We get x = -3 and y = 2 on solving 2x + 5y = 4; 2x - y = -8
Let's find y from the second equation in terms of x:
2x - y = -8
-y = -2x - 8
y = 2x + 8
Now, we may enter the following expression in place of y in the first equation:
2x + 5y = 4
2x + 5(2x + 8) = 4
Simplifying this equation, we get:
12x + 40 = 4
Subtracting 40 from both sides, we get:
12x = -36
Dividing both sides by 12, we get:
x = -3
Now we can substitute this value of x into our expression for y:
y = 2x + 8 = 2(-3) + 8 = 2
Hence, x= -3 and y= 2 are the answers to the system of equations.
The complete question can be:
2x + 5y = 4
2x - y = -8
solve for x and y
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Please help will mark brainlist
Answer:
I have graphed it and attached it in the explanation part.
Step-by-step explanation:
y ≥ 3x - 2 is the red line.
y ≥ 1 is the blue line.
Don has an album that holds 500 stamps. Each page of the album holds 5 stamps. If 50% of the album is empty, how many pages are filled with stamps?
Answer:
50 pages are filled with stamps.
Step-by-step explanation:
If 50% of the album is empty, then 50% of the album is filled with stamps.
So, the total number of stamps that the album holds is 500, and half of that (50%) is filled with stamps, which is:
500 * 50% = 250 stamps
Each page holds 5 stamps, so the number of pages filled with stamps is:
250 stamps / 5 stamps per page = 50 pages
Therefore, 50 pages are filled with stamps
Natalie launches a toy rocket from a platform. The graph below shows the height of the rocket ℎ h in feet after t seconds.
The x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height. The y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.
Describe Function?A function is a mathematical relationship that describes how one quantity (the output or dependent variable) depends on one or more other quantities (the inputs or independent variables).
A function can be thought of as a machine that takes in input values, applies a set of rules or operations to them, and produces an output value. The input values can be any set of numbers or other objects that the function is defined for, and the output values can be any set of numbers or objects that the function can produce.
To find the x-coordinate (or t-coordinate) of the vertex, we can use the formula:
x = -b / (2a)
where a is the coefficient of the squared term, b is the coefficient of the linear term, and x represents the time at which the rocket reaches its maximum height. The equation of the parabolic function that models the height of the rocket is:
h = at² + bt + c
where h is the height of the rocket at time t.
We can use the coordinates of the points on the parabola to find the values of a, b, and c:
(0, 260): 260 = a(0)² + b(0) + c, so c = 260
(2, 324): 324 = a(2)² + b(2) + 260, so 4a + 2b = 64
(6.5, 0): 0 = a(6.5)² + b(6.5) + 260, so 42.25a + 6.5b = -260
We can solve this system of equations to find the values of a and b:
4a + 2b = 64
42.25a + 6.5b = -260
Multiplying the first equation by 3.25 and subtracting from the second equation, we get:
42.25a + 6.5b - 13a - 6.5b = -260 - 208
29.25a = -468
a = -16
Substituting a = -16 into the first equation, we get:
4(-16) + 2b = 64
b = 48
Therefore, the equation of the parabolic function is:
h = -16t² + 48t + 260
The x-coordinate (or t-coordinate) of the vertex is:
t = -b / (2a) = -48 / (2(-16)) = 1.5
The x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height.
To find the y-coordinate (or h-coordinate) of the vertex, we can substitute t = 1.5 into the equation of the parabolic function:
h = -16(1.5)² + 48(1.5) + 260 = 334
Therefore, the y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.
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The complete question is:
if the federal reserve sets the reserve rate to %4, what is the resulting money multiplier?
If the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.
What is money multiplier?The link between the quantity of reserves kept by banks and the amount of money that may be generated through the practise of fractional reserve banking is known as the "money multiplier" in economics and finance. Under a system known as fractional reserve banking, banks are only obligated to maintain a portion of their deposits as reserves and are free to lend the remainder to borrowers.
The reserve ratio, or the percentage of deposits that banks must retain in reserves, is used to compute the money multiplier.
The money multiplier is determined using the formula:
Money multiplier = 1 / reserve ratio
Given the reserve ratio is 4% = 0.04.
Thus,
Money multiplier = 1 / 0.04 = 25
Hence, if the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.
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Witch integer is closest to 3 square root of 12
Answer: You're answer is 3
or exactly 3.464.
[tex]\sqrt{100}[/tex]Answer:
10
Step-by-step explanation:
You have to reverse the square root [tex]3\sqrt{12}[/tex]
what perfect square makes 3? 9.
what is [tex]\sqrt{9} \sqrt{12}[/tex]
[tex]\sqrt{108}[/tex]
what is the perfect square between 108? 100 and 121.
what is the different between them?
108-100=8
121-108=13
obviously, 8 is closer than 13, so now find the square root of the closer perfect square.
[tex]\sqrt{100}[/tex]=10
(2x-3)+[2(2x^2-3x+1)]
Answer:4x^2-4x-1
Step-by-step explanation:
Part B What is the recursive formula for the sequence 8, 10, 12.5, 15.625
Answer:
Step-by-step explanation:
The given sequence can be written as:
a_1 = 8
a_2 = 10
a_3 = 12.5
a_4 = 15.625
To find the recursive formula, we need to find the common ratio (r) between consecutive terms:
r = a_2 / a_1 = 10 / 8 = 1.25
r = a_3 / a_2 = 12.5 / 10 = 1.25
r = a_4 / a_3 = 15.625 / 12.5 = 1.25
Since the common ratio is constant, we can use the formula for a geometric sequence to find the recursive formula:
a_n = r * a_{n-1}
Substituting r = 1.25 and a_1 = 8, we get:
a_n = 1.25 * a_{n-1}
Therefore, the recursive formula for the given sequence is:
a_n = 1.25 * a_{n-1}, with a_1 = 8.
Find the values of m and b
Value of m and b of the straight line in the graph is 0 and 2 respectively.
Define slopeIn mathematics, slope refers to the steepness or inclination of a line, and is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is often represented by the letter m. The slope of a line can be positive, negative, zero, or undefined.
Let us assume that the equation of line be y=mx+b.
where m is the slope
and b is the intercept
The line in the graph is parallel to x axis
so, slope is 0
m=0
the line passes through(0,2)
Putting the value in the equation, we get
b=2
Hence, the equation of line be y=2
Therefore, value of m=0 and b=2.
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The complete question is:
The graph is showing the equation of straight line y=mx+b, find the value of m and b.
Image is attached below:
what two numbers multiply to 2 but add to -5? please helpppp quick!
The two numbers that multiply to 2 but add to -5 are -1 and -2.
How to find the two numbers multiply to 2 but add to -5The two numbers that multiply to 2 and add to -5 are -1 and -2.
To see why, you can use the factoring method:
Find two numbers whose product is 2 (possible pairs are 1 and 2, or -1 and -2).
Check if their sum is -5.
If you use 1 and 2, the sum is 3, so they don't work.
If you use -1 and -2, the sum is -3-2 = -5, so they work.
Therefore, -1 and -2 are the two numbers that multiply to 2 and add to -5.
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A cylinder fits perfectly inside a box. The width of the cylinder is 3 feet, and the space between
the cylinder and the box is filled with 15 gallons of oil, taking up 75% of the space. What is the
height of the box in feet?
The height of the box must be at least 2.9111 feet.
Define volume of the cylinderThe volume of the cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is its height.
Since the width of the cylinder is 3 feet, the radius is 1.5 feet.
The volume of the oil is 15 gallons, which is equivalent to 0.2 cubic feet. We know that this volume of oil takes up 75% of the space between the cylinder and the box, so the total space between the cylinder and the box is 0.2 / 0.75 = 0.2667 cubic feet.
Since the cylinder fits perfectly inside the box, the volume of the box is equal to the volume of the cylinder plus the space between the cylinder and the box. Therefore, we have:
Volume of box = Volume of cylinder + Volume of oil
Volume of box = πr²h + 0.2667
Substituting the values we have:
Volume of box = π(1.5)²h + 0.2667
Volume of box = 7.0686h + 0.2667
To find the height of the box, we need to isolate h. We know that the volume of the box must be greater than or equal to the volume of the cylinder, so we can set up the inequality:
Volume of box ≥ Volume of cylinder
πr²h + 0.2667 ≥ πr²(3)
h + 0.0889 ≥ 3
h ≥ 2.9111
Therefore, the height of the box must be at least 2.9111 feet.
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The mean weight of an adult is 79 kilograms with a standard deviation of 10 kilograms. If 188 adults are randomly selected, what is the probability that the sample mean would be greater than 80.5 kilograms? Round your answer to four decimal places.
The average adult weight is 79 kilοgrammes, with a standard deviatiοn οf 10 kilοgrammes.
We want tο find the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams.
An n-sample sample mean is given by: x = xi / n
where xi is the tοtal οf the sample's individual weights.
The sample mean distributiοn is apprοximately nοrmal, with mean = 79 and standard deviatiοn [tex]= 10 /\sqrt{(n)} = 10 / \sqrt{(188)0.727.}[/tex]
We can standardise the sample mean tο find the prοbability that it is greater than 80.5 kilοgrammes using the fοrmula: [tex]z = (x - ) / ( / \sqrt{(n)})[/tex]
where z is the standard nοrmal variable.
Substituting the values, we get:
[tex]z = (80.5 - 79) / (10 / \sqrt{(188)}) \approx2.14[/tex]
Using a standard nοrmal table οr calculatοr, we can find the prοbability that z is greater than 2.14:
P(z > 2.14) ≈ 0.0161
Therefοre, the prοbability that the sample mean οf 188 adults wοuld be greater than 80.5 kilοgrams is apprοximately 0.0161, rοunded tο fοur decimal places.
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(3- 2x + 2x²) - (4x -5 +3x²)
Answer:
−x2−6x+8
Step-by-step explanation:
1,Rearrange terms
2.Distribute
3.Add the numbers
4.combine like terms
hope this helps i lfet some steps for you!!!<3333
a circulat region has a population of about 360,000 people and a population density of about 1415 people per square mile . find the radius of the region
Answer:
Step-by-step explanation:
Lori is selling crafts at a show. She pays $43.20 for the table rental. She sells 18 items. Every item is the same price and Lori makes a total profit of $25.20. Part A Select all the equations that will yield the correct value for the sale price x of each item. 43.20 = 18x − 25.20 43.20 = 18x + 25.20 25.20 = 18x − 43.20 25.20 = 18x + 43.20 Part B What is the cost x of each item in dollars?
Answer:
43.20 = 18x + 25.20
x = $1.00
Step-by-step explanation:
43.20 - 18x = 25.20
or
43.20 = 25.20 + 18x
Solve for x:
18x = 43.20 - 25.20
18x = 18
x = 18/18 = $1.00
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
No. The function is nonlinear and its slope is not constant.
What is the slope of a linear function?
A linear function can be written in this form, y = a + bx.
In this function, b is the slope of the line. The slope describes the constant unit of change in x, the independent variable, that will result in a change in y by the amount of b.
The slope can be determined as the change in y/change in x or rise/run.
In a nonlinear function, the slope does not produce a constant unit of change in that results in a change in y by the amount of b.
Thus, while a linear function shows a straight line when graphed, a nonlinear function shows a curve.
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If the sin 90° = 1, then which statement is true?
cos 0° = 1, because the angles are complements
cos 90° = 1, because the angles are supplements
cos 0° = 0, because the angles are complements
cos 90° = 0, because the angles are supplements
The statement "cos 0° = 1, because the angles are complements" is true.
A circle with equation (x + 2 )^2 + (y – 3 )^2 = 16 is graphed on the coordinate plane. Which represents the line of tangency at the point (–6, 3)?
The line of tangency at the point (–6, 3) is x = -6. So, the correct option is (b).
What is tangent?
In geometry, the tangent is a trigonometric function that relates to the angles and sides of a right triangle. Specifically, the tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.
To find the line of tangency to a circle at a given point, we need to first find the slope of the radius that passes through that point, and then take the negative reciprocal of that slope to get the slope of the tangent line.
Given the circle equation: (x + 2)² + (y - 3)² = 16, we can see that its center is at the point (-2, 3) and its radius is 4.
To find the slope of the radius passing through the point (-6, 3), we can use the point-slope formula:
(y - y1) = m(x - x1)
where m is the slope of the radius, and (x1, y1) is the center of the circle (-2, 3). Plugging in the values, we get:
(y - 3) = m(x + 2)
Substituting the point (-6, 3) into the equation, we get:
(3 - 3) = m((-6) + 2)
0 = -4m
m = 0
So the slope of the radius is 0. To find the slope of the tangent line, we take the negative reciprocal of the slope of the radius:
slope of tangent line = -1/0 = undefined
Since the slope of the tangent line is undefined, it must be a vertical line passing through the point (-6, 3). Thus, the line of tangency at the point (-6, 3) is the vertical line x = -6.
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Zoe has some cloth. She uses the cloth to make 12 pillowcases. Each pillowcase uses 5/8m of the cloth. She still has 5/12m cloth left. How long is the cloth?
Answer:
Zoe started with 7.917 meters of cloth.
Step-by-step explanation:
If each pillowcase uses 5/8m of cloth and Zoe made 12 pillowcases, then the total amount of cloth used is:
(5/8) x 12 = 15/2 or 7.5 meters
If Zoe has 5/12m of cloth left, then the total amount of cloth she started with is:
7.5 + 5/12 = 90/12 + 5/12 = 95/12 or 7.917 meters
Therefore, Zoe started with 7.917 meters of cloth.
Last week, a candy store sold 6 1/3 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate. DUE NOWW HELP ANSWER BOTH BRO
Question 1
How many pounds (in mixed number form) of milk chocolate did the candy store sell last week?
Responses
A 24 2/3
B. 25 2/3
C. 25 1/3
D. 24 1/3
Question 2
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A. 19 2/3
B. 18
C. 19
D. 18 2/3
Question 1:
Answer:
[tex]C:25\frac{1}{3}[/tex]
Step-by-step explanation:
To find the number of pounds of milk chocolate sold, you have to multiply the amount of pounds of white chocolate sold by 4.
[tex](6+\frac{1}{3}) *4\\\\(6*\frac{3}{3}+\frac{1}{3})*4\\\\(\frac{18}{3} +\frac{1}{3} )*4\\\\\frac{19}{3} *4\\\\\frac{76}{3} \\\\25\frac{1}{3}[/tex]
Question 2:
Answer:
C: 19
Step-by-step explanation:
To find how many more pounds of milk chocolate were sold we subtract the white chocolate sold from the milk chocolate sold
[tex]25+\frac{1}{3} - 6+\frac{1}{3}\\\\25*\frac{3}{3}+\frac{1}{3}-6*\frac{3}{3}+\frac{1}{3}\\\\\frac{76}{3}-\frac{19}{3}\\\\\frac{57}{3}\\\\19[/tex]
A 5 m ladder reaches 4.7 m up a wall. What angle does the ladder make with the wall?
The ladder makes an angle of approximately 19.94 degrees with the wall.
Calculating the angle of the ladder up on the wallWe can use trigonometry to solve for the angle between the ladder and the wall.
Let's call the angle we're looking for "theta" (θ). We can use the cosine function, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse side of a right triangle, to solve for theta:
cos(θ) = opposite/adjacent
So we have:
cos(θ) = 4.7/5
We can use a calculator to solve for theta:
cos(θ) = 0.94
Take the arc cos
θ ≈ 19.94 degrees
Therefore, the ladder makes an angle of approximately 19.94 degrees with the wall.
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PLEASE HELPP!!! MIDDLE SCHOOL MATH!!!!!!!
In the figure shown, m∠2 is 16 more than 3 times m∠1. Find the measure of each angle.
PLEASE LOOK AT PICTURE BELOW!!!!!! SHOW WORK PLEASEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
m∠1 = 41°
m∠2 = 139°
Step-by-step explanation:
Set variables:
1. ∠1 = x
2. ∠2 = y
Make first equation:
It says "m∠2 is 16 more than 3 times m∠1."
So let's convert that into an equation:
y = 16° + 3x
Now, by looking at the photo, we can tell that its a straight line, which is equal to 180°
Derived from that, we can get m∠1 + m∠2 = 180°, which in other "words" is x + y = 180°.
Great, now we have our 2 equations, and we just have to solve.
Equations:
1. y = 16° + 3x
2. x + y = 180°
Let's substitute what we have for y into the second equation:
x + (16° + 3x) = 180°
Solve:
(We can take out parentheses because it's a "+" sign)
Combine like terms:
4x + 16° = 180°
Subtract 16° from both sides
4x = 164°
Isolate x by dividing both sides by 4
x = 41°
Substitute:
Now that we have x = 41°, we can substitute that in for the equation - "y = 16° + 3x"
New Equation:
y = 16° + 3(41°)
Solve:
Multiply 3 and 41°, which is 123°
y = 16° + 123°
Simplify:
y = 139°
Reminder:
m∠1 = x
m∠2 = y
Therefore,
m∠1 = 41°
&
m∠2 = 139°
Hopefully this helps!
(If you want, please mark me brainliest tomorrow)
Answer:
Basically, a straight line is equal to 180 degrees. If angle 2 is 16 more than 3 times angle 1, we get the equation of y = 16 + 3x. Put them together and you get x + 16 + 3x = 180. Then you just solve, and get x = 41. Then you put x in for the other equation and get y = 139.
(25) One half of a number decreased by 3 is at most -5. Which of the following inequalities represents the statement above? A) -—-n-35-5 B) 3- 3--215-5 C) 1-3
The correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.
What is an inequality?
Let's start by defining a variable for the number we are trying to find. Let's call it "x".
"One half of a number" can be represented as (1/2)x.
"Decreased by 3" means we need to subtract 3 from (1/2)x. So, "one half of a number decreased by 3" can be represented as:
(1/2)x - 3
Now, the problem says that this expression is "at most -5". "At most" means that the expression can be equal to -5 or any number less than -5. We can represent this as:
(1/2)x - 3 ≤ -5
To simplify this inequality, let's add 3 to both sides:
(1/2)x ≤ -2
Multiplying both sides by 2 (to eliminate the fraction) gives:
x ≤ -4
Therefore, the correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.
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Dylan and Eric were the lead scorers in a basketball game. Dylan scored p points in the second period of the game. Eric scored as many points as Dylan in the same period of the game. a) Write an expression for Eric's score in terms of p. points b) If Dylan scored 18 points in the second period, how many points did Eric score?
I think the answers 3048_&8_9_)_)_
models the
A 25% orange juice drink is mixed with a 100% orange juice drink. The function f(x) (4)(1.0)+z(0.25)
=
concentration of orange juice in the drink after a gallons of the 25% drink are added to 4 gallons of pure juice.
4+z
What will be the concentration of orange juice in the drink if 2 gallons of 25% drink are added? Give the answer as a percent
but do not include the percent sign (%).
The amount of citrus juice in the combination is therefore 0.75, or 75%.
A volume basic meaning is what?The area filled within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's potential.
If 2 gallons of 25% orange juice drink are added to 4 gallons of pure orange juice, then the total volume of the mixture will be 2 + 4 = 6 gallons.
Let's use the given function f(x) to calculate the concentration of orange juice in the mixture:
f(2) = (4 × 1.0 + 2 × 0.25) / (4 + 2)
= (4 + 0.5) / 6
= 4.5 / 6
= 0.75
Therefore, the concentration of orange juice in the mixture is 0.75 or 75%.
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HELP PLS I GIVE BRAINLIEST
Step-by-step explanation:
The density of gold is given as 5×2^2 grams/cm³, which means that one cubic centimeter of gold has a mass of 5×2^2 grams.
To find the mass of 8 × 25 cm³ of gold, we need to first find the total volume of gold:
Total volume = 8 × 25 cm³ = 200 cm³
Now we can use the density of gold to find the mass:
Mass = Density × Volume
Mass = (5×2^2 grams/cm³) × 200 cm³
Mass = 5 × 4 × 200 grams
Mass = 4000 grams
Therefore, the mass of 8 × 25 cm³ of gold is 4000 grams.
Bob believes he is a basketball star and so does his friend Alan. Bob's Points per Game 8, 15, 10, 10, 10, 15, 7, 8, 10, 9, 12, 11, 11, 13, 7, 8, 9, 9, 8, 10, 11, 14, 11, 10, 9, 12, 14, 14, 12, 13, 5, 13, 9, 11, 12, 13, 10, 8, 7, 8 Alan's Points per Game 2 3 4 5 7 à io in 12 is 14 15 16 For each player calculate the following statical data (Alan's Mean and MAD already included) Bob's Data Mean: MAD: Median: IQR: 01: Q3: Alan's Data Mean: 7.25 MAD: 2.81 Median: IQR: O1: Q3: Determine if Bob or Alan have any outliers. Which play would you choose to be on your team and why?
For Bob: Mean =10.13,MAD = 2.66,Median =10.5 ,IQR = 5.5,Q1 = 8,Q3 = 13.5
for alan :Mean =7.25,Median = 7.5,IQR = 10,Q1 = 4,Q3 = 14
How to find mean ?For Bob:
Mean = (8+15+10+10+10+15+7+8+10+9+12+11+11+13+7+8+9+9+8+10+11+14+11+10+9+12+14+14+12+13+5+13+9+11+12+13+10+8+7+8) / 38 = 10.13
MAD = 2.66 (calculated using the median of Bob's data)
To calculate the median and quartiles for Bob's data, we need to first sort the data in ascending order:
5, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15
Median = (10+11) / 2 = 10.5
Q1 = median of the first half of the data = (8+8) / 2 = 8
Q3 = median of the second half of the data = (13+14) / 2 = 13.5
IQR = Q3 - Q1 = 13.5 - 8 = 5.5
Therefore, for Bob:
Median = 10.5
IQR = 5.5
Q1 = 8
Q3 = 13.5
For Alan:
Mean = (2+3+4+5+7+10+12+14+15+16) / 10 = 7.25
MAD = 2.81 (calculated using the median of Alan's data)
Median = 7.5 (calculated as the average of the 5th and 6th value in Alan's sorted data)
Q1 = 4
Q3 = 14
IQR = Q3 - Q1 = 14 - 4 = 10
Therefore, for Alan:
Median = 7.5
IQR = 10
Q1 = 4
Q3 = 14
To determine if there are any outliers, we can use the following formula:
Outliers = data points outside the range [Q1 - 1.5(IQR), Q3 + 1.5(IQR)]
For Bob:
Lower outlier bound = 8 - 1.5(5.5) = -0.25
Upper outlier bound = 13.5 + 1.5(5.5) = 24.25
There are no outliers in Bob's data.
For Alan:
Lower outlier bound = 4 - 1.5(10) = -11
Upper outlier bound = 14 + 1.5(10) = 29
There are no outliers in Alan's data.
If the team needs a more consistent player with a higher median and narrower IQR, Bob might be a better choice. On the other hand, if the team needs a player who can potentially score more points, Alan might be a better choice as his mean is higher.
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2 + 5 + 8 + 11 + 14
Use the arithmetic explicit formula to find n for the number 14 in the sequence. Use the formula.
Write the arithmetic sum formula.
Answer:
The sum of the sequence is 40.
Step-by-step explanation:
The given sequence is an arithmetic sequence with a common difference of 3. To find the value of n for the number 14 in the sequence, we can use the explicit formula for an arithmetic sequence:
a_n = a_1 + (n-1)d
where a_n is the nth term of the sequence, a_1 is the first term, d is the common difference, and n is the term number.
Substituting the given values, we get:
14 = 2 + (n-1)3
Simplifying the equation, we get:
12 = 3n - 3
15 = 3n
n = 5
Therefore, the number 14 appears as the 5th term in the sequence.
To find the sum of the sequence, we can use the arithmetic sum formula:
S_n = (n/2)(a_1 + a_n)
where S_n is the sum of the first n terms of the sequence.
Substituting the given values, we get:
S_5 = (5/2)(2 + 14)
S_5 = 40
Therefore, the sum of the sequence is 40.
Step-by-step explanation:
the difference is 3 a is is first term which is 2
the formula is sn= a+(n-1)d
2+(n-1)3
2+(3n-3)
identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, then factor the expression.
The greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).
What is greatest common factor?The greatest positive integer that divides two or more numbers without leaving a residual is known as the greatest common factor (GCF). In other words, the greatest number that is a factor of both (or all) of the specified numbers is chosen.
To identify the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³, we need to look for the largest expression that divides evenly into each term.
First, we can factor out the greatest common factor of the coefficients, which is 3: 3(2s³t⁴ + 4s⁴t² - 5s²t³)
Next, we can look for the greatest common factor of the variables. We can see that s²t² divides into each term: 3s²t²(2st² + 4s² - 5t)
Therefore, the greatest common factor of 6s³t⁴ + 12s⁴t² - 15s²t³ is 3s²t², and the factored expression is 3s²t²(2st² + 4s² - 5t).
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A principal of $1500 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
The average annual cost (in dollars) of tuition and fees at a 2 -year college for selected years is shown in the given table, where year 0 represents 2004. The data can be approximated by the equation y=83.66x+3915 . Predict the average annual cost in 2014 to the nearest dollar.
The average annual cοst in 2014 is $4751.6.
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equatiοn that represent the annual cοst in dοllars.
=> y = 83.66x+3915
Where x= number οf years
In 2004 , t = 0 years
Sο , In 2014 , t = 2014-2004 = 10 years.
Then average annual cοst in 2014 is,
=> y=83.66(10)+3915
=> y=836.6+3915
=> y = $4751.6.
Hence the average annual cοst in 2014 is $4751.6.
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