The majority of human physical, mental, and personality factors have a mean in the middle of the distribution, where there are also the most cases. For example, in baseball, the rookie of the year often has a poor second season.
Correct answer is b) regression to the mean.
Regression to the mean is the propensity of outcomes that are extreme by chance on the first measurement to move closer to the average when tested a second time. Results that are susceptible to regression to the mean are those that are vulnerable to some degree of chance. When exceptional scores are the result of chance or a fluke, it's improbable that those extreme scores will be obtained again.
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help please Consider the functions:
Answer the equations about these functions in the table below.
Select f(x), g(x), both options, or neither.
The x-intercept of (-2, 0) has both functions. The behavior of the function g(x) for x ⇒ -∞ then g(x) → ∞. The y-intercept of the function f(x) is (0, 6). And both functions have real roots.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = x³ - 2x² - 5x + 6
g(x) = - x³ + 4x
The factor of the function f(x) is given as,
f(x) = 0
x³ - 2x² - 5x + 6 = 0
(x + 2)(x - 1)(x - 3) = 0
x = -2, 1, 3
The factor of the function g(x) is given as,
g(x) = 0
- x³ + 4x = 0
x = 0, 2, -2
The y-intercept of the function f(x) is given as,
f(0) = (0)³ - 2(0)² - 5(0) + 6
f(0) = 6
The y-intercept of the function g(x) is given as,
g(0) = - (0)³ + 4(0)
g(0) = 0
The graph of the function is given below.
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Matt ate 0.45 of his birthday cake. Convert the amount of cake Matt consumed into a fraction in simplest form.
Answer: 9/20
Step-by-step explanation:
45/100 ÷ 5/5 = 9/20
To convert 0.45 into a fraction, we can consider it as 45/100. Then to get the simplest form of the fraction, we divide both the numerator and denominator by their greatest common factor which is 5. So, the simplest form of the fraction is 9/20. Therefore Matt ate 9/20 of his birthday cake.
Tommy is buying a home, its purchase price is $200,000. She has to put
down 5%, with an APR of 6.4%. What will her monthly payment be.
The required monthly payment for 6.4% of interest is $16846.6.
What is interest?Interest is the cost of borrowing money or the fee you charge to lend it. Most frequently, interest is shown as an annual percentage of the loan amount. The interest rate for the loan is denoted by this proportion.
According to question:We have,
Purchasing price = $200,000
Down payment = 5% of $200,000
= $10000
Remaining Amount = $190000
Interest of one year = 6.4%
Amount of interest = 6.4% of $190000
Amount of interest = $12160
Total amount = f $190000 + $12160
Total amount = $202160
Monthly payment = $16846.6
Thus, required monthly payment is $16846.6.
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Evaluate : 2 (x-4) + 3x - x^2 for x = 3.
A. 6
B.- 6
C. 2
D. -2
Answer: -2
Step-by-step explanation:I'am in a rush right now sorry
If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of f[g(0)]
Answer:
f(g(0)) = 12
Step-by-step explanation:
to find f(g(0)) , evaluate g(0), then substitute the value obtained into f(x)
g(0) = 0 + 4 = 4 , then
f(4) = 3(4) = 12
Please help me ASAP pleaseee please
It is given that ABCD is a rectangle. We have to give reasonings for the statements.
What is the rectangle?
A rectangle is a four-sided polygon with four right angles. The opposite sides of a rectangle are equal in length (congruent) and the opposite angles are equal in measure (congruent). The opposite sides are parallel to each other. A rectangle can be defined as a special case of parallelogram where all angles are right angles.
Given: ABCD is a rectangle
Prove: triangle ADC is congruent to triangle BCD
1. Given ABCD is a rectangle
2. By definition of rectangle, opposite sides are congruent (AD is congruent to BC)
3. By definition of rectangle, opposite angles are right angles (angle ADC and angle BCD are right angles)
4. By definition of right angle, adjacent angles are congruent (angle ADC is congruent to angle BCD)
5. By reflexive property, an object is congruent to itself (DC is congruent to DC)
6. By SAS Congruence (Side-Angle-Side), if two triangles have two congruent sides and the included angle congruent, the two triangles are congruent. Since AD=BC and angle ADC= angle BCD, and DC=DC, then triangle ADC is congruent to triangle BCD.
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4. The gas tank of a hybrid car fills up with 16 gallons of gas. The car can drive for an average of
85 miles per gallon. The equation d = 85g represents the distance (d, in miles) that can be
driven with g gallons of gas left in the tank. What is a reasonable range for this problem
situation?
If the vehicle has 10 gallons of fuel left, it has driven 600 miles.
What is the equation?The term "equation" refers to mathematical statements with at least two terms that contain variables or integers that are equal.
The amount of gas in the tank should be x gallons, and the distance travelled by car should be d miles.
Due to the car's 16-gallon fuel tank
So, 16 - x would be the remaining fuel in the tank.
It gets 85 miles per gallon of gas when travelling on a highway.
⇒ d = (16-x)85
if the tank still holds 10 gallons of fuel
In the equation above, if x = 10, we get
⇒ d = (16-10)85.
⇒ d = (20)85.
⇒ d = 600.
If the vehicle has 10 gallons of fuel left, it has driven 600 miles.
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-1
5
X
f(x)
slope:
y-intercept:
0
4
of f ==
off=
1
3
2
2
of g =
of g =
3
1
The slope and the intercept of the function f(x) = -x + 5 are given as follows:
Slope: -1.Intercept: 5.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y at which the graph of the function crosses the y-axis.The function for this problem is defined as follows:
f(x) = -x + 5.
Comparing to the standard definition of a linear function, we have that:
The slope is of -1.The intercept is of 5.Missing InformationThe problem asks for the slope and the intercept of the function f(x) = -x + 5.
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A traffic light at a certain intersection is green 55% of the time, yellow 10% of the time, and red 35% of the time. A car approaches this intersection once each day. Let Y denote the number of days up to and including the third day on which a red light is encountered. Assume that each day represents an independent trial.
Find P(Y=7)
Find the mean of Y
Find the Variance of Y
The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479
According to the question,
we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)
Here,
Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.
And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,
The distribution here is a geometric one, where
P(Y = 3)
= P(Not red light in initial 2 lights) x P(red light in third light)
= [(1 - 0.35)² X 0.35]
= 0.1479
so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.
Note:
mean and variance of this question is not possible to find out.
the complete question ends till the probability to find the first red light on the third day.
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5 people all of different age are sitting around a round table, what is the probability they are sitting in age order.
The probability that they are sitting around a round table in age order is 1/12. There are 10 ways for five people to sit in age order.
What is probability?Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceFive people all of different age are sitting around a round table.
Find the probability they are sitting in age order!
Let's name the 5 people 1, 2, 3, 4, 5.
There are two ways in putting them in the age order, ascending or descending.
Ascending: 12345, 23451, 34512, 45123, 51234.Descending: 54321, 43215, 32154, 21543, 15432.There are 10 ways that they are sitting around a round table in the age order.
n(Age order) = 10
The total arrangements for 5 people sitting around a round table is
5! = 1 × 2 × 3 × 4 × 5
5! = 120 ways
n(S) = 120
The probability that they are sitting in age order would be
P(Age order) = n(Age order) / n(S)
P(Age order) = 10/120
P(Age order) = 1/12
Hence, the probability that five people are sitting around a round table in age order is 1/12.
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I need help please ans thank you
The length of all a triangle's sides added together yields the perimeter of a triangle.
What's perimeter formula?The length of all a triangle's sides added together yields the perimeter of a triangle.
The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.
perimeter=(length + width)2.
JKL - Delta RST^ prime , RS = 14 ST = 12 , TR = 10 , and LJ = 14 2. ADEF, if triangle DEF sim triangle ABC , AB = 27 BC = 16 CA = 25 , and FD = 15 3
RST perimeter=(length + width)2.
14+ 12+10+14 = 50
triangle ABC
27 + 16 + 25 =68
triangle PQR sim triangle LMN , LM = 16 , MN = 14 , NL = 27 ,
16+14 + 27 = 57
if triangle KTM sim triangle FGH . . FG = 30 GH = 38 , HF = 38
30 + 38 + 38 =106
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Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is
34
3434 inches, and Udon is
12
1212 inches shorter than Mian. Which of the following systems of equations could be used to find
m
mm, the length of Mian in inches, and
u
uu, the length of Udon in inches?
The length of Mian in inches is 23 and the length of Udon in inches is 11
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is 34 in and Udon is 12 inches shorter than Mian.
Let Mian be represented by M and that of Udon by U,
Therefore, according to question, establishing the equation,
M + U = 34
M - U = 12
Adding both the equations,
2M = 46
M = 23
U = 11
Hence, the length of Mian in inches is 23 and the length of Udon in inches is 11
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Which of the following lines is parallel to y = 1/5x + 4
5 y - x = 6
y + 5 x = 4
5 y - 2 x = 15
The line that is parallel to y = 1/5x + 4, is A. 5 y - x = 6.
What are parallel lines ?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.
As mentioned parallel lines will have the same slope so the line that is parallel to y = 1/5x + 4 would have the same slope of 1 / 5.
Converting the first option to slope intercept form gives:
5 y - x = 6
5 y = 6 + x
y = 6 / 5 + x / 5
y = 1.2 + 1 / 5 x
This slope is the same as y = 1/5x + 4 so they are parallel.
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For the given function f(x)=3x-5 find f(k)
Answer:111
Step-by-step explanation: how to do it:is try
Answer: f(k) = 3k - 5
Step-by-step explanation:
For f(x) functions, you're simply plugging in whatever value is in the parenthesis. For example, if you were asked to find f(1), you would plug in 1 for x.
f(1) = 3(1) - 5 = -2. In this case, you're just plugging in a different variable.
someone help me please and thank you
Answer: i know what school ur from my school page looks the same (we in CCA) XDD
anyways this question is very vague. but i think its c.
Step-by-step explanation:
again its very vague but i tried i think its c
400x(9x10 to the power of 15)
Answer: 3.6e+18
Step-by-step explanation: (400 x 9 = 3,600) 10 to the power of 15= 1,000,000,000,000,000 or quadrillion. 9x1,000,000,000,000,000=9e+15x400=3.6e+18
Help Me, Now! Lacey pays $15 for each hour of golf lesson and $10 for equipment rental. If the lesson is more than 3 hours long she only pays $5 for equiptment rental. Is the total cost of Lacey's lesson a function of the number of hours scheduled? Is This a function? (Write Yes Or No)
The total cost of Lacey's lesson a function of the number of hours scheduled is [tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex] and this one refers the function.
In math the term called function is known as a correspondence from one value x of the first set A to another value y of the second set B and it relates inputs to outputs.
Here we have know that Lacey pays $15 for each hour of golf lesson and $10 for equipment rental.
And here we have also know that If the lesson is more than 3 hours long she only pays $5 for equipment rental.
Let us consider that x be the amount time she has been taking lessons.
Then the function can be written as,
[tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex]
While we looking into it we have identified that the given situation will create the function.
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What is a perfect square
A perfect square is a number obtaining by squaring a whole number
What is a perfect square?A perfect square can be defined as a number that is being expressed as the product of an integer by itself.
It is also seen as the second exponent of an integer.
In determining the perfect of a number, when you multiply an integer which could be a “whole” number, positive, zero or negative) by itself, the product of the multiplication is termed a square number, or a perfect square.
Perfect square is also described as a number made by squaring a whole number.
Some perfect squares in mathematics are;
Number 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 139, 144, etc
Hence, a perfect square is described as a number that is the product of an integer with itself.
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Prove whether the quadrilateral is a parallelogram using the slope formula:
K(2, 7), L(6, 12), M(13, 13), N(9, 8)
Parallelograms are quadrilaterals with two sets of parallel sides
Slope Formula: y2-y1/x2-x1
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
We can identify this as a parallelogram since it has congruent angles and sides, which are found on a parallelogram.
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Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?
a-3) a² + ab +3²
a + b) a ² - ab +6²
o a+ba? +la+b+Dab? - 53
a-ba? +da+b+Dab? - b
The long division problem can be used to prove the formula for factoring the difference of two perfect cubes (a-b)(a²+ab+b²).
The difference of two perfect cubes: a³-b³ = (a-b)(a²+ab+b²)
let the two perfect cubes be a³ and b³. Factoring the difference between these two perfect cubes we have: a³ - b³
First, we need to factorize (a-b)³:
(a-b)³ = (a-b) (a-b)²
(a-b)³ = (a-b)(a²-2ab+b²)
(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³
(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²
(a-b)³ = a³-b³ - 3a²b+3ab²
(a-b)³ = (a³-b³) -3ab(a-b)
Then we will make a³-b³ the subject of the formula from the result equation;
a³-b³ = (a-b)³+ 3ab(a-b)
a³-b³ = a-b{(a-b)²+3ab}
a³-b³ = a-b{a²+b²-2ab+3ab}
a³-b³ = (a-b)(a²+b²+ab)
a³-b³ = (a-b)(a²+ab+b²)
The long division problem that can be used is (a-b)(a²+ab+b²).
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6y + 14 math help people
The number of terms in the algebraic expression 6y + 14 is 2 terms
How to determine the number of terms in the algebraic expressionsFrom the question, we have the following parameters that can be used in our computation:
6y + 14
Consider an expression given as
ax + b
The number of terms in the expression is 2 and the terms are ax and b
Using the above as a guide, we have the following:
6y + 14 has 2 terms
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Complete question
Identify the number of terms and then the resend themselves for each algebraic expression
6y + 14
You sell soup mixes for a fundraiser. For each soup mix you sell, the company that makes the soup receives x dollars,and you receive the remaining amount. You sell 16 soup mixes for a total of (16x+ 96) dollars. How much money do you receive for each soup mix that you sell? (MUST SHOW WORK)
Using subtraction and division operations, the amount you receive for each soup mix sold is $6.
What are mathematical operations?Subtraction and division operations are two of the four basic mathematical operations. The other two are multiplication and addition.
Mathematical operations combine variables, numbers, and mathematical operands to solve mathematical problems.
The number of soup mixes sold = 16
The total sales revenue = 16x + 96
The amount for the company that makes the soup = 16x
The amount that the seller receives = 96 (16x + 96 - 16x)
The amount the seller receives per soup mix = The total revenue received divided by the number of units sold
= 6 (96/16)
Thus, for each soup mix that you sell, you receive $6.
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1.20 housing proposal across dorms. on a large college campus first-year students and sophomores live in dorms located on the eastern part of the campus and juniors and seniors live in dorms located on the western part of the campus. suppose you want to collect student opinions on a new housing structure the college administration is proposing and you want to make sure your survey equally represents opinions from students from all years. (a) what type of study is this? (b) suggest a sampling strategy for carrying out this study.
(a) The study is observational type.
(b) Stratified sampling can be used for carrying out this study.
(a) In the given problem, We want to hear students' opinions about the new housing structure and ensure that the survey reflects all students' views equally. The critical thing to note here is that you need to collect opinions. Not the reason behind the opinion. So researchers don't care how the data goes up. So this is an observational study.
(b) In the case of sampling strategy we can use stratified sampling. Stratified sampling refers to a type of sampling technique. In stratified sampling, researchers divide the population into separate groups called strata. A probability sample (often a simple random sample) is then drawn from each group. The same number of samples can be used each year.
Therefore, To make sure the survey equally represents opinions from students from all years (a) the study is the observational type and (b) Stratified sampling can be used for carrying out this study.
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Here are two sets of numbers, A and B.
Set A
Set B
281
268
392
512
413
225
290
422
у
mean of Set A: mean of Set B = 7:12
Work out the value of y.
After solving the value of y is 541.
The value of set A is 281, 268, 225, 290. So
The mean of set A = (281 + 268 + 225 + 290)/4
The mean of set A = 1064/4
The mean of set A = 266
The value of set B = 392, 512, 413, 422, у
The mean of set B = (392 + 512 + 413 + 422 + у)/5
The mean of set B = (1739 + y)/5
The ratio of Mean of Set A : Mean of Set B = 7 : 12
So, 7x = 266
Divide by 7 on both side, we get
x = 266/7
x = 38
Now, 12x = 12 × 38 = 456
The mean of set B = 456
(1739 + y)/5 = 456
Multiply by 5 on both side, we get
1739 + y = 2280
Subtract 1739 on both side, we get
y = 541
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The complete question is:
Here are two sets of numbers, A and B.
Set A Set B
281 268 392 512 413
225 290 422 у
Mean of Set A : Mean of Set B = 7 : 12.
Work out the value of y.
What is 88% of %33.00
what equation is graphed in the figure
The equation that is graphed is (c) y = x² + 2 if x < 1 and y = -x + 2 if x ≥ 1
How to determine the graphed functionFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
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How much water must be added to 7 gallons of a 8% insecticide solution to reduce the concentration to 7%?
1 gallon of water must be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7%.
Let x = amount of water required
7 gallons + x gallons = (x + 7) gallons of mixture
For x gallons of water, we have 0 gallons of insecticide
For 7 gallons of 8% insecticide solution, we have 0.08(7)=0.56 gallons of insecticide
According to the question, we get the equation as follows
0.07(x + 7) = 0.56
7(x + 7) = 56
x + 7 = 8
x = 1 gallon
Therefore, the amount of water that needs to be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7% is 1 gallon.
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Factor.
5x + 25
7m +42
Three players scored a total of 70 points during a basketball game. Jan
scored twice as many points as Tritt and ten points fewer than Sarah. Let x
represent the number of points that Jan scored. Which equation could be
used to solve for the number of points that Jan scored in the game?
Ox+(0.5x)+(x+10) = 70
O 0.5x+(x+10) = 70
O 3x = 70
Ox+(x+10)+2x = 70
The equation that can be used to solve for the number of points that Jan scored in the game is:
x + 2x + (x-10) = 70
Given that Jan scored twice as many points as Tritt, we can use the equation
2x = Tritt.
Given that Jan scored ten points fewer than Sarah, we can use the equation
x = Sarah - 10.
Also, we know that the total number of points scored by all three players is 70, so we can use the equation:
x + Tritt + Sarah = 70
If we replace Tritt with 2x and Sarah with x-10, we get:
x + 2x + (x-10) = 70
So the equation that can be used to solve for the number of points that Jan scored in the game is:
3x -10 = 70
We get x = 30, which means Jan scored 30 points in the game.
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the ages of 32 recruits in the police academy are normally distributed with a mean of 27 and a standard deviation of 2.
label the normal curve
Mean is 27 and SD is 2 then the normal curve with highest range would be at domain 27.
What is mean?The mean is the average of a set of numbers. It is calculated by adding all the numbers in the set together, and then dividing by the number of values in the set. It is calculated by adding up all the numbers in the set, dividing by how many values there are in the set, and then multiplying by that number. The average of a group of numbers is called the mean.
Mean is 27 and SD is 2
a) P(23<x<27)= P((23-27)/2<z<(27-27)/2)=P(-2<z<0)=P(z<0)-P(z<-2) or P(z<0)-(1-P(z<2))
From normal distribution table we get 0.5-(1-0.9772)=0.4772
b) P(x>31)=P(z>(31-27)/2)=P(z>2) or 1-P(z<2)=1-0.9772=0.0228
c) P(x<29)= P(z<(29-27)/2)=P(z<1)=0.8413
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