Answer:
1. $29.4 million
2. 145.24
3. 145.24
4. 12.05
5. D. No, because the sample is not representative of the whole population.
Step-by-step explanation:
1. The computation of range of the sample data is shown below:-
Range of the sample data = Maximum value - Minimum value
= 42 - 12.6
= $29.4 million
2. For the computation of variance of the sample data first, we need to find out the mean which is shown below:-
Mean = [tex]\frac{(42 + 40 + 39 + 32 + 21 + 18 + 16 + 14 + 13.7 + 12.6) }{10}[/tex]
= 24.83
The Variance of the sample data
= [tex]\frac{(42 - 24.83)^2 + ..... + (12.6 - 24.93)^2}{10 - 1}[/tex]
= [tex]\frac{1307.161}{9}[/tex]
= 145.24
3. The computation of the standard deviation of the sample data is shown below:-
The Standard deviation of the sample
= [tex]\sqrt{145.24}[/tex]
= $12.05155592
or
$12.05
4. No, as the sample does not represent the whole population.
can someone do this ???
This year, Arvin and Mariah were in charge of making orange juice for campers. They planned to make the juice by mixing water and
frozen orange juice concentrate. To find the mix that would taste best, they decided to test some mixes.
Mix A: 2 cups concentrate
3 cups cold water
Mix B: 5 cups concentrate
9 cups cold water
Mix C: 1 cup concentrate
2 cups cold water
Mix D: 3 cups concentrate
5 cups cold water
1. Which mix will make juice that is the most 'orangey"? Explain your reasoning.
2. Which mix will make juice that is the least 'orangey"? Explain your reasoning
Answer:
Mix A is the most orangey, Mix C is the least orangey
Step-by-step explanation:
Mix A largest proportion of concentrate to water
Mix C is the smallest proportion of concentrate to water
If A(4 -6) B(3 -2) and C (5 2) are the vertices of a triangle ABC fine the length of the median AD from A to BC. Also verify that area of triangle ABD = Area of triangle ACD
Answer:
a) The median AD from A to BC has a length of 6.
b) Areas of triangles ABD and ACD are the same.
Step-by-step explanation:
a) A median is a line that begin in a vertix and end at a midpoint of a side opposite to vertix. As first step the location of the point is determined:
[tex]D (x,y) = \left(\frac{x_{B}+x_{C}}{2},\frac{y_{B}+y_{C}}{2} \right)[/tex]
[tex]D(x,y) = \left(\frac{3 + 5}{2},\frac{-2 + 2}{2} \right)[/tex]
[tex]D(x,y) = (4,0)[/tex]
The length of the median AD is calculated by the Pythagorean Theorem:
[tex]AD = \sqrt{(x_{D}-x_{A})^{2}+ (y_{D}-y_{A})^{2}}[/tex]
[tex]AD = \sqrt{(4-4)^{2}+[0-(-6)]^{2}}[/tex]
[tex]AD = 6[/tex]
The median AD from A to BC has a length of 6.
b) In order to compare both areas, all lengths must be found with the help of Pythagorean Theorem:
[tex]AB = \sqrt{(x_{B}-x_{A})^{2}+ (y_{B}-y_{A})^{2}}[/tex]
[tex]AB = \sqrt{(3-4)^{2}+[-2-(-6)]^{2}}[/tex]
[tex]AB \approx 4.123[/tex]
[tex]AC = \sqrt{(x_{C}-x_{A})^{2}+ (y_{C}-y_{A})^{2}}[/tex]
[tex]AC = \sqrt{(5-4)^{2}+[2-(-6)]^{2}}[/tex]
[tex]AC \approx 4.123[/tex]
[tex]BC = \sqrt{(x_{C}-x_{B})^{2}+ (y_{C}-y_{B})^{2}}[/tex]
[tex]BC = \sqrt{(5-3)^{2}+[2-(-2)]^{2}}[/tex]
[tex]BC \approx 4.472[/tex]
[tex]BD = CD = \frac{1}{2}\cdot BC[/tex] (by the definition of median)
[tex]BD = CD = \frac{1}{2} \cdot (4.472)[/tex]
[tex]BD = CD = 2.236[/tex]
[tex]AD = 6[/tex]
The area of any triangle can be calculated in terms of their side length. Now, equations to determine the areas of triangles ABD and ACD are described below:
[tex]A_{ABD} = \sqrt{s_{ABD}\cdot (s_{ABD}-AB)\cdot (s_{ABD}-BD)\cdot (s_{ABD}-AD)}[/tex], where [tex]s_{ABD} = \frac{AB+BD+AD}{2}[/tex]
[tex]A_{ACD} = \sqrt{s_{ACD}\cdot (s_{ACD}-AC)\cdot (s_{ACD}-CD)\cdot (s_{ACD}-AD)}[/tex], where [tex]s_{ACD} = \frac{AC+CD+AD}{2}[/tex]
Finally,
[tex]s_{ABD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ABD} = 6.180[/tex]
[tex]A_{ABD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ABD} \approx 3.004[/tex]
[tex]s_{ACD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ACD} = 6.180[/tex]
[tex]A_{ACD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ACD} \approx 3.004[/tex]
Therefore, areas of triangles ABD and ACD are the same.
Solve the problem by entering and solving equation.
A rectangular picture frame has a perimeter of 56 inches. The height of the frame is 16 inches. What is the
width of the frame?
The solution is
+W)=
The width of the frame is
inches.
Answer:
12 inches
Step-by-step explanation
The perimeter of a rectangle is the sum of each of the sides. So, it would be Perimeter= width+width+height+height. Let's make x as the width as the variable. We already know the value of the perimeter and the height. We can then substitute these values in the above equation.
So, that would be 56=x + x +16 +16
Then we would solve for x. First combine like terms.
56=2x+32
Then, subtract 32 from each side.
24=2x
Finally, divide by 2 on both sides to get the answer.
x=12
Answer:
12 inches
Step-by-step explanation:
none none none none none none none
What is the solution to this system of equations
Sorry, Please rewrite it again.
Wich ratio is equivalent to 4:5
A 10/15
B 4/10
C 16/20
D 15/8
Answer:
16/20
Step-by-step explanation:
4:5
Multiply each side by 4
4*4: 5*4
16:20
16/20
Answer:
The answer is C. 16/20.
Step by step explanation:
This is because if you were to multiply 4 and 5 by 4, you would get 16/20. That means that both ratios are the same. Hope this helps! :)
This screen is 6 inches by 8 inches. What is the screen size?
Answer:
The area of the screen is 48 square inches
Step-by-step explanation:
6x8=48
Answer:
The real answer is 10!
Step-by-step explanation:
I just did the question!
Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 15$ and $XY = 9$, then what is $AB$?
Answer:
AB=5.4 units
Step-by-step explanation:
We using the theorem of intersecting tangent and secant to solve this.
By this theorem:
[tex]XY^2=XB \times AX\\9^2=15(15-XB)\\81=225-15XB\\15XB=144\\XB=9.6\\$Therefore:\\AB=AX-XB\\AB=15-9.6\\AB=5.4$ units[/tex]
Answer:
Its 9.6, the other guy got it wrong, he already got it but accidentally added a step. Its 9.6 :)
Step-by-step explanation:
trust me :).
You get dressed in the morning without looking at the colours of the clothes you choose. Your shirts are white or blue, your pants are black, red, or yellow, and your shoes are brown or black. How likely are you to choose a white shirt, black pants, and brown shoes?
Answer:
add up all the colors
Step-by-step explanation:
HELPPP
Which expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared?
RootIndex 4 StartRoot 2 cubed EndRoot
StartRoot 2 Superscript 5 EndRoot
RootIndex 4 StartRoot 4 cubed EndRoot
StartRoot 4 Superscript 5 EndRoot
Answer:
its d i just the test
Step-by-step explanation:
StartRoot 4 Superscript 5 EndRoot expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared.
Whats does equivalent mean?Definition of equivalent
1: equal in force, amount, or value also: equal in area or volume but not superposable a square equivalent to a triangle.
2a: like in signification or import. b: having logical equivalence equivalent statements. 3: corresponding or virtually identical especially in effect or function.
What does equivalent me an example?The definition of equivalent is something that is essentially the same or equal to something else. An example of an equivalent is (2+2) and the number 4. Since 2+2= 4, these two things are equivalent. adjective.
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A lawn mowing company is trying to grow it's buisness. It had 30 clans when it started its buisness and wants to increase by 6 new clients each week. Use ab arithmetic sequence to write a function to represent the real world situation and determine the range of the function for the first four weeks of data.
Answer:
The situation per week is 30 + 6n
where n is the number of weeks
Range of the function is 18 for the first four weeks of data
Step-by-step explanation:
Here, we are to use an arithmetic sequence for a representation.
The first term here is a which is 30 clients while the common difference of d is 6 new clients per week
So we can write the nth term of the sequence as;
Tn = a + (n-1)d
Tn = 30 + (n-1)6
Tn = 30+ 6n -6
Tn = 24 + 6n
where n is the number of weeks
Now for the second week we shall have a total of a+ d clients = 30 + 6 = 36
For the third we have 24 + 6(3) = 24 + 18 = 42
For the fourth, we have 24 + 6(4) = 24 + 24 = 48
Thus the range mathematically means the difference between the highest and lowest for that four weeks = 48-30 = 18
Answer:
A lawn-mowing company is trying to grow its business. It had 18 clients when they started its business and wants to increase by 4 new clients each week.
Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
f(x) = 4x + 18; 0 ≤ y ≤ 4
For the function Y=-3Cos4x +6 State the Amplitude, Period, Frequency, and Vertical Shift.
Answer:
Amplitude = -3
Period = [tex]\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
Frequency = [tex]\frac{1}{\pi/2}=\frac{2}{\pi}[/tex]
Vertical Shift = 6.
Step-by-step explanation:
Consider the function:
[tex]y=A\ sin (B(x+C))+D[/tex]
Here,
A = amplitude; It is the measure of how high is the peak from the center line.
2π/B = period; A period is the distance between one peak to the next.
C = phase shift; it represents how far the function is shifted horizontally from the initial point.
D = vertical shift; it represents how far the function is shifted vertically from the initial point.
The frequency of a function is the number of times something happens per unit time.
[tex]\text{Frequency}=\frac{1}{Period}[/tex]
The function provided is:
[tex]y=-3\ cos\ 4x+6[/tex]
On comparing the provided function with the general one it can be determined that:
Amplitude = -3
Period = [tex]\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
Frequency = [tex]\frac{1}{\pi/2}=\frac{2}{\pi}[/tex]
Vertical Shift = 6.
What is the common ratio Between successive terms in the sequence? 1.5,1.2,0.96,0.768
Answer:
0.8
Step-by-step explanation:
0.768/0.96= 0.8
0.96/1.2 =0.8
4432 buttons are made in three hours it takes 6 hours to make enough buttons to fill three boxes. When box B has been filled there are 3363 buttons remaining box C holds half of the amount of button as box A how many are there in A than C
Answer:
Box A has 1121 buttons more than Box C
Step-by-step explanation:
4432 boxes are made in three hours
Then in six hours, we would be making double of this
The number of boxes made is 4432 * 2 = 8864 boxes
Now,
we have boxes A B C to fill
Filling box B, we have 3363 boxes left to fill A and B
Now C holds half of what A hold
so we can say the ratio of buttons in C to A is 1:2
The number of buttons in C would thus be
1/3 * 3363 = 1121
Number of buttons in A would be 2/3 * 3363 = 2 * 1121 = 2242 buttons
Now the number of buttons with which the buttons in A exceeds that in C would be 2242 -1121 = 1121 buttons
The distance it takes a truck to stop can be modeled by the function Image description d = stopping distance in feet v = initial velocity in miles per hour f = a constant related to friction When the truck's initial velocity on dry pavement is 40 mph, its stopping distance is 138 ft. Determine the value of f, rounded to the nearest hundredth.
Answer: 0.39
Step-by-step explanation:
We are required to determine the the value of f, rounded to the nearest hundredth
The value of f, rounded to the nearest hundredth is 0.39
Given function:
[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]
Where,
d = stopping distance in feet
v = initial velocity in miles per hour
f = a constant related to friction
When
v = 40 mph
d = 138 ft
f = ?
[tex]d(v) = \frac{2.15 {v}^{2} }{64.4f} [/tex]
[tex]138= \frac{2.15 {(40)}^{2} }{64.4f} [/tex]
138(64.4f) = 2.15(1600)
8,887.2f = 3440
f = 3440 / 8,887.2
f = 0.3870735439733
Approximately to the nearest hundredth f = 0.39
Therefore, the value of f, rounded to the nearest hundredth is 0.39
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Is the solution shown below correct? Explain.
9x+2=8x2+6x
Negative 8 x squared + 3 x + 2 = 0. x = StartFraction negative 3 plus-or-minus StartRoot (3) squared minus (4) (negative 8) (2) EndRoot Over negative 16 EndFraction. x = StartFraction negative 3 plus-or-minus StartRoot 9 minus (64) EndRoot Over negative 16 EndFraction. x = StartFraction 3 plus-or-minus StartRoot 55 Endroot i Over 16 EndFraction.
Answer:
It is wrong
Step-by-step explanation:
What we have is as follows;
9x + 2 = 8x^2 + 6x
Bringing 9x + 2 yo the right hand side, we have;
8x^2 + 6x -9x -2 = 0
8x^2 -3x -2 = 0
So what is used here is the quadratic formula and we want to try to see if it was used correctly.
The form we have in the question is however;
-8x^2+ 3x + 2 = 0
which is obtained by taking the right hand side of the equation to the left
Now;
using the quadratic formula;
x = -b ± √(b^2 -4ac)/2a
where a is -8
b = 3
c = 2
Thus we have
-3 ± √(9 - 4(-8)2)/2(-8)
-3 ± √(9 + 64)/(-16)
So where is wrong is in the square root
what we are supposed to have is 9 + 64 = 73 and not otherwise
Answer:
Step-by-step explanation:
No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.
Three semicircles are placed in a rectangle, as shown below. The width of the 3 rectangle is 15 . Find the area of the shaded region. Use the value 3.14 of pie , and do not round your answer.
Answer:
Step-by-step explanation:
Width of rectangle = 15 cm
width of rectangle is equal to the radius of each semicircle.
radius of each semicircle (r) = 15 cm.
Diameter of each semicircle = 30 cm
Length of rectangle = 3 x 30 = 90 cm.
[tex]Area \: of \: shaded \: region \\ = Area \: of \: rectangle \\ \: \: \: \: \: - 3 \times area \: of \: one \: semicircle \\ = l \times w - 3 \times \frac{\pi {r}^{2} }{2} \\ \\ = 90 \times 15 - 3 \times \frac{3.14 \times {15}^{2} }{2} \\ \\ = 1350 - 3 \times \frac{3.14 \times 225 }{2} \\ \\ = 1350 - \frac{2119.5}{2} \\ \\ = 1350 - 1059.75 \\ \\ \purple { \boxed{ \therefore \: Area \: of \: shaded \: region = 290.25 \: {cm}^{2}}} \\[/tex]
What is the length of the uhn known leg in the right triangle
Answer:
Triangle?
Step-by-step explanation:
But to find it (hypotenuse) you use the other sides of the right triangle and solve using the pythagorean theorem.
a^2+b^2=c^2
c= hypotenuse
To find any other side, just plug it in to solve for that variable.
a=one of the other sides
b = the third side
PLZZZ HELP MEEE!!!!!!!!!!
Answer:
Step-by-step explanation:
Graph shown in the attachment,
- Since every value of x corresponds to a distinct value of y, so the graph represents a function.
- Every input value of x of the table has a output value of y, therefore, it's a function.
- In the set of ordered pairs (5, 8) and (5, 2), input value x = 5 has two output values for y,
y = 8 and y = 2
Therefore, it's not a function and (5, 8) should be changed to make the relation a function.
Simplify (4x - 6) - (5x + 1).
a)x+7
b)-X +7
c)X-7
d)-X-7
Answer:
Step-by-step explanation:
4x - 6 - 5x - 1
-x - 7
the answer is d
Answer:
D . -x - 7
Step-by-step explanation:
(4x-6) - (5x+1) = 4x-6-5x-1
4x-5x-1-6
4x-5x= -x
1-6 = -7
-x - 7
∠MNQ and ∠PNR are vertical angles. What is the value of x?
Answer:
Step-by-step explanation:
I don’t know the answer
The value of x such that ∠MNQ and ∠PNR are vertical angles is 40
How to determine the value of x?The given parameters are:
MNQ = 3x - 6
PNR = 114
Vertical angles are equal.
So, we have:
3x - 6 = 114
Add 6 to both sides
3x = 120
Divide both sides by 3
x = 40
Hence, the value of x is 40
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Which graph matches the equation y+3=2(x+3)?
Answer:
The leftmost graph [with the points (-3,-3) and (0,3)]
Step-by-step explanation:
y+3=2(x+3)
y+3=2x+6
y=2x+3
The y-intercept is 3, meaning that the line passes through the point (0,3), and it's slope is 2, so it travels 2 units up and 1 unit over. Thus the correct graph is the top left graph, with the two points (-3,-3) and (0,3).
The graph is considered as the creation of a diagram that depicts a relationship connecting two or more items, and further discussion can be defined as follows:
Given:
[tex]\bold{y+3=2(x+3)}[/tex]
To find:
graph=?
Solution:
[tex]\bold{y+3=2(x+3)}[/tex]
Solving the given equation:
[tex]\to \bold{y+3=2(x+3)}\\\\\to \bold{y+3=2x+6}\\\\\to \bold{y=2x+6-3}\\\\\to \bold{y=2x+3}\\\\[/tex]
In this, the y-intercept is 3, indicating that the line crosses through the point (0,3), and the slope is 2, showing that it moves 2 units up and 1 unit over. And as a result, the proper graph is the upper left graph, with two points [tex]\bold{(-3,-3)\ and\ (0,3)}[/tex].Please find the graph in the attached file.
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Make K the subject of the formula
[tex]t = \frac{mu {}^{2} }{k} - 5mg[/tex]
Answer:
Step-by-step explanation:
[tex]t = \frac{mu^{2} }{k} -5mg\\kt = mu^{2} -5mg\\k = \frac{mu^{2} -5mg}{t}[/tex]
To make k subject of the fomula :
Step 1 : cross multiply
Step 2 : Divide both side of the equation to isolate k
The solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is t = (mu²)/k - 5mg. The value of the expression for the value of k will be,
The value of k will be written as,
t = (mu²)/k - 5mg
k = (mu² - 5mgk)/t
Therefore, the solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
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i need help help pls
Answer:
MAD = 2
Step-by-step explanation:
First We'll find the mean of data
Mean = [tex]\frac{20}{5}[/tex]
Mean = 4
Then, we'll find absolute deviation
=> |4-3| = 1
=> |4-2| = 2
=> |4-1| = 3
=> |4-1| = 3
=> |4-3| = 1
Now, taking the mean of these absolute deviations:
MAD = [tex]\frac{1+3+3+2+1}{5}[/tex]
MAD = [tex]\frac{10}{5}[/tex]
MAD = 2
How many Positive Integers are there between 20 to 100 exclusively?
Select one:
a. 70
b. 80
c. 81
d. 79
Answer:
79
Step-by-step explanation:
There is a cool easy way to solve this kind of problem. If a range is given, and the entire range increases in incrememnts of 1, then you can find the number intergers inclusive by taking the first number and subtracting it from the last and adding 1. Since in this problem you want it exclusive, we can rewrite the range to 21-99.
99-21 +1 = 78 + 1 = 79
help plzzzz asap i need the answer right now
The probability that a biased coin will land on Heads is 0.43
Azmol is going to throw the coin 600 times.
Work out an estimate for the number of times the coin will land on Tails.
Answer:
[tex]342[/tex]
Step-by-step explanation:
The probability of heads landing is 0.43.
The probability of tails landing is 1-0.43=0.57.
Azmol throws the coin 600 times, so:
[tex]600 \times 0.57[/tex]
[tex]=342[/tex]
An urn contains 4 red, 6 green, and 2 yellow balls. If 3 balls are randomly selected what is the probability that you pick one of each color?
The bookstore is selling a series of 4 books for 97.50 what is the unit price for one book
Answer:
Step-by-step explanation:
97.50/4 equals 24.375 but if you are rounding it is 24. :)
The unit price for one book is 24.375 .
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Cost of four books = 97.50
Therefore,
the price of one book = [tex]\frac{97.50}{4} =24.375[/tex]
Hence, the unit price for one book is 24.375 .
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Pls help me!!!!! I'm dead!!!!! I have like 40 of these things. Pls ;)
Answer:
4 and 5 are coefficients the rest are terms
Step-by-step explanation:
coefficients are the numbers not the letters
Answer:
Coefficient: 4, 5Term: 4p, 5b, 8cStep-by-step explanation:
The terms are the elements of the sum:
5b, 8c, 4p
The coefficients are the constant multipliers:
5, 8, 4
___
In your list of items to "drag and drop", you have ...
Coefficient: 4, 5
Term: 4p, 5b, 8c