The population variance is a measure of the spread of values from their mean.
We need to define the population variance. The population variance is the variance of the population. Population variance describes how data points are distributed. It is the square of the average distance between each data point in the population and the mean.
In probability theory and statistics, variance is defined as the expectation of a random variable's squared deviation from its population mean or sample mean.
An average is a single number that represents a set of numbers, generally the sum of the numbers divided by the number of numbers in the set.
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A private college report contains these statistics:
75% of incoming freshmen attended public schools.
85% of public school students who enroll as freshmen eventually graduate.
80% of other freshmen eventually graduate.
What percent of students who graduate from the college attended a public high school?
The percentage of students that graduated from college that also attended a high school is given as 0.7792 or 77.92 percent.
How to solve for the probability?We have the Prob(attended public school | graduated)
The probability that a person attended public school and graduated as
Prob (P and G) = 0.80 x 0.75
= 0.6
The probability that a person graduated is given as
0.8*0.75 + (1 - 0.8 * 0.85)
= 0.6 + 0.17
= 0.77
Prob(P and G ) /Prob(G)
= 0.6 / 0.77
= 0.7792
The percentage is given as 77.92%
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Identify the horizontal asymptote of f(x) = 3 over 5 x. y = 3 over 5 y = 0 y = 5 over 3 no horizontal asymptote
y = 0 is the horizontal asymptote for the given equation f(x)
To find : Horizontal Asymptote of function f(x)
Horizontal Asymptote
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote. The end behavior of the function is determined using the horizontal asymptote.
Given that,
A function is provided as
f(x) = 3/5x
x serving as the denominator
By setting the denominator equal to 0, we can easily determine the vertical asymptote i.e,
Make x=0,
Specifically, the vertical asymptote is at y=0 or x=0
Identifying the horizontal asymptote
Write x in terms of y, then look for any instances where y differs.
We are able to write the given function
x=3/5
Here, y=0 renders x undefinable.
Thus y=0 is the horizontal asymptote.
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Answer:
B
Step-by-step explanation:
Got it right.
solve for x
2(x - 3 1/2)=10 3/4
exact form
x=71/8
Decimal Form:
x=8.875
Mixed Number Form:
x= 8 7/8
Answer:
Step-by-step explanation:
8 7/8
Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator
and denominator by ___
The correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'
In this question, we have been given a statement 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by ____'
We need to complete given statement.
We know that, the denominator in unit rate is always 1.
So, to find unit rate we need to divide the denominator with the numerator in such way that the denominator becomes 1.
Sally's unit rate is 39/3 miles per hour
numerator = 39 and denominator = 3
We need to make denominator 1 so divide numerator as well as denominator by 3.
So, the unit rate would be, 13/1 = 13 miles per hour
Therefore, the correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'
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ANSWER THIS FOR BRAINLISTEST
hii help pls n thanks
Answer:
(1,8.5)
Step-by-step explanation:
find the midpoint of x and yx=(-1+3)÷2
=1
y=(9+8)÷2
=8.6
(1 , 8.5)
What is the inverse?
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{f(x)}{y}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\sqrt{4y+5}}\implies x^2=4y+5\implies x^2-5=4y \\\\\\ \cfrac{x^2-5}{4}=y\implies \cfrac{1}{4}(x^2-5)=\stackrel{f^{-1}(x)}{y}\qquad x\geqslant 0[/tex]
now, I don't see any good reason why x ⩾ 0 or x ⩽ 0 , since any negative or positive values are perfectly valid.
Answer:
[tex]\textsf{C)} \quad f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt{4x+5}[/tex]
The domain of the given function is restricted to x ≥ -⁵/₄.
Therefore, the range of the given function is restricted to f(x) ≥ 0.
The inverse of a function is its reflection in the line y = x.
To find the inverse of a function, swap x and y:
[tex]\implies x=\sqrt{4y+5}[/tex]
Rearrange the equation to make y the subject:
[tex]\implies x^2=4y+5[/tex]
[tex]\implies 4y=x^2-5[/tex]
[tex]\implies y=\dfrac{1}{4}(x^2-5)[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\dfrac{1}{4}(x^2-5)[/tex]
The domain of the inverse of a function is the range of the original function.
Therefore, the domain of the inverse function is x ≥ 0.
Therefore, the inverse of the given function is:
[tex]f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0[/tex]
Find the product of 4√6 and √10 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.
Answer:
8√15
Step-by-step explanation:
4√6 × √10 = 4√(6 × 10) = 4√60 = 8√15
Jaheim made a bag of trail mix with 1/2 cup of almonds,6/7cup of apple slices, and 1/8cup of pumpkin seeds. About how much trail mix did Jahiem make?
Jahiem made about 3/2 cups of trail mix.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, Jaheim made a bag of trail mix with 1/2 cup of almonds, 6/7 cup of apple slices, and 1/8 cup of pumpkin seeds.
The total amount of trail mix is:
1/2 cup of almonds + 6/7 cup of apple slices + 1/8 cup of pumpkin seeds
= 1/2 + 6/7 + 1/8
= (28 + 48 + 7)/56
= 83/56
≈ 3/2
Hence, Jahiem made about 3/2 cup of trail mix.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4 , 20 , 100
THe given series is GP series
common ratio n =5
The series is given 4,20,100...
then common ratio is 20/4=5
and another is 100/20=5
so common ratio is same
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Identify any reasonable constraints on the domain.
Describe the domain using inequality or set-builder
notation. SEE EXAMPLE 3
19. Cameron earns an hourly wage at his job. He
makes a table of the number of hours he works
each week and the amount of money he earns.
The domain should be non-negative since time cannot be negative.
If the number of hours worked is [tex]h[/tex], the domain in inequality notation is [tex]h \geq 0[/tex].
Complete the description of a real-world situation that could be modeled by the equation 30 +1.25x = 15
+25X.
A pet sitter charges a flat fee of $
sitter charges a flat fee of $15 plus $
two pet sitters the same?
plus $1.25 per hour to keep a dog during the day. A second pet
per hour. After (select)
Is the charge for the
Answer:
The question is possibly mistyped. The response below explains why, but also answers the questions based on a imagined relationship, instead of the one given.
Step-by-step explanation:
The equation 30 + 1.25x = 15 + 25X cannot be interpreted in the manner the questions are written. It is really only an expression, since there is no y in the equation, only x. We can, however, solve for x:
30+1.25x = 15 + 25x
30 - 15 = 25x - 1.25x
15 = 13.75x
x = (15/13.75)
x = 1.0909
There is no other information to discern what x represents. It could be light years to a particular comet, grams of a reagent, hours until the meat is cooked, or anything the imagination allows.
If, however, the equation were something like:
y = 1.25x + 15
we could answer the questions, as follows;
A pet sitter charges a flat fee of $15
sitter charges a flat fee of $15 plus $1.25/hr
The rest of the questions are not coherent.
==========
"two pet sitters the same?
plus $1.25 per hour to keep a dog during the day. A second pet
per hour. After (select)
Is the charge for the"
If f (x) = -3x - 2, find f (3).
Answer:
f(-3) = |(-3)-2| = |-5| = 5
Orlando and Tanya are experimenting
with different mix ratios. Determine
whether each mix below will result in a
more concentrated (more
"grapefruity") or a less concentrated
(less "grapefruity") mix than the
original mix instructions. (The original
mix is the "Mix one can of concentrate
with 4 cans of cold water.")
Answer:
Whichever ratio has more water will be less concentrated (less "grapefruity"), and whichever ratio has more of the concentrate will be more concentrated (more"grapefruity").
Graph this using the slope and y-intercept
Answer:
(5,0) (0,1)
Step-by-step explanation:
what is the major difference between the two sample t-test and paired t-test? when should we use one versus the other? g
Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.
A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test we can find the mean difference between pairs of measurements is zero or not. So paired t-test is used, when data is in the form of matched pairs
Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs
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assume that the heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.5 inches. a) what percentage of women have heights between 64 and 66 inches? b) find the third quartile q3; that is, find the 75th percentile.
The percentage of women that have heights between 64 and 66 inches is 42.06%
The third quartile is 65.1875 inches
Part a
Given: mean=63.5 inches
std. deviation=2.5 inches
To find percentage: we calculate probability and convert to percentage
P(64<X<66) would mean
Z statistic=64-63.5/2.5=0.2
=66-63.5/2.5=1
From Z table, we find corresponding probability values.
Therefore, P(64<X<66)=P(0.2<Z<1)=0.84134-0.42074
=0.4206
Thus percentage=0.4206*100
=42.06%
Part b
Finding the third quartile, Q3
Q3=mean+(0.675)*std. dev
Q3=63.5+(0.675*2.5)
=65.1875 inches
Hence, the third quartile is 65.1875 inches
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A line passes through the points (–14, 1) and (–4, 11). What is its equation in slope-intercept form?
Answer:
slope: (11-1)/(-4+14)
m: 10/10
M: 1
11 = -4 + b
b = 15
y = x + 15
For the question, let x be a rational number not equal to zero and let z be an irrational number. Determine whether the operation results in a value that is always rational, never rational, or sometimes rational.
x+z
x + z can't be result in a value that's rational.
x + z is never rational.
Given,
In the question:
Let x be a rational number not equal to zero and let z be an irrational number.
To determine whether the operation results in a value that is always rational, never rational, or sometimes rational.
Now, According to the question;
Assume, x + z results in a value that is rational
m = x + z
z = m - x (m, x is rational)
∴ m - x is a rational.
but z is an irrational number.
So, x + z can't be result in a value that's rational.
x + z is never rational.
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Andrea mixes 2 cups of water with 2/3 of lemonade concentrate. Nicholas mixes 1.5 cups of water with 1/3 cup of lemonade concentrate. whose lemonade mixture tastes stronger. (bonus points to the first person to show there work!)
x - 4 minus -8x² - 8.
The value of the expression (x-4) minus -8x² - 8 is [tex]8x^{2}[/tex]+x+4.
According to the question,
We have the following information:
x - 4 minus -8x² - 8
Now, we will convert this into an expression only using mathematical signs. So, we have the following expression:
(x-4)-(-8x² - 8)
Now, we know that the multiplication of two negative integers gives us the positive results and the multiplication of one positive and one negative integer give us the negative results.
So, we have the following expression after multiplying -1 into the bracket :
x-4+8[tex]x^{2}[/tex]+8
[tex]8x^{2}[/tex]+x+4
Hence, the value of the expression (x-4) minus -8x² - 8 is [tex]8x^{2}[/tex]+x+4.
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Find the value of x
6x-10
8x -20°
slove the simultaneous equation 9x+4y=51
x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given equation is nine times of x plus four y equal to fifty one
9x+4y=51
We have to convert this equation to slope intercept form
4y=51-9x
4y=9x-51
Divide both sides by 4
y=9/4x-51/4
x intercept is 9/4 and y intercept is -51/4
Hence x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.
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A recipe calls for 3 ounces of flour for every 2 ounces of sugar.Find the constant of proportionality
Answer:the answer is 3:2
Step-by-step explanation:
it is ratio of flour to sugar so the answer is 3:2
Answer:
1.5
Step-by-step explanation:
A recipe calls for 3 ounces of flour for every 2 ounces of sugar.Find the constant of proportionality
we have a ratio of 3 : 2
the constant of proportionality is:
3 : 2 = 1.5
HELP ASAP !!!!
Write and graph linear equations
Answer:
first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1
Step-by-step explanation:
examine the diagram below. Identify the error in the diagram
Answer:
Either this is not a right triangle or one of the side has the wrong measurement.
Step-by-step explanation:
This is either not a right triangle or one of the measurements is off
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]14^{2}[/tex]
25 + 144 = 196
169 ≠196
Complete an equation in slope-intercept form for the line that passes through (6, 5) and is parallel to the line x + 3y = 9.
The slope-intercept form is y = -1/3x +7 .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.The standard form equation can be found by using the given point values in the given equation to find the new constant.
x +3y = (6) +3(5) = 21
Solving for y puts this equation into slope-intercept form.
3y = -x +21 . . . . . . . subtract x
y = -1/3x +7 . . . . . . divide by 3.
This is slope-intercept form.
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cans of corn on sale at 10 for AED 32 find the cost of 15 cans
The cost of 15 cans will be AED 48.
According to the question,
We have the following information:
Cost of 10 cans = AED 32
Now, in order to find the cost of 15 cans, first we will find the cost of 1 can by dividing the total cost of 10 cans by the number of cans.
So, we have the following expression:
Cost of 1 can = 32/10
Cost of 1 can = AED 3.2
Now, we will find the cost of 15 cans using multiplication:
Cost of 15 cans = 15*3.2
Cost of 15 cans = AED 48
Hence, the cost of 15 cans will be AED 48.
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Why is it 4 and 1/2? Where did you get the 1/2 and shouldn’t it be 5/10?
The reason for 1/2 and not 5/10 is it is a norm in math to reduce fractions to the least terms
What is equivalent form of fractions?This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator
Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.
In the given problem, 1/2
1 is the numerator2 is the denominator5/10 is an equivalent form of 1/2, this means that they are equal.
5/10 is shown to be equal to 1/2 by dividing by 5, this reduces the fraction to the least term which is 1/2. Using calculator can still show it that both numbers equal 0.5
In mathematics, it is preferred to reduce fractions to it's least form except it was stated.
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Select the equation that is NOT equivalent to 5x3 = 2x + 15.
● -3=-3x+15
● 7x - 3= 15
● 5x = 2x + 18
The equation which is not equivalent to 5x - 3 = 2x + 15 is 7x - 3 = 15
Given equation is 5x - 3 = 2x + 15.
5x - 3 = 2x + 15
5x - 3 - 5x = 2x + 15 - 5x ..........(Subtract 5x from both sides)
-3 = -3x + 15
this equation is an equivalent equation to 5x - 3 = 2x + 15.
Consider given equation,
5x - 3 = 2x + 15
5x - 3 + 3 = 2x + 15 + 3 ............(Add 3 on both sides)
5x = 2x + 18
this equation is an equivalent equation to 5x - 3 = 2x + 15.
Therefore, the equation which is not equivalent to 5x - 3 = 2x + 15 is 7x - 3 = 15
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