Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:
x + y = 5 (the total length of the rope is 5 feet)
And from the problem statement, we have:
3x - 7 = 5y
Now we can use the first equation to solve for y:
y = 5 - x
Substituting this expression for y into the second equation:
3x - 7 = 5(5 - x)
Expanding the right side:
3x - 7 = 25 - 5x
Adding 5x to both sides:
8x - 7 = 25
Adding 7 to both sides:
8x = 32
Dividing both sides by 8:
x = 4
So the length of the longer rope piece is 4 feet.
What is the kinetic energy of a 3 kg ball that is rolling at 2 m/s
The kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules. The kinetic energy of an object is the energy it possesses due to its motion.
The kinetic energy of an object is the energy it possesses due to its motion. The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, the mass of the ball is 3 kg and its velocity is 2 m/s, so we can plug these values into the formula:
Kinetic Energy = [tex](1/2) * 3 kg * (2 m/s)^2[/tex]
Kinetic Energy = [tex](1/2) * 3 kg * 4 m^2/s^2[/tex]
Kinetic Energy = 6 J
So the kinetic energy of the 3 kg ball rolling at 2 m/s is 6 joules.
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What is the length of the radius of the above sphere if the volume is 14,130 in3?
Solve this equation and you will have the solution:
4 • 3.14 • r3 ÷ 3 = 14,130
Your last step when solving this equation is to find the cube root of a both sides!
The length of the radius of the sphere is 15 in.
What is a sphere?It is a three-dimensional figure and has a diameter and a radius and the volume of a sphere is 4/3πr³.
We have,
Volume of the sphere = 14130 in³
So,
4/3πr³ = 14130 _____(1)
Solve for r.
4/3 x 3.14 x r³ = 14130
keep r on one side and the rest on the other side.
r³ = 14130 x 3 / 4 x 3.14
Cube root on both sides.
r³ = 3375
∛r³ = ∛3375
[ 15 x 15 x 15 = 3375 ]
So,
r = 15
Thus,
The radius of the sphere is 15 in.
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a square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. a square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. what is x y ?
The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.
Note that triangle ABC and triangle FBE are similar,(by AAA)
As [tex]\angle B[/tex] is common in both, and [tex]\angle F= \angle A[/tex] as they both are 90°
so, the [tex]\angle C[/tex] will also be equal to [tex]\angle E[/tex]
so [tex]\frac{BF}{FR} = \frac{AB}{AC}[/tex]
This can be written as [tex]\frac{4-x}{x} = \frac{4}{3}[/tex]
solving: 12 - 3x = 4x
7x = 12 or x = 12/7
Similarly, triangle A'B'C' and triangle RB'Q are similar,
so RB' = [tex]\frac{4}{3}y[/tex] and C'S= [tex]\frac{3}{4}y[/tex]
Thus, C'B' = C'S+ SR+ RB'
or [tex]\frac{4}{3}y + y + \frac{3}{4} = 5[/tex]
solving y = 60/37
Now, x/y = [tex]\frac{12}{7} \times \frac{37}{60}[/tex] = 37/35
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The number of bacteria in a lab experiment can be modeled by the function y(t)=270(1.129)^4t. Write an equivalent function of the form y(t)=ab^t. Round your final values to 4 decimal places.
Please help! 15 Points!
Answer:
Option C
Step-by-step explanation:
2*-1 = -2
2*0 = 0
When the data is asymmetrical, you use _ (IQR/SD) to measure the spread.
Fοr distributions with a nοrmal shape or symmetry, the mean and standard deviation are emplοyed; for asymmetrical distributiοns, the median and interquartile range are used.
Do you calculate spread using IQR or standard deviation?Because it is unaffected by οutliers, the IQR is frequently regarded as a mοre accurate measure of spread than the range. The variance and standard deviatiοn are indicators of hοw widely the data are dispersed from the mean. Each οbserved data value's prοximity to the mean is summarised.
Why are skewed data sets used for IQR?The strοngest indicator of variability in data sets with οutliers or skewed distributions is the interquartile range. It's unlikely to be impacted by οutliers because it's based οn numbers that come frοm the centre half of the distribution.
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10. The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight. It changed by the same amount each hour. Write and solve an equation to find h, the hourly change in temperature.
The hourly change in temperature is -1.5
What do you understand by Fahrenheit?Fahreheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
The 18th- cenetury German physicist Daniel Gabreil Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.
Given:
The temperature underwent a change of -18°F between noon and midnight.
To find:
The hourly change (h) in temperature
There are 12 hours between noon and midnight
So,
According to Question
Equation:
12h = -18
h = -18/12
h =-3/2
h = -1.5
The hourly change in temperature is -1.5
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The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight, then the hourly change in temperature is -1.5.
What is Fahrenheit?
Fahrenheit temperature scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
The 18th-century German physicist Daniel Gabriel Fahrenheit originally took as the zero of his scale the temperature of an equal ice-salt mixture and selected the values of 30° and 90° for the freezing point of water and normal body temperature, respectively, these later were revised to 32° and 96°, but the final scale required an adjustment to 98.6° for the latter value.
Given:
The temperature underwent a change of -18°F between noon and midnight.
To find:
The hourly change (h) in temperature
There are 12 hours between noon and midnight
So,
According to Question
Equation:
12h = -18
h = -18/12
h =-3/2
h = -1.5
Therefore, The hourly change in temperature is -1.5
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Madison took a taxi from her house to the airport. The taxi company charged a pick-up fee of $3.20 plus $5 per mile. The total fare was $98.20, not including the tip. Write and solve an equation which can be used to determine
m, the number of miles in the taxi ride.
Answer:
19 miles
Step-by-step explanation:
hope this helps!!
Clarice has animated a 3D airplane with visible passengers in the windows. She wants the plane to move on a predetermined path across the screen. What form of animation should she use?
this is just for fun I already know the answer but I will give branly and a lot of points to who ever answers
2+2
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation: Because 1+1=2
2+2=4 therefore 2*2 also equal 4 and 2^2= 4
what is the van't hoff factor for a solution of (nh4)3po4? write your answer in number format such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.
In this solution, each molecule of (NH₄)₃PO₄ dissociates into three ammonium ions (NH₄₊) and one phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. Hence, the Van 't Hoff factor for this solution is 4.
The Van 't Hoff factor (i) is a measure of the degree to which a substance ionizes in a solution, and is defined as the ratio of the number of ions formed to the number of molecules (or formula units) dissolved. For the case of a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4. The Van 't Hoff factor is a measure of the extent to which an ionic substance dissociates into individual ions when dissolved in water. It is defined as the ratio of the number of ions formed to the number of formula units or molecules of the substance that are dissolved. For a solution of (NH₄)₃PO₄, the Van 't Hoff factor is 4 because each molecule dissociates into 3 ammonium ions (NH₄₊) and 1 phosphate ion (PO4₃₋), resulting in a total of 4 ions per molecule. The Van 't Hoff factor is important in determining the colligative properties of solutions, such as boiling point elevation and freezing point depression.
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1. suppose that the students in your class want to have a party at which they will serve punch to drink. the punch the students want to serve is sold in half-gallon containers. if 25 students attend the party and if each student drinks 8 fluid ounces of punch, then how many containers of punch will you need? describe two different ways students could correctly solve this problem. for each method of solving the problem, explain simply and clearly why the method makes sense.
As per the volume, we need to to purchase 4 containers of punch.
To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:
Total volume of punch = number of students * volume of punch per student
= 25 * 8 fluid ounces
= 200 fluid ounces
Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:
Number of containers of punch = Total volume of punch / Volume of punch per container
= 200 / 64
= 3.125
Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.
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Solve the following system of inequalities graphically on set of axes below. State the coordinates of a point in the solution set.
Answer:
see below for a graph
(-8, 4) is in the solution set
Step-by-step explanation:
You want the graph and a solution point for the inequalities y ≤ -6/5x -4 and y ≥ 2/5x +4.
GraphThe solid boundary line of the first inequality will cross the y-axis at -4, and will have a "rise" of -6 units for each "run" of 5 units. Shading is below this boundary line.
The solid boundary line of the second inequality will cross the y-axis at +4 and will have a "rise" of 2 units for each "run" of 5 units. Shading is above this boundary line.
Solution setThe boundary lines make an X shape on the graph, crossing at the point (-5, 2). The solution set is in the left quadrant.
Point (-5, 2) is in the solution set, as are points in the doubly-shaded space to its left. (-8, 4) is one of those.
__
Additional comment
The boundary lines are solid because the "or equal to" case is included in each.
The ≤ symbol tells you y-values that satisfy the first inequality will be less than (or equal to) those on the boundary line.
The ≥ symbol tells you y-values that satisfy the second inequality will be greater than (or equal to) those on the boundary line.
I get 64% off a table the sale price is $72, what is the original price?
The original price of the table was $200 before the 64% discount was applied.
What is the percentage?
Percentage is a way of expressing a fraction or proportion out of 100. It is commonly used to compare two quantities, indicate the change or growth of a quantity over time, or express the probability or chance of an event occurring.
If you received a 64% discount on the sale price of a table, and the sale price is $72, we can calculate the original price of the table as follows:
Determine the percentage of the original price that corresponds to the sale price after the discount:
If the sale price is 100% - 64% = 36% of the original price, after the 64% discount.
Use the percentage found in step 1 to calculate the original price:
Let x be the original price
x * 36% = $72
0.36x = $72
x = $72 / 0.36
x = $200
Therefore, the original price of the table was $200 before the 64% discount was applied.
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person a starts walking north at 4 ft/s from a point p. five minutes later, person b starts walking south at 5 ft/s from a point 500 feet due east of p. at what rate are the people moving apart 15 minutes after person b starts walking?
The rate at which the people are moving apart 15 minutes after person B starts walking is √2660 feet per second. To the nearest tenth of a foot per second, this is 51.3 feet per second.
Let's call the rate at which the people are moving apart "d".
15 minutes after person B starts walking, person A has been walking for 15 + 5 = 20 minutes, for a total distance of 20 * 4 = 80 feet north from point P.
At the same time, person B has been walking for 15 minutes, for a total distance of 15 * 5 = 75 feet south from point 500 feet due east of P.
The distance between the two people is the square root of the sum of the squares of their north-south and east-west separations, or:
d = √(80^2 + (500)^2) = √(80^2 + 250000) = √250100 = 500
Since the rate at which they are moving apart is the derivative of their separation with respect to time, we can find it by taking the derivative of the above equation with respect to time:
d/dt = √(2 * 80 * 4dt / dt + 2 * 500 * 5dt / dt) = √(160 + 2500) = √2660
To the nearest tenth of a foot per second, this is 51.3 feet per second.
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En una empresa líder en investigación se quiere estimar la proporción de personas a favor de una nueva reforma política en el distrito A. ¿A cuántas personas se necesitará para la estimación, si de una muestra piloto se obtuvo que el 64. 1% de las personas están a favor de la reforma política, se desea estar seguro con un 97% de confianza y tener a lo más 4. 7% de error de estimación?
A sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
To estimate the sample size, we can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
where:
n = sample size
Z = the Z-score for a given confidence level (for 97% confidence, Z = 2.33)
p = the proportion in the pilot sample (0.641)
E = the maximum allowed error of estimation (0.047)
Plugging in the values, we get:
n = (2.33^2 * 0.641 * (1 - 0.641)) / 0.047^2
n = (5.3929 * 0.359) / 0.00222009
n = 1.928 / 0.00222009
n = 869.75
Since the sample size must be a whole number, we round up to the nearest whole number.
n = 870
Therefore, a sample of at least 870 people is needed to estimate the proportion of people in favor of the political reform in District A with a 97% confidence level and a maximum estimation error of 4.7%
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The image of a trapezoid is shown. An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters. What is the area of the trapezoid? 70 m2 38 m2 35 m2 19 m2
The area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.
What is trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. In a trapezoid, the parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases.
There are several types of trapezoids, including isosceles trapezoids, where the legs are of equal length, and right trapezoids, where one leg is perpendicular to both bases. Trapezoids are commonly used in geometry and can be used to find the area of various shapes, such as triangles and rectangles.
To find the area of the trapezoid, we can use the formula:
Area = (1/2) x (sum of bases) x height
Since the trapezoid is isosceles, the length of the two parallel sides are the same. Let's call that length "x". We can use this information to set up an equation:
3 + 4 + 7 + x = 2x
Simplifying, we get:
14 + x = 2x
x = 14
So the length of both parallel sides is 14 meters.
Now we can plug in the values into the area formula:
Area = (1/2) x (3 + 14) x 5
Area = 8.5 x 5
Area = 42.5
Therefore, the area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.
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Answer: B 38m squared.
Step-by-step explanation:
I took the test and got this question correct.
1. A number is divided in the ratio 5:9. If the 1st is 35, find the other.
Step-by-step explanation:
solution
let first part be 5x and second part be 9x
so ,
5x = 35
x = 35\5
x = 7
Now 9x = 9*7 = 63
this might help you thank you
write the equation for the given graph.
The absolute value function on the graph is:
f(x) = -|x + 4| - 5
What is the equation of the absolute value function?Remember that an absolute value function that has a vertex at (a, b) will be written as:
f(x) = |x - a| + b
Here the vertex is at (-4, -5), replacing that in the general formula we will get:
f(x) = |x + 4| - 5
And we also can see that the absolute value function opens downwards with slopes of 1, then there must be a leading coefficient of -1, the actual function is:
f(x) = -|x + 4| - 5
That is the graphed function.
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Ann spent 50% of her allowance on food 30 % of it on stationary and saved the remaining amount her allowance was $15 how much money did she save
At the end, Ann saves a total amount of 3 dollars according to the money she spent and on allowance according to the percentages.
Total Allowance of Ann = 15 dollars
Spent on food by Ann = [tex]\frac{15}{100}[/tex]*50
On food = 50 × [tex]\frac{15}{100}[/tex] = 7.5 dollars
Spent on stationary = 30% of Allowance
On stationary = 30 X[tex]\frac{15}{100}[/tex] = 4.5 dollars
Therefore, Money saved by Ann = Total Allowance - Money spent
Money saved = 15 dollars - 7.5 dollars - 4.5 dollars = 15-(7.5+4.5) dollars
Money saved = 3 dollars
Therefore, money saved by Ann is 3 dollars.
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What is the area of this compound figure?
The area of this compound figure is 85 cm².
What is the area of the compound figure?
The area of the compound figure given is calculated by subtracting the small area of the figure from the big figure.
A (total) = 9 cm x 15 cm
A (total) = 135 cm²
The area of the small figure is calculated as follows;
A (small) = ( 9 cm - 4 cm ) x ( 15 cm - 5 cm )
A (small) = ( 5 cm ) x ( 10 cm )
A (small) = 50 cm²
The area of this compound figure = ( 135 cm² - 50 cm² ) = 85 cm²
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Evaluate: -2[-4+3(2-32+4⋅2-3)-3]
Answer:
68
Step-by-step explanation:
-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3] Start in the center and work your way out.
-2[-4 + 3(2 - 32 + 8 -3) - 3]
-2[-4 + 3(-30 + 8 - 3) -3]
-2[-4 + 3(-22 -3) -3]
-2[-4 + 3(-25)-3]
-2[-4 -27 -3}
-2[-31 - 3]
-2(-34)
68
HELP ASAP, GUITAR CLASS, WILL MARK FIRST ANSWER BRAINLIEST,
What is the name of the note shown above?
A
B
C
G
Answer:
C
Step-by-step explanation:
The spaces go F A C E. The note shown is C.
What is the answer to question 5
Anwer: EG=EF+EG => 6x+12+48=144
6x=144-12-48
6x=84
x=14
d)x=14
Jemma filled one-fourth of a barrel with compost on Saturday. Then she filled the remaining space with 4,200 g4,200 g4, comma, 200, start text, space, g, end text of compost on Sunday.
How many kilograms of compost are in the barrel?
.....kilograms?
The kilograms of compost in the barrel is 5.6 kg
How to determine the kilograms of compost in the barrel?From the question, we have the following parameters that can be used in our computation:
Amount filled on day 1 = 1/4
Remaining space = 4200 grams
The number of kilograms in the barrel is calculated as
Remaining space = (1 - 1/4) * Original space
Substitute the known values in the above equation, so, we have the following representation
(1 - 1/4) * Original space = 4200 grams
Convert to kg
(1 - 1/4) * Original space = 4.2 kg
So, we have
Original space = 4.2 kg/(1 - 1/4)
Evaluate
Original space = 5.6 kg
Hence, the original space is 5.6 kg
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Deshaun rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 80 cents for each mile driven. Deshaun had to pay $250.55 when he returned the truck. For how many miles did he drive the truck?
Answer:
287 miles
Step-by-step explanation:
20.95+ .80x =250.55
250.55-20.95=229.6
.80x=229.6
229.6/.80=x
x=287 miles
a certain bacteria population obeys the population growth law. it is observed that the doubling time for the population is 4 hours. the length of time it will take for the population to increase to 3-times its original population is
According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:
[tex]P = P_0 * 2^{t/t_d)}[/tex]
where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.
To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:
[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]
Dividing both sides by [tex]P_0[/tex] gives:
[tex]3 = 2^{t/t_d}[/tex]
Taking the logarithm of both sides (using any base) gives:
[tex]log(3) = log(2^{t/t_d} )[/tex]
Using the logarithmic identity
[tex]log(a^b) = b*log(a),[/tex]
we can rewrite this as:
[tex]log(3) = (t/t_d)*log(2)[/tex]
Solving for t, we get:
[tex]t = t_d * (log(3)/log(2))[/tex]
Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:
[tex]t = 6 * (log(3)/log(2)) hours[/tex]
Simplifying using the change of base formula
[tex](log(a)/log(b) = log_b(a))[/tex], we get:
[tex]t = 6 * log_2(3)[/tex] hours
Therefore, the answer is (f) None of the above.
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Correct question should be
Click on image for question
over the course of a year, malachi gets 2 haircuts at a price of $12.00 each, 3 haircuts at a price of $15.00 each, and 1 haircut at a price of $25.00. for malachi,what is the weighted mean cost of a haircut?
The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.
We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.
To begin, let's figure out how much each haircut will cost overall:
2 haircuts at $12.00 each = $24.00
3 haircuts at $15.00 each = $45.00
1 haircut at $25.00 = $25.00
Total cost = $24.00 + $45.00 + $25.00 = $94.00
Next, We must determine the total number of cuts:
2 haircuts + 3 haircuts + 1 haircut = 6 haircuts
Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:
The weighted mean cost of a haircut = Total cost / Total number of haircuts
= $94.00 / 6 haircuts
= $15.67 per haircut (rounded to the nearest cent)
Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {1, 3, 7}
A ∪ B?
The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}
The event A has data - A = {6, 8, 10}
The event B has data - B = {5, 6, 9, 12}
The event C has data - C = {1, 3, 7}
The probability formula is -
Probability = No. of outcomes that is favorable / Total number of outcomes
The value for A∪B is -
A∪B = 3/4
The value of A∪B in data set is the values that are present in U data set and in A and B data set.
So, the value is - {5, 6, 8}
Therefore, the value is 3/4 or {5, 6, 8}.
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Need help with this question urgent please
The equation y < - 4 · x - 1 represents the inequality seen in the figure.
How to determine an inequality
According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:
y < m · x - b
m = Δx / Δb
Where:
m - Slopeb - InterceptWe know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:
m = (- 1 - 3) / [0 - (- 1)]
m = - 4
b = - 1
y < - 4 · x - 1
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