Addy’s monthly water bills for last year are $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26. Express the formula for the mean using sigma notation and calculate the mean water bill for the year. Extend Your Understanding
Answer:
Σ( xi ) / n ; $29
Step-by-step explanation:
Given the following data:
X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26
Number of observations (n) = 12
Mean formula (m) = ( Σ xi ) / n
Where i = each individual value in X
Mean water bill for the years is thus :
m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12
m = 348 / 12
m = 29
Hence, the mean water bill for the year is $29
Suppose the following are the city driving gas mileages of a selection of sport utility vehicles (SUVs). 19, 20, 19, 20, 18, 21, 17, 19, 24, 23, 21, 21, 17, 20, 20, 18 (a) Find the sample standard deviation (rounded to two decimal places). (b) In what gas mileage range does Chebyshev's inequality predict that at least 75% of the selection will fall
Answer:
answer below
Step-by-step explanation:
from the question the
mean = ∑x/n
∑x = 317
n = 16
mean = 19.8125
x x-Ц x-Ц²
19 -0.8125 0.66015625
20 0.1875 0.03515625
19 -0.8125 0.66015625
20 0.1875 0.03515625
18 -1.8125 3.28515625
21 1.1875 1.41015625
17 -2.8125 7.91015625
19 -0.8125 0.66015625
24 4.1875 17.53515625
23 3.1875 10.16015625
21 1.1875 1.41015625
21 1.1875 1.41015625
17 -2.8125 7.91015625
20 -0.8125 0.66015625
20 -0.8125 0.66015625
18 -1.8125 3.28515625
∑(x-Ц)² = 56.44
s.d = 1.9
b.
19.81 + 2*1.9= 23.61
19.81-2*1.9 = 16.01
=
Mr. Beeson has $220 in the bank and $12 in his billfold. He has bills of $76 and $188 to pay. Use a
integer to express his total balance.
Answer:
Your answer is -32
Step-by-step explanation:
First you add $220 and $12 together giving you $232
Then you subtract $76 from the $232 giving you $156
Then subtract $188 from $156 giving you a total of -$-32
If the two solids shown have the same height and the same cross-sectional area at every level, then what is the radius of the oblique cylinder?
Answer:
8
Step-by-step explanation:
If the two solids have the same height and same cross-sectional area at every level, this means that the radius of the oblique cylinder is the same as the radius of the right cylinder.
Since the radius of the right cylinder is 16/2=8, this means that the radius of the oblique cylinder must also be 8.
Algebraically, the area of the cross-section is given by:
[tex]A=\pi r^2[/tex]
If the areas of them are the same:
[tex]A_{right}=A_{oblique}[/tex]
Then:
[tex]\pi r_{right}^2=\pi r_{oblique}^2\\r_{right}=r_{oblique}[/tex]
Althea paid five dollars each for two bracelets and later sold each for $15. She paid eight dollars each for three bracelets and sold each of them for nine dollars. Write an expression that represents the profit Althea made.
Answer:
2(15 - 5) + 3(9 - 8)
Step-by-step explanation:
Profit for each $5 bracelet: 15 - 5
Profit for 2 $5 bracelets: 2(15 - 5)
Profit for each $8 bracelet: 9 - 8
Profit for 3 $8 bracelets: 3(9 - 8)
Total profit: 2(15 - 5) + 3(9 - 8)
Answer:
2(-5)+3(-8)+2(15)+3(9)=23
Step-by-step explanation:
For this expression, every time she payed for something we will use a negative number, and whenever she sold it we will use a positive number.
Lets start off with what she payed for, she bought two 5 dollar bracelets, and three 8 dollar bracelets.
2(-5)+3(-8)
Now we will see what she sold. She sold two bracelets for 15 dollars, and then sold three bracelets for 9 dollars.
2(15)+3(9)
Now we combine these to find out her profit.
2(-5)+3(-8)+2(15)+3(9)=23
(8-8i)(2+i)= (simplified)
Answer:
24-8i
Step-by-step explanation:
(8-8i)(2+i)=8*2+8i-8i*2-8i^2=16+8i-16i-8*(-1)=16-8i+8=24-8i
Given the preimage: A(3, 2), B(3, 6), C(11, 6), D(11, 2). Translate down 4 units. What is B'?
Answer:
B' is (3,2)
Step-by-step explanation:
In the original B coordinate pair, 6 is the y-coordinate. When we talk about shifting images or points up or down, we will normally see a change in the y-coordinate. In this case, the image is being translated 4 units down, so subtract 4 from 6 to get 2 as your y-ccoordinate for B'. Since no horizontal shift is being made, the x-coordinate from the original B point stays the same and B' becomes (3,2).
Answer:
b is (3,2)
Step-by-step explanation:
ggchvvbggggghhh
What is 12+24=2(6+ )
Answer:
[tex]\huge \boxed{x=12}[/tex]
Step-by-step explanation:
Let the unknown number be x.
12+24=2(6+x)
Switch sides.
2(6+x)=12+24
Expand brackets.
12+2x=12+24
Subtract 12 from both sides of the equation.
12+2x-12=12+24-12
2x=24
Divide both sides of the equation by 2.
(2x)/2=24/2
x=12
12+24=2(6+x )
36=2(6+ )
36\2=(6+x)
18=(6+x)
18-6=x
12=x
the answer is 12
Please help slove for AB.
Answer:
Based on triangles of angles: 45-45-90:
chord/2=(radius√2)/2
chord/2=(10√2)/2
chord/2=5√2
chord=10√2
Step-by-step explanation:
Hope it helps ;)
find the values of x and y please and thank you
Answer:
x=26
y=9
Step-by-step explanation:
5x-17+3x-11=180
8x=180+17+11
8x=208
x=26
3(26)-11=78-11=67
2y+5=90-67
2y=90-67-5
2y=18
y=9
There are three different colored balls: orange, green and purple. The probability of randomly choosing orange ball from a bag is 45%. The probability of randomly choosing a green ball from bag is 0.10. Explain how likely it is, in relation to 0, for Jared to randomly choose a purple ball from the bag. * l
Answer:
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probabiity = expected outcome/total outcome
Let the total outcome be 100% = 1.0
Given three different colored balls: orange, green and purple. If the probability of randomly choosing orange ball from a bag is 45%. The probability of randomly choosing a green ball from bag is 0.10
The probability of choosing both orange ball and green ball is 0.45+0.10 = 0.55.
Since the total outcome of probability is 1, then the probability for Jared to randomly choose a purple ball from the bag will be expressed as;
Pr(purple) = 1 - [Pr(green)+Pr(orange)]
Pr(purple) = 1 - [0.45+0.10]
Pr(purple) = 1 - 0.55
Pr(purple) = 0.45
Hence it is 45% likely for Jared to randomly choose a purple ball from the bag.
0,01,9,12,18,3,27,4,36,5,45 Types of variable input variable (input variable) .
Answer:
please mark my answer brainliest
Step-by-step explanation:
these types of input variables are called integer...
(20x^3-7x^2+3x-7)/-13x^2-5
Answer:
x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60
see atachement it's more legible.
Step-by-step explanation:
Solve for x:
(20 x^3 - 7 x^2 + 3 x - 7)/(-13 x^2 - 5) = 0
Hint: | Multiply both sides by a polynomial to clear fractions.
Multiply both sides by -13 x^2 - 5:
20 x^3 - 7 x^2 + 3 x - 7 = 0
Hint: | Look for a simple substitution that eliminates the quadratic term of 20 x^3 - 7 x^2 + 3 x - 7.
Eliminate the quadratic term by substituting y = x - 7/60:
-7 + 3 (y + 7/60) - 7 (y + 7/60)^2 + 20 (y + 7/60)^3 = 0
Hint: | Write the cubic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
20 y^3 + (131 y)/60 - 36253/5400 = 0
Hint: | Write the cubic equation in standard form.
Divide both sides by 20:
y^3 + (131 y)/1200 - 36253/108000 = 0
Hint: | Perform the substitution y = z + λ/z.
Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:
-36253/108000 + (131 (z + λ/z))/1200 + (z + λ/z)^3 = 0
Hint: | Transform the rational equation into a polynomial equation.
Multiply both sides by z^3 and collect in terms of z:
z^6 + z^4 (3 λ + 131/1200) - (36253 z^3)/108000 + z^2 (3 λ^2 + (131 λ)/1200) + λ^3 = 0
Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.
Substitute λ = -131/3600 and then u = z^3, yielding a quadratic equation in the variable u:
u^2 - (36253 u)/108000 - 2248091/46656000000 = 0
Hint: | Solve for u.
Find the positive solution to the quadratic equation:
u = (36253 + 30 sqrt(1462809))/216000
Hint: | Perform back substitution on u = (36253 + 30 sqrt(1462809))/216000.
Substitute back for u = z^3:
z^3 = (36253 + 30 sqrt(1462809))/216000
Hint: | Take the cube root of both sides.
Taking cube roots gives 1/60 (36253 + 30 sqrt(1462809))^(1/3) times the third roots of unity:
z = 1/60 (36253 + 30 sqrt(1462809))^(1/3) or z = -1/60 (-36253 - 30 sqrt(1462809))^(1/3) or z = 1/60 (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)
Hint: | Perform back substitution with y = z - 131/(3600 z).
Substitute each value of z into y = z - 131/(3600 z):
y = 1/60 (30 sqrt(1462809) + 36253)^(1/3) - 131/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = -1/60 (-30 sqrt(1462809) - 36253)^(1/3) - (131 (-1)^(2/3))/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = 131/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + 1/60 (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3)
Hint: | Simplify each solution.
Bring each solution to a common denominator and simplify:
y = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (36253 + 30 sqrt(1462809))^(1/3)) or y = -1/60 (-1/(36253 + 30 sqrt(1462809)))^(1/3) ((30 sqrt(1462809) + 36253)^(2/3) + 131 (-1)^(1/3)) or y = 1/60 (131 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3))
Hint: | Perform back substitution on the three roots.
Substitute back for x = y + 7/60:
Answer: x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60
i need help on this, i don’t understand it.
Answer:
D
Step-by-step explanation:
From law of indices,( X^3)^2= x^3×2=x^6
Then the other one, also from law of indices, square
root of 5 is the same as 5 raised to power 1/2, then we multiply the powers, that will give us 5 and we have our complete expression which is x^6-5
Find the average value of the function y = 6 - x2 over the interval [-1, 4]
Answer:
The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].
Step-by-step explanation:
The average value of a function over an interval is represented by this integral:
[tex]\bar y = \frac{1}{b-a}\cdot \int\limits^{b}_{a} {f(x)} \, dx[/tex]
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds of the interval, dimensionless.
[tex]f(x)[/tex] - Function, dimensionless.
If [tex]a = -1[/tex], [tex]b = 4[/tex] and [tex]f(x) = 6 - x^{2}[/tex], the average value of the function is:
[tex]\bar y = \frac{1}{4-(-1)}\int\limits^{4}_{-1} {6-x^{2}} \, dx[/tex]
[tex]\bar y = \frac{6}{5}\int\limits^{4}_{-1} \, dx - \frac{1}{5}\int\limits^{4}_{-1} {x^{2}} \, dx[/tex]
[tex]\bar y = \frac{6}{5}\cdot x |_{-1}^{4} - \frac{1}{15}\cdot x^{3}|_{-1}^{4}[/tex]
[tex]\bar y = \frac{6}{5}\cdot [4-(-1)]- \frac{1}{15}\cdot [4^{3}-(-1)^{3}][/tex]
[tex]\bar y = \frac{5}{3}[/tex]
The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].
please help square root math
Answer:
2<∛13<3 1<∛6<2
Step-by-step explanation:
Lets find the integers a and b ∛13 lies between.
a<∛13<b
a³<13<b³
=> a=2 so 2³=8 and b=3 so 3³=27 8<13<27
Similarly a<∛6<b
a³<6<b³
a=1 and b=2
B is the midpoint of AC. Find the coordinates of C. B(-3,-3) and A(-1,-1)
Step-by-step explanation:
Let coordinates of B be ( x , y )
X coordinate of B = (-1 + x) / 2 = - 3
Y coordinate of B = (-1 + y) / 2 = -3
Therefore, coordinates of B are ( - 5, - 5 ).
is ray AB same as ray BA?
Answer:
Yes
Step-by-step explanation:
Because a - - - - - - - - - - b
Same as b-----------------a
If a=mg-kv2/m,find,correct to the nearest whole number the value of v when a=2.8,m=12,g=9.8 and k=8/3
Answer:
The value of [tex]v[/tex] is ± 22.729.
Step-by-step explanation:
Let be [tex]a=m\cdot g -\frac{k\cdot v^{2}}{m}[/tex], the variable [tex]v[/tex] is now cleared:
[tex]\frac{k\cdot v^{2}}{m}=m\cdot g -a[/tex]
[tex]k\cdot v^{2} = m^{2}\cdot g- m\cdot a[/tex]
[tex]v^{2} = \frac{m^{2}\cdot g - m\cdot a}{k}[/tex]
[tex]v =\pm \sqrt{\frac{m^{2}\cdot g-m\cdot a}{k} }[/tex]
If [tex]a = 2.8[/tex], [tex]m=12[/tex], [tex]g = 9.8[/tex] and [tex]k = \frac{8}{3}[/tex], the value of [tex]v[/tex] is:
[tex]v=\pm \sqrt{\frac{(12)^{2}\cdot (9.8)-(12)\cdot (2.8)}{\frac{8}{3} } }[/tex]
[tex]v \approx \pm 22.729[/tex]
The value of [tex]v[/tex] is ± 22.729.
solve for n: 2n+3=-3.2
Answer:
2n+3=3.2
2n=3.2-3
2n=0.2
n=0.2/2
n=0.1
The solution of the given equation for n will be -3.1.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
2n + 3 = -3.2
2n = -3.2 - 3
n = -6.2/2
n = -3.1
Hence "The solution of the given equation for n will be -3.1".
For more about the equation,
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Solve for x.
x + 3x + 5 =21
Answer:
x=4
Step-by-step explanation:
In order to solve for x, we must isolate x on one side of the equation.
x+3x+5=21
First, combine like terms. x and 3x are both terms with variables, and can be combined.
(x+3x) + 5=21
4x + 5=21
5 is being added to 4x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.
4x+5-5= 21-5
4x= 16
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.
4x/4=16/4
x= 16/4
x=4
Let's check our solution. Plug 4 in for x and solve.
x+3x+5=21
4+3(4)+5=21
4+12+5=21
16+5=21
21=21
This solution checks out, so we know our answer is correct.
x is equal to 4, x=4.
Answer:
x = 4
Step-by-step explanation:
x + 3x + 5 = 21
4x + 5 = 21
4x = 21 - 5
4x = 16
x = 16/4
x = 4
verify:
4 + 3*4 + 5 = 21
4 + 12 + 5 = 21
Hitomi, Ben, and Gayle bought 3 pumpkins that weighed 15 pounds altogether. Ben and
Gayle's pumpkins each weighed the same amount.
Hitomis pumpkin weighed pounds. How much did Gayle's pumpkin weigh?
Answer:
5
Step-by-step explanation:
15/3=5 when the y are 3 it division
Answer:
What the other guy said
Step-by-step explanation:
A triangle has vertices at (−4,−6),(3,3),(7,2). Rounded to two decimal places, which of the following is the closest approximation of the perimeter of the triangle?
19.34
29.12
12.36
15.52
The answer is
29.12
hope this helps
HELP ME WITH THIS ONE PLEASE ✊
(The problem is in the picture)
Answer/Step-by-step explanation:
Length of rectangle = [tex] l [/tex]
Width of rectangle = [tex] \frac{1}{3} of l - 1 = \frac{1}{3}l - 1 = \frac{l}{3} - 1 [/tex]
A. Expression for finding area of the rectangle:
Area of rectangle is given as [tex] length*width [/tex]
[tex] Area = l(\frac{l}{3} - 1) [/tex]
Or
[tex] Area = l*\frac{l}{3} - l*1 [/tex]
[tex] Area = \frac{l^2}{3} - l [/tex]
b. Expression for finding perimeter:
Perimeter of rectangle is given as [tex] 2(Length + Width) [/tex]
[tex] Perimeter = 2(l + (\frac{l}{3} - 1)) [/tex]
Or
[tex] Perimeter = 2(l) + 2(\frac{l}{3} - 1) [/tex]
[tex] Perimeter = 2l + \frac{2l}{3} - 2) [/tex]
c. Quotient of Perimeter divided by area:
[tex] 2(l + (\frac{l}{3} - 1)) [/tex] ÷ [tex] l(\frac{l}{3} - 1) [/tex]
[tex]2(l + (\frac{l}{3} - 1))[/tex] ÷ [tex]\frac{l^2 - 3l}{3}[/tex]
Change the ÷ to × and flip the fraction on your right upside down.
[tex]2(l + (\frac{l}{3} - 1)) * \frac{3}{l^2 - 3l}[/tex]
[tex]2l + 2(\frac{l}{3} - 1) * \frac{3}{l^2 - 3l}[/tex]
Use _________ to isolate the variable. A reciprocals B subtraction C an expression D inverse operations
For example, let's say we had the equation x+10 = 30
We are adding 10 onto some unknown number x to get 30. To find x, we undo what is happening to x, so we subtract 10 from both sides. Subtraction is the inverse operation of addition.
Answer:
d, i took the test i can confirm its correct lol
Step-by-step explanation:
15. Jim had 103 red and blue marbles. After giving of his blue marbles and 15 of his red marbles
to Samantha, Jim had as many red marbles as blue marbles. How many blue marbles did he
originally have?

This question above is incomplete
Complete Question
Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?
Answer:
70 Blue marbles
Step-by-step explanation:
Let red marbles = R
Blue marbles = B
Step 1
Jim had 103 red and blue marbles.
R + B = 103.......Equation 1
R = 103 - B
Step 2
After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles
2/5 of B to Samantha
Jim has = B - 2/5B = 3/5B left
He also gave 15 red marbles to Samantha
= R - 15
The ratio of what Jim has left
= Red: Blue
= 3:7
= 3/7
Hence,
R - 15/(3/5)B = 3/7
Cross Multiply
7(R - 15) = 3(3/5B)
7R - 105 = 3(3B/5)
7R - 105 = 9B/5
Cross Multiply
5(7R - 105) = 9B
35R - 525 = 9B............ Equation 2
From Equation 1, we substitute 103 - B for R in Equation 2
35(103 - B) - 525 = 9B
3605 - 35B - 525 = 9B
Collect like terms
3605 - 525 = 9B + 35B
3080 = 44B
B = 3080/44
B = 70
Therefore, Jim originally had 70 Blue marbles.
What is the probability of drawing a spade or a jack from a standard deck of 52 cards?
Answer:
4/13
Step-by-step explanation:
There are 4 jacks in the deck and 13 spades. However 1 jack is a spade so we have a total of 16 cards which are either a jack or a spade. Therefore there are (13 + 4 - 1)/52 cards which are not a jack or a spade. Divided 16/52, thus the probability is 4/13.
The probability of drawing a spade or a jack from a standard deck of 52 cards is;
P(drawing either a spade or jack) = 4/13
We are told that the standard deck of cards has 52 cards.
Thus;
N = 52
Now,in a pack of cards there are usually 4 Jacks and 13 spades.
However, among the 4 Jacks, 1 of them is a spade. This means that 1 card will be both a spade and a jack. Thus,
Possible number of Jack's and spades = 13 + 4 - 1 = 16
Thus;
P(drawing either a spade or jack) = 16/52 = 4/13
Read more at; https://brainly.com/question/20971273
Match the parent function name with the equation. Linear Quadratic Radical Absolute Value Rational Exponential Log Cubic Cube Root
Step-by-step explanation: The correct graph is #6. Cubic Function
The given graph shows the cigarette consumption (in billions) in the United States for the years 1900 to
2007
Choose the best estimate for the number of cigarettes smoked in 2000.
420 billion
Qi 400 billion
380 billion
450 billion
Answer:
The answer is below
Step-by-step explanation:
The graph used to estimate the consumption (in billions) in the United States for the years 1900 to 2007 is attached.
The year is plotted on the x axis and the number of cigarettes is on the y axis. To estimate the number of cigarattes smoked in year 2000, we have to find the y coordinate that corresponds to an x coordinate of 2000. This is done by drawing a line vertically to touch the graph from the point 2000 on the x axis. The point it touches the graph is then traced to the y axis to get the consumption as shown in the graph attached.
From the graph the number of cigarettes smoked in 2000 is about 420 billion cigarettes
Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?
X: 1,3,5
——————
G(X): 0,4,8
A)The function f(x) has a higher y-intercept
B)The function gx has a higher y intercept
C) They both have the same y intercept
D) The relationship between y intercepts cannot be determined
Answer: D) relationship between y intercepts cannot be determined
The graph of f(x) is a vertical line. It is completely parallel to the y axis, so it never crosses the y axis. We need the graph to cross the y axis somewhere in order to form a y intercept. Therefore f(x) does not have a y intercept. So we cannot compare y intercepts if f(x) doesn't have one at all.