Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample
Answers
The measures of the frequency distribution is;
(A) Range = 7
(B) Mean = 29
(C) Mode = 12
(D) Median = 29
(E) Variance = 7.612
(F) Standard Deviation = 2.759
How to solve frequency distribution?
A) The range of a frequency distribution is;
Range = Highest Value - Lowest Value
Thus;
Range = 32 - 25
Range = 7
B) Mean is expressed as;
x' = ∑fx/∑f
x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]
x' = 928/32
x' = 29
C) Mode is the value with the highest frequency and so in this case;
Mode = 12
D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29
E) Variance = 7.612
F) The standard deviation is;
σ = √Variance
σ = 2.759
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Related Questions
For each system choose the best description of a solution if applicable give the solution
Answers
ANSWER
The system has no solution
EXPLANATION
We want to find the solution to the system of equations given:
[tex]\begin{gathered} x+4y-4=0 \\ -x-4y=4 \end{gathered}[/tex]From the first equation, make x the subject of the formula:
[tex]x=4-4y[/tex]Substitute that into the second equation and simplify:
[tex]\begin{gathered} -(4-4y)-4y=4 \\ -4+4y-4y=4 \\ \Rightarrow4y-4y=4+4 \\ 0=8 \end{gathered}[/tex]As we can see, the two sides of the equality sign have two different values.
This implies that the system of equations has no solution.
What is 3/7 + 4/18 estimated 0 1/2!or 1
Answers
1 .
Notice that 3/7 is close to 1/2 and 5/9 is also close to 1/2.
Therefore, an estimate for 3/7 + 5/9 is 1/2 + 1/2 = 1.
To estimate fractions using mental math, start by simplifying the fraction to the lowest possible denominator. Then, look at the fraction and round it to the nearest fraction that you feel comfortable working with which could be ¼, ⅓, ½, ¾, or even 1.
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he volume of a cylinder with height
h
h and radius
r
r can be found using the formula
V
=
π
r
2
h
V=πr2h
Find the volume of a cylinder with radius 6 feet and height 9 feet, rounded to 1 decimal place.
Answers
Answer:
1018.3
Step-by-step explanation:
The volume of a cylinder=πr2h
=22\7*6*6*9
=1018.3
therefore, the of the cylinder is 1018.3
Help me to find the measure of angles 1 2 and 3!
Answers
Given:
Given the diagram
Required: The measure of angles 1, 2 and 3.
Explanation:
The sum of interior angles of a triangle is 180 degrees. So,
[tex]\begin{gathered} x+55^o+70^o=180^o \\ x=180^o-55^o-70^o \\ =55\degree \end{gathered}[/tex]The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.
[tex]\begin{gathered} x+m\angle1=180\degree \\ 55\degree+m\angle1=180\degree \\ m\angle1=180\degree-55\degree \\ =125\degree \end{gathered}[/tex]The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,
[tex]m\angle2=55\degree[/tex]Angle y and 150 degrees are supplementary angles. So,
[tex]\begin{gathered} y+150\degree=180\degree \\ y=180\degree-150\degree \\ =30\degree \end{gathered}[/tex]The sum of the interior angles of a triangle equals 180 degrees.
[tex]\begin{gathered} m\angle2+m\angle3+y=180\degree \\ 55\degree+m\angle3+30\degree=180\degree \\ m\angle3=180\degree-55\degree-30\degree \\ =95\degree \end{gathered}[/tex]Final Answer:
[tex]m\angle1=125\degree,m\angle2=55\degree,m\angle3=95\degree[/tex]Find the numerical value if x=4 and y=34x2(squared)+7y=?
Answers
To find the numerical value of the expression, we have to replace the variables for their given values. This way:
[tex]\begin{gathered} 4x^2+7y \\ 4(4)^2+7(3) \\ 4\cdot16+21 \\ 64+21 \\ 85 \end{gathered}[/tex]The numerical value of the expression is 85.
what is the ansss??? btw this is a practice assignment.
Answers
A) Check the graph below, please. B) Horizontal translation to the left in 2 units. C) Vertical shift 4 units
1) Given that we have the function h(x) = |x+2| and g(x)= |x| + 4
A) Let's set a pair of tables, and pick 3 arbitrary values for x and then plug into each one
h(x) = |x+2|
x | y = |x+2|
-1 | 1 y =|-1 +2| = |1| = 1
0 | 2 y =|0+2| = |2| = 2
1 | 3 y =|1+2| = |1| = 1
g(x) =|x| + 4
x | y
-1 | 5
0 | 4
1 | 5
Let's plot those absolute value functions:
B) Considering the parent function f(x) =|x| we can notice that h(x) is a translation to the left, in two units. This we can see better this way:
Note that f(x) is in red, and h(x) in pink or light red.
C) Considering that f(x) = |x| we can see that g(x) = is a vertical shift 4 units up.
In a study of randomly selected women science majors, the following data were obtained on two groups, those who left their profession within a few months after graduation (leavers) and those who remained in their profession after they graduated (stayers). Test the claim that those who stayed had a higher science grade point average than those who left. Use α = 0.05.
Answers
X₁: science GPA for those who left their profession after graduation
X₂ science GPA for those who remained in their profession after graduation.
The working hypothesis is that the GPA of those who stayed is higher than those who left.
Which is the same as saying that the GPa of those who left is less than those who stayed.
μ₁ represents the population mean of the science GPA of those who left.
μ₂ represents the population mean of the science GPA of those who remained.
Part one
You can express the working hypothesis as follows:
[tex]\mu_1<\mu_2[/tex]The hypothesis does not include the equal sign, so this hypothesis can be considered as the alternative hypothesis.
The null hypothesis of this test will be the complement of the alternative hypothesis, and always carries the equal sign within. So if the alternative hypothesis states that "the mean of the leavers is less than the mean of the stayers", then the null hypothesis will be that "the mean of the leavers is greater than or equal to the mean of the stayers" you can symbolize this as:
[tex]\mu_1\ge\mu_2[/tex]Since the null hypothesis carries the equal sign you can also write it as:
[tex]\mu_1=\mu_2[/tex]Both options are equally valid.
So, the second answer is null hypothesis.
Part two
Considering that we are studying the population means of two normal variables and that we know the population standard deviation for both populations, the test statistic to use is the standard normal for the difference of means which is defined as follows:
[tex]Z=\frac{(\bar{X_1}-\bar{X_2})-(\mu_1-\mu_2)}{\sqrt[]{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}N(0,1)[/tex]Subindex 1 indicates the values corresponding to the "leavers":
X₁bar= 3.16
n₁= 103
σ₁= 0.52 → σ₁²= 0.2704
Subindex 2 indicates the values corresponding to the "stayers":
X₂bar= 3.28
n₂= 225
σ₂= 0.46 → σ₂²= 0.2116
Under the null hypothesis both population means are equal, which means that their difference is equal to zero:
If μ₁ = μ₂, then μ₁ - μ₂ = 0
Replace all values on the formula to determine the Z-value under the null hypothesis, i.e. the test statistic:
[tex]undefined[/tex]
Find the domain & range(Select the correct answer below & fill in the box to complete the choice.)A. The domain is the interval ____(Write your answer in interval notation.)B. The domain is the set {_____}(Use a comma to separate answers as needed. Write each answer only once.)——————————————————A. The range is the set {_____}(Use a comma to separate answers as needed. Write each answer only once.)B. The range is the interval ____(Write your answer in interval notation.)
Answers
The domain of a function is the set of x values the function uses as inputs; from a graph the domain is the x-values that the graph take on the x-axis; in this case, since we have an infinite amount of x-valeus the function uses we will write the domain as an interval. The domain is:
[tex](-\infty,\infty)[/tex]Similarly, the range is the set of values the function takes on the y-axis, from the graph we notice that the range is:
[tex](-\infty,6\rbrack[/tex]
HELP FAST. Please explain how to find the answer for the equation step by step.
Answers
The equation for the given summation is:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
How to find the equation?Here we have a summation of unknown terms of the form:
uₙ
That summation goes between n = 1 and n = 4, this means that we will have a sum of 4 terms, such that:
[tex]\sum_{n=1}^4 u_n[/tex]
Means that we need to sum the terms u₁, u₂, u₃, and u₄, then we can write the equation:
[tex]\sum_{n=1}^4 u_n = u_1 + u_2 + u_3 + u_4[/tex]
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Questiona + 4 = 10. If a must be equal to one of the values below, what is the value of a?Select the correct answer below:4679
Answers
1) In this question, we can solve it in two different ways. Either algebraically, or by mental Math.
2) Algebraically we have:
[tex]\begin{gathered} a+4=10 \\ a+4-4=10-4 \\ a=6 \end{gathered}[/tex]By mental math, we just need to ask ourselves how much can I add to 4 and get 10,? The answer will be six.
3) Thus, the answer is 6
Here are the approximate populations of three cities in the United States, expressedin scientific notation: San Jose: 1.1 x 10^6; Washington: 7 x 10^5 ; Atlanta: 4.8 x 10^5.a. Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. Doyou agree with her? Explain your reasoning.Your answer
Answers
Lin says that about 6.2 x 10^5 more people live in San Jose than in Atlanta. To find if she is right you substract the population of Atlanta from the population in San Jose:
Substraction of numbers in scientific notation:
1. Turn the numbers to get the same power of base 10.
You move to the left the decimal to increase the power of base 10 and move to the right to g
[tex]undefined[/tex]Calculate the root mean square velocity, in m/s, of Ne at 273.0 K. Assume ideal gas behavior.
I meant to put this in chemistry
Answers
The root mean square velocity of Neon, in m/s as required in the task content is; 18.45 m/s.
What is the root mean square velocity of Neon as required?It follows from the task content that the root mean square velocity of Neon is to be determined.
Since the molar mass of Neon is; 20 while the gas constant, R = 8.314 and T = 273K.
It follows from the root mean square velocity formula that we have;
R.M.S = √(3RT/M)
R.M.S = √{(3×8.314×273)/20}
R.M.S = √340.46
R.M.S = 18.45 m/s.
Hence, the root mean square velocity of Neon, Ne under the given condition is; 18.45 m/s.
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The total value of the invoice is Q.10,000.00, the customs agent will be paid 3 per thousand. What amount will we pay you?
Answers
3 per thousand?
10000 ------------------------- 1000
x ------------------------ 3
x = (3 x 10000)/1000
x = 30000/1000
x = 30
The answer is 30
consider a quadrilateral and its diagonals.wich conjecture below would best describe a quadrilateral whose diagonals divide into four isosceles triangles
Answers
Isosceles triangle have 2 equal lengths
Square or Rectangle have 4 equal teiangles
Isosceles trapezoid also divides
Then answer is
Isosceles trapezoid. Option A)
Eva and her friend are making friendship bracelets. Eva has 11 meters of yarn, and she gives
2 meters of the yarn to her friend. Each bracelet uses 1 1/2 meters of yarn. How many bracelets can Eva make with the yarn she has left?
Let n equal the number of bracelets Eva can make.
Write an equation that represents the situation.
Answers
6 bracelets Eva can make with the yarn she has left with .
The equation is [tex]\frac{3n}{2}=9[/tex]
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic expression is 2x + 4 = 8, which results from operations like addition, subtraction, multiplication, and division on variables and constants. Algebraic expressions are obtained as the mathematical statement.
Eva has 11 meters of yarn and she gives 2 meters of the yarn to her friend
Now she left with 11 -2 = 9
As Each bracelet uses [tex]\frac{3}{2}[/tex] meters of yarn
n braclet = [tex]\frac{3n}{2}[/tex]
9= [tex]\frac{3n}{2}[/tex]
n = [tex]\frac{18}{3}[/tex]
=6
6 bracelets Eva can make with the yarn she has left with .
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find the absolute value of each number -1/3, 6 & -0.2
Answers
The absolute number of an integer is the distance that separates the number from position zero "0" so, if it is a distance it cannot be a negative value.
Then the absolute value of these numbers is:
Balloon A is released 5 feet above the ground. Balloon B is released at ground level. Both balloons rise at a constant rate. Which situation can you represent using an equation of the form y = kx? Explain.
Table for Balloon A shows that the balloon reaches 9ft in 1s, 13ft in 2s, 17ft in 3s. Table for Balloon B shows that the balloon reaches 4ft in 1s, 8ft in 2s and 12ft in 3s.
Answers
Answer: Balloon B
Step-by-step explanation:
The distance, in feet, is always four times the time, in seconds.
(g) distance from the x-axis is equal to the distance to the y-axis.
Answers
Part a
Remember that the ordinate is the y-coordinate and the abscisa is the x-coordinate
so
(x, 2x+1)
y=2x+1
Part b
[tex](\frac{1}{2}y^2,y)[/tex]x=(1/2)y^2
Part c
x^2+y^2=25
Part e
y=2
Part f
x=7
Part g
x=y
Part h
[tex]\sqrt[\square]{x^2+y^2}=5[/tex]Part i
[tex]\sqrt[\square]{(x-2)^2+(y-3)^2}=5[/tex]Simplify these below with explainations please. Thank you
Answers
Answer:
3x^5y^8
Step-by-step explanation:
so the cube root of 27 is 3
to find the cube root of x^15 divide the exponent by 3 which gets you x^5
do the same thing for y^24 and that gets you y^8
mhm and i think thats right
TRIGONOMETRY Find the magnitude and the direction of the resultant vector
Answers
Step 1:
Write the given vectors
[tex]\begin{gathered} \bar{V}\text{ = ( 10 , 9 )} \\ \bar{W}\text{ = (-6 , -2 )} \end{gathered}[/tex]Step 2
Resultant vector = [ 10 + (-6) , 9 + (-2) ]
= ( 4 , 7 )
Resultant vector = 4i + 7j
Step 3
[tex]\begin{gathered} \text{Magnitude = }\sqrt[]{4^2+7^2} \\ \text{Magnitude = }\sqrt[]{16\text{ + 49}} \\ \text{Magnitude = }\sqrt[]{65} \\ \text{Magnitude = 8.1} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \text{Direction }\theta=tan^{-1}(\frac{4}{7}) \\ \text{Direction = 29.7} \end{gathered}[/tex]After 6 weeks, a plant is 11 inches tall. After 8 weeks, it is 13 inches tall. After 10 weeks, it is 15 inches tall.
Write an equation to describe the relationship between the height of the plant, y, and the number of weeks it has been growing, x
Answers
The equation to describe the relationship between the height of the plant and the number of weeks is
y = x + 5
Given,
The height of the plant = x
The number of weeks = y
The height of plant at 6th week = 11 inches
The height of plant at 8th week = 13 inches
The height of plant at 10th week = 15 inches
We have to find the equation to describe the relationship between the height of the plant and the number of weeks.
Lets see,
x = 6 and y = 11, y – x = 11 – 6 = 5
x = 8 and y = 13, y – x = 13 – 8 = 5
x = 10 and y = 15, y – x = 15 – 10 = 5
That is,
y – x = 5.
y = x + 5
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Altred is saving up money for a down payment on a house. He currently has $4739, but knows he can get a loan at a lower interest rate if he can put down $5336. If heinvests the $4739 in an account that earns 5.1 % annually, compounded monthly, how long will it take Alfred to accumulate the $5336? Round your answer to two decimal places, if necessary.
Answers
Given the word problem, we can deduce the following information:
Principal amount = $4739
Future amount = $5336
Interest = 5.1 % =0.051
To determine the time to accumulate the $5336, we use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A=Future amount=$5336
P=Present amount=$4739
r=interest rate = 0.051
n=number of compounding periods =12
t=time in years
We also note that the number of compounding periods must be 12 since the investment is compounded monthly.
We plug in what we know:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 5336=4739(1+\frac{0.051}{12})^{12t} \\ Simplify\text{ and rearrange} \\ 5336=4739(\frac{12.051}{12})^{12t} \\ 12t=\frac{\ln\frac{5336}{4739}}{\ln\frac{12.051}{12}} \\ t=\frac{\operatorname{\ln}\frac{5,336}{4,739}}{12\operatorname{\ln}\frac{12.051}{12}} \\ Calculate \\ t=2.33 \end{gathered}[/tex]Therefore, the answer is 2.33 years.
A cyclist rides his bike at the speed of 11 ft per second what is the speed in miles per hour how many miles will the cyclist travel in 5 hours in your computations use the fact that one mile is equal to 5280 ft do not round your answers
Answers
The speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
According to the question,
We have the following information:
A cyclist rides his bike at the speed of 11 ft per second.
Now, it is given that we have to use 1 mile = 5280 ft.
So, we have:
1 ft = 1/5280 miles
We know that there 3600 seconds in 1 hour.
1 seconds = 1/3600 hour
So, we have the speed in miles per hour:
11*(1/5280)/(1/3600)
(11*3600)/5280
7.5 miles per hour
Time taken = 5 hours
Speed = 7.5 miles per hour
Distance = speed*time
Distance = 7.5*5
Distance = 30 miles
Hence, the speed of the cyclist in miles per hour is 7.5 miles per hour. The distance covered by the cyclist in 5 hours is 30 miles.
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A man walked 5 miles right and read a sign that said "20 miles north to Atlanta". How far is Atlanta from the starting point?
Answers
ANSWER
Atlanta is 20.62 miles away from the starting point
EXPLANATION
This is a diagram of this problem
We're looking for the hypotenuse of this right triangle. Using the Pythagorean theorem:
[tex]\begin{gathered} d^2=5^2+20^2 \\ d=\sqrt[]{25+400} \\ d=\sqrt[]{425} \\ d\approx20.62\text{ miles} \end{gathered}[/tex]21/24 simplified plsssssssssssssssssssssssss
Answers
(Divide both 21 and 24 by the greatest common factor, 3)
Answer:
7/8
Step-by-step explanation:
The test statistic for an ANOVA hypothesis test is an F-statistic. Is the P-value the area to the right or left the F-statistic?
Answers
The test statistic for the anova is an F test and it is said to be positively skewed which would be to the right of the F test statistic.
What is the ANOVA?This is the term that is used to refer to the short form of the term that says analysis of variance.
The ANOVA is used to show the variation that would be in existence of a group of observations.
The F test is known to be positively skewed at all times. So we would have it that the P value would have to be to the right and not to the left in the ANOVA hypothesis.
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12345678912345678912456789
Answers
Answer:
3 is missing in there numbers,the last pair
WILL GIVE BRAININESS HELP PLEASE Which function is increasing at the highest rate?
Answers
The first equation is increasing at highest rate.
Which function has highest increasing rate?
We can know which function has the highest rate of increase by looking at its slope. The function with the highest slope will have the highest rate.
In equation first m = 2 and is highest among every slope.
12x - 6y = -24
-6y = -12x -24
y = 2x +4
m = 2 (increasing)
In second equation m = 1
m = (-4 + 5)/(2-1) = 1
for a straight line function , the slope is given by
m = ( y₂ -y₁)/(x₂-x₁)
m = ( -3 -3)/(2- (-1)) = -6 /3 = -2
Therefore the function is decreasing
8,0) (0,-4)
m = (-4 -0) /(0-8) = 4/8 = 1/2
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A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
Answers
Answer:
47/68
Step-by-step explanation:
total candies=136
not red candies=94
94/136=47/68
Solve the following polynomial equation by grouping and factoring. 36y^3−49y=0
Answers
Given:
[tex]36y^3-49y=0[/tex]solve for y:
[tex]\begin{gathered} 36y^3-49y=0 \\ y(36y^2-49)=0 \\ y=0;36y^2-49=0 \end{gathered}[/tex]Value of y is zero and
[tex]\begin{gathered} 36y^2-49=0 \\ 36y^2=49 \\ y^2=\frac{49}{36} \\ y=\pm\sqrt[]{\frac{49}{36}} \\ y=\pm\sqrt[]{1.361111} \\ y=\pm1.166 \\ y=1.166,y=-1.166 \end{gathered}[/tex]