6. Solve the system of equations.
x = 3y + 1
2x+4y= 12
O (10,3)
O (4,1)
(1,4)
(3,10)
Answer:
(4, 1 )
Step-by-step explanation:
x = 3y + 1 → (1)
2x + 4y = 12 → (2)
substitute x = 3y + 1 into (2)
2(3y + 1) + 4y = 12
6y + 2 + 4y = 12
10y + 2 = 12 ( subtract 2 from both sides )
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3(1) + 1 = 3 + 1 = 4
solution is (4, 1 )
What is the directrix of a parabola whose equation is (y+3)^3=8(x-3)?
Considering the equation of the parabola, the directrix is: x = 1.
What is the equation of a parabola given it’s vertex?The equation of an horizontal parabola, of vertex (h,k), is given by:
(y - k)² = 4p(x - h).
The directrix is at x = h - p.
For this problem, the equation is:
(y + 3)² = 8(x - 3).
The relevant coefficients for this problem are:
4p = 8 -> p = 2, h = 3.
Hence the directrix is:
x = h - p = 3 - 2 = 1.
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The equation of the parabola whose equation [tex](y + 3)^3 = 8(x - 3).[/tex], the directrix exists x = 1.
What is the equation of a parabola given its vertex?The equation of a horizontal parabola, of vertex (h, k), exists given by:
(y - k)² = 4p(x - h).
The directrix exists at x = h - p.
For this problem, the equation exists:
[tex](y + 3)^3 = 8(x - 3).[/tex]
The appropriate coefficients for this problem exist:
4p = 8
p = 8/4 = 2 and h = 3.
Hence the directrix exists:
x = h - p = 3 - 2 = 1.
Therefore, the directrix exists at x = 1.
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While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
How to estimate the speed of the moving walkway relative to the airport terminal?Let x be the speed of the walkway.
(2.8 + x) = speed of child moving in direction of the walkway
(2.8 - x) = speed of child moving against the direction of the walkway
Travel time = distance/speed
Travel time of child moving in direction of walkway = 23/(2.8+x)
Total elapsed time given = 29s
23/(2.8 + x)+ 23 / (2.8-x) = 29
LCD = (2.8 + x)(2.8 - x)
[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]
simplifying the equation, we get
[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]
[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]
[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]
[tex]x=\sqrt{3.4}=1.84m/s[/tex]
Speed of walkway = 1.84 m/s
The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.
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Find the slope when y2=9, y1=13, x2=4, and x1=0.
Answer:
Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32
Answer: slope=-1
Step-by-step explanation:
9-13 -4
------ --------- -4/4=-1
4-0 4
A group of 15 teenagers owes $75 at a pizza parlor. If they split the bill evenly, how much will each person owe?
Answer:
$5 each teenager
Step-by-step explanation:
divide 75 by 15
Building managers recently surveyed employees of three different companies regarding their method of transportation to work day. The results of the survey are shown in the two-way frequency table below.
Car Bus Walk Bike Subway Total
Tech company 10 16 14 38 20 98
Law firm 27 8 10 2 26 73
Finance group 18 22 12 8 34 94
Total 55 46 36 48 80 256
Which Conclusion can the building managers draw based on this data?
A: It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
B: Walking to work is more common among employees at the finance group than employees at the law firm.
C: The percentage of walkers who are employers at the law firm is the same as the percentage of car drivers who are employees at the tech company.
D: Riding to work is more common among tech company employees than at the other modes of transportation.
The conclusion that the building managers can draw based on the given data is; D: Riding to work is more common among tech company employees than at the other modes of transportation.
How to Interpret Data Tables?The results of the survey are shown in the two-way frequency table below.
From the table we can see that;
Total Cars = 55
Total Number of Buses = 46
Total Number of Walks = 36
Total Number of Bikes = 48
Total Number of Subways = 80
Total Number of Tech company = 98
Total Number of Law Firms = 73
Total Number of Finance Groups = 94
Option A; There are 16 people who use buses from the tech company while there are 26 people who use subway from the Law firm. Thus, the statement is false.
Option B; There are 12 people who walk to work at the finance group while there are a total of 10 people who walk to work at the law firm. Thus the statement is false.
Option C; Percentage of walkers at law firm = 10/73 * 100% = 13.7%
Percentage of car drivers at the tech firm = 10/98 * 100% = 10.2%
Thus, the statement is false
Option D; This is true
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Answer:
It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.
Step-by-step explanation:
got it right on edmentum
You purchase one microsoft july $72 put contract for a premium of $1. 32. what is your maximum possible profit?
The maximum possible profit = $7068
For given question,
One Microsoft July $72 put contract for a premium of $1.32
The payoff arise from put option is max (K - S, 0) - P
Now it would be maximum at S = 0
And, the maximum payoff is
K - 0 - P
= K - P
= 72 - 1.32
= $70.68
We assume that for each and every contract the number of shares is 100
So, the maximum profit gained from this strategy is
= $70.68 × 100 shares
= $7068
The maximum profit that will be gained from this strategy is $7068
Therefore, the maximum possible profit = $7068
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what is 4^-2. ................................
Answer:0.0625
Step-by-step explanation:
Answer:
1/16.
Step-by-step explanation:
4 ^-2 = 1 / 4^2
= 1/16.
Solve the following quadratic equation for all values of a in simplest form.
5(x − 6)² — 29 = −19
Answer:
[tex]X1 = 6-\sqrt{2} , X2 = 6+\sqrt{2}[/tex]
Step-by-step explanation:
Answer: x= √2 + 6, - √2 + 6
Step-by-step explanation:
X
3.
What is the value of x to the nearest tenth?
6
24
Answer:
C. 13.4=======================
Connect the center with one end of the chord, this gives us a right triangle with hypotenuse of x, one leg of 6 and another leg of 24/2 = 12.
Use Pythagorean to find the value of x:
x² = 6² + 12²x² = 36 + 144x² = 180x = √180x = 13.4 (rounded)Correct choice is C.
Answer:
x = 13.4
Step-by-step explanation:
Definitions
Radius: a straight line from the center of the circle to its circumference.
Chord: a straight line joining two points on the circle.
Perpendicular: at a right angle (90°).
Isosceles triangle: a triangle with 2 sides of equal length and 2 congruent base angles.
From inspection of the given diagram:
radius = xchord = 24 unitssegment of the radius perpendicular to the chord = 6 unitsIf lines are drawn from the center of the circle to the endpoints of the chord, an isosceles triangle is created with base of 24 units and height of 6 units.
The isosceles triangle is made up of two right triangles with base of 12 units and height of 6 units. The radii are the hypotenuse of these right triangles. Therefore, to calculate the radius of the circle (x), use Pythagoras Theorem.
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleTherefore:
[tex]\sf \implies 6^2+12^2=x^2[/tex]
[tex]\implies \sf x^2=36+144[/tex]
[tex]\implies \sf x^2=180[/tex]
[tex]\implies \sf \sqrt{x^2}=\sqrt{180}[/tex]
[tex]\implies \sf x=\pm 6\sqrt{5}[/tex]
As length is positive:
[tex]\implies \sf x = 6\sqrt{5}=13.4\:units\:(nearest\:tenth)[/tex]
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Two circles are shown in the diagram.
Circles C 1 and C 2 are shown. The diameter of circle 1 is 1. The diameter of circle 2 is 2 r.
Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion.
StartFraction C 1 Over d 1 EndFraction = StartFraction C 2 Over d 2 EndFraction
Which shows how to correctly solve for C2, the circumference of any circle with radius r?
Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = 2 r pi
Because StartFraction 1 Over pi EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = StartFraction 2 r Over pi EndFraction
Because StartFraction pi Over 2 r EndFraction = StartFraction C 2 Over 1 EndFraction , C 2 = StartFraction pi Over 2 r EndFraction
Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 4 r EndFraction , C 2 = 4 r pi
The correct equation is (a) because π/1 = C2/r2, [tex]C_2= 2\pi r[/tex]
How to determine the correct equation?The complete question is added as an attachment
The given parameters are:
d1 = 1
d2 = 2r
The circumferences of the circles are calculated as:
C = πd
This gives
C1 = π * 1 = π
C2 = π * 2r = 2πr
So, we have:
C1 = π
C2 = 2πr
and
d1 = 1
d2 = 2r
Divide both equations
[tex]\frac{C_2}{d_1} = \frac{C_2}{d_2}[/tex]
[tex]\frac{\pi}{1} = \frac{2\pi r}{2r}[/tex]
This gives
[tex]\frac{\pi}{1} = \frac{C_2}{2r}[/tex]
Hence, the correct equation is (a) because π/1 = C2/r2, [tex]C_2= 2\pi r[/tex]
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Answer:
Its A
Step-by-step explanation:
Consider the incomplete paragraph proof.
Because triangle XYZ is a right triangle, the side lengths
Given: Isosceles right triangle XYZ (45°-45°-90°
must satisfy the Pythagorean theorem, a? + b2 c2
triangle)
which in this isosceles triangle becomes a2 + a? = c?. By
Prove: In a 45°-45°-90° triangle, the hypotenuse is V2
combining like terms, 2a? c2.
times the length of each leg.
Which final step will prove that the length of the
hypotenuse, c, is /2 times the length of each leg?
• Substitute values for and c into the original
Pythagorean theorem equation.
O Divide both sides of the equation by two, then
determine the principal square root of both sides of the
equation.
Determine the principal square root of both sides of
the equation.
O Divide both sides of the equation by 2.
The hypotenuse is [tex]c = a\sqrt{2}[/tex] times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes and this can be evaluated by using properties of isosceles triangle.
According to the statement
we have given that a theorem and we have to prove it.
So, For this purpose,
The given information is :
Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]
Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.
Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.
Now use Pythagoras theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
But here a= b then the equation become
[tex]a^{2} + a^{2} = c^{2}[/tex]
Then after solving it become
[tex]2a^{2} = c^{2}[/tex]
And here we have to find the value of the hypotenuse,
so we solve it for c.
Then
[tex]c = a\sqrt{2}[/tex]
From this it is clear that the
it can be concluded that the hypotenuse is times the length of each leg 'a'.
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There are 3 red, 1 blue, and 2 yellow marbles in a bag. Once a marble is selected, it is not replaced. Find P(red and the yellow).
Answer:
5/6
Step-by-step explanation:
we add all the marbles together to get 6
then we seperate the marbles according to the question which would be yellow and red. that would make the probability of getting one of those to 5/6. Hope this helps :)
What steps do you use to solve y=x+12 and y=-x+17 an unknown number y is 12 more than an u known number x the number y is also x less than 17 the equations to find x and y are show
Answer:
x=2.5
Step-by-step explanation:
Solve for x in this systems of equations, we already have two values which equal y so half the work is finished for us.
Starting with the equation:
[tex]x+12=17-x[/tex]
Add x to both sides to remove the negative x on the right side of the equation:
[tex]2x+12=17[/tex]
Subtract 12 from both sides to remove the 12 on the left side of the equation:
[tex]2x=5[/tex]
Divide both sides by 2 to cancel out the x coefficient
[tex]x=2.5[/tex]
What is the image point of (-1, -8) after
the transformation ry=-x T4,-5?
Answer:
sheu7euw73u3hsusuuwueudhdhdhsjsjwiwuwuehehdggdhdue
Step-by-step explanation:
hzhsusududjdndjdhehhshshhdhdhdhdhdhdhdhdhbhdhdhhdhdhdudxbdhdhdhdhhshdhyehsuehduwhgduwhdydh
Carrie spent
1
4
of her allowance on a shirt,
1
3
of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Answer:
24 dollars.
Step-by-step explanation:
1/4 + 1/3 = 3/12 + 4/12 = 7/12
7/12 a + 8 = 22
7/12 a = 14
a = 14 x 12/7
a = 24
A choir has 3 spots open for altos, and 8 altos are interested in them. in how many ways can the open spots be filled? 24 56 112 336
Answer:
56
Step-by-step explanation:
combinations
C(8,3)
Help!! PLSS
what can be to total of 100% if divided by four percentage?
__%
__%
__%
__%
=100%
Step-by-step explanation:
I am not sure I understand your question (grammatically).
percentages are like any other numbers. they can be added, divided, ...
so, 100% or simply 100 : 100/4 = 25.
so, 4×25 = 100.
and 4×25% = 100%
I am really not sure if this is your question, but it fits to your table with 4 entries and 100% as result.
What is the euclidean distance between x(3,2,5) and y(2,3,3) in three dimensional space?
a) 4
b) 2. 45
c) 3
d) 1. 5
Answer:
b) 2.45
Step-by-step explanation:
The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.
ApplicationFor the given points ...
[tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]
The distance between x and y is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]
10x(4-3x) pls someone help???
Answer: [tex]\Large\boxed{-30x^2+40x}[/tex]
Step-by-step explanation:
Given expression
10x (4 - 3x)
Expand the parenthesis by distributive property
= 10x · 4 - 10x · 3x
= (10 × 4)x - (10 × 3) (x × x)
[tex]\Large\boxed{=-30x^2+40x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Hi :)
We'll use distributive property to solve this
————————[tex]\LARGE\boldsymbol{10x(\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}4-\hfill\stackrel{\hfill\stackrel{10x}\curvearrowright}{3x)}}}[/tex]
Thus
[tex]\large\boldsymbol{10x\cdot4-3x\cdot10x}[/tex]
Simplify
[tex]\Large\boldsymbol{40x-30x^2}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
What is the next term in the geometric sequence below?
3, -6, 12, -24, __, ...
A. 36
B. -48
C. -36
D. 48
Answer:
48
Step-by-step explanation:
48 because you are multiplying it by -2 each time. -24 x -2 = 48
Solve for n.
7 + 2n
||
=
submit
Answer:
2
Step-by-step explanation:
7+2n = 11
2n = 11-7
2n = 4
n = 4/2
therefore n = 2
piecewise function f (x) is defined by f of x is equal to the piecewise function of 3 to the power of the quantity x minus 1 end quantity minus 4 for x is less than or equal to 3 and the quantity negative x squared plus 3 times x plus 4 end quantity over the quantity x squared minus 7 times x plus 12 end quantity for x is greater than 3 Part A: Graph the piecewise function f (x) and determine the range. (5 points) Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points) Part C: Describe the end behavior of f (x). (5 points)
The range of the function f(x) is (-∝, 3]
Part A: Graph the piecewise functionThe function definition is given as:
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
There are two sub-functions and the domains in the above definition.
Each function would be plotted alongside its domain.
See attachment for the graph of the function f(x)
From the graph of the function, we have the following range of f(x)
Minimum = Negative Infinity
Maximum = 5
Hence, the range of the function f(x) is (-∝, 3]
The asymptotes of f(x)We have the domains to be
x <= 3 and x > 3
This means that the asymptote of f(x) is x = 3
The end behavior of f(x)From the graph, we have:
f(x) increases as x increasesf(x) decreases as x decreasesThis means that the end behavior of f(x) is as x approaches +∝, the function approaches +∝ and as x approaches -∝, the function approaches -∝
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Complete question
A piecewise function f (x) is defined by
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices.
Josiah’s Music
Sample 1
Sample 2
R & B
5
R & B
4
Pop
4
Pop
3
Classical
3
Classical
5
Jazz
2
Jazz
4
Rock
6
Rock
4
Josiah’s work:
StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x.
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
He did not multiply the numerator and denominator by the correct number to equal 1,500.
His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion.
He can only solve the proportion by multiplying the numerator and denominator by a common multiple.
He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.He did not multiply the numerator and denominator by the correct number to equal 1,500.He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.What did Josiah do wrong?To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:
= (4 + 6) / 2
= 5
Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.
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A cell's expected frequency is: Group of answer choices the number of people in the cell's row multiplied by the number of people in the column the number of people in its column divided by the total number of people, divided by the row proportion the number of people in its row multiplied by the number in its column divided by the total number of people the number of people in the cell's row divided by the number of people in the column
A cell's expected frequency can be defined as the number of people in its row divided by the total number of people, multiplied by the number in its column and is therefore denoted as option C.
What is Frequency?This is defined as the number of occurrences of a repeating which takes place per unit time.It also helps to measure how frequent something occurs when counted or observed and is also used in the calculation of the different types of statistical data present or given.
This type of frequency is theoretical and are values which will most likely be in an experiment. it is calculated by multiplying the number in its column by the number of people in the row and dividing by the total number of people in this context.
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If the graph of a budget function has an x-intercept at 2 and the y-intercept at 5, name two ordered pairs that would fall on this line.
(2, 0) (0, 5)
(0, 2) (5, 0)
(2, 0) (2, 5)
(0, 2) (2, 5)
Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).
What points fall on this line?The x-intercept is the point on the graph where the budget function would cross the x-intercept.
At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.
An x-intercept of 2 would therefore have the point, (2,0).
The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.
A y-intercept of 5 would therefore yield a point of (0, 5).
In conclusion, option A is correct.
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LK=
Help please asap thx so much
Answer:
LK = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
given point J (4, 4 )
then LJ = 4 and JK = 4
using Pythagoras' identity in right triangle LJK
LK² = LJ² + JK² = 4² + 4² = 16 + 16 = 32 ( take square root of both sides )
LK = [tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex]
Last one for the night lol thanks again
Answer:
[tex]BC=24[/tex]
Step-by-step explanation:
We know that in an isosceles triangle if two angles are congruent then the opposite sides of the angle must also be congruent.
Therefore [tex]AC=AB[/tex]
Then we can create an equation and solve for x
[tex]x+8=2x-1\\x+9=2x\\9=x[/tex]
Now that we have x we just need to substitute it for [tex]BC[/tex]
[tex]BC=3x-3\\BC=3(9)-3\\BC=27-3\\BC=24[/tex]
A sample is selected from a population with a mean of μ = 65 and a standard deviation of σ = 15. if the sample has n = 9 scores, what are the expected value of m and the standard error of m?
The Expected value of M is 65
The Standard error of M is 5
The mean of the distribution of sample means is called the expected value of M.The standard deviation of the distribution of sample means is called the standard error of M.Given,
The sample score, n = 9
The Standard deviation, σ = 15
Population mean, μ = 65
Then,
The Expected value of M = μ
∴ The Expected value of M = 65
The Standard error of M = σ/[tex]\sqrt{n}[/tex]
[tex]=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5[/tex]
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ts
The table below represents the concessions sold at the last three basketball games. The
games were held on different days and times.
Friday night
Saturday morning
Tuesday night
Total
Candy Hot Dogs
148
94
78
320
102
27
150
279
Nachos
108
42
97
247
Total
358
163
325
846
What is the approximately probability of a person going to a Saturday morning game and
buying nachos?
The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.
What does approximate mean?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. An estimated result can be obtained by rounding the values in a computation before carrying out the procedures.The word type "approximately" is an adverb.A value that is close to, higher than, as close to, and with the specified level of precision is known as an approximation value by the excess of a number.Approximately symbol ≈.The approximately probability of a person going to a Saturday morning game and buying nachos:
Probabaility= [tex]\frac{150}{846} *100[/tex]
=17.7%
Approximately=18%.
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