Step-by-step explanation:
x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Cube root of x^3 is x.
Cube root of 8 is 2
So
a=x
b= 2.
[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]
Set these equations equal to zero
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
[tex] {x}^{2} - 2x + 4 = 0[/tex]
If we do the discriminant, we get a negative answer so we would have two imaginary solutions,
Thus the only real root is 2.
If you want imaginary solutions, apply the quadratic formula.
[tex]1 + i \sqrt{ 3 } [/tex]
and
[tex]1 - i \sqrt{3} [/tex]
question is attachment
The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]
To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.
It is given by the formula:
[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]
We have that the mean of the values is:
at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]
at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]
Using the above definitions we have that
at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]
at 12 AM
[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]
In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.
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i needs help with it
Answer:
a) initial height = 0 m
b) 8 s
c) vertex = (4, 32)
maximum height = 32 m
Step-by-step explanation:
Given equation:
[tex]h=-2t^2+16t[/tex]
where:
h is the height of the arrow about the ground (in metres)t is the time (in seconds)Part (a)The initial height of the arrow will be at the beginning of its journey, so when t = 0
Substitute t = 0 into the equation and solve for h:
[tex]\implies h=-2(0)^2+16(0)[/tex]
[tex]\implies h=0[/tex]
Therefore, the initial height of the arrow is 0 m.
Part (b)The arrow will hit the ground when the height is 0 m.
Substitute h = 0 into the given equation:
[tex]\implies -2t^2+16t=0[/tex]
Factor out -2t:
[tex]\implies -2t(t-8)=0[/tex]
Therefore:
[tex]\implies -2t=0 \implies t=0[/tex]
And:
[tex]\implies t-8=0 \implies t=8[/tex]
Therefore, the arrow will hit the ground at 8 seconds.
Part (c)The vertex is the turning point of a parabola - it's minimum or maximum point.
As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.
There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.
We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4
To find the y-coordinate, substitute t = 4 into the equation and solve for h:
[tex]\implies h=-2(4)^2+16(4)[/tex]
[tex]\implies h=-32+64[/tex]
[tex]\implies h=32[/tex]
Therefore, the coordinates of the vertex are (4, 32)
The maximum height is the y-coordinate of the vertex.
Therefore, the maximum height is 32 m
190 divided by 2 over 3
Eduardo and his friends want to start a band, so he decides to take guitar lessons. He purchases a 6-lesson package at Sharp Notes music store, which comes out to $22.50 per lesson.
Question 1 of 6
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 23 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
Answer:
They could make at most 5 teams and its not possible to make everyone on team.
Step-by-step explanation:
If there are 4 players on a team, then we use 23 ÷ 4 = 5.75, 0.75 is not enough for 1, so there are 3 players remaining after making 5 teams.
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³
Answer:
V = (s^3)/6 (Answer B )
Step-by-step explanation:
If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.
The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).
In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6 (Answer B)
According to the U.S. Census Bureau, the mean of the commute time to work for a resident of CA is 21.5 minutes. Assume that the standard deviation of the commute time is 4.8 minutes to complete parts (a) through (c).
Part 1
(a) What minimum percentage of commuters in has a commute time within standard deviations of the mean?
enter your response here%
(Round to one decimal place as needed.)
Using Chebyshev's Theorem, the minimum percentage of commuters in has a commute time within 2 standard deviations of the mean is of 75%.
What does Chebyshev’s Theorem state?When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].Hence, the minimum percentage of commuters in has a commute time within 2 standard deviations of the mean is of 75%.
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Help please I need it asap and thank you
Answer: 2.5
Step-by-step explanation:
The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.
Over which interval is the graph of the parent absolute value function decreasing?
(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)
The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
What is the parent absolute value function?An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.
The absolute value function is f(x) = |x| is defined as,
f(x )
x = x < x = 0 < x = -x
Observe that the graph is V-shaped.
The vertex of the graph is (0,0).
The domain is the set of all real numbers.
The x-intercept and the y-intercept are both 0.
Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
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What is the lowest value of the range of the function
shown on the graph?
O -∞
O -2
0 0
03
The question is incomplete. Below you will find the missing graph.
The lowest value of the range of the function shown on graph is (B) -2.
A graph is the pictorial representation of the function or mathematical relation (Equation or Inequality etc).
The lowest value of the graph is the value of y when y=f(x) gives the least value.
From the given graph we can clearly see that at x=3 the graph of the given function approaches the least value which is -2.
So the lowest value of the range of the function shown on the graph is -2.
Hence the correct option is (B).
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Match each value on the left with the number on the right that includes that value.
The graph shown below expresses a radical function that can be written in the form F(x) = a(x+ k)^1/n+ C. What does the graph tell you about the value of a in this function?
For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.
Given the value of function F(x)=[tex]a(x+k)^{1/n}+C[/tex].
We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :
a[tex](x+k)^{1/n}[/tex]+C=0
a[tex](x+k)^{1/n}[/tex]=-C
a=-C/[tex](x+k)^{1/n}[/tex]
Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.
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Select the graph that represents the correct answer to the equation.
5y = 3x - 5
Given:
The given equation is 5y=3x-5
Find: Draw the graph
Explanation:
It is given that 5y=3x-5. Substitute x=0 into the given equation we have
[tex]5y = 3x - 5[/tex]
[tex]5y = 3(0) - 5[/tex]
[tex]5y = - 5[/tex]
[tex]y=-1[/tex]
Now, substitute x=5 into the given
equation we have
[tex]5y = 3(5)-5[/tex]
[tex]5y = 15-5[/tex]
[tex]5y = 10[/tex]
[tex]y = 2[/tex]
The points are (0,-1) and (5,2).
Therefore, the required graph is
Hence, the required graph is obtained.
Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.
40/(-10) 40/10 40/40 40/(-40)Please refer to the attached picture.
We have a rectangular shape as shown in the picture.
Total number of square units = 40
Each row has 10 units cube.
Each cube = 40/10
Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
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Would it be
A.
B.
C.
D.
Answer:
A. is the answer
PLEASE GIVE STEP BY STEP EXPLANATION !!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The two types of transformations that can be used to transform f(x) to g(x). g (x) = f(x) + 16 and g (x) = f(x + 8)
ABC has vertices at A (12, 8), B (4, 8)
What is the equation about?f(x)= 0, -1 ,5,14
g(x)= -6, -1, -1, 14
g(x)=f(x)+k
-6= 0+k
k= -6
A) g (x) = f(x) + 16 and
g(x) = f(x + 8)
B) g(x)=f(x)+k
-1= -1+ k
k= -1+1=0
g(x)=f(x)+k
-1= 5+k
k= -1-5=-6
g(x)=f(x)+k
14= 14+k
k= 0
k= -6,0,-6,0
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In the figure below, lines I and mare parallel. What is the value of x?
1
(4x13)
X=
m
(2x + 37)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 25°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 4x - 13 = 2x + 37[/tex]
[ Alternate Exterior Angle ]
[tex]\qquad \tt \rightarrow \: 4x - 2x = 37 + 13[/tex]
[tex]\qquad \tt \rightarrow \: 2x = 50[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{50}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = 25 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Mama bear wants to bake a cake with chocolate frosting for her twins birthday party. She uses a package containing 495 grams of coco powder for the frosting. What will be the weight of the chocolate frosting if it is 55% cocoa powder?
The weight of the chocolate frosting if it is 55% cocoa powder will be 272.25 grams.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Mama bear wants to bake a cake with chocolate frosting for her twin's birthday party.
She uses a package containing 495 grams of cocoa powder for the frosting.
Then the weight of the chocolate frosting if it is 55% cocoa powder will be
⇒ 0.55 × 495
⇒ 272.25 grams
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find the slope of the line on the graph write your answer as a whole number or a fraction not a mixed number or decimal
Answer: 3/4
Step-by-step explanation:
in the game of roulette, a player can place a $ 7 bet on the number 28 and have a 1/38 probability of winning. if the metal ball lands on 28, the player gets to keep the $7 paid to play the game and the player is awarded $245. otherwise, the player is awarded nothing and the casino takes the player's $7. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose?
Answer: The player expects to lose 184.21 dollars.
=========================================================
Explanation:
X = net winnings in dollars
Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.
If the player wins, then they walk away with 7+245 = 252 dollars
If the player loses, then their "winnings" is -7
So either X = 252 or X = -7 are the only two options.
Let's form a table showing those options with their corresponding probabilities.
[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]
Now multiply each X value and P(X) value across the rows.
252*(1/38) = 6.631579
-7*(37/38) = -6.815789
These values are approximate.
[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]
Add up the results of the third column
6.631579 + (-6.815789) = -0.18421
This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.
Do this 1000 times and the player should expect to lose about
1000*(0.18421) = 184.21 dollars
Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.
Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21
Which is the domain and range of the parabola with the equation y = 0.5(x2 – 8x – 6)?
D: (–∞, ∞); R: (–∞, –11]
D: (–∞, ∞); R: [–11, ∞)
D: (–∞, –11]; R: (–∞, ∞)
D: [–11, ∞); R: (–∞, ∞)
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.
Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.
This means that the first option must be wrong since the range has a maximum, not a minimum.
Therefore, the correct answer is Option 2.
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.
update I GOT A 100% woop woop
NEED ASAP !!!!!
Which table represents a linear function?
Urgent algebra 2 help needed
Answer:
The area for the trapezoid is
A=h/2(a+b)
A=8/2(10+15)
A=100 cm square
Hope it helps!
find the value of the hypotenuse for each of the following right triangles.
Answer:
I have done the 1st 2 sums in proper systematic manner. The remaining sums I'll be writing only the main formula and substitution. I hope you will write the missing sentences .
Step-by-step explanation:
Hope you will understand the sums..Also I would appreciate it if you could marke my answer as BRAINLIEST and THANK ME.｡◕‿◕｡
Answer:
Step-by-step explanation:
1. hypotenuse = 89
2. hypotenuse = 85
3. hypotenuse = 97
4. hypotenuse = 153
5. hypotenuse = 34
6. hypotenuse = 113
7. hypotenuse = 916
8. hypotenuse = 170
9. hypotenuse = 394
10. hypotenuse = 61
AB and CD intersect at point E if measure angle AED equals 6x-24 and measure angle CEB equals 4y+32 find the values of x and y such that AB is perpendicular to CD
The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
AB and CD intersect at point E.
If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.
Then the values of x and y such that AB is perpendicular to CD will be
6x – 24 = 90
6x = 114
x = 19
Then we have
4y + 32 = 90
4y = 58
y = 14.5
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Two angles are complentary if the sum of their measures is 90 °. Find two complentary angles such that one of the angles is 165° less than 4 times the other angle
Answer:
51° and 39°
Step-by-step explanation:
x + 4x - 165 = 90
5x = 90 + 165
5x = 255
x = 255 / 5
x = 51
4 x 51 = 204
204 - 165 = 39
2 angles are 51 and 39
In a recent year, 17.7% of all registered doctors were female. If there were 54,400 female registered doctors that year, what was the total number of registered doctors?
Answer:
The total number of registered doctors in this year are 307345.
Step-by-step explanation:
Let the total number of doctors who registered in this year are x
Given that the total number of female doctors in total registered doctors are 54400
According to the question 17.7 percent of the total registered doctors are the female doctors
Hence the total number of registered doctors who are females are 17.7% of x
which is written as 17.7*x÷100
According to the question 17.7x÷100= 54400
as we are given that the total number of female doctors are 54400
now
17.7x = 54400×100
x= 54400×100÷17.7
x= 307344.633 ≈ 307345
Therefore there are 307345 doctors who registered that year.
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pls help how do i solve for x in this equation??
Answer:
x = -2
Step-by-step explanation:
1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2
What is the simplified form of this expression? 3x + (8x − 16)
28.6% of city employees ride the bus to work. Last year, 29.7% of city employees rode the bus to work. What is the relative change from last year to this year?
(Express your answer rounded correctly to the nearest tenth of a percent!)
A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.
Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,
Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%
Hence, the relative change from last year to this year is 3.7%.
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