No, [tex]4x^{2} +8=12[/tex] is not a linear equation
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
No, [tex]4x^{2}+8=12\\4x^{2} -4=0[/tex]is not a linear equation because An equation is said to be linear if the maximum power of the variable is consistently 1.
This is a quadratic equation, because quadratic equation has a maximum power of 2.
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The volume of the rectangular prism shown is 612 cubic centimeters. Find the dimensions of the prism.
The dimensions of the rectangular prism are approximately 6 cm (width), 14 cm (height), and 1 cm (length).
To find the dimensions of the rectangular prism with a volume of 612 cubic centimeters, we can use the given expressions for the width, height, and length of the prism and set up an equation based on the volume formula.
The formula for the volume of a rectangular prism is V = length * width * height.
Given:
Width (w) = w cm
Height = w + 8 cm
Length = w - 5 cm
Volume (V) = 612 cubic centimeters
Now, set up the equation using the provided information:
V = (w - 5) * w * (w + 8)
Substitute the volume value:
612 = (w - 5) * w * (w + 8)
Now, we have a cubic equation in terms of w. To find the value of w, we can solve the equation:
w³ + 3w² - 40w - 612 = 0
By factoring or using numerical methods, we find that w ≈ 6. Therefore, the width of the prism is approximately 6 cm.
Now, we can find the height and length using the given expressions:
Height = w + 8 ≈ 6 + 8 ≈ 14 cm
Length = w - 5 ≈ 6 - 5 ≈ 1 cm
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Use the tax table below to answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Consider cases where the number of withholding allowances is less than 6. Which will cause the amount of federal income tax withheld to increase?
a.
Gross pay stays the same and withholding allowances increase.
b.
Gross pay increases by more than $20 and withholding allowances stay the same.
c.
Gross pay increases by more than $20 and withholding allowances increase.
d.
Gross pay decreases by more than $20 and withholding allowances stay the same.
Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
What is the Percentage?A percentage is a relative figure that has the ability to represent 1/100th of any quantity.
Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.
By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.
So, Luce is single and makes $763 twice weekly.
She does not request any compensation from federal withholding.
The value of this amount ranges from $760 to $780.
If we look at the table in the issue, the federal tax for this slab is $86.
Federal taxes now make up 19% of all state taxes.
Hence, the $86 in federal tax at a rate of 19% is:
Tax = 86 * 19/100
Tax = 16.34
Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
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Correct question:
Use the tax table to help answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?
a. $12.92
b. $15.13
c. $15.77
d. $16.34
How much money is pictured below?
Answer:
$1
Step-by-step explanation:
1 quarter: 25 cents
3 nickels: 15 cents
6 dimes: 60 cents
25+15+60= 100 cents, and 100 cents make up exactly 1 dollar.
a box of a dozen donuts contains 5 glazed, 3 blueberry, and 4 chocolate donuts. what is the probability that you randomly choose a chocolate donut from the box? state your answer as a reduced fraction.
A box of a dozen donuts, the probability that you randomly choose a chocolate donut from the box is 1/3 ....
What is Probability?Probability is the study of occurrence of chance of a particular result. It is calculated by ratio of favourable outcomes and the total possible outcomes.
We have box of a dozen donuts contains,
The number of glazed donuts in box = 5
The number of blueberry donuts in box = 3
The number of chocolate donuts in box = 4
So, the total number of donuts = 12
We have to calculate probability that you randomly choose a chocolate donut from the box, say P(X) .
That is one donut is selected randomly from box.
P(X) = Number of favourable cases/ Total number of possible outcomes
= 4/12 = 1/3
Thus, the required probability is 1/3.
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You are planning a trip to an amusement park with a new water slide. It costs $25
for admittance to the park, plus $5 each time you ride the new water slide. Let w
represent the number of times you go down the slide and c represent the total cost
in dollars.
Write the amount that you will spend as a function of the number of times you
ride the new water slide. What is the total cost if you go down the slide 6 times?
Answer
55
Step-by-step explanation:
5w+25= c
5(6)+25=55
it has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. chickens are delivered to grocery stores in crates of 24. assume the chickens are chosen for inclusion in a crate at random. what is the probability that a randomly selected crate has more than 4 contaminated chickens?
Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.
What is the binomial probability distribution formula?
The formula is:
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
Cₙ,ₓ = n!/x!(n-x)!
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
About 30% of frozen chickens are contaminated, hence p=0.3.
Chickens are delivered to grocery stores in crates of 24, hence n=24
The probability that a certain crate has more than 4 contaminated chickens is:
P(X>4)=1-P(X≤4)
In which:
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
Then
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002
P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020
P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097
P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305
P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687
Hence
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
= 0.0002+0.0020+0.0097+0.0305+0.0687
= 0.1111
0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
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Solve for the shaded region
The Area of the Shaded Region is 184.61 sq. mm
What is Area?
The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Solution:
Area of the Shaded Region = Area of Rectangle - 2 * Area of Circles
Area of Recatangle = Length * Breadth = 21 * 13 = 273 sq. mm
2 * Area of Circle = 2* πr² = 2 * 22/7 * 7.5/2 * 7.5/2
= 88.39 sq. mm
Area of the Shaded Region = 273 - 88.39 = 184.61 sq. mm
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1+1=2
2+2=4
5+5=10
34+35=?
The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (startfraction pi over 20 endfraction t). How long does it take for the waterwheel to complete one turn?.
The waterwheel takes 40 seconds to make one turn.
To find the period of the function, we need to find the time it takes for the function to repeat itself. In this case, we want to find the time it takes for the waterwheel to complete one turn.
The function h = 15 cos (π/20) t models the height of the cloth in relation to sea level as a function of time.
The cosine function has a period of 2π, so the period of the function h = 15 cos (π/20) t will be 2π divided by (π/20) which simplifies to 40 seconds.
Therefore, it takes 40 seconds for the waterwheel to complete one turn.
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Which of the following is the solution to the following system of inequalities?
x+2y<=4
3x-y>=2
See the picture for the graphs. Any help is appreciated!! This is honors algebra 2 on Apex learning.
Answer: B.
Step-by-step explanation:
x+2y≤4
3x-y≥2
a teacher has a grading policy for a group assignment such that each team can earn up to 100 points, which will then be divided between four team members based on the quality of each team member's contribution to the group. this situation would be what type of game for team members?
This situation would be known as a positive-sum game for team members.
In game theory, a scenario is said to as a positive-sum game if the sum of the profits and losses is more than zero. When resources are somehow expanded and a strategy is developed that satisfies the wants and requirements of everyone involved, a positive sum results. One instance would be when two parties engage in a competition and, regardless of the outcome, both sides stand to profit financially. In situations of distributive bargaining, where various interests are discussed in order to satisfy everyone's wants, positive-sum outcomes take place.
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Domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Given:
range: 68,71,74,77,80
Domain:1,2,3,4,5
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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Grace has 2 quartera . Jen have 4 dimesss were ans 1 nickels. Keesha has 3 dimes and 3 nickels. Terry has 1 quarters , 1 dime who has the most money
Answer: grace has the most money
Step-by-step explanation:
Because
Grace has 2 quarters = 50 cents
Jen has 4 dimes and 1 nickel = 45 cents
Keesha has 3 dimes and 3 nickels = 33 cents
Terry has 1 quarter and 1 dime = 26 cents
so as you can see grace has the most money
a paired samples test for the difference between two means can be used for segmentation purposes. true false
The statement "a paired samples test for the difference between two means can be used for segmentation purposes " is true
The given statement is
"A paired samples test for the difference between two means can be used for segmentation purposes"
The segmentation is the process of dividing the similar characteristics objects and group them together.
Here the a paired sample test for the difference between two mean is used for the segmentation process. It can be used for the segmentation purpose because A paired samples test for the difference between two means are samples in which natural or matched couplings occur
Therefore, the give statement is true
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y = 2x - 2 please help me
Answer: x = − [tex]\frac{y}{2}[/tex] - 1
Steps for solving linear equation.
y = − 2x − 2
Swap sides so that all variable terms are on the left-hand side.
−2x − 2 = y
Add 2 to both sides.
−2x = y + 2
Divide both sides by −2.
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{y + 2}{-2}[/tex]
Dividing by −2 undoes the multiplication by −2.
x = [tex]\frac{y+2}{-2}[/tex]
Divide y + 2 by −2.
x = -[tex]\frac{y}{2}[/tex] - 1
Graph:
can someone explain what algebra is please
Answer: Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.
can someone help me i will give brainlest
Answer:
code : fasmej ??
Step-by-step explanation:
1. F
2. A
3. S
4. M
5. E
6.J
Find the minimum value of the function f ( x ) = x 2 + 8 x + 9.6 f(x)=x 2 +8x+9.6 to the nearest hundredth.
The maximum and minimum values of the given function will be equal to -1.47 and -6.52.
What is the quadratic equation?The 2nd equation in x is known as a quadratic function. ax² + bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
As per the equation given in the question,
f(x) = x² + 8x + 9.6
D = b² - 4ac
= 8² - 4(1)(9.6)
D = 25.6
Now, find the roots,
-(b ± √D)/2a
-(8 ± 5.05)/2
So, the roots are,
-(8 + 5.05)/2 = -1.47, (x + 1.47)
-(8 - 5.05)/2 = -6.52, (x + 6.52)
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Find an equivalent expression to 3(4m 2 2) 2 2(m 1 5)
The expression equivalent to 3(4 m -2) - 2(m + 5) is 10 m - 16.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Given:
3(4 m -2) - 2(m + 5)
Solve the above equation using distributive property,
x (a - b) = xa - xb
12 m - 6 - 2 m - 10
10 m - 16
Thus, 3(4 m -2) - 2(m + 5) = 10 m - 16.
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The complete question is: Find an equivalent expression to 3(4 m -2) - 2(m + 5).
what is the perimeter of a square with a diagonal of 10 centimeters? round to the nearest whole number.
Answer:
P≈28.28cm = 28 cm
Step-by-step explanation:
Using the formulas
P=4a
d=√2a
Solving forP
P=2 √2d=2·√2·10≈28.28427cm
you are dealt a hand of three cards, one at a time. find the probability that your cards are all face cards.
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884We know that Total number of cars is 52 .
26 red and 26 is black.
13 are hearts ,
13 are diamonds,
13 are clubs,
13 are spades.
(a) The first club you get is the third card dealt,
Probability P (first club get is the third card dealt) = P(Non-club x Non club x club)
So,
P = [tex]\frac{39}{52} * \frac{38}{51} * \frac{13}{50}[/tex]
P = 0.145
(b) Your cards are all black,
[tex]P_{all are black}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{all are black}[/tex] = 0.116
(c) You get no hearts,
[tex]P_{no heart}[/tex] = [tex]\frac{39}{52} *\frac{38}{51} *\frac{37}{50}[/tex]
[tex]P_{no heart}[/tex] = 0.413
(d) You have at least one red card,
[tex]P_{at least one red}[/tex] = 1 - [tex]P_{no red}[/tex]
[tex]P_{no red}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{no red}[/tex] = 0.116
[tex]P_{at least one red}[/tex] = 1 - 0.116
[tex]P_{at least one red}[/tex] = 0.884
Therefore,
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884To learn more about Probability visit :
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ERADES
4
Declan is training to take part in a 10 km race.
He runs the same distance every day for 30 days. A
For the first 20 days, his mean running time was 56.2 minutes.
His mean running time for all 30 days was 54.4 minutes.
Work out Declan's mean running time for the last 10 days of his training.
unning time for first 20
Answer: 54.5
Step-by-step explanation: 54.5
Simplify −2r(−16r + 3r − 18).
Answer: 26r^2 + 36r
Step-by-step explanation:
−2r(−16r + 3r − 18)
32r^2 - 6r^2 + 36r
26r^2 + 36r
Answer:
26[tex]r^2[/tex] + 36r
Step-by-step explanation:
Combine like terms:
-2r(-13r - 18)
Use the distributive property:
-2r(-13r) + (-2r)(- 18)
26[tex]r^2[/tex] + 36r
suppose the population of a country increases at a steady rate of 3% per year. if the population is 35 million at a certain time, what will it be (in millions) 40 years later? (round your answer to the nearest tenth of a million.)
Answer:
110 billion or 1.10x10^8 to the nearest 10th.
Step-by-step explanation:
The population, P, that results from a constant yearly increase from a starting value (S) at a rate (R, as a decimal)) for x years is given by the expression:
P(x) = S*e^(1+R)x
P(40) = (35x10^6)*(1.03)^40
P(40) = (35x10^6)*(1.03)^40
P(40) = (35x10^6)*3.26
P(40) = 1.14x10^8
The popultion will be 114,000,000 [114 billion or 1.14x10^8)
110 billion or 1.10x10^8 to the nearest 10th.
13. If f(x)=x² + 3x-2, find f(-2).
By using the substitution property, the value of f(-2) is -4.
What is the substitution property of equality?
In an expression or equation, one value can be substituted for another and the result will still be the same. This is known as the substitution property of equality. If the values of x and y are the same, then x and y can be substituted for one another.
Given, f(x) = x² + 3x - 2
To find the value of f(-2), apply substitution property
f(-2) = (-2)² + 3(-2) - 2 = 4 - 6 - 2 = -2-2 = -4
Hence, the value of f(-2) is -4.
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Write the expression as a number in scientific notation.
the quantity 3.6 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity
2.6 × 107
2.16 × 101
2.16 × 10−1
2.6 × 10−7
The expression is written as a number in scientific notation as 2.16 × 10^1. Option B
What is scientific notation?Scientific notation can be described as a form of expressing or representing large numbers or very small numbers in a more simpler form.
It is also called index form or standard form.
From the information given, we have;
3.6 times ten to the fifth power = 3. 6 × 10^51.5 times ten to the negative eighth power = 1. 5 × 10^82.5 times ten to the negative fourth power = 2. 5 × 10^4Now, let's substitute the values
3. 6 × 10^5 × 1. 5 × 10^8/2. 5 × 10^4
Multiply the decimals and add the powers
5. 4 × 10^5/2. 5 × 10^4
Divide the values and subtract the powers, we get
2. 16 × 10^5-4
2. 16 × 10^1
Hence, the value is 2. 16 × 10^1
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Answer:
The expression is written as a number in scientific notation as 2.16 × 10^1. Option B
Step-by-step explanation:
Write the equation of the line that passes through the points (-7,7)(−7,7) and (-2,-6)(−2,−6).
The equation of the line y = - (13 / 5) · x - 56 / 5 passes through the points (x₁, y₁) = (- 7, 7) and (x₂, y₂) = (- 2, - 6).
What is the equation of a line that passes through two points?In this question we must derive the equation for a line that passes through two points on Cartesian plane. This can be done by means of the following two formulas:
Secant line formula
m = Δy / Δx
Equation of the line in slope-intercept form
y = m · x + b
Where:
Δx - Change in the independent variable.Δy - Change in the dependent variable.m - Slope of the lineb - Intercept of the lineFirst, write the given points:
(x₁, y₁) = (- 7, 7), (x₂, y₂) = (- 2, - 6)
Second, determine the slope of the line:
m = (- 6 - 7) / [- 2 - (- 7)]
m = - 13 / 5
Third, calculate the intercept of the equation of the line:
b = y - m · x
b = - 6 - (- 13 / 5) · (- 2)
b = - 6 - 26 / 5
b = - 30 / 5 - 26 / 5
b = - 56 / 5
Fourth, write the resulting equation of the line:
y = - (13 / 5) · x - 56 / 5
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Solve for x
A) 5
B) 6
C) 4
D) 3
Answer:
D
Step-by-step explanation:
given a line parallel to a side of a triangle and intersecting the other 2 sides the it divides those sides proportionally , that is
[tex]\frac{x}{15}[/tex] = [tex]\frac{2}{10}[/tex] ( cross- multiply )
10x = 15 × 2 = 30 ( divide both sides by 10 )
x = 3
find an equation for a line perpendicular to y=2x-3, passing through the origin.
Use the results from the simulation to predict the number of times a
card with the number 10 would be drawn when the total number of
cards drawn in the simulation is 1,440.
The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be 240 tines.
How to illustrate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
In thi situation, the simulation shows that the number of times 10 is drawn is 1/6. The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be:
= 1/6 × 1440
= 240 times.
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Complete question
The simulation shows that the number of times 10 is drawn is 1/6. Use the simulation to predict the number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440.