The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.
What is the equation of the polynomial with zeroes 2, 3 and 5?It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).
Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;
f(x) = (x - 2) (x - 3) (x - 5)
Therefore, by simplification; we have;
f(x) = (x² - 5x + 6) (x - 5)
f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.
f(x) = x³ - 10x² + 31x - 30.
Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.
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Write the standard form of the equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5
The equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5 in standard form is 5y + 2x = -5
How to find the equation of a line?The equation of a line can be represented in standard form or slope intercept form as follows;
Slope intercept form,
y = mx + b
where
m = slopeb = y-interceptLine are parallel when they have the same slope.
Therefore, the slope of the equation has a slope of - 2 / 5 x.
The line passes through (-5, 1).
Hence, let's find y-intercept.
y = - 2 / 5 x + b
1 = - 2 / 5 (-5) + b
1 - 2 = b
b = -1
Therefore, y = -2 / 5x - 1.
The equation in standard form should be in the form Ax + By = C.
Hence,
y + 2 / 5 x = -1
5y + 2x = -5
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Help! Consider the following three systems of linear equations.
Answer:
b & d
Step-by-step explanation:
An astronaut has an annual income of $161,141.00.
The income tax an astronaut must pay is 8%.
What is the amount of income tax in dollars and cents that the
astronaut must pay?
Ibram got a job selling bags of peanuts at the local fairground. He is paid a fixed amount of $340 per week plus $0.84 per item sold. This is represented by the equation P = 0.84 + 340 where P is the amount he is paid for the week and n is the number of bags of peanuts he sold. How much will Ibram be paid if he sells 380 bags of peanuts? If Ibram sells 380 bags of peanuts, he will earn S How many bags of peanuts did Ibram sell if he earned $1,087.60? for the week. If Ibram has earned $1,087.60, he sold bags of peanuts.
Answer:
Assuming the bags sold were for 1 week period.
1. $659.20 for 1 week and 380 bags of peanuts
2. 890 bags
Step-by-step explanation:
The equation is missing the variable, n (the number of bags sold). I'll take the liberty to add it after the $0.84/bag term, where it belongs:
P = 0.84n + 340
The 340 is $340/week. n must be in units of "bags/week."
1. How much will Ibram be paid if he sells 380 bags of peanuts?
P = $0.84n + $340
n = 380 bags (we will assume in 1 week).
P = $0.84n + $340
P = $0.84(380) + $340
P = $659.20
2. How many bags of peanuts did Ibram sell if he earned $1,087.60?
P = $0.84n + $340
P = $1087.60
$1087.60 = $0.84n + $340
$1087.60 - $340 = $0.84n
$0.84n = $1087.60 - $340
$0.84n = $747.60
n = 890 bags ( ! - I'm impressed)
Rupert has a bag containing 2 green, 3 purple and 2 orange marbles. He selects two marbles from
his bag in succession, without replacement.
Using a tree diagram, determine the probability that Rupert picked the two green marbles.
The probability that Rupert picked 2 green balls is 1/21.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.
Main Body:
total balls = 7 , green balls =2
1st try:
probability of getting green ball = 2/7
As there is no replacement so now,
total balls = 6 , green balls = 1
2nd try:
probability of getting green ball = 1/6
total probability = (2/7)*(1/6)
= 1/21
Hence the answer is 1/21.
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1. Harper is going to create a graph of the equation y = -0.5x + 12. Which of the following will be true about the graph?
The graph will contain the origin.
The graph will increase from left to right.
The graph will cross the x-axis at (12, 0).
The graph will have a slope of -0.5.
The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.
What is a slope?A slope is defined as the difference between a chosen point on the vertical and horizontal axis.
The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;
y = mx + b
Where m = the measure of the steepness of the straight line graph.
From the equation of the graph that was given;
y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.
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elect the correct answer. A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?
The expected value of a player's winnings on each roll is: $30.
How can we calculate the expected value of a player's winnings on each roll?We can calculate the expected value of a player's value on each winning by first understanding that there are only two multiples of three on the six-sided die. These multiples are 3 and 6.
So, if 3 is obtained facing upward, the player wins 3 × 20 = $60
Also, if the player obtained 6 facing upward, the player wins 6 × 20 = $120
So, the total amount is $180.
However, the question expects us to calculate the expected value of a player's winnings on each roll. Thus, we will have $180 ÷ 6 = $30.
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How long will it take for $3, 900 to double if it is invested at 8% annual interest compounded 2 times a year?
Enter in exact calculations or round to 3 decimal places.
It will take___years to double.
How long will it take if the interest is compounded continuously?
Compounded continuously, it would only take___ years.
The number of years to double the investment is 8.824 years.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $3,900
R = 8%
n = 2
A = 2P = 2 x 3,900 = $7,800
Now,
A = P [tex](1 + r/n)^{nt}[/tex]
7,800 = 3,900 [tex](1 + 0.04)^{2t}[/tex]
78/39 = [tex](1.04)^{2t}[/tex]
2 = [tex](1.04)^{2t}[/tex]
Taking logs on both sides.
log 2 = 2t log(1.04)
0.30 = 2t x 0.017
0.30/0.017 = 2t
17.65 = 2t
Divide both sides by 2.
t = 17.65 / 2
t = 8.824 years.
Thus,
The number of years to double the investment is 8.824 years.
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1. Calculate arithmetic mean from the following data. 50, 60, 70, 80, 65, 70, 90
Answer:
Here ,
sigma x=50+60+65+70+70+80+90=485
N=7
now,
Mean =sigma x÷N
=485÷7
=69.28
two foods contain proteins, carbohydrates, and fats. food a costs $1 per pound and contains 30% protein, 10% fat, and 50% carbohydrates. food b costs $1.50 per pound and contains 20% protein, 4% fat, and 75% carbohydrates. what is a combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat at the lowest cost? (x, y)
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given,
Function:
C = x + 1.5y
Subjected to:
30x + 20y ≥ 13/10 ×100 ≥ 130
10x + 4y ≥ 1/5 × 100 ≥ 20
50x + 75y ≥ 3 × 100 ≥ 300
Feasible region:
(0, 13/2), (3,2) (6,0)
C = x + 1.5y
(0, 13/2) ⇒ C = 0+ (1.5)(13/2)
(0.13/2) ⇒ C = 9.75
(3,2) ⇒ C = 3+ (1.5)(2)
(3,2) ⇒ C = 6
(6,0) ⇒ C = 6 + 0
(6,0)⇒ C = 6
A combination of x pounds of food a and y pounds of food b that provides at least 1 1 2 pounds of protein, 3 3 4 pounds of carbohydrates, and 1 5 pound of fat lowest cost is at (x,y) is (3,2).
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What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
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help meeeeeeeeeeeeeee pleaseee
The vertex of the graph is (2, -1), the axis of symmetry of the graph is x = 2 and the parabola opens downward
How to determine the properties of the function?The vertex
The graph represents the given parameter
From the graph, we can see that:
The maximum point on the graph is located at
(2, -1)
The vertex of a graph is the maximum or the minimum of the graph
This means that
Vertex = (2, -1)
The axis of symmetry
The graph represents the given parameter
In (a), we have
Vertex = (2, -1)
Remove the y-coordinate
x = 2
The axis of symmetry of a graph is the x coordinate of the vertex
This means that the axis of symmetry is x = 2
The direction of the parabolaFrom the graph, we can see that the parabola opens downward
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if a seed is planted, it has a 65% chance of growing into a healthy plant. if 12 seeds are planted, what is the probability that exactly 3 don't grow?
There is a 136.13 probability that 3 won't increase.
Only 0.65% of seeds will grow into robust plants.
There is a 0.35 probability that a seed won't grow into a robust plant.
In this case, n = 12 and r = 3.
11 seeds will sprout if 1 seed doesn't germinate. Raising 0.65 to the power of 11 and 0.35 to the power of 3 will result in the following: 11 seeds develop, and we use the 11th power; 3 seeds do not grow, so we use the power of 3:
So, the response is:
[tex]{}^{12}C_3[/tex] × [tex]{(chance of successful growth) }^{11}[/tex]x [tex](chance of Unsuccessful growth)^3[/tex]
= [tex]{}^{12}C_3[/tex] × [tex]0.65^{11}[/tex] × [tex]{0.35}^3[/tex]
= 362880 × 0.008750 × 0.042875
= 136.13
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A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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A number cube with six sides numbered 1 through 6 is rolled. the probability of rolling a 5 is 16. what is the probability of not rolling a 5?
The probability of not rolling a 5 is [tex]\frac{1}{6}[/tex]
For any event A, the probability of not getting A is given by
[tex]P(not A)= 1- P(A)[/tex]
A number cube with six sides numbered 1 through 6 is rolled.
Then we have,
The total number of possible outcomes [tex]= 6[/tex]
Also, it is given that, The probability of rolling a 5 is
P(rolling 5)=[tex]\frac{1}{6}[/tex].
Now, the probability of not rolling a 5 will be
[tex]P(\text{not rolling a 5})= 1- P(\text{rolling 5})[/tex]
[tex]=1-\frac{1}{6}[/tex]
[tex]=\frac{5}{6}[/tex]
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Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
As per the given percentage, Sherry want to invest $2,000 amount in mutual fund and $13,200 amount in bonds.
Percentage:
Percentage means the number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Given,
Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.
Here we need to find if she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account.
It is given that the total amount is 15200.
So, let us consider x be the amount invested in mutual funds then 15200 - x be the amount invested in bonds.
Therefore, it can be written in the following matrix,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}[/tex]
Now, we have know that the total interest amount after 1 year is 548,
So, it can be written like the following expression
amount invested x percentage = final amount
Therefore,
[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}\times\begin{bmatrix}\frac{1}{100} \\\frac{4}{100}\end{bmatrix}=548[/tex]
It can be simplified as,
[tex]\begin{bmatrix}x\times(\frac{1}{100})+(15200-x)\times(\frac{4}{100}) \end{bmatrix}=[548][/tex]
=> x/100 + 60800-4x/100 = 548
=> x + 60800 - 4x = 54800
=> -3x = 54800 - 60800
=> -3x = -6000
=> x = 2000
=> 15200 - 2000 = 13200
Therefore, she invests $2,000 in mutual funds and $13, 200 in bonds.
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3 math questions for 50 points.
The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
Which bird is closer to the ground after 8 minutes?
The
eagle
is closer to the ground.
How much closer?
feet
hurry
The hawk is closer to the ground after 8 minutes
It is 130 feet closer
How to determine the valuesWe have the equation as;
y = −20x+350. This represents the altitude y in feet of a hawky=−10x+400. This represents the altitude y in feet of the eagleAlso, x represents the descending time in minutes
Now, let's substitute the value of x as 8 minutes in the equations
If x = 8
For equation (1)
y = - 20(8) + 350
expand the bracket
y = - 160 + 350
y = 190 feet
For equation (2)
y = -10(8) + 400
expand the bracket
y = -80 + 400
y = 320 feet
The hawk is closer after 8 minutes
The distance from the ground(eagle) - The distance from the ground(hawk)
320 - 190
130 feet
Hence, the hawk is closer to the ground
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(jk−1)÷j when j=−4 and k=−0.9
The evaluation of the expression for the given values of j and k is -0.65
Evaluating an ExpressionFrom the question, we are to evaluate the given expression for the given values of j and k.
From the given information,
The given expression is
(jk - 1) ÷ j
and
j = -4 and k = -0.9
Now, substitute the values of j and k into the expression
(jk - 1) ÷ j
((-4)(-0.9) - 1) ÷ -4
= (3.6 - 1) ÷ -4
= 2.6 ÷ -4
= - 0.65
Hence, the value of the expression is -0.65
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help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The object has fallen [tex] \boxed{\sf 289} [/tex] feet from ts intial position.
Step-by-step Explanation:
Given:
Formula:
[tex] \rm v = \sqrt{2gh} [/tex]
Where,
v = velocity (in feet per second)
h = Height fallen (in feet)
g = acceleration due gravity (in feet per second squared) = approximately 32 ft/s²
To find:
How far an object has fallen if its velocity (v) is 136 ft/s
Solution:
By substituting the value of g & v in the formula we get:
[tex]\rm \implies 136 = \sqrt{2 \times 32 \times h} \\ \\ \rm \implies 136 = \sqrt{64h} \\ \\ \rm \implies 64h = {136}^{2} \\ \\ \rm \implies h = \dfrac{ {136}^{2} }{64} \\ \\ \rm \implies h = \dfrac{18496}{64} \\ \\ \rm \implies h = 289 \: ft[/tex]
4) Identify all the zeros that make the function
true. f(x) = 2x² - 8
0
-2
2
-4
4
-8
The zero of the function f(x) = 2x² - 8 is ± 2.
Zeros of the function
Zero of the function means the values of x when f(x) is equal to 0. Which means that when f(x) = 0, x is a zero of the function.
Given,
Here we have the function f(x) = 2x² - 8.
Here we need to find the zero of the function.
As per the definition of the zeros of the function,
We have to apply the value of f(x) = 0, then we get,
2x² - 8 = 0
Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,
2x² = 8
Now, move the number 2 to the right hand side then it will be dividing the number 8,
x² = 8/2
x² = 4
x = √4
Therefore, the value of x is ± 2.
So, the zeros of the function is either +2 or -2.
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a simple random sample of 25 observations is dervied from a normally distributed population with a population standard deviation of 8.2. compute the margin of error with 80% confidence.
The margin of error with 80% confidence interval is 2.099
Given that,
A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.
To find : The margin of error with 80% confidence
Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
Here we have
n=25,σ=8.2
For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is
ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992
Thus, with 80% confidence, the error margin is 2.099.
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which number line shows -4, -1, 1, and 2 correctly plotted.
A number line which shows -4, -1, 1, and 2 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical values -4 and -1 would be plotted on the left hand side of zero (0) while the numerical values 1 and 2 would be plotted on the right hand side of zero (0) using a number line.
In this scenario, a number line would be used for the comparison of two or more numbers such as -4, -1, 1, and 2, and this is plotted in the graph shown in the image attached below.
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Mr karki divided a sum of Rs 1,80,000 between his son and daughter in the ratio of 4:5 find the sum obtained by eachof them.
Answer:
Rs 80,0000 and Rs 100,000
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide the amount by 9 to find the value of one part.
Rs 1,80,000 ÷ 9 = Rs 20,000 , then
4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives
5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives
The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.
Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.
Let the common multiple be x
∴ The son obtained Rs. 4x --------1
And daughter obtained Rs. 5x --------2
As the total sum is Rs. 1,80,000
∴ 4x + 5x = 180000
9x = 180000
x = 180000/9
∴ x = Rs. 20000
Putting the value of x in 1 and 2 we get,
The sum obtained by son = 4x = 4*20000 = Rs. 80000
And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000
Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.
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which is a reasonable estimate for the amount of kernels serena needs to make 6 cups of popcorn
Answer:
four tablespoons to make 6 cups of popcorn.
Step-by-step explanation:
1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.
2. One plane
points_____
passes through three noncollinear
A. Point, Line, and Plane Postulates do not
address this topic directly.
B. always
C. never
D. sometimes
a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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How long would the minute hand of a clock have to be if its end were to move at 100km/hour?
To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers
What is angular velocity?Angular velocity is the rate and direction of rotation of a body about an axis.
The required linear speed of the minute hand = 100 km/hour
The formula to convert angular speed to linear speed is presented as follows;
[tex]\omega = \dfrac{v}{r}[/tex]Which gives;
[tex]r = \dfrac{v}{\omega}[/tex]The angular speed of the minute hand = 2·π rad/hour
The required length of the minute hand is therefore;
[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]
The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km
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tan 30 x cos 30 in exact value
a coin is altered so that the probability that it lands on heads is less than 1 2 12 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1 6 16. what is the probability that the coin lands on heads?
The probability that the coin lands on heads is D = (3±√3)/6
Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.
Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.
The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities
(4+2)x2(1-x)2 = 1/6
6x2(1-x)2 = 1/6
x2(1-x)2 = 1/36
x(1-x) = ±1/6
As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence
x(1-x) = 1/6
6x2 – 6x +1 = 1/6
Using the quadratic formula, we can determine that the roots of this equation are
(3±√3)/6
Therefore the probability that the coin lands on heads is D = (3±√3)/6
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