EXPLANATION
Let's see the facts:
Revenue --> R(x) = 2sqrt (x) - 4 [x=number of items sold]
Cost --------> C(x) = 6 - sqrt (x)
The company will be profitable when the Revenue exceeds the cost.
Profitable condition: Revenue > Cost
Setting the two functions equal to each other and solving for x:
\(2\sqrt[]{x}-4\text{ = 6 - }\sqrt[]{x}\)Adding +sqrt(x) to both sides:
\(2\sqrt[]{x}+\sqrt[]{x}-4\text{ = 6 }\)Adding +4 to both sides:
\(2\sqrt[]{x}+\sqrt[]{x}\text{ = 6 }+4\)Adding similar terms and simplifying:
\(3\sqrt[]{x}=10\)Dividing both sides by 3:
\(\sqrt[]{x}=10/3\)Applying the power of 2 to both sides:
\(x=(10/3)^2\)Simplifying:
x=11.11
The answer is about 111. In order for a company to be profitable, their revenue must exceed their cost. Setting the two functions equal to each other and solving for x gives the minimum number of items that need to be sold in order to be profitable. OPTION B.
On Thursday, a local hamburger shop sold a combined total of 378 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Thursday?
Answer:
252 Cheese Bugers were sold on Thursday
Step-by-step explanation:
378 divided by 3=126
126+126= number of hamburgers
126= number of chese bugers
126+126=252
find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = 6 cos θ, y = 6 sin θ θ = π/4
find:
dy/dx=
d^2y/dx^2 =
slope
concavity:
The value of dy/dx is -cotθ, d^2y/dx^2 is -6cosec³θ, slope is -cotθ, concavity is -6cosec³θ.
Parametric Equations Point x = 6cosθ, y = 6sinθ and θ = π/4
We have to determine the value of dy/dx.
We can define dy/dx as;
dy/dx = (dy/dθ)/(dx/dθ)
We first define dy/dθ and dx/dθ.
x = 6cosθ y = 6sinθ
dx/dθ = -6sinθ dy/dθ = 6cosθ
Now put the value
dy/dx = 6cosθ/(-6sinθ)
dy/dx = -cotθ
Now we have to determine the value of d²y/dx².
d²y/dx² = d/dx(dy/dx)
We can write it as
d²y/dx² = \(\frac{\frac{d}{d\theta}(\frac{dy}{dx})}{dx/d\theta}\)
We first determine the value of d/dθ(dy/dx)
d/dθ(dy/dx) = d/dθ(-cotθ)
d/dθ(dy/dx) = cosec²θ
Now put the value
d²y/dx² = cosec²θ/(-6sinθ)
d²y/dx² = -6cosec³θ
Now we have to determine the slope.
Slope = dy/dx
Slope = -cotθ
Now we have to determine the concavity.
Concavity = d²y/dx²
Concavity = -6cosec³θ
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Ten upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 9. The smallest domino, #0, is 3.00 inches tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 15% taller than the one before. What is the height of domino #9?
Answer:
8.604 in.
Step-by-step explanation:
We can use the formula for compound interest to find the height of domino #9:
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).
Substituting the given values:
A = 3.00 in * (1 + 0.15)^9
Simplifying:
A = 3.00 in * 2.86797199
A ≈ 8.604 in
Therefore, the height of domino #9 is approximately 8.604 inches.
the perimeter of a different regular polygon is 75b - 20 the length of one of its sides is 15b-4 how many sides does this regular polygon have
The number of sides of the polygon, is 5
What are perimeters?The perimeter of an object is the outer boundary length, is calculated by adding all its sides.
Given that, the perimeter of a different regular polygon is 75b - 20 the length of one of its sides is 15b-4 we need to find the number of sides of the polygon,
Let the number of sides of the polygon be x,
Therefore,
(15b-4)x = 75b-20
x = 75b-20 / 15b-4
x = 5(15b-4) / 15b-4
x = 5
Hence, the number of sides of the polygon, is 5
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Need the answer to this pls
Answer:
0
Step-by-step explanation:
1. First, we should know the slope-intercept form of any equation: y = mx + b.
y = y-coordinatem = slopex = x-coordinateb = y-intercept2. In the equation y = -2/3(x), it appears that the variables we can see are y, m, and x. However, the y-intercept, b, is still there with the value of 0.
Additionally, this is a proportional relationship because it follows the format y = kx. Proportional relationships always have a y-intercept of 0.Therefore, the y-intercept is 0.
the following pair of triangles are similar. find the value of x 10 x x+2 x+14
The numerical value of x in the similar pair of triangle is 10.
What is the numerical value of x?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
From the diagram,
Side A of the small triangle = 10
Side B of the small triangle = x + 2
Side A of the Big triangle = 10 + x
Side B of the big triangle = x + 14
Hence;
Ratio of Side A to Side B of the small triangle = 10 / x + 2
Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14
Since the triangle area similar, equate the two ratio and solve for x.
10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )
Cross multiply
10( x + 14 ) = ( 10 + x )( x + 2 )
Expand using FOIL method
10x + 140 = 10x + 20 + x² + 2x
10x + 140 = x² + 12x + 20
x² + 12x + 20 = 10x + 140
x² + 12x + 20 - 10x - 140 = 0
x² + 2x - 120 = 0
Factor the left side of the equation
( x - 10 )( x + 12 ) = 0
Hence;
x - 10 = 0 and x + 12 = 0
x = 10 and x = -12
Since the dimension of the triangle cannot be negative,
x = 10
Therefore, the value of x is 10.
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If $22,000 is invested in an account earning 4.5% interest compounded continuously,
determine how long it will take the money to quadruple. Round to the nearest year.
Use the model A = Pet where A represents the future value of P dollars invested at
an interest rate r compounded continuously for t years.
OA) 31 years
B) 36 years
C) 3 years
D) 308 years
Answer:
approx 32years so pick answer A
Step-by-step explanation:
22000x4=88000
22000x1.045^t
22000x1.045^31=84,104
22000x1.045^32=89,979
A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 70 and a standard deviation of 10.How many different samples of size 5 can be taken from a finite population of size 10?
252 different samples can be taken.
-------------------------
The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.
-------------------------
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
-------------------------
In this question, samples of 5 from a set of 10, so:
\(C_{10,5} = \frac{10!}{5!5!} = 252\)
252 different samples can be taken.
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Define the terms population, population parameter, sample, raw data, and sample statistic as they apply to statistical studies.
Answer:
Find the definitions below.
Step-by-step explanation:
1. Population: This refers to all the constituents or members of a particular group of people or things under study.
2. Population Parameter: This is a value that provides information about a particular aspect of the population. An example is the population mean.
3. Sample: This is a group of objects or subjects chosen from a population for the purpose of a specific inquiry.
4. Raw data: This simply refers to unprocessed data. In this case, the data is obtained but has not been critically examined using statistical mesures.
5. Sample Statistic: This is the statistical information that is derived from a given sample in a population
Please help me
please say A,B,C or D
Ali, Basti and Cian stand at three points A, B and C respectively. Suppose that the measure of angle ABC is 50 degrees , the measure of angle BAC is 60 degrees and Ali is exactly 150 ft away from Basti. Find the distance between Basti and Cian.
To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.
Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.
Using the law of sines, we can set up the following equation:
sin(50°) / 150 = sin(60°) / x
To solve for "x", we can rearrange the equation:
x = (150 * sin(60°)) / sin(50°)
Using a calculator, we can evaluate the expression:
x ≈ (150 * 0.866) / 0.766
x ≈ 168.4 ft
Therefore, the distance between Basti and Cian is approximately 168.4 ft.
At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation:
Factor 20x^2+25x-30 using the decomposition method
The factorisation of 20x² + 25x - 30 is (4x - 3)(x + 2).
How to factorise?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number .
Therefore, let's factorise the polynomial as follows:
20x² + 25x - 30
divide through by 5
4x² + 5x - 6
4x² + 8x - 3x - 6
Hence,
4x(x + 2) - 3(x + 2)
(4x - 3)(x + 2)
Therefore,
20x² + 25x - 30 = (4x - 3)(x + 2)
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Refer to the following study and the SAS output:
Aerobic fitness is measured by the ability to consume oxygen. Collecting oxygen consumption measurements data to investigate aerobic fitness can be expensive and cumbersome. A study was conducted at North Carolina State University to examine which measurements from simple exercise tests could be used to predict aerobic fitness. The sample consisted of 31 men involved in a physical fitness course at North Carolina State University. The oxygen intake rate (ml per kg body weight per minute) was measured while the men were running. The other variables collected were age (years), weight (kg), time to run 1.5 miles (minutes), heart rate while resting (beats per minute, bpm), heart rate while running (bpm), and maximum heart rate recorded while running (bpm). It is important to note that the maximum heart rate was highly correlated with the heart rate while running, so the model presented here includes only one of these variables (the latter) to avoid multicollinearity issues. Using a 0.05 significance level, we need to determine whether aerobic fitness (oxygen intake rate) can be predicted from these simple exercise test measurements.
Analysis of Variance Sum of Squares Mean Source DF Square F Value Pr> F Model Error Corrected Total 139.21044 6.21317 30 851.
What type of analysis is this?
a. Linear regression
b. One-way ANOVA
c. Two-way ANOVA
d. ANCOVA
e. Logistic regression
How many model degrees of freedom are there in this problem?
a. 1
b. 5
c. 6
d. 24
e. 25
What percentage of the variation in oxygen intake rate can be explained by the linear association between oxygen intake rate and the collection of variables given in this problem?
a. 61.0%
b. 66.8%
c. 78.1%
d. 88.4%
e. 90.4%
What is the best-predicted oxygen intake rate of a 48-year-old man weighing 77.5 kg with a resting heart rate of 52 bpm who runs 1.5 miles in 10 minutes with a running heart rate of 170 bpm?
48.9
60.6
71.8
83.5
Cannot be determined from the given information
Answer:
1- c. Two-way ANOVA
2- a. 1
3- c. 78.1%
4- 48.9
Step-by-step explanation:
ANOVA is a statistical technique designed to test mean of one or more quantitative populations. In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA.
Oxygen intake rate varies for different people. It also depends on the age factor. Oxygen intake rate is indicator of normal function of cells. A 48 year old man breath slower than a younger man. The babies breathe faster than adults.
Help 20 points (show your work)
The measure of angle ADC in the geometric system is equal to 55°.
How to determine the value of an angle related to a geometric system
In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:
m ∠ CDE + m ∠ EDF = 180°
(2 · x + 1) + (x - 7) = 180°
3 · x - 6 = 180°
3 · x = 186°
x = 62
m ∠ CDE = 2 · x + 1
m ∠ CDE = 2 · 62 + 1
m ∠ CDE = 125°
m ∠ ADC = 180° - 125°
m ∠ ADC = 55°
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Can someone PLEASEE help me
Which equation represents a linear equation
Answer:
I'm thinking it's A or C
Step-by-step explanation:
I'm sorry I can't decide ;-;
Answer:
The 4th answer.
Step-by-step explanation:
It has the equivalence that each point will be substracted 5 from y and 20 from x, but it won't change the line of the result. Sure, the position, but not the line.
C. The temperature was -12 degrees Celsius and rose to 2
degrees Celsius. What was the change in temperature?
Answer:
Step-by-step explanation:
The change in temperature is the difference between the final temperature and the initial temperature. In this case, the initial temperature was -12 degrees Celsius and the final temperature was 2 degrees Celsius. Therefore, the change in temperature is:
Change in temperature = Final temperature - Initial temperature
Change in temperature = 2 degrees Celsius - (-12) degrees Celsius
Change in temperature = 2 degrees Celsius + 12 degrees Celsius
Change in temperature = 14 degrees Celsius
So the change in temperature is 14 degrees Celsius.
Besides 40 and 1, what is one factor of 40?
Answer:
Step-by-step explanation:
40 x 1 = 40
20 x 2 = 40
10 x 4 = 40
8 x 5 = 40
What is the density of the oak board? Show your work.
What is the density of the oak board? Show your work.
Answer:
it is 5.5 inches wide, 1.5 inches thick and 3 feet long
Answer: Im not really sure if this is correct but it's what I put so I hope it is. If it's incorrect please let me know.
Step-by-step explanation:
We first need to find its mass and volume.
Mass: 8.05
Volume: Turn 3 feet into inches: 36
36in × 1.5in × 5.5in =297
Density : 8.05lb ÷ 297 cubic inches = 0.027 cubic inches
I’ll mark you as brainliest!
two person A and B spent a total of pkr 486 .Person A spent twice as much money as person B. How much money did person A spend
9514 1404 393
Answer:
pkr 324
Step-by-step explanation:
Person A spent 2/3 of the total money spent, so ...
(2/3)(pkr 486) = pkr 324 . . . spent by person A
Suppose we want to chose 2 objects without replacement from 3 objects how many ways can this be done with choice matter and with choice does not Matter
There are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
What is the factοrial?The prοduct οf all pοsitive integers less than οr equal tο a given pοsitive integer and denοted by that integer and an exclamatiοn pοint. Thus, factοrial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factοrial zerο is defined as equal tο 1.
If the chοice matters (i.e., the οrder οf the chοsen οbjects matters), then there are 3 pοssible chοices fοr the first οbject and 2 pοssible chοices fοr the secοnd οbject.
Thus, there are 3 * 2 = 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters.
If the chοice dοes nοt matter (i.e., the οrder οf the chοsen οbjects dοes nοt matter), then there are 3 chοοse 2 = 3!/((3-2)!*2!) = 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
Therefοre, there are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
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A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
Suppose you and a friend are playing a game. You can choose any two cards from the deck without looking. If the two cards you choose are both spades, you win!
You pull out one card, and then another, without putting the first one back.
What is the approximate probability that you win? Are your two choices independent or dependent events?
6%, Independent
6%, Dependent
11%, independent
11%, Dependent
The probability that you win is 6%, and the two choices are dependent events option (B) is correct.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
The probability of the first draw:
Probability = favorable outcomes/total outcomes
First draw: 1/4
For the second draw:
Second draw = 12/51
The probability that you win = (1/4)(12/51) = 3/51
In percent:
= (3/51)x100
= 5.88 = 6%
Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.
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Each of the 9 parking lots at an automobile plant holds the same number of new cars. The lots are full. If there are 431 cars in the lots, about how many cars are in each lot? Show how you estimated.
Answer:
50, I just took a number that was the closet to this and divided it by 9
(450/9=50)
what does (-3)+9/8 equal i cant get it im kinda stupid lol
Answer:
-15/8 or -1 7/8, 1.875
Step-by-step explanation:
If f(x) is a function which is continuous everywhere then we must have m= ?
The function is continuous only if m = 7.
How to find the value of m?If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2
That means that:
f(-2) = f(-2) (trivially)
Replacing the two pieces of the function we will get:
m*(-2) - 6 = (-2)^2 + 10*(-2) - 4
now we can solve that equation for m.
-2m - 6 = 4 -20 - 4
-2m = -20 + 6 = -14
m = -14/-2 = 7
m = 7
that is the value of m.
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Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r/1+1/1+1rRewrite this formula as a simple fraction. Use your formula to calculate the new tax rate after 1 year, 2 years, 5 years, and 15 years. 1 year____2 years____5 years___15 years____
Would tax rates increase or decrease over time? O increase O decrease Congress claims that this law would ultimately cut peoples' tax rates by 75%. Do you believe this claim? Explain.
The simple fraction is \(= \frac{x + 1}{2x + 1}r\)
In math, what is a fraction?
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction.
Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
\(= \frac{r}{1 + \frac{1}{\frac{1 + 1/x }{} } }\)
\(= 1 + 1/x\)
= x + 1/x we have
= \(\frac{1}{x + 1/x}\)
\(= \frac{x}{x + 1}\)
\(= 1 + \frac{x}{x + 1}\)
\(= \frac{ 2x + 1}{x + 1}\)
r%*x+1/(2x+1)
\(= \frac{x + 1}{2x + 1}r\)
reduce to the appropriate fraction. The denominator was then brought up and the numerator down as I normalized.
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The complete question is -
Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r 1 1 1 1 x . Rewrite this formula as a simple fraction.
if P = (4,2), Find: Rx=3 (P). Pls help!!
The coordinates of the reflected point P' will be (4, -3).
When a point is reflected over the x-axis, its y-coordinate changes sign.
In this case, the point P has coordinates (4,3).
To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.
So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.
Therefore, the coordinates of the reflected point P will be (4, -3).
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Answer:
Step-by-step explanation:
Sketch a graph of f(x)={- 5 if x < -2 2x-1 if-2 < x≤ 2 0 if x>2. (piecewise)
A graph of the given piecewise-defined function is shown in the image below.
What is a piecewise-defined function?In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.
In conclusion, this piecewise-defined function has a removable discontinuity.
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