Answer:
t = nRT/M + 5ab/M
Step-by-step explanation:
I'm going to assume that the t and T are seperate variables.
basically all you have to do is isolate t by dividing each side with factors that do not contain the t
What type of correlation exists between the temperature and the number of fruit bars sold? What is the real-world meaning of the slope of the line of best fit for the given scenario? There are approximately more fruit bars sold for every degree(s) the temperature rises
Answer:
There's no figure, but okay! The type of correlation that exists between the temperature and the number of fruit bars sold is a positive correlation.
The real-world meaning of the slope of the line of best fit for the given scenario is that: As the temperature increases, so too does the number of fruit bars sold.
I hope that helps you!! ^-^
Answer:
What type of correlation exists between the temperature and the number of fruit bars sold?
✔ positive
What is the real-world meaning of the slope of the line of best fit for the given scenario?
There are approximately ✔ 2.2 more fruit bars sold for every ✔ 1 degree(s) the temperature rises.
Step-by-step explanation:
got it right in edg 2021, hope this is of help :)
2/5 divided 1/3 give answer in simplest form as a mixed number
Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x=0.) f(x)=1+x8∑n=0[infinity]() provided ∣x∣< [-/5 Points] Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x=0.) f(x)=1+x25∑n=0[infinity]([) provided ∣x∣<∣
To find the power series representation for the function f(x) = 1 + x^8, we can expand it as a Taylor series centered at x = 0. We have: f(x) = 1 + x^8
To find the power series representation, we'll express it in terms of the variable t, where t = x^8:
f(x) = 1 + t
Now, we can rewrite the function in terms of the variable t and find its power series representation:
f(x) = 1 + t = 1 + x^8
The power series representation centered at x = 0 is:
f(x) = 1 + x^8 = 1 + (x^8)(1) = 1 + x^8
The interval of convergence for this power series representation is given by the condition |x| < √(R), where R is the radius of convergence. In this case, since the power series only consists of a single term, the interval of convergence is the set of all real numbers (-∞, +∞).
Similarly, for the function f(x) = 1 + x^25, we can find its power series representation centered at x = 0:
f(x) = 1 + x^25
Again, expressing it in terms of the variable t where t = x^25:
f(x) = 1 + t
The power series representation centered at x = 0 is:
f(x) = 1 + x^25 = 1 + (x^25)(1) = 1 + x^25
The interval of convergence for this power series representation is also (-∞, +∞) since it consists of a single term.
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Write an inequality for the graph
A candy store allows customers to select 3 different candies to be packaged and mailed. If there are 13 varieties available, how many possible selections can be made?
There are 286 different possible selections of three candies from 13 varieties.
To find out how many possible selections can be made, we can use the combination formula: nCk = n! / (k! (n-k)!), where n is the total number of candies available and k is the number of candies to be selected.
In this case, n = 13 (the number of candy varieties) and k = 3 (the number of candies to be selected). So the number of possible selections can be calculated as follows: 13C3 = 13! / (3! (13-3)!) = 286. Therefore, there are 286 different possible selections of three candies from the 13 varieties available in the candy store.
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Determining the location of a terminal point given the signs of Determine the quadrant in which the terminal side of 0 lies. (a)sine < 0 and cot 0 < 0 (Choose one) (b) cos > 0 and esce < 0 (Choose one) quadrant I quadrant II quadrant III quadrant IV ?
Based on the given information, the terminal side of angle 0 lies in quadrant III.
To determine the quadrant in which the terminal side of angle 0 lies based on the given information, we can analyze the signs of the trigonometric functions:
(a) Since sine < 0 and cotangent < 0, we can determine the quadrant as follows:
Sine < 0 implies that the y-coordinate (vertical component) of the point on the unit circle corresponding to angle 0 is negative.
Cotangent < 0 implies that the x-coordinate (horizontal component) of the point on the unit circle corresponding to angle 0 is negative.
In quadrant III, both the x and y-coordinates are negative. Therefore, quadrant III is the correct answer in this case.
(b) The information provided in this option is incorrect. "esce" is not a recognized trigonometric function, and "cos > 0" does not provide enough information to determine the quadrant.
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Find the outward flux of the given field across the given cardioid. F = (5xy - 4x/1 + y^2)i + (e^x + 4 tan^-1 y)j r = a(1 + cos theta), ...
The outward flux of the given vector field F across the given cardioid, you need to perform a surface integral, integrating (F · n) over the surface of the cardioid, where \(F = (5xy - 4x/(1 + y^2))i + (e^x + 4 tan^-1 y)j\) and r = a(1 + cos theta).
How we find the outward flux?To find the outward flux of the given vector field F across the given cardioid, we need to calculate the surface integral of the vector field over the surface of the cardioid.
The vector field F is defined as:
F = \((5xy - 4x/(1 + y^2))i + (e^x + 4 tan^(^-^1^)^y^)^j\)
The cardioid is defined in polar coordinates as:
r = a(1 + cos theta)
To perform the surface integral, we need to express the vector field and the surface element in terms of the polar coordinates (r, theta).
First, let's calculate the outward unit normal vector n for the cardioid surface. The outward normal vector is given by:
n = (cos theta)i + (sin theta)j
Next, we need to express the vector field F in terms of the polar coordinates. We have:
x = r * cos theta
y = r * sin theta
Substituting these values into the components of F, we get:
F = \((5r^2 * sin theta * cos theta - 4r * cos theta / (1 + (sin theta)^2))i + (e^(^r ^* ^c^o^s ^t^h^e^t^a^) + 4 * tan^(^-^1^)^(^r ^* ^s^i^n ^t^h^e^t^a^)^)^j\)
Now, let's calculate the surface element dS in terms of polar coordinates. The surface element is given by:
dS = r * dr * dtheta
To perform the surface integral, we need to integrate the dot product of F and n over the surface of the cardioid. The outward flux (Φ) is then given by the double integral:
Φ = ∫∫(F · n) dS
Substituting the expressions for F, n, and dS, the integral becomes:
Φ = ∫∫\(((5r^2 * sin theta * cos theta - 4r * cos theta / (1 + (sin theta)^2))(cos theta) + (e^(^r ^* ^c^o^s ^t^h^e^t^a^) + 4 * tan^(^-^1^)(r * sin theta))(sin theta)) * (r * dr * dtheta)\)
The limits of integration for theta will depend on the specific range for which the cardioid is defined.
Solving this double integral will give us the outward flux of the vector field across the cardioid. Please note that the integration process can be quite involved and may require numerical methods if no closed-form solution is available.
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For the given rectangular equation, write an equivalent polar equation. x² - y² = 4
The equivalent polar equation for x² - y² = 4 is cos(2θ) = 4 / r². To convert the rectangular equation x² - y² = 4 into an equivalent polar equation.
We can substitute x and y with their corresponding polar coordinate representations.
In polar coordinates, we have:
x = r * cos(θ)
y = r * sin(θ)
Substituting these into the rectangular equation:
(x² - y²) = 4
(r * cos(θ))² - (r * sin(θ))² = 4
Expanding and simplifying:
r² * cos²(θ) - r² * sin²(θ) = 4
Using the trigonometric identity cos²(θ) - sin²(θ) = cos(2θ), we can rewrite the equation as:
r² * cos(2θ) = 4
Dividing both sides by r², we obtain the equivalent polar equation:
cos(2θ) = 4 / r²
Therefore, the equivalent polar equation for x² - y² = 4 is cos(2θ) = 4 / r².
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ex 17. Determine whether each of these conditional statements is true or false. a) If1 + 1 = 2, then 2 + 2 = 5. b) If1 +1= 3, then 2 + 2 = 4. c) If 1+1=3, then 2 + 2 = 5. d) If monkeys can fly, then 1 + 1 = 3.
a) False - The consequent (2 + 2 = 5) does not hold true when the condition (1 + 1 = 2) is satisfied.
b) False - Neither the condition (1 + 1 = 3) nor the consequent (2 + 2 = 4) is true.
c) False - The consequent (2 + 2 = 5) does not follow when the condition (1 + 1 = 3) is met.
d) True - Since the condition (monkeys can fly) is false, the statement (1 + 1 = 3) holds true due to the structure of the conditional statement.
In the given conditional statements, we need to determine whether each statement is true or false based on the provided conditions.
a) If 1 + 1 = 2, then 2 + 2 = 5. This statement is false because the initial condition (1 + 1 = 2) is true, but the consequent (2 + 2 = 5) is false. In mathematics, if the condition is true, the consequent should also be true, but in this case, it is not.
b) If 1 + 1 = 3, then 2 + 2 = 4. This statement is false because both the condition (1 + 1 = 3) and the consequent (2 + 2 = 4) are false. The initial condition is not satisfied, so the statement cannot be true.
c) If 1 + 1 = 3, then 2 + 2 = 5. This statement is false for the same reason as statement a) - the initial condition is true, but the consequent is false.
d) If monkeys can fly, then 1 + 1 = 3. This statement is true because it follows the structure of a conditional statement where the condition (monkeys can fly) is false, and therefore the statement is always true.
In summary, statement a), b), and c) are false, while statement d) is true.
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Given f(x) = 3x+9 and g(x) = 5x-1, find f(g(x)).
Step-by-step explanation:
In this equation, given
f(x) = 3x + 9 and g(x) = 5x -1
So the question is what is the value of f if we put the value of g(x) in f(x)
So to solve the equation we need to replace the value of x in f(x) with g(x)
So it was obtained as below
f(g(x)) = 3(5x-1) + 9
= (15 x - 3) + 9
= 15 x + 6
respectively Q 1
=160−10P 1
OR r 1
=16−0.1Q 1
aWD 1/P 6
=16 6
−2T −
Q 2
=200−20P 2
ORP 2
=10−0,050,…H1AP 2
=15−0:0% Saga's Total Cost function is: TC =120+4Q With third degree price discrimination, the condition for peofit marimizater is MR 1
=MR 2
=MR=MC Find P 1
,Q 1
,P 2
,Q 1
Total Revenue, Total Cost, and Total proft wit sree discrimination. Find P,Q,TR,TC&π In the absence of price discrimination. Marks: 7
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.
Given the demand equations and the total cost function:
Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1
Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2
Total Cost: TC = 120 + 4Q
To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:
MR1 = MC:
16 - 0.2Q1 = 4
0.2Q1 = 12
Q1 = 60
MR2 = MC:
10 - 0.1Q2 = 4
0.1Q2 = 6
Q2 = 60
Substituting the quantities back into the demand equations, we find:
P1 = 16 - 0.1(60) = 10
P2 = 10 - 0.05(60) = 7
The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:
TR = P1 * Q1 + P2 * Q2
TR = (10 * 60) + (7 * 60)
TR = 600 + 420
TR = 1020
The total cost (TC) is given by the total cost function:
TC = 120 + 4Q
TC = 120 + 4(60 + 60)
TC = 120 + 480
TC = 600
Finally, the profit (π) can be calculated by subtracting total cost from total revenue:
π = TR - TC
π = 1020 - 600
π = 420
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
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HELPPP also remeber simplifyyy
Answer:
9/1
Step-by-step explanation:
A lock has a code of 4 numbers between 1 and 20. If no numbers in the
code are allowed to repeat, how many different codes could be made?
There are 116,280 different codes that can be made with 4 numbers between 1 and 20 without repeating any number.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
To find the number of different codes that can be made with 4 numbers between 1 and 20 without repeating any number, we can use the permutation formula, nPr = n! / (n-r)! where n is the total number of items and r is the number of items we want to choose.
In this case, we have n = 20 (the total number of numbers we can choose from) and r = 4 (the number of numbers we need to choose).
So, the number of different codes that can be made is:
20P4 = 20! / (20-4)! = 20! / 16! = 20 × 19 × 18 × 17 = 116,280
Therefore, there are 116,280 different codes that can be made with 4 numbers between 1 and 20 without repeating any number.
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1 Select the correct answer. What is the simplified form of this expression? (-3x² + 4x) + (2x²-x-11)
a. -x2 + 5x − 11
b. -x² + 3x - 11
c. -x² + 3x + 1
d. -x2 + 5x + 11
Blynomials: Mastery Test
The value of the given expression is - x² + 3x - 11 and option b is the correct answer.
What is binomial expression?Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form. Therefore, A binomial is a two-term algebraic statement that includes a constant, exponents, a variable, and a coefficient.
The given expression is:
(-3x² + 4x) + (2x²-x-11)
-3x² + 4x + 2x² - x - 11
Subtract the like terms:
- x² + 3x - 11
Hence, the value of the given expression is - x² + 3x - 11 and option b is the correct answer.
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find the number degree of freedom, Critical value X², X² Given 95% confidence; n = 25, s = 0.24 Degree of freedom, df = 24 Critical value: X= [Select] X²= [Select] [Select] 39.364 32.852 12.401
The number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
To find the number of degrees of freedom and the critical value X² for a 95% confidence level with n = 25 and s = 0.24, we need to determine the appropriate values based on the chi-square distribution.
The number of degrees of freedom (df) is equal to n - 1, where n is the sample size. In this case, df = 25 - 1 = 24.
To find the critical value X² for a 95% confidence level and 24 degrees of freedom, we need to consult a chi-square distribution table or use statistical software. The critical value corresponds to the chi-square value that leaves 5% (0.05) in the right tail.
Looking up the chi-square distribution table or using software, we find that the critical value for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
Therefore, the number of degrees of freedom is 24, and the critical value X² for a 95% confidence level and 24 degrees of freedom is approximately 36.415.
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Which of the following is a quadratic function?
f(x) = 0x + 3x - 6
f(x) = 2x + 5
f(x) = 3 - 4x^2
f(x) = 2^x
Answer:
f(x) = 3 - 4x^2
Step-by-step explanation:
Quadratic Equation form: f(x) = ax² + bx + c
Quadratic function has a x (variable) with and exponent of 2.
They also leave a curve line on a coordinate plane. As you can see on the picture. ↓
What is the remainder when the two-digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
Answer:
22Step-by-step explanation:
You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.
(1) Digit sum is 5The sum of digits of a 2-digit number will be 5 if that number is one of ...
{14, 23, 32, 41, 50}
In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.
(2) Mod 9 value is 5In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:
{59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9
The remainders when divided by 3 are all 2 for these numbers as well.
__
Additional comment
The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.
Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.
Given: -4(-3n – 8)=10n + 20
Prove: n=-6
Answer:
i'm not sure if i messed up or not, but n can't equal -6?
Step-by-step explanation:
-4(-3(-6)-8)=10(6)+ 20
-4(18-8)=60+20
-4(10)=80
40=80
PLEASEE HELPP ME DO THISS
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. Find the solutions to the given equation on the interval 0≤x<2π. −8sin(5x)=−4√ 3
The solutions to the given equation on the interval 0≤x<2π. −8sin(5x)=−4√ 3 The solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:
x = π/3 and x = 2π/3.
To find the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π, we can start by isolating the sine term.
Dividing both sides of the equation by -8, we have:
sin(5x) = √3/2
Now, we can find the angles whose sine is √3/2. These angles correspond to the angles in the unit circle where the y-coordinate is √3/2.
Using the special angles of the unit circle, we find that the solutions are:
x = π/3 + 2πn
x = 2π/3 + 2πn
where n is an integer.
Since we are given the interval 0 ≤ x < 2π, we need to check which of these solutions fall within that interval.
For n = 0:
x = π/3
For n = 1:
x = 2π/3
Both solutions, π/3 and 2π/3, fall within the interval 0 ≤ x < 2π.
Therefore, the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:
x = π/3 and x = 2π/3.
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if you had a 5% chance of winning 1 dollarr and a 95% chance of winning 1 cent and you gambled 100 times how much will you make statistically
Statistically, you can expect to make approximately $5.95 from gambling 100 times under the given conditions. However, it's important to note that the expected value represents the average outcome over many trials and individual results can still vary significantly.
To determine how much you can expect to make statistically from gambling 100 times with a 5% chance of winning $1 and a 95% chance of winning 1 cent, we can calculate the expected value.
Let's break it down:
5% of the time, you win $1. This contributes 0.05 \(\times\)$1 = $0.05 to the expected value.
95% of the time, you win 1 cent. This contributes 0.95 \(\times\) $0.01 = $0.0095 to the expected value.
Now, let's calculate the total expected value over 100 trials:
Expected value per trial = $0.05 + $0.0095 = $0.0595
Expected value over 100 trials = $0.0595 \(\times\)100 = $5.95
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2x+3y= -4
x+9y=13
find the solution of the system of equations.
Answer:
(-5, 2)
Step-by-step explanation:
2x + 3y = -4
x + 9y = 13
We can solve this by substituting or using elimination.
Substituting:
2x + 3y = -4
-2x = -2x Subtract 2 from both sides.
3y = -2x - 4
3 = 3 Divide both sides by 3.
y = -2/3x - 4/3
x + 9(-2/3x - 4/3) = 13 Replace the y with -2/3x - 4/3.
x - 6x - 12 = 13 use the distributive property.
-5x - 12 = 13
+12 = + 12 Add 12 to both sides.
-5x = 25
-5 = -5 Divide both sides by -5.
x = -5
Now that we know what x is, we substitute -5 for the variable x in any of the two equations.
x + 9y = 13
-5 + 9y = 13 Replaced x with -5
+5 = +5 Add 5 to both sides.
9y = 18
Divide both sides by 9 to get:
y = 2
The other way to solve:
Elimination:
2x + 3y = -4
x + 9y = 13
Make the variable y cancel out.
-3(2x + 3y = -4) use the distributive property.
-6x - 9y = 12
-6x - 9y = 12
x + 9y = 13
Add the equation.
-5x = 25
Divide both sides by -5.
x = -5
Plug in -5 for x.
2(-5) + 3y = -4
-10 + 3y = -4
+10 = +10 Add 10 to both sides.
3y = 6
Divide both sides by 3:
y = 2
We get the same answer in both strategies, you could use either one.
- 10x - y = 27
- 4x - y = 9
Find the solution of the system equation.
Find (f-g) (x)
(image attached)
The function (f - g)(x) is given as follows:
C. (f - g)(x) = |7x + 1| - 6.
How to obtain the subtraction function?The functions for this problem are defined as follows:
f(x) = |7x + 1| - 8.g(x) = -2.To obtain the subtraction of f(x) by g(x), we merely subtract the definitions, as follows:
(f - g)(x) = f(x) - g(x).
Hence:
(f - g)(x) = |7x + 1| - 8 - (-2)
(f - g)(x) = |7x + 1| - 8 + 2.
The like terms in the expression are given as follows:
-8 + 2 = -6.
Hence the subtraction function for this problem is defined as follows:
(f - g)(x) = |7x + 1| - 6.
Meaning that option C is the correct option.
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Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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graph the absolute value of each number on a number line-5,-4,-3,-2,-,1,0,1,2,3,4,5.
It is correct to state that the Absolute Values of the above numbers will be:
5,4,3,2,1,0,1,2,3,4,5. Because positive values cannot be represented on the Negative spectrum of the Coordinate system, we are left with 0,1,2,3,4,5 which means is represented by 0 ≤ x ≤ 5. See the attached real number line attached.
What is a Number Line and why is it important?A number line is a graphical depiction of numbers on a straight line, with each point representing a distinct actual number. It is essential for visualizing numerical concepts and procedures.
The absolute value of a number, independent of its sign, is the number's distance from zero. It is expressed as a positive number and is useful for determining the size of a quantity or the distance between two points on a number line.
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A piece of string is 28 cm long. It is used to from a square. (a) what is the length of each side of square? (b) what is the area of the square.?
Answer:
7 cm and 49 cm²
Step-by-step explanation:
(a)
A square has 4 equal sides , then
28 cm ÷ 4 = 7 cm
The length of each side of the square is 7 cm
(b)
The area (A) of a square is
A = s² ( s is the side length ) , then
A = 7² = 49 cm²
Answer:
Step-by-step explanation:
Perimeter of square will be equal to the length of the string
Perimeter of square = 28 cm
4*side = 28
Divide both sides by 4
Side = 28/4
Side = 7 cm
b) Area of square = side * side
= 7 * 7
=49 cm²
Which equation has an X intercept of 3 and a y intercept of 5?
y = -\(\frac{5}{3}\)x+5 equation has an X intercept of 3 and a y intercept of 5 .
The point on a line where it crosses an axis is referred to as the "intercept." The slope of the line passes through a point called an intercept on the y-axis.
The equation for a line, which is written as y = mx+c, which stands for slope and y-intercept, respectively, reflects this.
The two main intercepts are X-intercept and Y-intercept. Where the line crosses the x and y axes, respectively, is where the line's x-intercept and y-intercept are situated.
In this case, you are given both intercepts.
Plot a line from the third x-axis point.
On the y-axis, place the coordinates y = 5.
The necessary line is a straight line that passes through these two places is
y = -\(\frac{5}{3}\)x+5
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a shipment of nine smartphones contains two with cracked screens. if sold in a random order, what is the probability that the first seven sold have undamaged screens?
To determine the probability that the first seven smartphones sold have undamaged screens.
We need to consider the number of ways to choose seven undamaged smartphones out of the total remaining undamaged smartphones.
Given that there are nine smartphones in total, with two having cracked screens, there are 9 - 2 = 7 undamaged smartphones.
The probability of choosing an undamaged smartphone on the first sale is 7/9, as there are seven undamaged smartphones out of the remaining nine.
After the first sale, there are six undamaged smartphones remaining out of the remaining eight smartphones. The probability of choosing an undamaged smartphone on the second sale is 6/8.
Continuing this pattern, the probability of choosing an undamaged smartphone on the third, fourth, fifth, sixth, and seventh sales is calculated as follows:
Third sale: 5/7
Fourth sale: 4/6
Fifth sale: 3/5
Sixth sale: 2/4
Seventh sale: 1/3
To find the overall probability, we multiply the individual probabilities together:
(7/9) * (6/8) * (5/7) * (4/6) * (3/5) * (2/4) * (1/3)
Simplifying the expression:
(7 * 6 * 5 * 4 * 3 * 2 * 1) / (9 * 8 * 7 * 6 * 5 * 4 * 3)
The common factors cancel out:
1/ (9 * 8)
Finally, calculating the result:
1/72
Therefore, the probability that the first seven smartphones sold have undamaged screens is 1/72.
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Answer:
20%
Step-by-step explanation:
1,200 is 80% of 1,500