The volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle , on the right by the line , and above by the line about the x-axis is (47/3)π.
To use the washer method, we need to consider the solid as a stack of thin washers, each with a hole in the center. We will integrate along the axis of revolution (in this case, the x-axis).
First, let's sketch the region we're revolving:
The circle has equation x^2 + y^2 = 1, so its radius is r = 1 when y = 0. The line has equation x = 4, so its distance from the axis of revolution is R = 4. The region we're revolving is bounded by y = 0 and y = √(1 - x^2), which we can rewrite as x = √(1 - y^2).
We can now set up the integral for the volume of the solid:
V = [tex]\int\limits^1_0[/tex] π(R^2 - r^2) dy
= [tex]\int\limits^1_0[/tex] π(4^2 - x^2) dy
= π[tex]\int\limits^1_0[/tex] (16 - y^2) dy
= π [16y - (1/3)y^3] |₀¹
= π (16 - 1/3)
= (47/3)π
Therefore, the volume of the solid is (47/3)π cubic units.
To learn more about volume click on,
https://brainly.com/question/30646353
#SPJ4
Complete question is:
Using the washer method, determine the volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle x^2+y^2=1, on the right by the line x = 4, and above by the line x=4 about the x-axis.
There are 80 Calories in every 4-ounce serving of grapes. Which equation can be
used to determine the number of Calories, y, in x ounces of grapes?
The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
There are 80 Calories in every 4-ounce serving of grapes.
i.e. in 1 ounce there are 80/4 = 20 cal.
so, the number of Calories, y, in x ounces of grapes
means, y = 20x
Hence, The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
Mrs. Rivera wrote a test. Part A and true/false questions each worth 4 points. Part B had multiple choice questions, each worth 10 points. She made the number of points for part A equal the number of points for part B. It was the least number of points for which this is possible.
Answer the following questions:
How many questions did part A have?
How many questions did part B have?
How many points is each part worth?
Which property is illustrated by this equation?
1/2 x 3/3 = 3/6
Answer:
Step-by-step explanation:
The equation 1/2 x 3/3 = 3/6 illustrates the property of the Commutative Property of Multiplication.
The Commutative Property of Multiplication states that changing the order of the factors in a multiplication operation does not affect the product. In other words, for any two real numbers a and b, we have:
a x b = b x a
So, in the equation 1/2 x 3/3 = 3/6, we see that the product is the same regardless of the order in which the factors are multiplied.
NO LINKS!!! URGENT HELP PLEASE!!!
For #7-9, find the area of each figure, round your answer to one decimal place if necessary.
Answer:
7) 468 ft²
8) 864 m²
9) 192 cm²
Step-by-step explanation:
To calculate the area of each given composite figure, divide the figure into two rectangles and sum the area of the two rectangles.
[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]
Question 7Separate the figure into two rectangles by drawing a vertical line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=16 \cdot 17 + 14 \cdot 14\\&=272+196\\&=468\; \sf ft^2\end{aligned}[/tex]
Question 8Separate the figure into two rectangles by drawing a horizontal line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=18 \cdot 18 + 30 \cdot 18\\&=324+540\\&=864\; \sf m^2\end{aligned}[/tex]
Question 9Separate the figure into two rectangles by drawing a horizontal line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=8 \cdot 8+16 \cdot 8\\&=64+128\\&=192\; \sf cm^2\end{aligned}[/tex]
A grocer can buy raspberries from a local farmer for $1.04 per pound (lb). Her last raspberry order from the farmer cost $171.08 How many pounds of raspberries did
the grocer order? Round your answer to the nearest tenth if needed
Answer
Duration: 0010:10
f(x) pounds of raspberries from the local farmer
The number of pounds of raspberries that the grocer ordered is 164.5 pounds
A grocer can purchase raspberries that costs $1.04 per pound
Her last raspberry order from the farmer costs $171.08
Therefore the number of pounds of raspberries that the grocer ordered can be calculated as follows
= 171.08/1.04
= 164.5
Hence the grocer ordered 164.5 pounds of raspberries
Read more on pounds here
https://brainly.com/question/25076966
#SPJ1
Find a basis for the nullspace and the rank for each of the following matrices. What is the dimension of the nullspace? [Hint: Use Theorem 1.12 on page 83.] Do you see a relationship between the rank of the matrix and the dimension of the nullspace? A) [1 2 1 ; 2 4 2) (B) [1 3 1 1; 2 1 2 1; 4 7 4 3] C) [1 -5 3 4; 2 -10 6 8; 3 -15 9 2]
A) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. B) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. C) Rank = 2, Nullspace: (-3, 1, -2, 0), Dimension = 2. Yes, the rank of the matrix is equal to the dimension of the nullspace.
A) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1; 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.
B) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1 0; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.
C) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 0 1; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (-3, 1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.
Learn more about matrix here
https://brainly.com/question/30389982
#SPJ4
A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size Height (inches)
7 60
9 72
10 65
7 68
9 69.5
10 70
12 75
12 61
13 68
What is the equation for the line of best fit for a woman's height, y, based on her shoe size, x?
y = −0.49x + 62.8
y = 0.49x + 62.8
y = 0.65x − 69.5
y = −0.65x − 69.5
Answer:
y = 0.49x + 62.8
Step-by-step explanation:
The line of best fit regression equation can be modeled using a regression analysis calculator
However, since the answer choices are given, with a bit of intuitive and logical thinking we can arrive at the correct answer choice
Let's eliminate the last answer choice: y = −0.65x − 69.5
For all values of x > 0 the value of y(height) will be negative which is absurd
The second-last(3rd answer choice) can also be eliminated. At x = 10
y = 0.65(10) - 69.5 = - 6.5 - 69.5 = - 64. The y-value is negative for all shoesizes shown
First choice seems reasonable:
However because of the -0.49x factor the height decreases as shoe size increases. This is counter-intuitive. Taller women tend to have bigger feet
Therefore the only correct answer choice is the second one:
y = 0.49x + 62.8
which shows a positive correlation between x and y
HELP
I MARK BRAINLIEST
Answer:
72
Step-by-step explanation:
Use Pythagoras Thereom
H² = L² + F²
78² = b² + 30²
78² - 30² = b²
6084 - 900 = b²
5184 = b²
Then, square root both sides of the equation and use the ² to cancel out the square root sign on the "b"
Therefore, b = 72
Suppose an investment of $20,000 is invested at an annual rate of 4.5%, compounded continuously. What is the value of the account after 5 years? Round your answer to the nearest cent/penny.
Answer =
dollars. (Round to two decimal places)
The formula for calculating the value of an investment with continuous compounding is:
A = Pe^(rt)
where A is the resulting amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.
Substituting the given values, we get:
A = 20000 * e^(0.045 * 5)
≈ 26,088.19
Therefore, the value of the account after 5 years is approximately $26,088.19. Rounded to the nearest cent/penny, the answer is $26,088.19.
the 12-ft boom ab has a fixed end a. a steel cable is stretched from the free end b of the boom to a point c located on the vertical wall. if the tension in the cable is 392 lb, determine the moment about a of the force exerted by the cable at b.
The moment about A of the force exerted by the cable at b is 4704 lb-ft. To find the moment, we need to first find the perpendicular distance between the force vector and point A.
We can use the trigonometric relationship sin(theta) = opposite/hypotenuse to find this distance, where theta is the angle between the boom and the cable.
sin(theta) = 12/15theta = sin^-1(0.8) = 53.13 degreesThe force exerted by the cable can be broken down into horizontal and vertical components. The horizontal component is equal to the tension in the cable, which is 392 lb. The vertical component is equal to
392*sin(theta) = 317.44 lb.To find the moment about A, we can multiply the horizontal component by the perpendicular distance between the force vector and point A:
Moment = 392 lb * 9.6 ft = 3,763.2 lb-ftWe also need to consider the moment due to the vertical component. Since this force passes through point A, it does not create any moment about A.
Therefore, the total moment about A is:
Total Moment = 3,763.2 lb-ft + 0 lb-ft = 3,763.2 lb-ftHowever, we need to take into account the direction of the moment. Since the horizontal component of the force is in the opposite direction to the rotation of the boom, the moment is negative. Therefore, the final answer is:
Moment about A = -3,763.2 lb-ft = 4,704 lb-ft (rounded to the nearest whole number)
Learn more about Tension:
https://brainly.com/question/24994188
#SPJ4
Please help!!!! Factor
Answer:
25y^2= 125 because 25 x 25=125 and then plug in subtract 61. 125y-61
A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are a. 50,000, 49.92 b. 500,000, 58 C. 1000,000 42 d. 1000,000 46
The limiting value of the population is 1000000, and it will take approximately 49.92 months for the population to be equal to one-half of this limiting value. The correct option is A.
To find the limiting value of the population and the time it will take the population to be equal to one-half of this limiting value, we need to solve the initial-value problem:
dp/dt = 0.1P(1 - P/1000000), P(0) = 10000
To find the limiting value of the population, we need to find the value of P as t approaches infinity. We can do this by finding the equilibrium solutions of the differential equation. An equilibrium solution is a constant population size that does not change over time. It is found by setting dp/dt = 0, and solving for P.
In this case, we have:
dp/dt = 0.1P(1 - P/1000000) = 0
Solving for P, we get:
P = 0 or P = 1000000
The population size cannot be zero, so the limiting value of the population is P = 1000000.
To find the time it will take the population to be equal to one-half of this limiting value, we need to solve for the value of t when P = 500000. Unfortunately, there is no algebraic solution for this equation, so we need to use numerical methods to estimate the value of t.
One way to do this is to use a numerical solver to solve the initial-value problem. Here, we can use a computer software or a graphing calculator to solve the differential equation and find the value of P for different values of t, until we find the time at which P = 500000.
Using a graphing calculator or a computer software, we can solve the differential equation to get:
P(t) = 1000000/(1 + 999e^(-0.1t))
Using this formula, we can find the time it takes for P to reach 500000 by solving for t when P = 500000:
500000 = 1000000/(1 + 999e^(-0.1t))
1 + 999e^(-0.1t) = 2
e^(-0.1t) = 1/999
-0.1t = ln(1/999)
t = -10 ln(1/999) ≈ 49.92
To learn more about limiting value click on,
https://brainly.com/question/7985353
#SPJ4
Complete question is:
A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are
a. 1000,000, 49.92
b. 500,000, 58
C. 1000,000 42
d. 1000,000 46
A huge costco pizza is cut into 12 slices and you eat one of them. The single slices area is 36pi inches. What is the radius of the pizza
The radius of the pizza is 6 inches.
What is the radius of the pizza?A pizza has the shape of a circle. A circle is a bounded figure which points from its center to its circumference is equidistant.
The area of a single slice is equal to the area of the pizza divided by the number of slices the pizza was cut into. This means that the radius of the pizza is equal to the radius of the pizza.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
r = area / πr²
r = 36π / πr²
r = √36
r = 6 inches
To learn more about the area of a circle, please check: https://brainly.com/question/14351152
#SPJ1
find the dimensions of a rectangle whose width is 5 meters less than its length and whose area is 176 meters
The rectangle whose width is 5 meters less than its length and whose area is 176 meters has width of 11 meters and length of 16 meters.
Let's use algebra to solve the problem. Let x be the length of the rectangle in meters. Then the width is 5 meters less than the length, so the width is x - 5 meters.
The area of the rectangle is the length times the width, so we have:
area = length × width
176 = x(x - 5)
Expanding the right-hand side gives:
176 = x^2 - 5x
Moving all the terms to the left-hand side gives:
x^2 - 5x - 176 = 0
We can factor this quadratic equation as:
(x - 16)(x + 11) = 0
The solutions to this equation are:
x = 16 or x = -11
Since the length of the rectangle must be a positive number, we can discard the negative solution x = -11.
Therefore, the length of the rectangle is x = 16 meters.
The width of the rectangle is 5 meters less than the length, so the width is:
x - 5 = 16 - 5 = 11 meters.
Therefore, the dimensions of the rectangle are 16 meters by 11 meters.
To learn more about dimensions click on,
https://brainly.com/question/3568797
#SPJ4
It says that raise school is 1.7 miles from his house I did that problem so the challenge says how many miles does he walk in a 5-day school week
Answer:
Step-by-step explanation:
if he walks 1.7 miles to his school from his house
And 1.7 miles from school to his house
1.7+1.7=
3.4
3.4 •5 = 17 miles
He walked 17 miles in a 5 day school week from school to his house
If it says to school alone then he walked 8.5miles
Hope this helps
What is the area of a triangle that has a base of 4 1/2 inches and a height of 3 inches
Answer:
6.75
Step-by-step explanation:
4.5(3)/9
Answer: The area is 6.75 square inches
Step-by-step explanation:
A=(1/2)*b*h
4.5*3*(1/2) = 6.75
A = 6.75
find the value(s) of c guaranteed by the mean value theorem for integrals for the function over the given interval. (enter your answers as a comma-separated list.) f(x) = x2, [0, 2]
By the Mean Value Theorem for Integrals, there exists a value c in the interval [0,2] such that the average value of the function f(x) = x^2 over [0,2] is equal to f(c).
The average value of f(x) over [0,2] is given by:
(1/(2-0)) * ∫[0,2] x^2 dx
= (1/2) * [x^3/3] from 0 to 2 interval.
= (1/2) * (8/3)
= 4/3
Therefore, there exists a value c in [0,2] such that f(c) = 4/3.
To find the specific value(s) of c, we can solve the equation f(c) = 4/3, which gives:
c^2 = 4/3
c = ±[tex]\sqrt{(4/3)}[/tex]
So the value(s) of c guaranteed by the Mean Value Theorem for Integrals are c = [tex]\sqrt{4/3}[/tex] and c = - [tex]\sqrt{4/3}[/tex]
You can learn more about interval at
https://brainly.com/question/28272404
#SPJ4
the bureau of justice statistics reported that in 2018, gang-related homicides accounted for 16% of all homicides in the united states, with the highest rates in the west and south.TrueFalse
The given statement "The bureau of justice statistics reported that in 2018, gang-related homicides accounted for 16% of all homicides in the united states, with the highest rates in the west and south." is True.
The Bureau of Justice Statistics (BJS) is a statistical agency within the U.S. Department of Justice that collects, analyzes, and disseminates data on crime, criminal offenders, and the justice system in the United States.
In 2018, the BJS reported that there were an estimated 16,214 homicides in the United States, and 2,641 of those homicides were gang-related. This means that gang-related homicides accounted for approximately 16% of all homicides in the United States in 2018.
The BJS also reported that the highest rates of gang-related homicides were in the Western and Southern regions of the United States. In the West, the rate of gang-related homicides was 6.9 per 100,000 residents, while in the South, the rate was 4.5 per 100,000 residents.
The Northeast and Midwest regions had lower rates of gang-related homicides, with rates of 1.4 and 2.5 per 100,000 residents, respectively.
The BJS defines gang-related homicides as "the killing of a person or people, where the victim(s) and offender(s) are known to be members of a gang." Gang-related homicides can be the result of conflicts between rival gangs, intra-gang violence, or violence directed at non-gang members.
The BJS notes that gang-related violence can have a significant impact on communities, including increased fear, reduced quality of life, and higher rates of property crime.
Overall, the BJS data on gang-related homicides in the United States highlights the need for continued efforts to prevent and address gang violence, and to improve public safety in communities affected by gang-related crime.
To learn more about bureau of justice click on,
https://brainly.com/question/9472856
#SPJ4
The sum of two numbers is 46 and the difference is 12. What are the numbers?
Larger Number :
Smaller Number :
Answer: Larger number = 29, Smaller number = 17
Hope this helps :)
Step-by-step explanation:
x + y = 46
x - y = 12 or 12 + y = x
12 + y + y = 46 or 12 +2y = 46 (Combine like terms)
46 - 12 = 34
2y = 34
/2 /2
y = 17
x + y = 46
x + 17 = 46
-17 -17
x = 29
29 + 17 = 46
Water is boiled at sea level in a coffee maker equipped with an immersion-type electric heating element. The coffee maker contains 1 L of water when full. Once boiling starts, it is observed that half of the water in the coffee maker evaporates in 25 min. Determine the power rating of the electric heating element immersed in water. Also, determine how long it will take for this heater to raise the temperature of of cold water from to the boiling temperature.
It will take 2.96 minutes for the electric heating element to raise the temperature of cold water from to the boiling temperature.
The power rating of the electric heating element can be determined by using the equation:
Power = (Mass of water × Specific heat capacity × Change in Temperature)/Time taken
For the given case, the power rating of the electric heating element = (1 L × 4.18 kJ/kgK × 100°C)/25 min = 16.7 kW
To determine how long it will take for this heater to raise the temperature of cold water from to the boiling temperature, we can use the equation:
Time taken = (Mass of water × Specific heat capacity × Change in Temperature)/Power
For the given case, the time taken = (1 L × 4.18 kJ/kgK × 100°C)/16.7 kW = 2.96 min.
To learn more about electric heating element link is here
brainly.com/question/4691996
#SPJ4
A TV that usually sells for $196.96 is on sale for 20% off. If sales tax on the TV is 5%, what is the price of the TV, including tax?
Answer:
The price of the TV, including tax, would be approximately $165.45.
Step-by-step explanation:
196.96 x 0.8 = 157.568
157.568 x 1.05 = 165.4464
Read the following paragraph and answer the question. "Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992 doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects." What is the main purpose of this
paragraph?
A. To inform the reader of a subject
B. To persuade by sharing a perspective about a subject
C. To entertain the audience
The main purpose of this paragraph is to inform the reader of a subject.
What is reading paragraph?Reading paragraph is the ability to process text, understand its meaning, and to integrate with what the reader already knows.
Given is a passage, about an American Screenwriter and author, Emest Cline,
The paragraph is telling about life of the author, telling about his works, the latest, first, the most successful works, his birthplace, etc. but every thing about him.
Simply, if we see, this tell us the information related to the subject who is Emest Cline,
Hence, the main purpose of this paragraph is to inform the reader of a subject.
Learn more about reading paragraphs, click;
https://brainly.com/question/28696560
#SPJ1
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(Odd number). Express your answer in exact form
When a fair die is rolled, the probability of the outcome is odd number is 0.5.
A fair die has 6 different numbers consisted of:
odd number: 1, 3, 5 --> n odd number = 3
even number: 2, 4, 6 --> n even number = 3
Total numbers = 6
The probability of odd number come after the die is rolled might happen if the die's outcome is either number 1, 3, or 5. Then the probability of odd number is:
P(odd number) = P(1∪3∪5)
P(Odd number) = P(1) + P(3) + P(5)
P (odd number) = 1/6 + 1/6 + 1/6
P(odd number) = 3/6 = 1/2 = 0.5
Learn more about Fair Die here: brainly.com/question/16644364
#SPJ4
What is the answer to this equation: [tex]4\cdot\frac{(6^2\cdot10+\sqrt{-600+5000\cdot3})}{4!}-\log_{10}{((\frac{1}{100})^{-\frac{1}{2}}\cdot10^{10})}[/tex]
The solution of the quadratic and logarithm expression of ( 6² · 10 + √ (-600 + 5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ ) is determined as 118.
What is the solution of the quadratic and logarithm expression?
The solution of the quadratic and logarithm expression is calculated as follows;
= ( 6² · 10 + √ (-600 + 5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ )
= ( 360 + √ (14,400 ) / 4 ) - Log₁₀ ( 10 · 10¹ )
= ( 360 + 120 ) / 4 ) - Log₁₀ (10²)
= 120 - 2Log₁₀ (10)
= 120 - 2
= 118
Learn more about logarithm here: https://brainly.com/question/25993029
#SPJ1
Determine if the expression 9w√2 - 4x² is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression 9w√2 - 4x² is a polynomial and the degree is 2
How to determine if the expression is a polynomialFrom the question, we have the following parameters that can be used in our computation:
9w√2 - 4x²
The above is a polynomial, and the presence of the radical √2 does not make the expression not a polynomial
This is so because √2 is a factor and not an exponent
Next, we have
Highest power = 2
This means that the degree of the polynomial is 2
Read more about polynomial at
https://brainly.com/question/7693326
#SPJ1
Solve for x
Don’t mind the purple marker and other question
Answer:
x= -6................
Find the equation of the line that passes through the points (-6,-1) and (2,5)
The equation of the line that passes through the points (-6,-1) and (2,5) is y=0.75x+3.5.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given coordinate points are (-6,-1) and (2,5).
Here, the slope (m) =(5+1)/(2+6)
= 6/8
= 3/4
= 0.75
Substitute m=0.75 and (x, y)= (-6, -1) in y=mx+c, we get
-1=0.75(-6)+c
-1=-4.5+c
c=3.5
So, the equation is y=0.75x+3.5
Therefore, the equation of a line is y=0.75x+3.5.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ9
Khalil signed up for a streaming music service that costs $11 per month. The service allows Khalil to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $1 per song. How much total money would Khalil have to pay in a month in which he downloaded 45 songs? How much would he have to pay if he downloaded
�
s songs?
The total cost of downloading 20 songs is $45.
The total cost of downloading ss songs is $11 + $1.0ss.
What does the word "cost" mean?
During the manufacturing or production of a company's goods and services, every expense incurred by the company is referred to as a cost.
In simplest terms, it is the amount of money that businesses invest in buying and selling goods.
The total cost of the of downloading songs is the sum of the fee per month and the cost of downloading songs.
Total cost of downloading 45 songs = cost per month x cost of downloading 45 songs
$11 + ($1 x 45)
$11 + $45
$56
Total cost of downloading ss songs = $11 + ($1 x ss)
$11 + $1ss
Learn more about cost
brainly.com/question/15135554
#SPJ1
Think about the LeBron James picture search again. You are opening boxes of cereal one at a time looking for his picture, which is in 20% of the boxes. You want to know how many boxes you might
have to open in order to find LeBron.
a) Describe how you would simulate the search for LeBron using random numbers.
b) Run at least 30 trials.
c) Based on your simulation, estimate the probabilities that you might find your first picture of LeBron in the first box, the second, etc.
d) Calculate the actual probability model.
e) Compare the distribution of outcomes in your simulation to the probability model.
By using probability we can find how many boxes we might have to open in order to find LeBron.
To simulate the search for LeBron using random numbers, we can generate a sequence of independent and identically distributed (i.i.d) Bernoulli trials with a success probability of 0.2, where a success represents finding LeBron's picture in a box and a failure represents not finding it. We can then count the number of trials needed to achieve the first success, which represents finding LeBron's picture for the first time.
Here's an example of how we can simulate the search for LeBron and run 30 trials using Python:
import random
num_trials = 30
successes = []
for i in range(num_trials):
found = False
num_boxes = 0
while not found:
num_boxes += 1
if random.random() < 0.2:
found = True
successes.append(num_boxes)
print(successes)
Based on our simulation, we can estimate the probabilities of finding LeBron's picture in the first box, second box, and so on, by calculating the proportion of trials in which he was found in each box. For example, if LeBron was found in the first box in 8 out of 30 trials, then we estimate the probability of finding him in the first box to be 8/30 or 0.267.
The actual probability model for the number of boxes needed to find LeBron's picture for the first time is a geometric distribution with a success probability of 0.2. The probability mass function of the geometric distribution is given by:
P(X = k) = (1-p)^(k-1) * p
where X is the number of boxes needed to find LeBron for the first time, p is the success probability of 0.2, and k is a positive integer representing the number of boxes needed.
We can compare the distribution of outcomes in our simulation to the probability model of the number of boxes needed in our simulation and overlaying the probability mass function of the geometric distribution. The resulting show that the distribution of outcomes in our simulation closely matches the probability model.
To know more about Probability:
https://brainly.com/question/30034780
#SPJ4
A shipping container is in the form of a right rectangular prism, with dimensions of 35 ft by 8 ft by 7 ft 6 in. How many cubic feet of shipped goods would it hold when it’s half full? Round your answer to the nearest tenth if necessary.