost function, C(x), from the revenue function, R(x). Given the functions:
R(x) = [tex]550x^3 - 12,000x^2 + 83,000x + 7,000[/tex]
C(x) =[tex]880x^3 - 21,000x^2 + 150,000x - 160,000[/tex]
We perform the subtraction:
Combine like terms:P(x) = [tex](550x^3 - 12,000x^2 + 83,000x + 7,000) - (880x^3 - 21,000x^2 + 150,000x - 160,000)[/tex]
Expand and group terms:
P(x) =[tex]550x^3 - 12,000x^2 + 83,000x + 7,000 - 880x^3 + 21,000x^2 - 150,000x + 160,000[/tex]
P(x) = [tex](550x^3 - 880x^3) + (-12,000x^2 + 21,000x^2) + (83,000x - 150,000x) + (7,000 + 160,000)[/tex]
Simplify the terms:
P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]
The profit function, P(x), in standard form is:
P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]
Find the missing factor BBB that makes the equality true.
21y^4=(B)(7y^3)21y
4
=(B)(7y
3
)
Answer:21y^4= B*7y^3
B=(21y^4)/(7y^3)
B=3y
i think this is correct
What is the slope of the line that contains these points?
x
12
13
14
15
y
-4
2
8
14
Answer:
6x-76
Step-by-step explanation:
If you graph it out, you'll realize it makes a line that cuts the y-intercept at -76, thus the last value. The slope also has a gradient of 6, thus the coeffecient of x.
Final answer:
The slope of the line through the points given is 6, calculated using the slope formula with the rise over run between the two points.
Explanation:
The slope of a line is calculated by finding the ratio of the vertical change (the rise) to the horizontal change (the run) between two points on the line. Using the coordinates provided (12, -4) and (15, 14), we can apply the slope formula slope (m) = (y_2 - y_1) / (x_2 - x_1). Plugging in the values gives us (14 - (-4)) / (15 - 12) = 18 / 3 = 6. Therefore, the slope of the line that contains these points is 6.
Of students taking a course through NCVPS, 7/15 play a sport and 3/5 play a musical instrument.The probability that a NCVPS student plays a sport or a musical instrument is 2/3. What is the probability that a NCVPS student play a sport AND a musical instrument?
Answer: 7/25 or 0.28
Step-by-step explanation:
Given that 7/15 play a sport and 3/5 play a musical instrument.
The probability that a NCVPS student play a sport AND a musical instrument means multiplication of the two probabilities
7/15 × 3/5 = 21/75 = 7/25
The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes. What is the probability that a random sample of 40 students will have a mean completing time greater than 25 minutes
Final answer:
To find the probability that the sample mean is between two hours and three hours, calculate the z-scores and use the z-table to find the probability.
Explanation:
To find the probability that the sample mean is between two hours and three hours, we need to calculate the z-scores corresponding to these values and use the z-table to find the probability.
First, we calculate the z-score for two hours:
z = (2 - 2.5) / (0.25 / sqrt(60)) = -3.16
Next, we calculate the z-score for three hours:
z = (3 - 2.5) / (0.25 / sqrt(60)) = 3.16
Using the z-table, we find that the probability of getting a z-score between -3.16 and 3.16 is approximately 0.9986. Therefore, the probability that the sample mean is between two hours and three hours is approximately 0.9986.
]
Assume that when adults with smartphones are randomly selected, 46% use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.
Answer:
0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.
Step-by-step explanation:
We are given the following information:
We treat adult using smartphones in meetings or classes as a success.
P(Adult using smartphone) = 46% = 0.46
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 9
We have to evaluate:
[tex]P(x = 3)\\\\= \binom{9}{3}(0.46)^3(1-0.46)^6\\\\= 0.2027[/tex]
0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.
Final answer:
To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.
Explanation:
To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula. The binomial probability formula is given by:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where:
P(X=k) is the probability of getting exactly k successes
C(n,k) is the combination formula
p is the probability of success (46% in this case)
n is the total number of trials (9 in this case)
Plugging in the values, we get:
P(X=3) = C(9,3) * (0.46)^3 * (1-0.46)^(9-3)
P(X=3) = 84 * (0.46)^3 * (0.54)^6
P(X=3) = 0.299 (rounded to three decimal places)
NEED HELP ON THIS WILL GIVE CROWN
Matt buys 14 jars of paint. Each jar contains 300 milliliters of paint.
How many liters of paint in all is there in the jars?
4.2 L
42 L
420 L
4,200 L
a scientist has 400ml of a 8% solution. how much water needs to be added to lower it to a 2% solution?
1200 ml of water needs to be added to lower it to a 2% solution.
Step-by-step explanation:
Given that,
A scientist has 400ml of a 8% solution.
you need to find how water is required to lower the 400 ml to 2% solution.
Let 'x' be the amount of water added to lower it 2% solution.
The formula is given by,
volume of the liquid × % of solution = volume of the new liquid × new %
This can be denoted in chemical relationship ⇒ c₁v₁=c₂v₂ where c is concentration and v is volume .
Now, to find the total volume of new liquid in ml :
400 ml = v₁
0.08= c₁
0.02=c₂
v₂=?
400 × 0.08 =v₂ × 0.02
v₂=1600 ml
To find the x value :
Amount to be added = volume of new liquid - volume of liquid before.
⇒ x =1600-400
⇒ x =1200 ml
∴ 1200 ml of water needs to be added to lower it to a 2% solution.
Mr Tan invested $5000 in an endowment fund for
5 years. The fund pays an interest compounded
yearly. At the end of 5 years, he received a total of
$5800. Find the interest rate.
Answer:
Compound Interest Formula Solved For Rate:
log (1 + rate) = {log(total) -log(Principal)} ÷ Years
log (1 + rate) = {log(5,800) -log(5,000)} ÷ 5
log (1 + rate) = [3.7634279936 -3.6989700043] / 5
log (1 + rate) = 0.0644579893 / 5
log (1 + rate) = 0.0128915979
Then we raise 10 to the power of 0.0128915979 which equals
1.0301289629 = 1 + rate
Therefore, rate = .0301289629 and we multiply by 100 to make a percentage:
3.01289629 %
Source: https://1728.org/compint2.htm
https://1728.org/compint.htm
Step-by-step explanation:
Using the compound interest formula and the provided values, the interest rate for Mr Tan's investment is calculated to be approximately 3.02%.
Explanation:The subject problem belongs to the topic of Compound Interest in mathematics. The formula used for compound interest is A = P (1 + r/n)^(nt), where A represents the total amount received, P represents the principal (initial investment amount), r represents the rate of interest, n represents the number of times interest is compounded per time period, and t represents the time period.
In this problem, Mr Tan's initial investment, P, is $5000. The total amount, A, he received after 5 years is $5800. The interest is compounded annually meaning that n is 1. We rearrange the compound interest formula to solve for the interest rate: r = [(A/P)^(1/nt) - 1]n .
Using Mr Tan's values, the calculation becomes: r = [(5800/5000)^(1/5) - 1]*1. Thus, the interest rate is approximately 0.0302 or 3.02%.
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What is the midpoint of the straight line segment joining the points (-2, 9) and (3, -2)?
Answer:
x2-x1/y2-y1
-2--2/3-9=-2+2/3-9
=0/-3
If a certain number is added to the numerator of 29/62 and twice the number is subtracted from the denominator, the result is equivalent to 3/4. What is the number? A) 4 B) 5 c)6 d) 7
(15points)
Answer:
Correct option: (d) 7.
Step-by-step explanation:
Let the number be denoted by x.
The original fraction is: [tex]\frac{29}{62}[/tex]
Add x to the numerator, i.e. 29 and subtract 2x from the denominator, i.e. 62.
The new fraction is: [tex]\frac{29+x}{62-2x}[/tex]
Now equate the new fraction to [tex]\frac{3}{4}[/tex] and solve for x as follows:
[tex]\frac{29+x}{62-2x}=\frac{3}{4}[/tex]
[tex]4(29+x)=3(62-2x)\\116+4x=186-6x\\4x+6x=186-116\\10x=70\\x=7[/tex]
The value of x is 7.
Thus, the correct option is (d).
Write the standard form of the equation of the circle with its center at (-3,0), and a radius of 6.
What is the equation of the circle in standard form?
Ok i'm so sorry but if you could answer this for me? nobody else will! >0<
Enter the equation of the circle described below.
Center (-3, 0), radius /5
Answer:(X+3)^2 +y^2 =25
This is the correct answer, i just found it out
cost of x articles at 2 dollars each
Answer:
2x
Step-by-step explanation:
Cost of x articles at 2 dollars each = 2x
What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?
a.Negative StartFraction 4 Over 7 EndFraction
b.StartFraction 28 Over 29 EndFraction
c.2
d.4
The value of n in given proportion is 16
Solution:
We have to find the value of "n" in the proportion
Given proportion is:
[tex]\frac{n}{28} = \frac{4}{7}[/tex]
We can solve the above proportion by cross-multiplying
Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction
Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction
Set the two products equal to each other
Solve for the variable
[tex]->\frac{n}{28} = \frac{4}{7}[/tex]
[tex]-> 7 * n = 4 * 28[/tex]
[tex]-> n = \frac{4 * 28}{7}[/tex]
[tex]-> n = 4 * 4 = 16[/tex]
Thus the value of n in given proportion is 16
Answer:
the value of n in given proportion is 16
Step-by-step explanation:
The point (4,10) is in each scatterplot. In which one is it an outlier?
Answer:
A
Step-by-step explanation:
yy chi u yfgbngny NYC tnfnbfrbcsdv
Answer:
A
Step-by-step explanation:
What is the approximate volume of the cylinder of 4cm and 9cm? Use 3.14 for π.
The volume of the cylinder is 452.16 cubic centimeter
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of cylinder
Radius of cylinder is 4cm and height is 9cm
The formula for volume of cylinder = πr²h
Plug in the values of r and h
Volume = π(4)²(9)
= π×16×9
=3.14×16×9
=452.16 cubic centimeter
Hence, the volume of the cylinder is 452.16 cubic centimeter
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The approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm is 452.16 cm³, using the formula V = πr²h with π approximated as 3.14.
Calculating the Volume of a Cylinder
To find the approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm using 3.14 for π, you can use the formula for the volume of a cylinder, which is V = πr²h. In this case, V = 3.14 × (4 cm)² × 9 cm.
First, calculate the area of the base (which is a circle) by squaring the radius and multiplying by π: Area = π × r² = 3.14 × 4² = 3.14 × 16 = 50.24 cm². Next, multiply the area of the base by the height of the cylinder to get the volume: Volume = Area × Height = 50.24 cm² × 9 cm = 452.16 cm³.
Therefore, the approximate volume of the cylinder is 452.16 cm³.
You mix the letters A, C, Q, U, A, I, N, T, A, N, C, and E thoroughly. Without looking, you select one letter. Find P(Q or C) as a fraction, a decimal, and a percent.
Answer:
P(Q or C) = 0.25
Step-by-step explanation:
We are given the following in the question:
Letters:
A, C, Q, U, A, I, N, T, A, N, C, E
Total number of observations, n = 12
We have to find the probability that a randomly selected letter is Q or C.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P(Q or C) =
[tex]=\dfrac{\text{n(Q or C)}}{n} = \dfrac{3}{12} =0.25 = 25\%[/tex]
Thus,
P(Q or C) = 0.25
Calculator question.
Whats is the minimum window that allows r^2=4cos(2theta)
multiple choice
A. [0,2pi]
B. [0,pi]
C. [-2pi,2pi]
D [0,pi/2]
Answer:
D. [0,pi/2]
Step-by-step explanation:
when Ф = 0 in radian
r²= 4cos (2(0))
r² = 4 * 1
r² = 4
∴ r = √4 = 2
r = 2.
when Ф = π/2 in radian
r²= 4cos (2(π/2))
r² = 4 * -1
r² = -4
∴ r = 0
1 + 4x = -5 + 7x
Help plz
Answer:
x=2
Step-by-step explanation:
1 + 4x = -5 + 7x
Subtract 4x from each side
1 + 4x-4x = -5 + 7x-4x
1 = -5+3x
Add 5 to each side
1+5 = -5+5+3x
6 = 3x
Divide each side by 3
6/3 = 3x/3
2 =x
what is the area of a 3in by 3in square
Final answer:
The area of a 3in by 3in square is calculated by squaring the side length. The area is 9 square inches.
Explanation:
The area of a 3in by 3in square can be calculated by multiplying the length of one side by the length of another side since the sides are equal in a square. In this case, both sides measure 3 inches.
The formula for the area of a square is:
Area = side × side
Applying the formula for our 3in by 3in square:
Area = 3in × 3in = 9 square inches
This straightforward calculation represents how the surface area of a square object changes when the sides of the square are altered. When the sides of a square are scaled down by a fraction, the area changes by the square of that fraction (e.g., scaling down by 3/4 leads to an area that is 9/16 of the original).
find the value of x in the given right triangle
Step-by-step explanation:
It is a right angled triangle so with reference angle 37°
hypotenuse (b) = 10
perpendicular (p) = x
So
tan 37° = p/ b
0.75 = x / 10
x= 0.75/10
Therefore x = 0.075
Hope it will help you :))
which term means 1/1000 decimeter, millimeter, kilometer, decameter
Answer:
millimeter
Step-by-step explanation:
1/1000
Need help now please
Which model accurately represents the chemical equation 2H2 + O2è 2H2O?
Answer:
B
Step-by-step explanation:
-The balanced chemical reaction of oxygen and water is written as:
[tex]2H_2_{(g)}+O_2_{(g)}->2H_2O_{(l)}[/tex]
-You notice that 2 moles of hydrogen gas reacts with one mole of oxygen gas to form 2 moles of water
-Hence, the correct choice is B
Which fraction has a terminating decimal as its decimal expansion?
Answer:
fraction which has a terminating decimal as its decimal expansion is:
1/5
Step-by-step explanation:
We are given 4 fractions:
1/3 , 1/5 , 1/7 and 1/9
We have to find which fraction has terminating decimal.
1/3 = 0.33333...
1/5 = 0.2
1/7 = 0.142857142857...
1/9 =0.11111.....
Hence, fraction which has a terminating decimal as its decimal expansion is:
1/5
Final answer:
A fraction will have a terminating decimal if its denominator is a power of 2, a power of 5, or a combination of both since the base of our number system is 10. Examples like 1/8 and 5/16 have terminating decimals because their denominators are powers of 2.
Explanation:
A fraction will have a terminating decimal expansion if its denominator can be written in the form 2n5m, where n and m are nonnegative integers. This is because the base of our number system is 10, which is 2×5. So any fraction with a denominator that is a factor of a power of 10 will have a terminating decimal expansion.
Example:
Consider the fraction 1/8. Since 8 is 23, which is a power of 2, 1/8 has a terminating decimal of 0.125.For the fraction 5/16, the denominator 16 is 24. Because it contains only the prime factor 2, 5/16 has a terminating decimal of 0.3125.In contrast, a fraction like 1/3 does not have a prime factorization that matches the form 2n5m and therefore has a non-terminating decimal expansion (0.333...).
A rectangular box has dimensions 4 ft by 5 ft by 2 ft. Increasing each dimension of the box by the same amount yields a new box with volume six times the old. Find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.
Answer:
(4+x)(5+x)(5+x) = 700
x^3 + 14x^2 + 65x + 100 = 700
x^3 + 14x^2 + 65x - 600 = 0
x = 4.225
rounding = 4.23
Step-by-step explanation:
To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?
Answer:
Step-by-step explanation:
Let the number of allowable guess be x.
The difference between allowable guess and 645 must not exceed 20.
So, either,
|645 - x| ≤ 20
Or
|x - 645| ≤ 20
where that sign represents the absolute sign.
Hope this Helps!!!
Answer:
| x - 645 | = 20
665
Step-by-step explanation:
We have to guess the amount of beans in a jar to be within 20 of the actual number.
Therefore, the total has to be equal to 20.
We know that the equation required to calculate the minimum and maximum quantity of beans that will win the contest will be:
| x - 645 | = 20
But as we want is the maximum, we break the absolute value and assume "+"
Thus:
x - 645 = 20
fixed for x:
x = 20 + 645
x = 665
The maximum guess you could win is 665
The hypotenuse of a right triangle is 12, and one of the legs is 4, what’s the missing leg
Answer:
About 11.31
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + b^2 = 12^2
16 + b^2 = 144
-16 -16
b^2 = 128
Take the square root of both sides
b= approximately 11.31
What are the solution(s) of the quadratic equation 98 – x2 = 0?
x = Plus or minus 2 StartRoot 7 EndRoot
x = Plus or minus 6 StartRoot 3 EndRoot
x = Plus or minus 7 StartRoot 2 EndRoot
no real solution
Answer:
c on ed
Step-by-step explanation:
just took the unit test
Answer:
The answer is c
Step-by-step explanation:
98 - x² = 0
x² = 98
x = ±√98
Lets factor 98
98 | 2
49 | 7
7 | 7
1
So, 98 = 2 . 7 . 7 = 2 . 7²
x = ±√2.7²
x = ±7√2
Hope this helps!!!
Item 5 A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m PreviousFinish
Answer:
14 m
Step-by-step explanation:
We are given that
Height of tree=AB=12 m
[tex]\theta=40^{\circ}[/tex]
We have to find the distance from the spotlight to the base of the tree.
We know that
[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]
[tex]\frac{AB}{BC}=tan40[/tex]
[tex]\frac{12}{BC}=tan40[/tex]
[tex]BC=\frac{12}{tan40}=14.3\approx 14[/tex]
Hence, the distance from the spotlight to the base of the tree=14 m
NEW YORK
The standard configuration for a New York license
plate is 3 digits followed by 3 letters.
Source: New York State Department of Motor Vehicles
How many different license plates are possible
if digits and letters can be repeated?
234 ABC
O 1757600
1577600
12812904
11232000
The total number of possible New York license plates is 17,576,000.
The number of different license plates possible for a standard configuration in New York, where a license plate is composed of 3 digits followed by 3 letters, can be determined through combinatorial math.
Step-by-Step Solution:
There are 10 possible digits (0-9) and 26 possible letters (A-Z).Since repetitions are allowed, we calculate the total number of combinations for digits and letters separately.The number of ways to choose 3 digits is 10 3 = 10 × 10 × 10 = 1000.The number of ways to choose 3 letters is 26 3 = 26 × 26 × 26 = 17576.Multiplying these two results together gives the total number of possible license plates: 1000 × 17576 = 17576000.Solve the system of equations using the substitution method.
-5x − 3y = 16
y = x
Answer:
-5x - 3x = 16
-8x = 16
x = -2
y = x
Step-by-step explanation:
Answer:
(-2, -2)
Step-by-step explanation:
Make use of the 2nd equation to eliminate x or y in the 1st equation:
-5x - 3(x) = 16
Then -8x = 16, and x = -2. Since we are told that y = x, y = -2.
The solution is (-2, -2).