The first error Emi made was dividing by N - 1 instead of N when computing the population variance.
The first error in computing the variance is Emi divided by N - 1 instead of N. In Emi's calculations for the data set, which includes the numbers 87, 46, 90, 78, and 89, the correct method should be to divide by N, because she is dealing with a population data set, not a sample.
For the population variance, we divide the sum of squared differences from the mean by the total number of data points in the population, which is N. However, Emi incorrectly divided by N - 1, which would only be correct if she were calculating the sample variance to estimate the population variance based on a subset of the population data.
ln(x+2)-ln(4x+3)=ln(1/2*x)
A die is tossed. find the odds against rolling a number greater than 11.
help me out with this
what is the product of r and t if R equals 5.33 and T equals 0.5
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Answer:
0.05
Step-by-step explanation:
Given :
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Solution :
Since ware required to find the probability that a student is a boy with red hair.
Total no. of boys with red hair = 2
Total no. of students = 4+4+10+2+5+6+8+1=40
Thus the probability that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]
⇒[tex]\frac{2}{40}[/tex]
⇒[tex]\frac{1}{20}[/tex]
⇒[tex]0.05[/tex]
Hence the probability that a student is a boy with red hair is 0.05
Write an equation of the line with the given slope, m, and y-intercept (0,b) m=-3/5 b=7/10
The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).
Explanation:To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.
Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).
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kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have
Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.
The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:
D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)Multiply the second equation by 100 to deal with whole numbers:
10D + 5N = 120From the first equation, we can express D as:
D = 14 - NSubstitute this into the second equation:
10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4So, Kaelyn has 4 nickels and the rest are dimes.
Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =
A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___
Help ASAP PLEASE!!! match the term with the appropriate definition.
Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?
Answer with explanation:
Pottery is on a Kiln.
Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).
Unit of time is second, minute and hour.
Rate of change of temperature of the pottery over time can be written as
[tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]
Internationally , Kelvin is used as S.I unit of Temperature.
So,Yanin can use
[tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]
as Rate of change of temperature of the pottery over time.
The period if a function is 4pi
How many cycles of the function occur in a horizontal length of 12pi?
(answer was 3)
QUESTION: Which type of transformation of the parent function would be shown by the graph?
Answer:
She's right the answer is a horizontal stretch.
Two events are independent when the following is true:
a. the outcome of one event determines the outcome of the other event
b. there is no correlation between the two events
c. the outcome of one event does NOT determine the outcome of the other event
d. The outcome of the event is determined by the theoretical probability of the event
Solution:
Independent Events:
Consider an experiment of Rolling a die, then getting an even number and multiple of 3.
Total favorable outcome = {1,2,3,4,5,6}=6
A=Even number = {2,4,6}
B=Multiple of 3 = {3,6}
A ∩ B={6}
P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]
P(A ∩ B)=[tex]\frac{1}{6}[/tex]
So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)
Hence two events A and B are independent.
Option (c). the outcome of one event does NOT determine the outcome of the other event
Answer:
C on edge or the outcome of one event does NOT determine the outcome of the other event
Step-by-step explanation:
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft
Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
where:
b is base of a triangle
h is height of a triangle
For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:
hypotenuse² = side² + side²
[tex]12^{2} = s^{2} + x^{2}[/tex]
[tex]x^{2} = 12^{2} - s^{2}[/tex]
[tex]x^{2} = 144 - s^{2}[/tex]
x = [tex]\sqrt{144 - s^{2} }[/tex]
To determine the Area of the right triangle as function of s:
A = [tex]\frac{b.h}{2}[/tex]
A = [tex]\frac{1}{2}[/tex](s.x)
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
Therefore, the area of the right triangle is:
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:
hypotenuse² = side² + side²
h² = 13² + 5²
h² = 169 + 25
h = [tex]\sqrt{194}[/tex]
h = 14
The minimum length the ladder has to have to reach the top is 14 ft.
Unsaved If you are studying the effects of UV rays on eyesight and you group 10 people together and make them wear sunglasses for 10 weeks and see if their eyesight is affected and then take another group and do not give them sunglasses and test their vision after 10 weeks, what is the treatment ? note this is not an ethical study.
sunglasses.
10 weeks.
eyesight.
vision test.
Answer:
Sunglasses
Step-by-step explanation:
Which ordered pair is the vertex of y = [x - 3]+ 2?
A.(2, –3)
B.(–3, 2)
C.(3, 2)
D.(2, 3)
HELP
______________________
Answer:
The answer is the third option/choice.
Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?
Answer:
4 ÷ 5
Step-by-step explanation: becuz i said so
On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from ticket sales on Sunday was $1750. The system of equations below represents the number of people and total sales for the county fair on Sunday, where x represents the number of child tickets and y represents the number of adult tickets.
The exponential function y = 2(3)x grows by a factor of 9 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?
Answer:
9
Step-by-step explanation:
What is the null hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2? h0: µ1 = 0?
No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:
Hₐ: µ₁ > µ₂
Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.
Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
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What is the area of sector GPH?
The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]
To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.
Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]
Using the formula for the area of a sector:
[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]
Substituting [tex]\(\theta = 90^\circ\):[/tex]
[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]
Simplifying the fraction:
[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]
So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.
please help with this word problem
Experts/ace/geniuses helppp asapp
If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?
Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?
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Which statement about a dilation with a scale factor of 3 is true?
The statement which is true about the dilation is:
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Step-by-step explanation:We know that the dilation transformation changes the size of the original figure but the shape is preserved.
The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.
The ratio of the corresponding sides of the two figure are equal.
i.e.
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Mr. Morris left work at 5:53 P.M. and drove 47 minutes to his home. What time did he arrive?
Answer:
6:40
Step-by-step explanation:
what is The desired outcomes of a specified event.
Answer:
Favorable Outcomes
Step-by-step explanation: