Answer:
15.94
Step-by-step explanation:
(2+h)² + h² =24²
4+4h+h²+ h² =24²
2+2h+h²= 576/2
h²+2h-286=0
solve h=15.94
Cost and revenue functions. Please tysm!!!
The profit function is P ( x ) = 2x² + 5x - 12 and the number of months during which the company is not making a profit is x = 1.5 years = 18 months
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the profit function be represented as P ( x )
Let the cost function of the company be C ( x ) = 17 - 8x - 2x²
Let the revenue function of the company be R ( x ) = 5 - 3x
Now , Profit = Revenue - Costs
Substituting the values in the equation , we get
P ( x ) = R ( x ) = C ( x )
P ( x ) = 5 - 3x - ( 17 - 8x - 2x² )
On simplifying the equation , we get
P ( x ) = 2x² + 5x - 12
Now , when the profit of the company is 0
2x² + 5x - 12 = 0
On factorizing the equation , we get
2x² + 8x - 3x - 12 = 0
2x ( x + 4 ) - 3 ( x + 4 ) = 0
Taking the common factors of the equation , we get
( 2x - 3 ) ( x + 4 ) = 0
The value of x cannot be negative , so
2x - 3 = 0
Adding 3 on both sides of the equation , we get
2x = 3
Divide by 2 on both sides of the equation , we get
x = 3/2 years
Therefore , the number of months x = 18 months
Hence , the equation is solved
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Please help me with this question.
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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7 Jon is using square ceramic tiles, each 20cm x 20cm, to cover a rectangular worktop in his greenhouse. He can fit exactly 6 tiles along the shorter edge of the worktop and 15 along the length. (a) How many tiles will he use, altogether, to cover the orktop? (b) What is the length of the worktop? Give your answer in metres (m). ............m
Answer:
(a) The number of tiles Jon will use to cover the worktop is 6 * 15 = 90 tiles.
(b) To find the length of the worktop, we first need to find the length of each tile, which is 20 cm = 0.2 m.
The length of the worktop is then 0.2 m * 6 tiles = 1.2 m.
The width of the worktop is 0.2 m * 15 tiles = 3 m.
So, the length of the worktop is 1.2 m and the width is 3 m.
can someone please give me 4 examples of problem of radical operation
Step-by-step explanation:
The answer is do ur homework ur self
Find all values of x where f(x)=-7.
Answer: A line parallel to the x-axis and at a distance of 7 units above the x-axis.
A house was valued at $388,000. Over several years, the value decreased by 19%, giving the house a new value.
(a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal.
New value = x Old value
(b) Use your answer in part (a) to determine the new value.
New value: s
X
5
(a) New value = 0.81 * Old value
(b) New value = 0.81 * $388,000 = $313,480.
What is the area of a circle that has a circumference of 24¯?
Answer:
Below
Step-by-step explanation:
Circumf = pi * 2 r
Circumf/(2pi ) = r
area = pi r^2
= pi * (circumf/2pi)^2
= circumf^2 / 4 pi =
24^2 / (4 pi) = 45. 8 units^2
Answer:
45.84 units^2
Which of the following variables use the ratio scale of measurement? Income Temperature Gender Social security number
Income normally uses a ratio scale of measurement.
Hence, option (a) is correct choice.
A ratio scale is a numerical scale with a genuine zero and equal gaps between adjacent points. A zero on a ratio scale, unlike an interval scale, indicates the complete absence of the variable being measured. Ratio scales include length, area, and population.
A ratio scale may be used to label variables, arrange them in order, and calculate the equal distance between variables. The ratio Scale enables unit conversion. British thermal units, such as Joules, kilograms, and grams, are ratio scale units.
As several elements of a given unit, interval scale may quantify size and magnitude. A ratio scale can be used to quantify size and magnitude by dividing one designated unit by another.
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A rectangle is 3 feet wide and has an area of 438 square feet. What is the
perimeter of the rectangle?
Answer:
Area is 438 Square Feet
Perimeter is 298
Step-by-step explanation:
Area is 438 Square Feet
Area= L x W
438 = L x 3
438 divided by 3 = 146
L=146
Perimeter is 2 (L x W)
2 (146x3)
Perimeter is 298
a child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling back down into the ground. Select the best description of the range of this function.
The range includes all numbers from 0 to 12.5. So correct option is D.
What do you mean by probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.
Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.
Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Please I need help , thanks
The statements that are true on the graph include:
The point ( -8, 9 ) lies on the line The point ( 0, 4 ) lies on the line The point ( 4, 0 ) lies on the line What points lie on the line ?At the point where the line hits x = 4, the y coordinates would be 0. This means that the point ( 4, 0 ) lies on the line. The point where the line crosses x = 0, y is the value of 4 which means that ( 0, 4 ) lies on the line.
The point ( - 8, 9 ) also lies on the line because as the line extends upwards, it would intersect the point ( - 8, 9 ).
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18. 60 minutes is 20% of
minutes.
Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. Shape of distribution:
Answer: The shape of the distribution of the age of first heart attack in the US population who have had at least one heart attack is likely to be positively skewed, with the majority of cases occurring in older age groups and a relatively small number of cases occurring in younger age groups. The frequency of heart attacks generally increases with age, reaching a peak in the older age groups.
Step-by-step explanation:
Over the last three evenings, Elsa received a total of 96 phone calls at the call center. The first evening, she received 8 more calls than the second evening. The third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answer:30, 22, 44
Step-by-step explanation: 2x+x+(x+8) represents how many calls for each evening. you simplify,
2x+x+(x+8)=4x+8
you know the total is equal to 96, so you do 4x+8=96.
x=22 calls for the SECOND evening. Next, you double and add 8 to get each evening.
EASY POINTS 12 POINTS!
Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
(x, y) = ????
Answer: y-int = (0,7)
x-int= (-7,0)
Step-by-step explanation:
-x+2y=7
2y=x+7
y-int = (0,7)
x-int= (-7,0)
on the graph, (1,4) (2, 4.5) (3, 5) etc
In a large IT company, 75% of programmers are male while 36% know Python. Twenty-seven percent of the programmers are male and know Python.
a- If a randomly selected programmer turns out to be male, what is the probability that he knows Python? Round your answer to four decimal places.
b- Are "being male" and "knowing Python" independent? Justify your answer using relevant probabilities.
Are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that In a large IT company,
75% of programmers are male while 36% know Python.
27% of the programmers are male and know Python.
We need to find the probability that he knows Python
P(M)=0.75
P(P)=0.36
P(MUP)=0.27
The probability that he knows Python is 0.36-0.27=0.09
Independent events are those events whose occurrence is not dependent on any other event.
Hence, are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python
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Two people are working on a joint project. Each person i puts in some effort x i ∈[0,1], which costs x i 2, and the outcome of the project is worth 2x1x2 . The worth of the project is split equally between them, regardless of their effort. a. Find the Nash equilibria of the game. b. Determine whether there are effort levels that yield a total payoff higher than that of the Nash equilibrium (Hint: factor the total payoff function).
a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Nash Equilibrium & Total Payoffa. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.
In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:
pi = (2x1x2) / 2 = x1x2
By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:
dpi/dx i = x2 - xi = 0
Since xi is in the range [0,1], we have xi = x2.
Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b. Total Payoff: The total payoff of the project is given by:
pt = x1x2 + x1x2 = 2x1x2
By factoring the total payoff function, we get:
pt = 2x1x2 = 2x1x1 = 2x12
So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.
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Hellllp I neeeeddd helllp asap
Answer:
B.80
Step-by-step explanation:
use of pythagoras theorem.
a^2 + b^2 = c^2
where c is hypotenuse
Answer:
D
Step-by-step explanation:
first we can see from question is finding perimeter which means first step we need is
24+24=48
second , we can know it from picture
ABD=[tex]\frac{1}{2}[/tex] times 60= 30, which means it is 1/2 marks
P=DB/BA
which we see DB=BE
so 2 time DB( or BE)=18 which is 18
so we just need use 24+24+18=66
Which expression is equivalent to g^2h√5g?
Shannon planted t fewer trees than toby. Toby planted 6 trees . Choose the expression that shows how many trees Shannon planted
Shannon planted 6 - t trees.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
Shannon planted t fewer trees than toby.
Toby planted 6 trees.
Shannon planted.
= t - 6 trees.
Therefore, the result is 6 -t.
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Categorize the type of sampling (simple random sample, stratified sample; systematic sample; cluster sample; or convenience sample) used: To judge the appeal of a proposed television sitcom, a random sample of 10 people from each of three different age categories was selected and those chosen were asked to rate a pilot show: simple random sample stratified sample systematic sample cluster sample
The type of sampling used to judge the appeal of the television sitcom is a b) stratified sample.
A stratified sample is a type of sampling where the population is divided into subgroups or strata based on certain characteristics, and then a random sample is taken from each of these strata. In this case, the population is divided into three age categories and a random sample of 10 people is selected from each category.
Stratified sampling is useful when the characteristics of each stratum are different and you want to make sure that the sample accurately reflects the entire population. By dividing the population into age categories, this method ensures that the sample is representative of the different age groups and their opinions on the pilot show.
Overall, stratified sampling is a useful method for accurately estimating the characteristics of a population by taking into account any relevant differences within it.
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Farthest Point. Which of the following points is farthest from P (–1, 3)? Show the necessary solutions.
a. R(2, 4)
b. S(-4, 1)
c. T(0, 5)
d. U(3, -2)
The farthest point from P is point U with a distance of 6.4 units
How to determine the farthest pointFrom the question, we have the following parameters that can be used in our computation:
P = (-1, 3)
To determine the farthest point, we make use of the distance formula represented as
distance = √[(y₂ - y₁)² + (x₂ - x₁)²]
So, we have
PR = √[(4 - 3)² + (2 + 1)²] = 3.2
PS = √[(1 - 3)² + (-4 + 1)²] = 3.6
PT = √[(5 - 3)² + (0 + 1)²] = 2.2
PU = √[(-2 - 3)² + (3 + 1)²] = 6.4
This means that the fartherst point is point U
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For every 50p Max saves, his mum gives him 20p. Max saves £5.50. How much does he have altogether, including the money his mum gives him?⭐⭐⭐⭐⭐
Max saves £5.50, which is 550p.
For every 50p Max saves, his mum gives him 20p, so for 550p, he gets 550/50 * 20p = 440p from his mum.
Altogether, Max has 550p + 440p = 990p, which is equivalent to £9.90.
In a scientific study there are 10 guinea pigs, 4 of which are pregnant. If 3 are selected at randorm without replacement, find the probability that all are pregnant. Enter your answer as a fraction or a decimal rounded to 3 decimal places.
P (3 are all pregnant) =
The probability that all 3 selected guinea pigs are pregnant is 0.033.
Let's consider the event "A" as "3 guinea pigs selected are all pregnant". The number of ways to choose 3 guinea pigs from the 4 pregnant ones is C(4,3) = 4. The total number of ways to choose 3 guinea pigs from the 10 is
C(10,3) = 120.
The probability of event "A" is given by
P(A) = C(4,3) / C(10,3) = 4 / 120 = 1/30.
Therefore, the probability that all 3 guinea pigs selected are pregnant is 1/30 or 0.033 rounded to 3 decimal places.
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I earns 875,00 in five working days so how many days must I work in order to earn R3500,00
The number of days you will need to work in order to earn R3500,00 given the ratio of amount earned in 5 days is 20 days
How many days will I earn R350,000?If in 5 working days, you earn R87,500
Then, you will earn R350,000 in x working days
The task content can be solved using the concept of equivalent ratio;
Number of days : amount earned
5 : 87,500 = x : 350,000
5/87500 = x / 350,000
cross product
5 × 350,000 = x × 87500
1,750,000 = 87,500x
divide both sides by 87,500
x = 1,750,000 / 87,500
x = 20
Hence, you need to work for 20 days in order to earn R350,000
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Solve with full solution
Q1. A ladder 9 m long reaches to a point below the top of building. From the foot of the ladder, the angle of olevation of the building is 60°. Find the height of the building. Here the ladder makes the angle 45° with ground. (Ans=11.02m)
Q2. A vertical pole is divided in the ratio 9:1 .If both segments of pole subtend equal angles to each other at a distance of 20m away from the foot of pole, find height of pole. (Ans=178.8m)
Answer:
Q 1 : Solution:
Let the height of the building be h.
We know that tan(60) = h/9 (angle of elevation formula)
h = 9tan(60) = 9sqrt(3)/3 = 3*sqrt(3) = 3.464101615 m (approx)
Q 2 : Solution:
Let the height of the pole be h.
Let the shorter segment be x, and the longer segment be 9x.
We know that tan(theta) = x/(20) = 9x/(20+h) (angle subtended formula)
By cross multiplying and simplifying, we get:
x = (20h)/(h+180)
The ratio of the segments is x:9x = 1:9, so x = (20h)/(h+180) = 1/10 * h
h = 10x = (20h)/(h+180)
h^2 + 180h - 20h^2 = 0
h(20-h) = 0
h = 0 or h = 20
Since the pole has a height, h = 20m is not possible, so the height of the pole is h = 178.8m
Six less than six times a number is the same as eight times the number. Find the number.
The number is
Answer:
below
Step-by-step explanation:
6x -6 = 8 x
-6 = 2x
x = -3
Answer:
X = -3
Step-by-step explanation:
Let's slowly create an equation
Six less than six times a number = eight times the number
if x = that number...
Six less than six times of x = eight times of x
6 less than 6 times of x is 6x-6
8 times x is simply 8x
So 6x - 6 = 8x
We can rearrange this equation by adding 6 to one side and subtracting 8x from the other
6x - 8x = 6
Combining like terms makes it -2x = 6
Last step is dividing by -2, giving us x = -3
The First and third term of geometric progression
are 5 and 80 respectively. What is the 4th term
of geometric progress.
Answer:
±320
Step-by-step explanation:
You want the 4th term of the geometric progression that has first and third terms 5 and 80.
Common ratioThe general term of a geometric sequence is ...
an = a1·r^(n-1)
for first term a1 and common ratio r.
We are given the 1st and 3rd terms, so we can find the common ratio from ...
80 = 5·r^(3-1) . . . . . use a3 = 80, a1 = 5, n = 3
16 = r^2 . . . . . . divide by 5
±4 = r . . . . . . . . take the square root
Fourth termThe 4th term will be the product of the 3rd term and the common ratio:
a4 = a3·(±4) = 80·(±4) = ±320
The fourth term is -320 or +320.
Help need a answer asap
The polynomial
negative -19x^2+181x+14,420
represents the electricity generated (in gigawatts) by geothermal sources during 2002-2007. The polynomial
866x^2–78x+10,190 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002 - 2007
Step-by-step explanation:
To find the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007, we need to add the two given polynomials.
The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 would be:
negative -19x^2+ 181x + 14,420 + 866x^2 – 78x + 10,190
Simplifying, we get:
847x^2 + 103x + 24,610
So the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is 847x^2 + 103x + 24,610.
If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the _____ probability distribution.
a. Poisson
b. exponential
c. binomial
d. hypergeometric
To calculate the probability of arrival of ten customer in one hour at a service station then use of option a. Poisson probability distribution is more applicable.
Poisson probability distribution represents the discrete probability of any event.This represents the occurring of the independent event in a fixed interval of time.It is also called constant mean rate.Here arrival of ten customer in fixed time interval of one hour we have to calculate.It implies that the Poisson probability distribution is the best way to calculate the given situation.Therefore, the required probability for the given situation is Poisson probability distribution .
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