The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.
To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula
z = ( x- μ)/ σ
where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get
z = ( 42,000- 40,000)/ 3,000 = 0.67
Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.
thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.
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The correct question is given below-
A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?
Calculator This figure shows A ABC. BD is the angle bisector of ZABC. What is AD? Enter your answer, as a decimal, in the box. units A 4.5 B D 5 4
Using similar side theorem and taking the ratios of similar sides, the value of AD is 3.6 units
What is similar side theorem?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
In this problem, we can use the similar side theorem by taking ratios of similar sides.
4.5 / 5 = AD / 4
Cross multiply both sides
AD = (4.5 * 4) / 5
AD = 18/5
AD = 3.6
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26. A student is asked to solve the equation
4(3x - 1)² 17 = 83. The student's
solution to the problem starts as
-
4(3x - 1)² = 100
(3x - 1)² = 25
A correct next step in the solution of the
problem is
A. 3x1 = ±5
B. 3x - 1 = ±25
C. 9x² - 1 = 25
D. 9x² - 6x +1=5
Answer:
A.
Step-by-step explanation:
correct answer is A. 3x1=
Answer: A
Step-by-step explanation:
The next step you would take is take the square root of both sides to cancel out the square.
Which gets rid of the square on 1 side and you get ±5 on the other.
Help on all parts pls step by step preferably
Applying the inscribed angle theorem, we have:
a. x = 55° b. x = 60° c. x = 92° d. x = 84°
How to Apply the Central Angle Theorem and the Inscribed Angle Theorem?These theorem states that:
Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.
Intercepted arc measure = central angle measure.
Therefore, we have:
a. x = 180 - 35 - 90 [tangent theorem]
x = 55°
b. x = 1/2(120) [inscribed angle theorem]
x = 60°
c. x = 2(46) [inscribed angle theorem]
x = 92°
d. m(FE) = 2(42) = 84°
m(EB) = 180 - FE = 180 - 84
m(EB) = 96°
m(AB) = 180 - m(EB) = 180 - 96
m(AB) = 84°
x = m(AB) = 84° [central angle theorem]
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A construction crew is lengthening a road. The road started with a length of 56 miles, and the crew is adding
3 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has
worked. Write an equation relating L to D. Then use this equation to find the total length of the road after
the crew has worked 36 days.
Using A linear equation, It ia found that:
• The equation is: L = 56 + 3d
Where D is representing the number of day crew has worked and L presenting the total length of the road. So let's solve this.
Step by step Explanation:
= L = 56 + 3d
= L = 56 + 3(36)
= L = 54 + 108
= L = 162
A shareholders' group is lodging a protest against your company. the shareholders group claimed that the mean tenure for a chief exective office (ceo) was at least 8 years. a survey of 52 companies reported in the wall street journal found a sample mean tenure of 5.8 years for ceos with a standard deviation of 5.4 years (the wall street journal, january 2, 2007). you don't know the population standard deviation but can assume it is normally distributed. Formulate a hypotheses that can be used to challenge the validity of the claim made by the shareholders?
The null hypothesis would be that the mean tenure for CEO's is 8 years, while the alternative hypothesis would be that the mean tenure for CEO's is less than 8 years. This would be formulated as: Null hypothesis: μ = 8 years
Alternative hypothesis: μ < 8 years
The sample mean of 5.8 years is lower than the claimed mean of 8 years, suggesting that the shareholders' claim may not be valid. To test the validity of their claim, a hypothesis test can be conducted using the sample data and assuming a normal distribution of CEO tenure in the population.
To challenge the validity of the claim made by the shareholders, you can formulate a hypothesis test using the following steps:
Step 1: State the null hypothesis (H0) and alternative hypothesis (H1)
- Null hypothesis (H0): The population mean tenure for a CEO is at least 8 years (μ ≥ 8)
- Alternative hypothesis (H1): The population mean tenure for a CEO is less than 8 years (μ < 8)
Step 2: Collect and summarize the sample data
- Sample size (n): 52 companies
- Sample mean (x): 5.8 years
- Sample standard deviation (s): 5.4 years
Step 3: Since the population standard deviation is unknown and the sample size is large (n > 30), we can assume the sampling distribution is normally distributed and use a t-test to perform the hypothesis test.
Note that we cannot directly test the validity of the shareholders' claim based on the sample data alone. The hypothesis test will help determine whether there is enough evidence to reject the null hypothesis and support the alternative hypothesis, which would then challenge the claim made by the shareholders.
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4. Mrs. Minor has a goal to
sell at least 16 boxes of
candy for a fundraiser. She
has already sold 4. Which
inequality shows how many
more boxes Mrs. Minor will
need to sell?
The inequality that shows how many more boxes Mrs. Minor will have to sell is given as follows:
x ≥ 12.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.She needs to sell at least 16 boxes, and has already sold 4, hence the amount that needs to be sold is:
16 - 4 = 12 boxes.
Then the inequality is:
x ≥ 12.
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see photo for my question
The area of the parallelogram in the figure is given as follows:
A = 39.96 in².
How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:
A = bh.
The parameters for this problem are given as follows:
h = 3.7 in, b = 10.8 in.
Multiplying the base of the parallelogram by the height of the parallelogram, the area is given as follows:
A = 10.8 x 3.7
A = 39.96 in².
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50 points to whoever can solve this quickly-
The area of the small triangle is equal to 25 ft².
What is a scale factor?In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).
How to determine the area of the small triangle?In Mathematics and Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
(Scale factor of dimensions)² = Scale factor of area
Therefore, the area of the small triangle can be calculated as follows;
Area of small triangle = (12/28)² × 135
Area of small triangle = 24.80 ≈ 25 ft².
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What’s the shaded region
The calculated value of the area of the shaded region is 60.5 square meters
Calculating the area of the shaded regionFrom the question, we have the following parameters that can be used in our computation:
The figure
Where we have the shaded region to be the gray region
Also, we have
Shaded region = 2 triangles with base = 1/2 * 11 and height = 11
using the above as a guide, we have the following:
Area = 2 * area of 1 triangle
So, we have
Area = 2 * 1/2 * 11 * 1/2 * 11
Evaluate
Area = 60.5
Hence, the area of the shaded region is 60.5 square meters
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question 12 options: what is the probability that, if iii-2 and iii-3 marry and have 7 children, that they will have 2 colorblind children and 5 normal children?
The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.
We have,
To calculate the probability, we can use the binomial probability formula:
P(2 colorblind and 2 normal) = (4 choose 2) * (1/16)² * (15/16)²
Using the formula, we can calculate:
P(2 colorblind and 2 normal) = (4! / (2! * (4-2)!)) * (1/16)² * (15/16)²
= (6) * (1/256) * (225/256)
= 1350/65536
≈ 0.0206
Therefore,
The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.
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The complete question:
What is the probability that, if a couple with no known family history of colorblindness has 4 children, exactly 2 of them will be colorblind and the other 2 will have normal color vision, assuming that the probability of having a colorblind child is 1/16 due to a rare genetic mutation?
A scale model of a tower is 24 inches. The scale is 1. 5 in. : 10 ft. What is the actual height, in feet, of the tower?
To find the actual height of the tower, we need to use the scale factor. The ratio of the scale is 1.5 inches to 10 feet, which can be simplified to 1 inch to 6.67 feet (by dividing both sides by 1.5).
Therefore, the actual height of the tower in feet would be:
24 inches × (1 inch ÷ 6.67 feet) = 3.6 feet
So the actual height of the tower is 3.6 feet.
Two coins are flipped at the same time.
A probability model for the number of heads is shown.
A 2-column table with 3 rows. Column 1 is labeled outcome with entries 0 heads, 1 head, 2 heads. Column 2 is labeled probability with entries blank, blank, blank.
Complete the statements about the probability model.
The probability for the outcome of 0 heads is
✔ 0.25
.
The probability for the outcome of 1 heads is
✔ 0.5
.
The probability for the outcome of 2 heads is
✔ 0.25
Using probability, we can find:
Probability of getting zero heads = 0.25
Probability of getting 1 head = 0.5
Probability of getting 2 heads = 0.25
Describe probability?The ability of an event to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.
Here in the question,
2 coins are flipped at the same time.
The possible outcomes are as follows:
H H
H T
T H
T T
So, there are 4 outcomes of this event.
Now,
Probability that there are 0 heads in the event:
One event there is 0 heads = T T
Probability = 1/4
= 0.25
Now, events with one head are:
H T and T H
So,
Probability = 2/4
= 0.5
In the final event, we have 2 heads in one event = H H
So,
Probability = 1/4
= 0.25
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MARK YOU THE BRAINLIEST! Dilate with scale factor 1/3
The dilated points are:
G' = (1, 1)
H' = (1, 3)
J' = (4, 1)
Option C is the correct answer.
We have,
To dilate with a scale factor of 1/3, we need to multiply the coordinates of each point by 1/3.
The new coordinates of G will be:
x-coordinate: 3 × 1/3 = 1
y-coordinate: 3 × 1/3 = 1
So, the new coordinates of G are (1, 1).
The new coordinates of H will be:
x-coordinate: 3 × 1/3 = 1
y-coordinate: 9 × 1/3 = 3
So, the new coordinates of H are (1, 3).
The new coordinates of J will be:
x-coordinate: 12 × 1/3 = 4
y-coordinate: 3 × 1/3 = 1
So, the new coordinates of J are (4, 1).
Therefore,
The dilated points are:
G' = (1, 1)
H' = (1, 3)
J' = (4, 1)
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You have 5 baseball players and you want to assign then to a random batting order for an upcoming competition. What is the probability that Player A is assigned to go 1st, Players B is assigned to go 2nd, Player C is assigned to go 3rd, Player D is assigned to go 4th, and player E is assigned to go 5th?
The probability that the Players are assigned to go in the order given can be found to be 0.833 %.
How to find the probability ?First, we need to find out the number of ways that the baseball players can be assigned to go and this is:
= 5 × 4 × 3 × 2 × 1 = 120 ways
However, there is only one way in which Player A is assigned to go 1st, Players B is assigned to go 2nd, Player C is assigned to go 3rd, Player D is assigned to go 4th, and player E is assigned to go 5th.
The probability is therefore:
= 1 / 120
= 0.833 %.
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Please help me I need a 100
Answer:
Yes, 86.76 is a rational number. A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not zero).
86.76 can be expressed as the ratio of two integers: 8676/100, which can be simplified to 2169/25. Since 2169 and 25 are both integers, and the denominator is not zero, 86.76 is a rational number.
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
A rational number is any number that can be expressed as the ratio of two integers (i.e., a fraction where the numerator and denominator are both integers).
In this case, we can express 86.76 repeating as the fraction:
8676/100 = 8676 ÷ 100
Simplifying this fraction, we get:
8676/100 = 8676 ÷ 4 ÷ 25 = 2169/25
Since 2169 and 25 are both integers, we have expressed 86.76 repeating as a ratio of two integers, and therefore it is a rational number.
Where does the normal line to the paraboloid z = x2 + y2 at the point (3, 3, 18) intersect the paraboloid a second time?
The normal to the parabola[tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).
To find the normal to the paraboloid[tex]z = x^2 + y^2[/tex] at points (3, 3, 18), we first need to find the slope of the surface at that point. The gradient vector is given by
[tex]∇f(x,y,z) = < 2x, 2y, -1 >[/tex]
So the gradient vector at points (3, 3, 18) is
∇f(3, 3, 18) = <6, 6, -1>
This gradient vector is orthogonal to the plane tangent to the surface at the point (3, 3, 18). So the surface normal at this point is parallel to the gradient vector and can be expressed as
x = 3 + 6t
y = 3 + 6t
z = 18 - t
To discover where this line converges the parabola once more, we ought to substitute the x, y, and z equations into the parabola's condition.
[tex]z = x^2 + y^2[/tex]
So it looks like this:
[tex]18 - t = (3 + 6t)^2 + (3 + 6t)^2[/tex]
[tex]18 - t = 18t^2 + 36t + 18[/tex]
[tex]0 = 18t^2 + 37t[/tex]
t=0 or t=-37/18
The value t = 0 corresponds to the starting point (3, 3, 18), so we are interested in the second value t = -37/18. Substituting this value into the normal equation gives:
x = 3 + 6(-37/18) = -1/3
y = 3 + 6(-37/18) = -1/3
z=18-(-37/18)=360/18=20
therefore, the normal to the parabola [tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).
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Find the sum of the interior angles of a 16-sided polygon. 2,880° 2,160° 2,700° 2,520°
Answer: Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘
Step-by-step explanation:
Answer:
D) 2520°------------------------
To find the sum of the interior angles of a 16-sided polygon, you can use the formula:
S(n) = (n - 2) × 180° , where n is the number of sides of the polygon.In our case, n = 16.
Substitute the value of n into the formula:
S(16) = (16 - 2) × 180° = (14) × 180° = 2520°The matching choice is D.
if moving due west is given +16 then what is -18
Answer:
Step-by-step explanation:
If moving due west is +16, then moving due east is going to cover up for -16 and an additonal -2 to the east. which sums up to -18. Therefore -18 is 2units to the east.
4. Allie orders candles from an online company that offers a flat rate for shipping. She placed an order for 4 candles
for $35. A few months later, she placed an order for 12 candles for $49.
a. Define your Variables
b. What information were you given?
c. Create an equation using the information you were given.
d. How much was the shopping?
e. How many candles can she get for $60?
a) The variables are the variable unit cost of candles and the fixed cost of shipping.
b) The information given in the question include the total costs for 4 candles and 12 candles, including their shipping costs.
c) An equation representing the situation is given as
d) Allie can get 18 candles for $60.
What is an equation?An equation is a mathematical statement showing that two or more algebraic expressions are equal or equivalent.
Algebraic expressions combine variables, values, constants, and numbers without the equal symbol (=), but they use the mathematical operands.
The total cost for ordering 4 candles = $35
The total cost for ordering 12 candles = $49
The difference = 8 candles = $14
Unit cost of candles = $1.75 ($14 ÷ 8)
Shipping (fixed) cost for the first order = $28 ($35 - $1.75 x 4)
Shipping (fixed) cost for the second order = $28 ($49 - $1.75 x 12)
For ordering candles for $60, the number of candles Allie can get = 18 ($60 - $28) ÷ $1.75
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An inequality is shown.
Answer:
24
Step-by-step explanation:
We can simplify this equality by squaring both sides.
[tex](\sqrt{x})^2 < 5^2[/tex]
[tex]x < 25[/tex]
We know that the greatest integer less than 25 is 24. Therefore, this is the greatest integer solution to the inequality.
during winter, the average temperature inside your room is 70 degrees with standard deviation of 2 degrees. what is an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees?
For a sample of room temperature during winter, an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees is equals to the 0.25.
For a sample of temperature during winter, Average temperature of room
= 70 degree
Standard deviations = 2 degrees
We have to determine upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees. According to chebyehev's theorem, [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex].
here , σ = 2 , μ = 70, kσ = 4
=> k = 2
So, the required upper bound of probability is [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex]
≤ [tex]\frac{ 1 }{2²} [/tex]
≤ [tex]\frac{ 1 }{4} [/tex]
= 0.25
Hence, required upper bound value is 0.25.
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Find the hypotenuse length
The requried measure of the hypotenuse of the given right triangle is 37.
The hypotenuse of the right angle triangle can be evaluated by Pythagoras' theorem, which states that the sum of squares of the legs of a right triangle is equal to the square of the third side.
Hypotensue² = 12²+35²
Hypotensue = √1369 = 37
Thus, the requried measure of the hypotenuse of the given right triangle is 37.
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The circumference of a circle is 43.96 inches. What is the circle's diameter?
Use 3.14 for .
Answer:
14 inches
Step-by-step explanation:
You want the diameter of a circle that has a circumference of 43.96 inches.
CircumferenceThe equation for the circumference of a circle is ...
C = πd
Then the diameter is ...
d = C/π
d = (43.96 in)/3.14 = 14 in
The circle's diameter is 14 inches.
<95141404393>
Work out the length of QR????!
:)
Step-by-step explanation:
First, use law of SINES to find QS :
11.7 / sin 28 = QS / sin95
shows QS = 24.83 cm
Now use law of COSINES to find QR
QR^2 = 10.2^2 + 24.83^2 - 2 ( 10.2)(24.83) cos ( 110)
shows QR = 29.9 cm
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
Answer:
Step-by-step explanation: Hello! You know the area of a right triangle shown is 24 square feet. The formula for area of a triangle is A = 1/2(b)(h).
24 can be substituted for A.
24 = 1/2(b)(h).
From here, I will need to see the triangle shown. If you post an image of the triangle with this, I might be able to come back and help you.
Good luck!
Which values of xare solutions to the equation below? Check all that apply. 4x²-30=34 □ A. x= -√√8 B. X= 4 C. X = -8 ☐ D. x = √√√8 E. x = -4 F. x=8
Starting with the given equation:
4x² - 30 = 34
Adding 30 to both sides:
4x² = 64
Dividing both sides by 4:
x² = 16
Taking the square root of both sides:
x = ±4
Therefore, the solutions to the equation are x = 4 and x = -4.
Checking each option:
A. x = -√√8 is not a solution.
B. x = 4 is a solution.
C. x = -8 is not a solution.
D. x = √√√8 is not a solution.
E. x = -4 is a solution.
F. x = 8 is not a solution.
Therefore, the solutions to the equation are x = 4 and x = -4, which are options B and E.
A population of bacteria is growing according to the equation P (t) = 1600 e^0.21t, with t measured in years. Estimate when the population will exceed 7569.
The population will exceed 7569 at moments beyond 7.4 years hence from 8 years (to the nearest years)
What is an exponential function?Exponential function is a function of the form f(x) = a e^(kt)
Considering the given problem,
the initial value = a
the base factor = k
the exponents in time = t
Information given in the problem are
a = 1600k = 0.21t = ?f(x) = 7569solving for the time wen the population will exceed 7569
7569 = 1600 x e(0.21 * t)
7569 / 1600 = e(0.21 * t)
take ㏑ of both sides
㏑ (7569 / 1600) = ㏑ e(0.21 * t)
㏑ (7569 / 1600) = 0.21t
t = ㏑ (7569 / 1600) / 0.21
t = 7.40
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Write an inequality for the shaded region shown in the figure.
The inequality for the shaded region shown in the figure is; y ≥ x^2 - 1
We can see that the shaded region seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)
Then:
y ≥ ax^2 + bx + c
where ax^2 + bx + c is the general quadratic equation.
Now to find the equation for the parabola:
f(x) = ax^2 + bx + c
We also can see that the vertex of the parabola is at the point (0, -1)
This means
f(0) = -1 = a0^2 + b0 + c
-1 = c
c = -1
Then:
f(x) = ax^2 + bx - 1
Now we can see at the graph again, to see that the zeros of the parabola are at +1 and -1
Which means that:
f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1
f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1
Then we have two equations:
a + b - 1 = 0
a - b - 1 = 0
b = 0
these equations become:
a - 1 = 0
a - 1 = 0
Then solving for a, a = 1
Then the quadratic equation is:
f(x) = 1*x^2 + 0*x - 1
f(x) = x^2 - 1
And the inequality is y ≥ x^2 - 1
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find the area of the following figure
what is the probability that bo, colleen, jeff, and rohini win the first, second, third, and fourth prizes, respectively, in a drawing if 49 people enter a contest and no one can win more than one prize?
The probability of winning first, second, third, and fourth prizes in specific order by Bo, Colleen, Jeff, and Rohini is equals to 0.00000020.
Number of people enter in contest = 49
The number of ways to choose the first prize winner is 49.
Since the first prize winner is no longer eligible.
The number of ways to choose the second prize winner is 48.
Since the first and second prize winners are no longer eligible.
The number of ways to choose the third prize winner is 47 .
Since the first, second, and third prize winners are no longer eligible.
and the number of ways to choose the fourth prize winner is 46 .
The total number of ways to choose four prize winners out of 49 entrants is,
= 49 x 48 x 47 x 46
= 5085024
However, probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes in that specific order.
The probability of this happening is,
(1/49) x (1/48) x (1/47) x (1/46)
= 1/5085024
= 0.0000001967
= 0.00000020
Therefore, probability of Bo, Colleen, Jeff, and Rohini winning first, second, third, and fourth prizes in specific order is 0.00000020.
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