The equation 3x - 8y = 24 can be written in slope intercept form as y = [tex]\frac{3}{8}[/tex] x - 3.
What is Slope?Slope of a line is defined as the value of the change in the values of the y coordinates with respect to the change in the values of the x coordinate.
It can also be defined as the tangent of the angle that the line makes with the X axis.
The standard equation of a line in slope intercept form is, y = mx + c, where m is the slope and c is the y intercept.
y intercept is the y coordinate when the line touches with the Y axis. The x coordinate of that point will be zero.
The given equation is,
3x - 8y = 24
Subtracting both sides of the equation with -3x,
3x - 8y - 3x = 24 - 3x
-8y = 24 - 3x
Dividing both sides by -8, we get,
y = -3 + [tex]\frac{3}{8}[/tex] x
y = [tex]\frac{3}{8}[/tex] x - 3
Hence the standard equation in slope intercept form for 3x - 8y = 24 is y = [tex]\frac{3}{8}[/tex] x - 3.
To learn more about Slope, click on the link given below:
https://brainly.com/question/3605446
#SPJ5
How many three-letter codes can we make using only vowels, a, e, i, o, or u?
Answer and explanation:
Given : Vowels a,e,i,o or u.
To find : How many three-letter codes can we make using only vowels ?
Solution :
1) If we assume that repetition is allowed then
The three letter code can form
[tex]5\times 5\times 5=125[/tex] ways
Number of three-letter codes can we make using only vowels is 125.
2) If we assume that repetition is not allowed then
The three letter code can form
[tex]5\times 4\times 3=60[/tex] ways
Number of three-letter codes can we make using only vowels is 60.
How many numbers must be selected from the set $\{1, 3, 5, 7, 9, 11, 13, 15\}$ to guarantee that at least one pair of these numbers add up to 16?
A basketball player makes 60% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 4 shots. let x = the number of shots that he makes. what is the probability that he makes all 4 shots?
Using the binomial distribution, it is found that there is a 0.1296 = 12.96% probability that he makes all 4 shots.
-------------------------------
For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
Makes 60% of the shots, thus [tex]p = 0.6[/tex]4 shots, thus [tex]n = 4[/tex].The probability of making all of them is P(X = 4), thus:[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
0.1296 = 12.96% probability that he makes all 4 shots.
A similar problem is given at https://brainly.com/question/9000732
Hudson worked two jobs last summer to start saving for a car. He mowed lawns during the day and worked at a pizza place in the evenings. In one month, Hudson earned a total of $1,400. If he earned $360 more at the pizza place than mowing lawns how much did he earn at each job?
Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
What is a system of linear equation?A System of Linear Equations is when we have two or more linear equations working together.
Given that, Hudson mowed lawns during the day and worked at a pizza place in the evenings. Hudson earned a total of $1,400. also he earned $360 more at the pizza place than mowing lawns
Let he earn x at deliveries and y at mowing,
Therefore, establishing a system of equations,
x+y = 1400
x-y = 360
Adding both the equations,
2x = 1760
x = 880
y = 1400-880
y = 520
Hence, Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
Learn more about system of equations, click;
https://brainly.com/question/12895249
#SPJ3
The game called lotto sponsored by the louisiana lottery commission pays its largest prize when a contestant matches all 4 of the 41 possible numbers. assume there are 41 ping-pong balls each with a single number between 1 and 41. any number appears only once, and the winning balls are selected without replacement.
a. the commission reports that the probability of matching all the numbers are 1 in 101,270. what is this in terms of probability
Final answer:
The reported probability of 1 in 101,270 for matching all four lotto numbers is equivalent to a decimal probability of approximately 0.00000987.
Explanation:
The Louisiana Lottery Commission's lotto game entails participants matching all 4 numbers out of a pool of 41. The reported probability of achieving this feat is 1 in 101,270. To express this probability, we utilize the ratio of successful outcomes to total possible outcomes. Consequently, the probability of matching all four numbers is 1/101,270, equivalent to approximately 0.00000987 in decimal form. This minute probability underscores the challenging nature of the lotto game, highlighting the rarity of successfully predicting and matching the specified set of numbers within the given range.
Diameter of a cylindrical tank is 9 feet and the height of a tank is 25 feet. Find the approximate volume of the cylindrical tank to the nearest hundredth place
C. 1,589.63 cubic feet
D. 2,325.26 cubic feet
E. 6,358.50 cubic feet
F. 3,489.27 cubic feet.
There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
The population of a small town decreased from 983 to 901. What is the percent decrease, to the nearest tenth of a percent?
The population of the small town percent decreased by approximately 8.4%.
To find the percent decrease in the population of the small town, we can use the formula for percent decrease:
Percent Decrease = [(Initial Value - Final Value) / Initial Value] * 100
Given that the initial population was 983 and the final population was 901, we can plug these values into the formula:
Percent Decrease = [(983 - 901) / 983] * 100
Now, calculate the numerator:
Percent Decrease = [82 / 983] * 100
Divide and multiply:
Percent Decrease = 0.0835 * 100
Now, calculate the percent decrease to the nearest tenth of a percent:
Percent Decrease ≈ 8.4%
So, the population of the small town decreased by approximately 8.4%.
To know more about percent decrease click here :
https://brainly.com/question/2913116
#SPJ2
A right triangle has legs that are 15 feet and 25 feet long. What is the length of the hypotenuse? Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
how can you be able to find an area
Two secant segments intersect outside a circle as shown. What is the value of x?
True or False 68oz < 4lb 6oz
Answer:true!!!
Step-by-step explanation:
which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9
EXPERTS/ACE/GENIUSES HELP PLZ!!:)
( only #2 )
Explain as well!! Best answer will get brainlist... but make ur answer short and sweet plz.
(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3
scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 = 63
(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3
scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 = 16
if f(x) = 5x^3-2 and g(x)= 2x+1, find (f+g) (x).
The expression for (f + g)(x) is [tex]\rm 5x^3+2x-1[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
[tex]\rm f(x) = 5x^3-2[/tex][tex]\rm g(x) = 2x + 1[/tex]The following steps can be used in order to determine the value of (f + g)(x):
Step 1 - Write the given functions.
[tex]\rm f(x) = 5x^3-2[/tex] --- (1)
[tex]\rm g(x) = 2x + 1[/tex] --- (2)
Step 2 - Now, to determine the value of (f + g)(x), add both function f(x) and g(x).
f(x) + g(x) = (f + g)(x)
Step 3 - Substitute the value of f(x) and g(x) in the above expression.
[tex]\rm (f + g)(x) = 5x^3-2+2x+1[/tex]
Step 4 - Simplify the above expression.
[tex]\rm (f + g)(x) = 5x^3+2x-1[/tex]
For more information, refer to the link given below:
https://brainly.com/question/5245372
Ming says that 0.24 > 14 because 0.24 = 24. Which best explains Ming's error?
Answer:
Ming says that 0.24 > 14
1
4
because 0.24 = 24
2
4
. Which best explains Ming's error?
Step-by-step explanation:
If a student scored 82 points on a test where the mean score was 78.2 and the standard deviation was 6.7. the student's z score is .
Consider a game in which a coin will be flipped three times. for each heads you will be paid $100. assume that the coin comes up heads with probability 4/5.
Please help me with questions 26 and 27
The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle? A. length = 20 inches, width = 17 inches B. length = 17 inches, width = 14 inches C. length = 10 inches, width = 7 inches D. length = 34 inches, width = 10 inches
To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.
Explanation:Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.
Step-by-step:
Express the area as a product of the length and width: 'x(x - 3) = 340'.Expand and rearrange the equation: 'x^2 - 3x - 340 = 0'.Factor the quadratic equation: '(x + 17)(x - 20) = 0'.Solve for 'x': 'x = -17' or 'x = 20'. Since length cannot be negative, the length is 20 inches.Calculate the width: '20 - 3 = 17 inches'.The cost for a pack of 4 padlocks is $17.60 . Find the unit price in dollars per padlock. If necessary, round your answer to the nearest cent.
Answer:
18.00
Step-by-step explanation:
60+40=100
Make a box-and-whisker plot for the data. What is the upper quartile value? 56 32 48 52 51 53 48 38 35 42 40 46 54 50
Answer:
Step-by-step explanation:
The given data is:
56 32 48 52 51 53 48 38 35 42 40 46 54 50
In order to get the value of the upper quartile, first arrange he given data in ascending form, we get
32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56
The upper quartile is:48, 50, 52, 53, 54, 56
The value of upper quartile is given as:
[tex]\frac{52+53}{2}[/tex]
=[tex]\frac{105}{2}[/tex]
=[tex]52.5[/tex]
Thus, the value of the upper quartile will be 52.5.
The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
To find the height of the rectangular prism, divide the volume by the area of the base.
Explanation:To find the height of the rectangular prism, we need to divide the volume by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the length, width, and height, respectively. The formula for the area of the base is A = lw.
In this case, the volume is given as (x3-3x2+5x-3) and the area of the base is (x -2). So, we need to divide the volume by the area of the base, which gives us:
(x3-3x2+5x-3)/(x -2).
Learn more about rectangular prism height here:https://brainly.com/question/16027067
#SPJ12
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24 cubic units what is the height of the cylinder
the answer is c.6 i just took the test.
Which graph correctly solves the system of equations below? x2 + y2 = 25 y = x + 1
How do you solve 7(2-j)-5??
IF YOU ANSWER WITHOUT A PROPER ANSWER AND YOU JUST WANT POINTS YOUR ANSWER WILL BE REPORTED! 99 POINT QUESTION! So I want a full explanation, best answer gets to be the brainliest. How much is 457 - (-54) + 7700 * 325 = ? I feel generous today so I'm making this 99 points. Btw, this is my first question asked here on brainly.
Use the graph to find the local minimum and the local maximum for the given function.
In the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
What is Local Maxima and Local Minima?
The local maxima and minima are the input values for which the function gives the maximum and minimum output values respectively. The y - coordinate of local maxima is called local maximum and that of local minima is called as local minimum.
Given is a graph of a function.
In the graph the local maximum is the y - coordinate that has maximum value at any specific input. Similarly, local maximum is the y - coordinate that has minimum value at any specific input.
PART A
In the interval [-3, 0], the local minimum is -16
PART B
In the interval [0, 3], the local maximum is 4 and local minimum is -3.
Therefore, in the interval [-3, 0] the local minimum is -16 and In the interval [0, 3], the local maximum is 4 and local minimum is -3.
To solve more questions on Local maxima and minima, visit the link below-
https://brainly.com/question/8086834
#SPJ5
Two years ago Carol's living expenses were $ 1200 $ 1200 per month. This year the same items cost Carol $ 1400 $ 1400 per month. What was the annual inflation rate for the past two years?
what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
a. -6
b. 7
c. x+2
d. 2x-3
Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.
Explanation:
To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.
For the numerator 7x+14, we can factor out a 7:
7x + 14 = 7(x + 2)
For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:
2x² + x - 6 = (2x - 3)(x + 2)
Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).