After answering the presented question, we can conclude that The equation number of trials is predetermined: We're going to roll the dice 20 times.
What is equation?An equation is a statement in mathematics that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). For example, 2 + 3 = 5 is an equation because the expression on the left-hand side (2 + 3) is equal to the expression on the right-hand side (5).
Equations are used in many areas of mathematics, science, and engineering to describe relationships between quantities and to solve problems. For example, equations are used to model physical phenomena, such as the motion of objects, the behavior of fluids, and the propagation of waves. They are also used in finance, statistics, and many other fields to analyze data and make predictions.
In this case, the random variable X reflects the number of times a specific number appears after rolling a 20-sided die 20 times.
To see if this situation fits the binomial distribution model, we must look at the four conditions listed below:
The trials are impartial: Each throw of the dice is distinct from the others.
There are just two possibilities: Each roll can produce one of the 20 numbers or none at all.
The likelihood of success is constant: The probability of rolling a given number on a 20-sided dice is the same for each roll.
The number of trials is predetermined: We're going to roll the dice 20 times.
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5. Heidi's family is trying to decide on the shorter
of two routes for a trip from Georgetown to
Cypress City. One route begins in Georgetown
and goes 53 miles to Cycle City, then 28 miles
to Aspen and 98 miles to Cypress City. The
second route also begins in Georgetown and
goes 28 miles to Canon City, then 49 miles to
Grover and 85 miles to Cypress City. Which
route is shorter and by how much?
Answer: We can find the total distance of the first route by adding the individual distances:
53 + 28 + 98 = 179 miles
Similarly, we can find the total distance of the second route:
28 + 49 + 85 = 162 miles
Therefore, the second route is shorter by (179 - 162) = 17 miles.
Step-by-step explanation:
Find the height of the basketball hoop
Answer: 13.51 (not in inches format)
Step-by-step explanation:
tan(x) = 4.384/12
x = tan^-1 (4.384/12)
x = 20.068°
tan(20.068) = y/(12+25)
tan(20.068) = y/37
20.068 = tan^-1 (y/37)
y = 13.51
Answer:
Step-by-step explanation:
To solve this with similar triangles - you need to set up a proportion.
I changed it all to inches.
12 ft = 144 in
4.384 ft = 51. 84 inches
12 + 25 (you need to add the base of the triangle) = 37 ft = 444 inches
set up smaller triangle in proportion to bigger triangle
51.84"/144" = x/444
cross mulitply then divide
51.84 times 444 = 23016.96
23016.96 ÷ 144 = 159.84 inches
Change back to feet by dividing by 12
159.84 ÷ 12 = 13.32 ft
you have 40 scarves and 55 hats to make identical donation bags. you make the greatest amount of donation bags with no clothing left over. how many scarves and hats are in each donation bag?
To create identical donation bags, you will need 55 hats and 40 scarves. You produce the most donation bags without any extra apparel. Each donation package contains 11 hats and 8 scarves.
To make the greatest amount of donation bags with no clothing left over, we need to find the greatest common factor (GCF) of 40 and 55. We can do this by finding the prime factors of both numbers:
[tex]40 = 2 * 2 * 2 * 5[/tex]
55 = 5 x 11
The GCF is the product of the common prime factors, which is 5. This means we can make 5 identical donation bags.
To find out how many scarves and hats are in each donation bag, we can divide the total number of scarves and hats by the number of donation bags:
Number of scarves per bag = 40 / 5 = 8 scarves
Number of hats per bag = 55 / 5 = 11 hats
Therefore, each donation bag will contain 8 scarves and 11 hats.
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Miyako hits a jump and follows the path of a parabola.
Her height can be modeled by the equation h = -16t² + 32t + 15,
where his her height in feet after t seconds. Graph the function.
Interpret the key features of the graph in terms of the quantities.
A parabolic function is represented by h = -16T² + 32T + 151.
Describe the parabolic function?A function with the equation f(x) = ax²+ bx + c is said to be parabolic. It is a second-degree quadratic expression in x². A parabola-like form can be seen in the graph of a parabolic function. The range value for the parabolic function is the same for two different domain values. Parabolic motion refers to a variety of motions, such as the motion of a stone thrown under the influence of gravity.
. The function's greatest or minimum value is where the parabola's vertex is located. In this instance, the formula -b/2a,
where a = -16 and b = 321, can be used to get the vertex of the parabola. As a result, this parabola's vertex is located at t = 1 second and h = 31 feet.
The parabola's vertex is located at t = 1 second and h = 31 feet. These are the main characteristics of this graph.
The parabola's axis of symmetry is a vertical line that passes through its vertex.
Because the coefficient of t² is negative, the parabola begins to slope downward.
- The maximum height that Miyako reaches is 31 feet.
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write down a polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4).
The required polynomial of exact degree 5 which interpolates the four given points is equals to p(x) = x^3/2 -4x^2 + 63x/6 -6.
Polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4).
Apply Lagrange interpolation.
Standard form of the Lagrange interpolation polynomial of degree n passing through n+1 distinct points (x0, y0), (x1, y1), ..., (xn, yn) is,
L(x) = Σ [yi × Π (x - xj) / (xi - xj)], for i = 0, 1, ..., n
where Π is the product operator and j takes all values different from i.
For the given four points, we have n = 3, so the polynomial has degree n+1 = 4.
Using the formula, we have,
L(x) = (1× (x - 2)(x - 3)(x - 4) / ((1 - 2)(1 - 3)(1 - 4)))
+ (3× (x - 1)(x - 3)(x - 4) / ((2 - 1)(2 - 3)(2 - 4)))
+ (3× (x - 1)(x - 2)(x - 4) / ((3 - 1)(3 - 2)(3 - 4)))
+ (4× (x - 1)(x - 2)(x - 3) / ((4 - 1)(4 - 2)(4 - 3)))
Simplifying this expression, we get,
⇒L(x) = (-x^3 + 9x^2 - 26x + 24)/6 + (3x^3/2 - 12x^2 + 57x/2 - 18) +(-3x^3/2 + 21x^2 /2- 21x + 12) + (2x^3/3 - 4x^2 + 22x/3 - 4)
⇒L(x) = x^3/2 -4x^2 + 63x/6 -6
Therefore, the polynomial of degree exactly 5 that interpolates the four points (1, 1), (2, 3), (3, 3), (4, 4) is p(x) = x^3/2 -4x^2 + 63x/6 -6.
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GEOMETRY PLS HELP ASAP
Answer:
1) 5
Step-by-step explanation:
Trapezoid Midsegment Theorem:
EF = (DC + AB) / 2
2x + 2 = ((x + 3) +(5x - 9)) / 2
4x + 4 = 6x - 6
-2x = -10
x = 5
pls solve thisss......
The height of the cone is 15cm.
How to find the radius of the object?From the question;
Height of cylinder = 28cm
Let the radius of the solid object = Rcm
The slant height of the cone = 17cm
Cost of painting = Rs. 140 per 100 sq cm
Cost of painting 1 cm² = 140/100 = RS1.4
The total cost of painting = Rs. 2851.2
Total area of the object = total cost of painting/Cost of painting per sq cm
Total area of the object = 2851.2/1.4 = 2036.57143 cm²
Total surface area of object = CSA of Cylinder + CSA of cone + area of the circle at the bottom
Total surface area of the object = [tex]\pi rh + \pi rl + \pi r^2[/tex]
So, [tex]\frac{2851.2}{1.4}[/tex] = [tex]\pi rh + \pi rl + \pi r^2[/tex]
[tex]\frac{2851.2}{1.4}[/tex] = [tex]2\pi r * 28 + \pi r * 17 + \pi r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1232}{7}r =+\frac{374}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1606}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{2}[/tex]= [tex]1606r + 22r^2[/tex]
[tex]14256 = 1606r + 22r^2[/tex]
[tex]22r^2 + 1606r - 14256 =0[/tex]
Solving the quadratic equation, the possible value of radius are:
r = 8cm
r = -81cm
r = -81cm will be neglected because radius can not be negative.
Therefore, the radius of the object is 8cm
To find the height of the cone, we should know that the relation between radius, height and slant height of the cone is:
[tex]l^2 = r^2 + h^2[/tex]
[tex]h=\sqrt{l^2 - r^2}[/tex]
[tex]h=\sqrt{17^2 - 8^2}[/tex]
[tex]h=\sqrt{225}[/tex]
[tex]h=15cm[/tex]
Therefore, height of cone in the solid object is 15cm
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Find the area and perimeter 20 12
Y=-x+1
Y= 2/3x-4
How many solutions does it have?
Answer:
x = -5
Y = -22/3
Step-by-step explanation:
Y= 2/3x - 4 Y = -x + 1
We put -x + 1 in for y to solve for x
-x + 1 = 2/3x - 4
-5/3x + 1 = -4
-5/3x = -5
x = -5
Now put -5 in for x and solve for y
Y= 2/3(-5) - 4
Y = -10/3 - 4
Y = -22/3
So, there are only one solution x = -5 and y = -22/3
Solve The table shows the costs of a membership and fruit baskets at a discount warehouse club. Item Cost ($) Membership Fee 30 Fruit Basket 15 Mrs. Williams paid a total of $105 for her annual membership fee and several fruit baskets as gifts for her coworkers. Solve the equation 15x+30=105 to find the number of fruit baskets Mrs. Williams purchased.
PLS HELP!!! (AND HURRY)
Answer:
The given equation is:
15x + 30 = 105
Here,
15x represents the total cost of the fruit baskets purchased, and
30 represents the cost of the membership fee.
To find the number of fruit baskets purchased (x), we must isolate the variable on one side of the equation.
Subtracting 30 from both sides, we get:
15x = 105 - 30
15x = 75
Dividing both sides by 15, we get:
x = 5
Therefore, Mrs. Williams purchased 5 fruit baskets for her coworkers.
Find an for each geometric sequence.
a₁= 3r= 1/10 n=8
O a. 3
Ob. 2 4/10
Oc.
3
10,000,000
Od. 2 1/10
The geometric sequence for the value of a₁= 3 r= 1/10 n=8 is [tex]a_{8} = \frac{3}{10000000}[/tex] i.e option c is correct.
What does the term "geometric sequence" mean?
A geometric sequence is a set of integers where the ratio between each pair of succeeding terms is fixed. The geometric sequence's general ratio is the name of this constant.
We can use the following algorithm to determine the nth term (an) of a geometric sequence:
[tex]a_{n} = a_{1} * r^{n-1}[/tex]
where a1 is the first term in the series, r represents the common ratio, and n denotes the term's number.
Since a1 = 3, r = 1/10, and n = 8, we get:
[tex]a_{8} = 3 * (\frac{1}{10})^{8-1} = 3 *( \frac{1}{10})^{7}[/tex]
[tex]= 3 * \frac{1}{10^{7} }[/tex]
Now, we can condense this equation to get the solution:
a₈ = [tex]\frac{3}{10000000}[/tex]
The solution is therefore [tex]\frac{3}{10000000}[/tex] that option c.
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in an article in the journal of management, joseph martocchio studied and estimated the costs of employee absences. based on a sample of 176 blue-collar workers, martocchio estimated that the mean amount of paid time lost during a three-month period was 1.3 days per employee with a standard deviation of 1.4 days. martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.1 day per employee with a standard deviation of 1.6 days.
suppose we randomly select a sample of 100 blue-collar workers. based on martocchio
The probability shows that if the mean μ=1, then only 0.0027 is at least as small as the sample mean x=1.5. This also leads to the conclusion that if we believe that μ = 1, we must also believe that there is a 27 in 10,000 chance that our observed sample mean can be described as such.
To achieve the goal of this task, use the mean μ x and the standard deviation σ x.
The task has two conditions, the first is that the standard deviation σ is 1.3 days and the second is that the standard deviation σ is 1.8 days.
If the standard deviation σ is 1.3, then the mean μ is 1.4. And if the standard deviation is σ 1.8, then the mean is μ₁. In this case, the given standard deviation is μ 1.8, so use the second condition to achieve the task goal.
we know that:
μₓ = μ and σₓ = σ/√n
Given that:
μ = 1, σ = 1.8 and n = 100
So, by the formula of standard deviation σₓ,
σₓ = σ/√n = 1.8/√100
= 0.18
Calculate the probability with the mean μ=1, and standard deviation
σₓ =0.18.
P(x > 1.5) = P(z > 0.5/0.18)
= P( z > 2.78)
Looking at the z table, first, find the units and decimals in the first column of the z table. In this case, search for 2.7 first. Then look in which column the 100th value is placed. In this case, 0.08 and follow the number of lines placed 2.7.
Therefore, the value of 2.78 in table z is 0.9973 because z=0.9973, and the right tail area is 0.0027 or (1−0.9973).
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help asap!!!!!!!!!!!!!!!!!
Answer:
126 meters squared
Step-by-step explanation:
To find the surface area
For the top and bottom it will be: l x w x 2(because there's a top and bottom)
3x6x2 = 36
For the sides (left and right) it will be: l x h x 2 (There's left and right)
3x5x2 = 30
For the front and back it will be w x h x 2 (There's the front and the back)
6x5x2 = 60
Added it all together and you get 126
The surface area is 126 meters squared
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AC = 9 and AD = 4, solve for CD. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."
Since AB is tangent to circle E at A, we know that angle CAB is a right angle (tangent is perpendicular to the radius at the point of tangency). Therefore, triangle ADC is a right triangle.
Let's use the Pythagorean theorem to find the length of CE:
CE^2 = AC^2 + AE^2 (using Pythagorean theorem in triangle ACE)
CE^2 = 9^2 + EA^2 (since AE = EA, by definition of radius)
CE^2 = 81 + EA^2
We still need to find EA. Let's use the fact that EA is half the length of CD:
EA = CD/2
Now we can substitute this expression into the previous equation:
CE^2 = 81 + (CD/2)^2
CE^2 = 81 + CD^2/4
Next, let's use the Pythagorean theorem in triangle ADC:
AD^2 + DC^2 = AC^2
4^2 + DC^2 = 9^2
DC^2 = 9^2 - 4^2
DC^2 = 65
Now we can substitute this expression into the previous equation:
CE^2 = 81 + 65/4
CE^2 = 99.25
Taking the square root of both sides, we get:
CE ≈ 9.96
Therefore, CD = 2CE ≈ 19.9.
Answer: CD ≈ 19.9
Find the area of the Square
1 in
1 in
please explain I'll mark brainlisest
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
For the first question, the measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is IQR, because it is robust to outliers and can provide a better representation of the spread of data for skewed distributions. The option "IQR, because Desert Landing is symmetric" is incorrect because the graph of Desert Landing is not symmetric.
For the second question, we need to compare the measures of center (mean and median) of the two sets of data to determine which shop typically sells the most amount of coffee per hour. To do this, we can calculate the mean and median of each set of data:
For Coffee Ground, the mean is (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5)/12 = 6.25 gallons and the median is the middle value of the ordered set, which is 5 gallons.
For Wide Awake, the mean is (2.5+10+4+18+4+3+6.5+15+6+5+2.5)/11 = 6.136 gallons and the median is the middle value of the ordered set, which is 4.5 gallons.
Therefore, we can conclude that Wide Awake typically sells the most amount of coffee per hour, with a median value of 4.5 gallons. The option "Wide Awake, with a mean value of about 4.5 gallons" is incorrect because the mean value of Wide Awake is slightly lower than 4.5 gallons. The option "Coffee Ground, with a median value of 5 gallons" is incorrect because the median value of Coffee Ground is lower than the median value of Wide Awake. The option "Coffee Ground, with a mean value of about 5 gallons" is incorrect because the mean value of Coffee Ground is higher than 5 gallons.
19 3/5 × 20 2/5 secial product patterns to find the product
Answer: 19 3/5 x 20 2/5 = 9996/25 = 399 21/25
What are the coordinates of each point after quadrilateral ABCD is reflected across the y-axis?
est.
nas
ge
5. In a survey, of the students at one
25
school said they wanted to become
doctors and 16% of the students
at
the same school said they wanted to
become teachers. The rest of the
students were undecided. Which of
the following represents the students
who were undecided?
Percentage of students who were undecided is 59% of the students were undecided about their future careers.
what is Percentage?
A percentage is a fraction or ratio expressed as a fraction of 100. It is a way of expressing a part of a whole as a proportion of the whole. It is denoted by the symbol '%'. For example, if there are 100 students in a class and 20 of them are girls, then the percentage of girls in the class is 20%.
In the given question,
To solve the problem, we need to first find out the percentage of students who were undecided. We know that 25% of the students wanted to become doctors and 16% wanted to become teachers. The percentage of students who were undecided can be found by subtracting the sum of the percentages of those who wanted to become doctors and teachers from 100%:
Percentage of students who were undecided = 100% - (25% + 16%) = 59%
Therefore, 59% of the students were undecided about their future careers.
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Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of the bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 bass in the pond.
If P represents the actual population of the bass in the pond and t represents the elapsed time in years, then which of the following systems of inequalities can be used to determine the possible number of bass in the pond over time?
The inequalities that can be used to determine the possible number of bass in the pond over time are:
[tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]
Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 basses in the pond.
Inequalities
Given:
r=4.8/100=0.048
Initial amount:
Lower end=250
Upper end=275
Using this equation to determine the inequalities
A=p×e^rt
Where:
A=Amount
P=Population
r=Growth rate
t=Time
Let's plug in the formula
Inequalities:
[tex]P > =250e^{0.048t}P < =275e^{0.048t}[/tex]
Therefore the inequalities are : [tex]P > =250e^{0.048t} , P < =275e^{0.048t}.[/tex]
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what is the length of the missing leg? If necessary, round to the nearest tenth.
Answer:
48 yards
Step-by-step explanation:
Use the Pythagorean theorem:
[tex] {a}^{2} = {52}^{2} - {20}^{2} = 2704 - 400 = 2304[/tex]
[tex]a > 0[/tex]
[tex]a = \sqrt{2304} = 48 \: yd[/tex]
I need help, I wasn't in school for 2 weeks because of vacation and nobody is helping me in class!
(a) Since M is the midpoint of DE, we have ME = (1/2)b.
Also, CXE is a straight line, so C, X, and E are collinear.
Therefore, we have CX + XE = CE, or a - b + FE = b + (2a - b), which simplifies to FE = a.
(b) n = a/b - 1.
How do we calculate?X is the point on FM such that
FX:XM =n:1,
we have FX = nX and XM = X.
Since M is the midpoint of DE, we have ME = (1/2)b,
so that DX = DE - EX = b - (n + 1)X.
Using the fact that CXE is a straight line,
we have CX + XE = CE, or a - b + FE = b + (2a - b),
which simplifies to FE = a.
Therefore, we have FX + FE = AX, or nX + a = a + b + (n + 1)X.
Simplifying, we get b = (n + 1)X - nX = X.
We know that DX = b - (n + 1)X = 0, so X = b/(n + 1).
Therefore, we have n/(n + 1) = FX/X = (a-b)/b.
Calculating for n, we have n = a/b - 1.
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what is the average voter turnout during an election? a random sample of 38 cities was asked to report the percent of registered voters who actually voted in the most recent election.
A random sample of 38 cities was asked to report their voter turnout percentages, which can be used to estimate the average voter turnout in those cities. However, caution should be taken when making generalizations about the larger population of cities, since the sample size is relatively small.
The average voter turnout during an election can be calculated by taking the percentage of registered voters who actually voted in a sample of cities and finding the mean. In this case, a random sample of 38 cities was asked to report the percent of registered voters who voted in the most recent election. To calculate the average voter turnout, follow these steps:
1. Obtain the reported voter turnout percentages from each of the 38 cities in the random sample.
2. Add up all the percentages of voter turnout from the 38 cities.
3. Divide the sum of voter turnout percentages by the number of cities (38) to find the average voter turnout.
By following these steps, you will find the average voter turnout for the most recent election, based on the random sample of 38 cities. Keep in mind that the average voter turnout can vary depending on the election and location, as factors such as political climate, awareness, and accessibility can impact voter participation. This calculated average represents an estimation of the overall turnout and may not be completely representative of the entire population, but it provides a useful measure to understand voter engagement during elections.
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One of the sides of a parallelogram has the length
of 5 in. Can the lengths of the diagonals be
4 in. and 6 in.?
Answer:
Yes they can.
The only time they would have to be different lengths is if it was a square
What should Andre estimate for the probability of picking out a green block from this bag
The answer using probability are shown:
(A) 43/60 projection is used.
(B) He shouldn't alter the estimate in light of this knowledge.
What is probability?Simply put, the probability is the likelihood that something will occur.
When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.
Statistics is the study of occurrences that follow a probability distribution.
Mathematics' study of random events is known as probability, and there are four major kinds of probability: axiomatic, classical, empirical, and subjective.
So, he would calculate the amount by dividing the overall number of bricks by the proportion of green bricks. The likelihood of choosing a green block out of all 60 bricks would be that.
Then, the probability would be:
= 43/60
Andre shouldn't alter his assessment, in other words.
The explanation is that we do not know whether the bricks he saw were green in color; we are only told that she looked in the bag and found 6 bricks.
The only time Andre needs to adjust his guess is if it turns out that the six bricks Mai saw in the bag were, in fact, green.
The estimate should not be altered until this proof is received.
Therefore, the answer using probability are shown:
(A) 43/60 projection is used.
(B) He shouldn't alter the estimate in light of this knowledge.
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Complete question:
Andre picks a block out of a bag 60 times and notes that 43 of them were green. What should Andre estimate for the probability of picking out a green block from this bag? Mai looks in the bag and sees that there are 6 blocks in the bag. Should Andre change his estimate based on this information? If so, what should the new estimate be? If not, explain your reasoning.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3186
grams and a variance of 385,641
. if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be between 3682
and 4552
grams. round your answer to four decimal places.
please need help asap
The probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.
To find the probability that a newborn baby boy's weight Convert the weights to z-scores:
z = (X - μ) / σ, where X is the weight, μ is the mean, and σ is the standard deviation.
First, calculate the standard deviation:
σ = √variance = √385,641 ≈ 621
Now, calculate the z-scores for the given weights:
z1 = (3682 - 3186) / 621 ≈ 0.7986
z2 = (4552 - 3186) / 621 ≈ 2.1965
Use a standard normal table or a calculator with a standard normal probability function to find the probabilities corresponding to these z-scores:
P(Z ≤ 0.7986) ≈ 0.7879
P(Z ≤ 2.1965) ≈ 0.9858
Find the probability that the weight is between the two z-scores:
P(0.7986 ≤ Z ≤ 2.1965) = P(Z ≤ 2.1965) - P(Z ≤ 0.7986) ≈ 0.9858 - 0.7879 ≈ 0.1979
So, the probability that a randomly selected newborn baby boy's weight is between 3682 and 4552 grams is approximately 0.1979, or 19.79% when rounded to four decimal places.
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you flip it twice more and get heads twice more. now what is the conditional probability that the coin you chose is fake?
The conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is higher than the initial probability.
Let A be the event that the coin chosen is fake, and B be the event that the three flips resulted in heads. We are given that the probability of choosing the fake coin is 0.1, i.e. P(A) = 0.1, and the probability of getting heads with the fake coin is 1, i.e. P(B|A) = 1. The probability of getting heads with the fair coin is 0.5, i.e. P(B|A') = 0.5, where A' is the event that the coin chosen is fair. Using Bayes' theorem, we can calculate the conditional probability of A given B:
P(A|B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|A') * P(A'))
Plugging in the given values, we get:
P(A|B) = 1 * 0.1 / (1 * 0.1 + 0.5 * 0.9) = 0.18
Therefore, the conditional probability that the coin chosen is fake given that it was flipped three times and all three flips resulted in heads is 0.18, which is higher than the initial probability of 0.1. This means that the evidence of three consecutive heads increases the likelihood that the coin is fake.
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(Using trig to find an angle)
Solve for x. Round to the nearest tenth of a degree, if necessary.
Angle B is approximately 53.15 degrees using trigonometry.
EquationsWe can use trigonometry to solve for angle B in the right triangle BCD. We know that angle CBC is 37 degrees, and BD is 64.
First, we can use the Pythagorean theorem to find the length of BC, which is the hypotenuse of the right triangle:
[tex]BC^{2}[/tex] = [tex]BD^{2}+CD^{2}[/tex]
[tex]BC^{2}[/tex] = 64² + [tex]CD^{2}[/tex]
Since CD is opposite angle B, we can use trigonometry to relate CD to angle B. Specifically, we can use the tangent function:
tan(B) = CD/BD
Rearranging, we have:
CD = BDxtan(B)
Taking the square root of both sides, we have:
BC = 64[tex]\sqrt{(1+tan^{2}B)}[/tex]
Now we can use the fact that BC is the hypotenuse of the right triangle to relate it to angle CBC, which is 37 degrees. Specifically, we can use the sine function:
sin(CBC) = BD/BC
Substituting our expression for BC, we have:
sin(37) = 64/64√(1 + tan²(B))
Simplifying, we get:
sin(37) = 1/[tex]\sqrt{(1+tan^{2}B)}[/tex]
Squaring both sides, we have:
sin²(37) = 1/[tex](1+tan^{2}B)}[/tex]
Substituting the identity cos²(θ) + sin²(θ) = 1, we have:
cos²(37) = cos²(B)
Taking the square root of both sides, we have:
cos(37) = ±cos(B)
Since angle B is acute (it is less than 90 degrees because it is in a right triangle), we know that cos(B) is positive. Therefore, we can take the positive square root:
cos(B) = cos(37)
B = 53.15 degrees (rounded to two decimal places)
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URGENT PLEASE HELP ME !!!!!!
What are the coordinates of the point on the directed line segment from (-10,10) to (2,-8) that partitions the segment into a ratio of 2 to 1?
The coordinate of the segment in the ratio is (-2,-2).
What is ratio?
When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.
Partitions the line segment in the ratio A to B... then,
=> x-coordinate is : x1 +[tex]\frac{ A(x2-x1)}{(A+B)}[/tex]
=> y-coordinate is: y1 + [tex]\frac{A(y2-y1)}{(A+B)}[/tex]
Here A = 2 , B = 1 and [tex](x_1,y_1)=(-10,10)[/tex] , [tex](x_2,y_2)=(2,-8)[/tex] .
x-coordinate = -10+[tex]\frac{2(2+10)}{(2+1)}[/tex] = -10 + [tex]\frac{2(12)}{3}[/tex] = -10 + 2(4) = -10+8 = -2
y-coordinate = 10+[tex]\frac{2(-8-10)}{(2+1)}=10+\frac{2(-18)}{3}[/tex] = 10+2(-6) = 10-12 = -2.
Hence the coordinate of the segment in the ratio is (-2,-2).
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a candy distributor needs to mix a 10% fat-content chocolate with a 50% fat-content chocolate to create 100 kilograms of a 14% fat-content chocolate. how many kilograms of each kind of chocolate must they use?
The candy distributor needs to use 30 kilograms of 10% fat-content chocolate and 70 kilograms of 50% fat-content chocolate to create 100 kilograms of a 14% fat-content chocolate.
To solve this problem, we can use the method of mixture problems, which involves setting up a system of equations. Let x be the number of kilograms of the 10% fat-content chocolate and y be the number of kilograms of the 50% fat-content chocolate.
We have two equations based on the fat content and the total weight of the mixture:
0.1x + 0.5y = 0.14(100) (equation for fat content)
x + y = 100 (equation for total weight)
We can solve this system of equations using substitution or elimination. Using substitution, we can solve for x in terms of y from the second equation and substitute it into the first equation:
x = 100 - y
0.1(100 - y) + 0.5y = 0.14(100)
10 - 0.1y + 0.5y = 14
0.4y = 4
y = 10
Then we can substitute y = 10 back into the equation for x and get:
x = 100 - y = 100 - 10 = 90
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