By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.
What is integration ?
Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.
Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.
Given by the question:
The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:
[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]
To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):
[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]
= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]
= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]
=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12
=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]
= [tex]51600[/tex]
Therefore, the total revenue of the shop for a year is $51,600.
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AB and CD are tangents of circle O find each of the following
The lines CA and CD are tangents to the circle O, hence; EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
If OB = 6 and AB = 8, then;
OA = √(8² + 6²) {by Pythagoras rule}
OA = √100
OA = 10
EA = OA - OE(radius)
EA = 10 - 6 = 4
If DE = 16 and EA = 9, then;
OA = (diameter/2) + EA
OA = 8 + 9 = 17
AB = √(17² - 8²)
AB = √225
AB = 15
OB is perpendicular to line CA tangent to the circle so m∠ABO = 90°
OD is perpendicular to the line CD tangent to the circle so m∠ODC = 90°
If m∠DOB = 120° then;
120° = m∠ABO + m∠EAB {exterior angle of a triangle is equal to the two opposite interior angles}
m∠EAB = 120° - 90°
m∠EAB = 30°
In conclusion, for the lines tangent to the circle, we have that;
EA = 4, AB = 15, m∠ABO = 90°, m∠ODC = 90°, and m∠EAB = 30°
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The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years, given the household’s annual income, 78,300.
$231784 is the to raise a child from birth to 17 years in a household with an annual income of $78,300.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Let y represents the total cost in dollars f raising a child in the United States from birth to 17 years
x represents the households annual income
We have y = 1.55x + 110,419
We need to find the value of y for x=78300
y=1.55(78300) + 110,419
y=231784
Hence, $231784 is the to raise a child from birth to 17 years in a household with an annual income of $78,300.
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The same hammer is available from an online retailer. if a customer uses a discount code fhat offercs a 25% discount and free shipping, the hammer will cost $17.25. There is no sales tax if the customer buys the hammer online
Therefore , the solution of the given problem of percentage comes out to be the original price of the hammer is $23, and the customer saved $5.75 with the discount code.
What is a percentage?In mathematics, a percentage is any value that can be represented as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." Nonetheless, it is typically denoted by the "%" symbol. The proportional amount is flat and lacks any dimensions. As percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage. .
Here,
Let x be the original price of the hammer.
With the 25% discount, the customer pays 75% of the original price:
0.75x
And since there is free shipping, the customer pays only the price of the hammer:
0.75x = 17.25
Solving for x, we have:
x = 17.25 / 0.75 = 23
Therefore, the original price of the hammer is $23, and the customer saved $5.75 with the discount code.
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The ratio of red paint and blue paint in paint mixture is 3:4 . How much blue paint is needed to make 1400 ml of paint mixture
Answer:
Step-by-step explanation:
First 3 + 4 is 7. Then for the red paint ( 3 ) , this is written.
= [tex]\frac{3}{7}[/tex] * 1400
Then calculated.
= [tex]\frac{3}{7}[/tex] * [tex]\frac{1400}{1}[/tex] = [tex]\frac{4200}{7}[/tex] = 600 ml for the red paint.
Then its easy to find the blue paint, either the long way ( above ) or...
= 1400 ml - 600 ml = 800 ml for blue paint.
Have a wonderful day! :-)
Kristina paid mortgage interest of
$6,320.00 and Medical Expenses of
$19,500.00 during 2022. Her
GROSS INCOME was $32,500.
16. Should Kristina take the
standard deduction or itemize her
two expenses? Why?
A)She should take the standard
deduction because it would be larger than her itemized deductions.
B) She should take the itemized
deductions because they would be larger than the standard deduction.
C) It wouldn't matter. Choosing either one
wouldn't change the outcome of your tax calculations.
Answer:
B) She should take the itemized deductions because they would be larger than the standard deduction.
Step-by-step explanation:
Given Kristina will file a single so her standard deduction for 2022 is $12,950.
For itemized deduction, she can include her mortgage interest of $6,320.00.
For her medical expenses, it has to be more than 7.5% of her gross income of $32,500 => 7.5% of $32,500 = $2437.5.
so her deduction for medical expenses is $19,500 - $2437.50 = $17,062.5
so her total itemized deduction is $6,320.00 + $17,062.50 = $23,382.50
Her itemized deduction is larger than standard deduction for single filing. So itemized deduction is the best option for Kristina.
Solve (x – 3)2 = 49. Select the values of x.
Answer:
27.5
Step-by-step explanation:
(x – 3)2 = 49
(x – 3) = 49/2
(x – 3) = 24.5
x = 27.5
Solve only this problem :
Write an expression for the number of years after which there will be 15,000 dollars in the account.
The time is about 122 years and 9 months after which there will be 15,000 dollars in the account.
What is an exponential function?Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.
Given:
An expression,
1[tex](e)^{0.034t}[/tex] model the balance, in thousands of dollars, where t is time.
(a).
0.034 represents the rate at which the function is expressed.
So,
0.034t = log(15000)
t = log(15000)/0.034
t = 122.826213502 in years.
t = 122 years, 9 months.
Therefore, t = 122 years, 9 months.
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1. There is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by:
Pr(X = 0) = 0.55
Pr{X = 1) = 0.22
Pr(X = 2) = 0.13
Pr(X = 3) = 0.08
Pr(X = 4) = 0.02
Determine the following:
a. the probability that two or fewer bits are transmitted in error
b.the probability that at least one bit is transmitted in error
c.the expected value of the number of bits transmitted in error
d.the standard deviation of the number of bits transmitted in error
2. Consider the following function:
f(x) = kx 0 less than or equal to x less than or equal to 8
a.Find the value of k that makes the function a valid probability density function (pdf). Report your answer as a fraction.
b. Determine Pr(2 less than or equal to x less than or equal to 3).Report your answer as fraction
c. Determine the expected value.
All the probabilities are solved and are mentioned below.
What is probability mass function?In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value
Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -
Pr(X = 0) = 0.55
Pr{X = 1) = 0.22
Pr(X = 2) = 0.13
Pr(X = 3) = 0.08
Pr(X = 4) = 0.02
We can find the probabilities as -
{ 1 } - the probability that two or fewer bits are transmitted in error :
P{E} = P(0) + P(1) + P(2)/∑P{n}
P{E} = 0.9/1
P{E} = 0.9
{ 2 } - the probability that at least one bit is transmitted in error -
P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}
P{E} = 0.45/1
P{E} = 0.45
{ 4 } - the expected value of the number of bits transmitted in error -
n = 0 + 1 + 2 + 3 + 4
n = 10
{ 4 } - the standard deviation of the number of bits transmitted in error -
σ = 1.0677
Therefore, all the probabilities are solved and are mentioned above.
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A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she takes 10 shots. Let x = the number of shots that she makes. What is the standard deviation for x?.
The standard deviation is 1.32
We can use the binomial distribution to calculate the probability of making a certain number of shots. The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
Where σ is the standard deviation, n is the number of trials (in this case, 10), p is the probability of success on each trial (0.39, or 39%), and (1-p) is the probability of failure on each trial (0.61, or 61%).
So, plugging in our values:
σ = √(10 * 0.39 * 0.61)
σ ≈ 1.32
In other words, if the player takes 10 free throws, we would expect her to make between 2 and 6 of them about 68% of the time.
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Use a definition, postulate, or theorem to find the value of x in the figure described.
Point E is between points D and F. IfDE=x-1, EF = 4x + 5, and DF = 6x - 5, find x.
The solution is x =?
Thus, the value of x in the figure is 9.
What's collinear?Collinear refers to a term used in figure to describe a set of three or further points that lie on the same straight line. In other words, if you can draw a straight line that passes through two or further points, those points are said to be collinear.
We can use the member addition hypothetical to break for x. According to the member addition hypothetical, if three points A, B, and C are collinear, also AB BC = AC.
In this case, points D, E, and F are collinear, so we can write
DE EF = DF
Substituting the given values, we get
x- 1 4x 5 = 6x- 5
Simplifying the equation, we get
x 4 = 6x- 5
Abating 5x from both sides, we get
= x- 5
Adding 5 to both sides, we get
x = 9
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A carpenter who was installing a new roof on a garage noticed that for every 1-foot horizontal run, the roof was elevated by 4 inches. What is the pitch of this roof?
The pitch of the roof with one foot horizontal run and 4 inches elevation is 4 in per foot
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
The roof pitch (steepness) is given as a ratio of inch rise per horizontal foot, It is given by:
Pitch = rise / run
For every 1-foot horizontal run, the roof was elevated by 4 inches, hence:
Pitch = rise / run = 4 in / 1 ft = 4 in per foot
The pitch is 4 in per foot
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:
Step-by-step explanation:
A possible trigonometric function that would model the tide situation for this beach is:
h(t) = -2 + 3sin(πt/12)
where h(t) represents the height of the tide at time t in hours, and πt/12 represents the angle (in radians) corresponding to the time t on a unit circle with a period of 24 hours.
The constant -2 represents the lowest point of the tide (2 feet below sea level), and the coefficient of 3 in front of the sine function determines the amplitude of the tide, which is 3 feet (half the difference between the highest and lowest points of the tide, which is 4 - (-2) = 6 feet). The sine function oscillates between -1 and 1, so the range of the function h(t) is between -2 - 3 = -5 feet (when the sine function takes on its minimum value of -1) and 4 - 2 = 2 feet (when the sine function takes on its maximum value of 1), as expected for the given tidal range.
Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.
The value went from $45.00 to $68.75. What was the percent change?
The percent change from $45.00 to $68.75 is approximately 52.8%.
What does the phrase "percent change" mean?Finding the difference between two values in a time series and multiplying it by 100 after dividing it by the initial value yields the percentage change between the two values.
We employ the following formula to determine the percentage difference between two values:
(New Value - Old Value) / Old Value * 100% is the formula for percent change.
The former value in this instance was $45.00, whereas the new value is $68.75.
Adding these values to the formula yields the following results:
($68.75 - $45.00) / $45.00 * 100% is the percent difference.
percent modification: (23.75% / (45.00%) * 100%
52.8% change in percentage
As a result, the percentage increase from $45.00 to $68.75 is almost 52.8%.
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Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually. What is the annual interest rate?
The annual interest rate for the given compound interset is 6%
What is interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.
Given that, Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually.
A = P(1+r)ⁿ
2560 = 2250(1+r)²
2560 / 2250 = (1+r)²
1.13 = (1+r)²
Taking roots,
1+r = √1.13
r = 0.06
r = 6%
Hence, the annual interest rate for the given compound interset is 6%
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I need help please!!
Equation of line of reflection:
What is the answer to this question?
8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
X = -29/22
Step-by-step explanation:
I used PEMDAS to solve the question
Hello. Please, help with a question below
The Average rate of change is defined as
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).
What is unit rate?The rate at which one quantity changes per unit change with the other quantity is called unit rate.
Given is the average rate of change.
Average rate of change is defined as the change in the value of a quantity over the interval change in the other quantity.
Mathematically -
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁)
Therefore, the Average rate of change is defined as
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).
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Answer:
what basic business principle does the author of your reading material state that automakers igno red in recent years leading to the need for an industry bailout
All 155 students in the math club went on a field trip some students rode in cars which hold five students each and some students wrote in buses which holds 30 students each how many of each type of vehicle do they use if there were only 11 vehicles total
7 cars and 4 buses were used on the trip
How to find how many of each type of vehicle do they use if there were only 11 vehicles total
Let's start by defining some variables to represent the unknowns in the problem:
Let x be the number of cars used.
Let y be the number of buses used.
We know that there were a total of 11 vehicles used, so we can write an equation based on that:
x + y = 11
We also know that the total number of students who went on the trip is 155.
We can use this information to set up another equation:
5x + 30y = 155
This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).
Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.
Let's use substitution. Solve the first equation for x in terms of y:
x + y = 11
x = 11 - y
Substitute this expression for x into the second equation:
5x + 30y = 155
5(11 - y) + 30y = 155
Simplify and solve for y:
55 - 5y + 30y = 155
25y = 100
y = 4
Now that we know y, we can use the first equation to find x:
x + y = 11
x + 4 = 11
x = 7
Therefore, there were 7 cars and 4 buses used on the trip.
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The correct mix for a batch of concrete is 5:4:2 in terms of sand, gravel, and cement.
The batch is to have 2200 pounds of these ingredients. How many of each are needed?
Sand
Gravel
Cement
To make a batch of concrete with a total weight of 2200 pounds and a mix ratio of 5:4:2 for sand, gravel, and cement, we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement.
We must utilise the ratio of sand, gravel, and cement in the mix, which is 5:4:2, to calculate the amount of each ingredient required for a batch of concrete with a total weight of 2200 pounds.
Let's use the number "5x" to represent the quantity of sand in the batch, where x is a proportionality constant. The batch's cement and gravel contents are then, respectively, "4x" and "2x," respectively.
The problem states that the batch weighs 2200 pounds in total. As a result, we may construct the equation shown below:
5x + 4x + 2x = 2200
By merging similar phrases to simplify the left side, we obtain:
11x = 2200
When we multiply both sides by 11, we get:
x = 200
Knowing the value of x allows us to calculate the quantity of each ingredient in the batch:
Sand weight is 5x, or 5 * 200, or 1000 pounds.
The gravel weight is 4x, or 4 * 200, or 800 pounds.
There are 400 pounds of cement, or 2x = 2 * 200.
Therefore we need 1000 pounds of sand, 800 pounds of gravel, and 400 pounds of cement to build a batch of concrete that weighs 2200 pounds overall and has a sand, gravel, and cement mix ratio of 5:4:2.
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Name 1. Write equivalent fractions for 2/ 3 and 1/3 that could be used to find the sum of the fractions.
Answer:
4/6 and 2/6
Step-by-step explanation:
2/3 = 4/6
1/3 = 2/6
4/6 + 2/6 = 6/6 = 1
1.8A F. Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van
for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van,
he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in
the business bank account and £175 cash in hand. You are required to calculate his capital.
Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375
What do you mean by capital?
Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.
A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.
Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375
So, Total assets= £10,375
Payable= £1,600, loan from Rub= £2,500, Balancing figure= £6,275
Total liabilities= £10,375
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The common ratio in a geometric series is 4 44 and the first term is 3 33. Find the sum of the first 8 88 terms in the series.
The sum of the first 8 terms in the given geometric series is 65,535.
A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed non-zero constant called the common ratio.
In this case, the common ratio is 4, and the first term is 3. So, the first 8 terms of the series are:
3, 12, 48, 192, 768, 3072, 12288, 49152
To find the sum of the first 8 terms, we can use the formula for the sum of a finite geometric series:
S = a(1 - r^n) / (1 - r)
where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
Plugging in the given values, we get:
S = 3(1 - 4^8) / (1 - 4)
Simplifying the expression, we get:
S = 65,535
Therefore, the sum of the first 8 terms in the given geometric series is 65,535.
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--The question is incomplete, answering to the question below--
"The common ratio in a geometric series is 4 and the first term is 3. Find the sum of the first 8 terms in the series."
(a) The length of a rectangle is 6 cm more than its width, w cm. The perimeter of the rectangle is 37 cm. Form an equation in w and solve it to find the width of the rectangle.
The width of the rectangle whose perimeter is 37 cm is 6.25 cm.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The length of a rectangle is 6 cm more than its width, w cm.
So, the length = w + 6
The perimeter of the rectangle is 37 cm.
Then, Perimeter of the rectangle = 37
2(l+ w) = 37
2( w+ 6 +w )= 37
2(2w + 6)= 37
4w + 12 = 37
4w = 25
w = 6.25 cm
and, length = w+ 6 = 6 + 6.25 = 12.25 cm
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A line segment has a midpoint of (5,1/2). If one endpoint is (6,2).What is the other endpoint?
The other endpoint has its coordinate to be (4, -1).
How to determine the other endpointRepresent the coordinates of the other endpoint of the line segment be (x, y).
Since the midpoint of the line segment is (5, 1/2), we can use the midpoint formula to write an equation relating the coordinates of the two endpoints:
((6 + x)/2, (2 + y)/2) = (5, 1/2)
Simplifying this equation, we get:
(6 + x)/2 = 5
(2 + y)/2 = 1/2
Solving for x and y, we get:
x = 4
y = -1
Hence, the coordinates of the other endpoint of the line segment are (4, -1).
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Please help I need help so badly
Step-by-step explanation:
area3.14×18×18
1017.36ft²
circumference2×3.14×18
113.04ft
A -foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is , and that the angle of depression to the bottom of the monument is. How far is the person from the monument? round the answer to the nearest hundredth.
The distance between the man and the monument is 1060.16 feet.
Here we have the angle of elevation to be 18°
and the angle of depression to be 3°
Let the distance between the man and the monument be x feet
Now for any angle a, tana = opposite angle / adjacent angle
Hence we can sum up the building's height to be
x tan18 + x tan3 = 400
or, x(tan18 + tan3) = 400
or, x(0.3249 + 0.0524) = 400
or, 0.3773x = 400
or, x = 400/0.3773
or, x = 1060.16
Hence the distance between the man and the monument is 1060.16 feet.
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If f is one-to-one and f(7)=3, then f^1(3)= ___, and (f(7))^-1= ___
Answer:
[tex]f^{-1}(3) = \boxed{7}[/tex]
[tex]f(f(7))^{-1} = \boxed{7}[/tex]
Step-by-step explanation:
These follow from two of the properties of inverse functions:
If [tex]f[/tex] is a one-to-one function then
[tex]if\; f(x) = y \;then\; f^{-1}(x) = y}[/tex][tex]f^{-1}(f(x) = x\\\\f^{-1}(f(x) \;is\;the\;same\;as; ((f(x))^{-1}[/tex]What is the slope of the line on the graph?
C)2
The slope of the line on the given graph in the image below is: 2.
How to Find the Slope of a Line on a Graph?To find the slope of the line in a graph, use any two points on the line and plug in the coordinates of the two points in the slope formula which is given as:
Slope (m) = change in y / change in x = rise/run = y2 - y1 / x2 - x1
Picking two points on the line, (0, 1) and (1, 3):
Slope (m) = change in y / change in x = (3 - 1) / (1 - 0)
Slope (m) = 2/1
m = 2
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The variable y varies directly with the variable x.
A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 10, 14. Column 2 is labeled y with entries 3, 15, blank, where y is
If the value of x is 14, what is the value of y?
Now that we know k is 3/2, we can use the formula to find the value of y when x is 14:
y = (3/2)(14) = 21
Therefore, when x = 14, y = 21.
What is a variable defined as?A variable is a number in mathematics that can change depending on the issue. Several statements and equations in mathematics use the generic letters x, y, and z. Or to put it another way, a variable is a symbol that denotes an unknowable numerical value. Assume that x + 5 = 10. The term "x" is used here.
Since y varies directly with x, we know that the ratio of y to x is constant. Let's call this constant k. Then we can write:
y = kx
To find k, we can use the first two rows of the table:
When x = 2, y = 3, so:
3 = k(2)
k = 3/2
When x = 10, y = 15, so:
15 = k(10)
k = 3/2 (which matches the previous calculation)
Now we can use k to find y when x = 14:
y = (3/2)(14) = 21
Therefore, when x = 14, y = 21.
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g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.
Answer:
the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Step-by-step explanation:
The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:
C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960
Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.
For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:
C(13, 5) = 13! / (5! (13 - 5)!) = 1,287
So the total number of ways of choosing 5 cards from the same suit is:
4 * 1,287 = 5,148
Therefore, the probability of getting 5 cards from the same suit is:
5,148 / 2,598,960 ≈ 0.00198
So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
