so here we get two outcomes one is 2 and other is 4.
so there is total 2 outcomes.
total no. of possibility is 5
so the probability of waiting between 2 and 4 minutes to use the ATM is 2/5.
cyryl hikes a distance of 0.75 kilomiters in going to school every day draw a number line to show the distance
Answer:
Step-by-step explanation:
Sure! Here's a number line showing the distance of 0.75 kilometers:
0 -------------|-------------|------------- 0.75 km
The "0" on the left represents the starting point (such as home), and the "|---|" in the middle represents the distance of 0.75 kilometers to the destination (such as school).
There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability P_i, i, .., N. Hence, P_1 + P_2 +... + P_N = 1. Let T denote the number of coupons one needs to select to obtain at least one of each type. Compute P(T > n).
If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.
Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:
P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)
By the principle of inclusion-exclusion, we can write:
P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.
This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.
In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.
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You might need: Calculator, Z table
Suppose that 15% of the 1750 students at a school have experienced
extreme levels of stress during the past month. A high school newspaper
doesn't know this figure, but they are curious what it is, so they decide to
ask a simple random sample of 160 students if they have experienced
extreme levels of stress during the past month. Subsequently, they find
that 10% of the sample replied "yes" to the question.
Assuming the true proportion is 15%, what is the approximate probability
that more than 10% of the sample would report that they experienced
extreme levels of stress during the past month?
The approximate probability that more than 10% of the sample would report that they experienced extreme levels of stress during the past month, obtained using the z-score for the proportion of the sample, and the standard error, is about 96.327%
What is the z-score of a proportion?The z-score of a sample proportion, z can be obtained using the formula;
z = (p - π)/√(π·(1 - π)/n)
Where;
p = The sample proportion
π = The proportion of the population
n = The sample size
The percentage of the students out of the 1750 students that experienced extreme levels of stress in the school, p = 15%
The number of students in the sample used by the newspaper, n = 160 students
The number of students in the sample that replied "yes" = 10%
The true proportion of the students that experience stress = 15%
The probability that ,more than 10% of the sample would report that they experienced extreme levels of stress during the past month can be found as follows;
The standard error is; SE = √(p × (1 - p)/n)
Therefore;
SE = √(0.15 × (1 - 0.15)/160) ≈ 0.028
The z-score is therefore;
z = (0.1 - 0.15)/0.028 ≈ -1.79
z = -1.79
The z-score indicates the number of standard deviations the proportion of the sample is from the true proportion
The proportion on the of the sample which is larger than 10% is obtained from the area under the normal curve, to the right of the z-score of -1.79, which is obtained as follows;
The z-value at z = -1.79 is 0.03673, which indicates that the area to the left of the z-value is 0.03673, and the area to the right is; (1 - 0.03673) = 0.96327
The probability observing a sample proportion more than 10% if the actual proportion is 15% is therefore; 0.96327 = 96.327%
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Find the total labour charges for a job that takes; 2 1/2hours Time (h) 1/2 1 2 3 4 Charges 1,200 1400 1 800 2,200 2,600
Answer:
The total labor charges for the job are P3,500.
Step-by-step explanation:
To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.
For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.
So, the total labor charges for 2 1/2 hours of work are
P1,200 + P1,400 + P900 = P3,500
Therefore, the total labor charges for the job are P3,500.
The Khan Shatyr Entertainment Center in Kazakhstan is the largest tent in the world. The spire on top is 60 m in length. The distance from the center of the tent to the outer edge is 97.5 m. The angle between the ground and the side of the tent is 42.7°.
Find the total height of the tent (h), including the spire.
Find the length of the side of the tent (x)
i. The total height of the tent including the spire is 150 m.
ii. The length of the side of the tent x is 132.7 m.
What is a trigonometric function?Trigonometric functions are required functions in determining either the unknown angle of length of the sides of a triangle.
Considering the given question, we have;
a. To determine the total height of the tent, let its height from the ground to the top of the tent be represented by x. Then:
Tan θ = opposite/ adjacent
Tan 42.7 = h/ 97.5
h = 0.9228*97.5
= 89.97
h = 90 m
The total height of the tent including the spire = 90 + 60
= 150 m
b. To determine the length of the side of the tent x, we have:
Cos θ = adjacent/ hypotenuse
Cos 42.7 = 97.5/ x
x = 97.5/ 0.7349
= 132.67
The length of the side of the tent x is 132.7 m.
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If F1 =(3,0), F2 =(−3,0) and P is any point on the curve 16x^2 + 25y^2 = 400, then PF1 + PF2 equals to:861012
The value of PF1 + PF2 equals to 10 for any point P on curve ellipse of equation 16x^2 + 25y^2 = 400. So, the correct answer is B).
We can start by finding the coordinates of the point P on curve of the ellipse. We can write the equation of the ellipse as:
16x^2 + 25y^2 = 400
Dividing both sides by 400, we get:
x^2/25 + y^2/16 = 1
So, the center of the ellipse is at the origin (0,0) and the semi-axes are a=5 and b=4.
Let the coordinates of point P be (x,y). Then, we can use the distance formula to find the distances PF1 and PF2:
PF1 = sqrt((x-3)^2 + y^2)
PF2 = sqrt((x+3)^2 + y^2)
Therefore, PF1 + PF2 = sqrt((x-3)^2 + y^2) + sqrt((x+3)^2 + y^2)
We can use the property that the sum of the distances from any point on an ellipse to its two foci is constant, and is equal to 2a, where a is the semi-major axis. So, we have:
PF1 + PF2 = 2a = 2(5) = 10
Therefore, PF1 + PF2 equals to 10 for any point P on the ellipse 16x^2 + 25y^2 = 400. So, the correct option is B).
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can you find the slope of the given graph?
slope of graph=?
The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12
What is the slope of a graph?The slope of a graph is the derivative of the graph at that point.
Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).
To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.
So, f(x) = 3x² + 7
Differentiating with respect to x,we have
df(x)/dx = d(3x² + 7)/dx
= d3x²/dx + d7/dx
= 6x + 0
= 6x
dy/dx = f'(x) = 6x
At (-2, 19), we have x = -2.
So, the slope f'(x) = 6x
f'(-2) = 6(-2)
= -12
So, the slope is -12.
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The definition of differentiable also defines an error term E(x,y). Find E(x,y) for the function f(x,y)=8x^2 − 8y at the point (−1,−7).E(x,y)=
The value of error term E(x,y) = 8x^2 - 8x - 56.
The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:
f(x,y) - f(a,b) = L(x,y) + E(x,y)
where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).
In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).
First, we need to calculate f(-1,-7):
f(-1,-7) = 8(-1)^2 - 8(-7) = 56
Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):
∇f(-1,-7) = (16,-8)
The linear function L(x,y) is given by:
L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)
where · denotes the dot product.
Substituting the values, we get:
L(x,y) = 56 + (16,-8) · (x+1, y+7)
= 56 + 16(x+1) - 8(y+7)
= 8x - 8y
Finally, we can calculate the error term E(x,y) as:
E(x,y) = f(x,y) - L(x,y) - f(-1,-7)
= 8x^2 - 8y - (8x - 8y) - 56
= 8x^2 - 8x - 56
Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.
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Alberto believes that because all squares can be called
rectangles, then all rectangles must be called squares.
Explain why his reasoning is flawed. Use mathematical
terminology to help support your reasoning.
Alberto's statement is flawed because all squares can be called rectangles, but not vice versa
Reason why Alberto's statement is flawedAlberto's reasoning is flawed because all squares can be called rectangles, but not all rectangles are squares.
While it is true that squares meet the definition of rectangles, not all rectangles meet the definition of squares.
A square is a special type of rectangle with all sides equal in length.
Therefore, Alberto's argument violates the logical concept of implication, where the truth of one proposition (squares can be called rectangles) does not necessarily imply the truth of the converse (all rectangles must be called squares).
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calculate the are of given figure
true/false. the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables
The statement " the continuity correction must be used because the normal distribution assumes variables whereas the binomial distribution uses discrete variables" is true because continuity correction is used to adjust for the discrepancy between continuous and discrete variables when approximating a discrete distribution
The continuity correction is used when approximating a discrete distribution, such as the binomial distribution, with a continuous distribution, such as the normal distribution. The normal distribution assumes continuous variables, while the binomial distribution uses discrete variables.
The continuity correction helps to account for the fact that the normal distribution is continuous, whereas the binomial distribution is not. It adjusts the boundaries of the intervals used in the approximation, to better reflect the underlying discrete nature of the data.
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what is the Taylor's series for 1+3e^(x)+x^2 at x=0
The Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
What do you mean by Taylor's series ?
The Taylor's series is a way to represent a function as a power series, which is a sum of terms involving the variable raised to increasing powers. The series is centered around a specific point, called the center of the series. The Taylor's series approximates the function within a certain interval around the center point.
The general formula for the Taylor's series of a function f(x) centered at [tex]x = a[/tex] is:
[tex]f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...[/tex]
where [tex]f'(a), f''(a), f'''(a),[/tex] etc. are the derivatives of f(x) evaluated at [tex]x = a[/tex].
Finding the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] :
We need to find the derivatives of the function at [tex]x=0[/tex]. We have:
[tex]f(x) = 1 + 3e^x + x^2[/tex]
[tex]f(0) = 1 + 3e^0 + 0^2 = 4[/tex]
[tex]f'(x) = 3e^x+ 2x[/tex]
[tex]f'(0) = 3e^0 + 2(0) = 3[/tex]
[tex]f''(x) = 3e^x + 2[/tex]
[tex]f''(0) = 3e^0 + 2 = 5[/tex]
[tex]f'''(x) = 3e^x[/tex]
[tex]f'''(0) = 3e^0 = 3[/tex]
Substituting these values into the general formula for the Taylor's series, we get:
[tex]f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...[/tex]
[tex]f(x) = 4 + 3x + 5x^2/2 + 3x^3/6 + ...[/tex]
Simplifying, we get:
[tex]f(x) = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
Therefore, the Taylor's series for [tex]1 + 3e^x + x^2[/tex] at [tex]x=0[/tex] is :
[tex]1 + 3e^x+ x^2 = 5 + 3x + (3/2)x^2 + (1/3)x^3 + ...[/tex]
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Let g(x) = 3x^2 - 2x + 4. Evaluate g(5)
Answer:
g(5)=69
Step-by-step explanation:
g(5)=3(5)^2-2(5)+4
g(5)=75-10+4
g(5)=69
2. write how many degrees are angle between.
a) North and East _______
Answer:
N and E is 90 degrees
N and S is 180 degrees
N and W is 90 degrees
An initial deposit of $800 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $800 is added to the account.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is __________.
The balance of the account after the seventh deposit can be calculated using the formula below:
A = P (1 + r/n)ⁿ
where:
A = the balance of the account
P = The initial deposit of $800
r = the interest rate of 5%
n = the number of times the interest is compounded annually
n = 1
Therefore, the balance of the account after the seventh deposit is:
A = 800 (1 + 0.05/1)⁷
A = 800 (1.05)⁷
A = 800 (1.4176875)
A = 1128.54
Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.
How many degrees are there in 5/8 of a circle
Answer:
Step-by-step explanation:
First the max degree is 360
Then multiply by 5/8
360 x 5/8 = 1800/8
1800/8 = 225
Answer: 225
6TH GRADE MATH PLS HELP TYSM
Answer:
m = 1
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-1,0) (0,1)
We see the y increase by 1 and the x increase by 1, so the slope is
m = 1
Help please need to pass this
Answer:
45%
Step-by-step explanation:
86 people play an instrument out of 192 students.
86/192 = .4479
.4479 x 100% = 44.79% = 45%
Answer: 45 percent
Step-by-step explanation:
What is the integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y = x2 - 3x and y = x about the horizontal line y = 6? * 18 (6 - x2 + 3x)2-(6- x)?dx o Tejo (6-x2+3x)2 - (6 - x)?dx OTS (6 - 12 - (6 - x2 + 3xPdx Orla (6 - XP2 – (6-x2 + 3x)
The integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y = x₂ - 3x and y = x about the horizontal line y = 6 is 2πx(6 - x² + 3x)dx, which is integrated from x=0 to x=3, which gives us 81π/2.
To find the integral expression for the volume of the solid formed by revolving the region bounded by the graphs of y=x² - 3x and y=x about the horizontal line y=6, we can use the method of cylindrical shells.
First, we need to find the limits of integration, The graphs of y = x² - 3x and y=x intersect at x=0 and x=3. Therefore, we integrate from x=0 to x=3.
Next, we consider a vertical strip of width dx at a distance x from the y- boxes. the height of the strip is the difference between the height of the curve y= x² - 3x and the line y=6, which is 6 - (x² - 3x) = 6 - x² + 3x. the circumference of the shell is 2π times the distance x from the y-axis, and the thickness of the shell is dx. the volume of the shell is the product of the height, circumference, and thickness which is
dV = 2πx(6 - x² + 3x)dx
To find the total volume, we integrate this expression from x=0 to x=3.
V = ∫₀³ 2πx(6 - x² + 3x)dx, after simplifying the integrand we get :
V = 2π ∫₀³ (6x - x³ + 3x²)dx, integrating term by term we get :
V = 2π [(3x²/2) - (x⁴/4) + (x^3)] from 0 to 3, now evaluation at the limits of integration we get:
V = 2π [(3(3)²/2) - ((3)⁴/4) + (3)³] - 2π [(0)^2/2 - ((0)⁴/4) + (0)^3]= 2π [(27/2) - (27/4) + 27] - 0 = 81π/2
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Which of the columns in the table below is categorical data? Name Position Goals Bob Goal 0 Cindy Wing 5 Maurice Center 10 Luke Center 15 A. Name B. Goals C. Position
The categorical data in the table is column C, Position.
What is table?In mathematics and statistics, a table is a way of presenting data in a structured manner, typically with columns and rows. Tables are commonly used to organize and present large amounts of data in a clear and concise way, making it easier to read and analyze. Tables can be used to display numerical data, as well as categorical data, such as names, dates, and labels. They can also be used to summarize data and display relationships between different variables. Tables are often used in scientific research, business, finance, and other fields where data analysis is important.
Here,
In the table given, the only column that contains categories or groups is the "Position" column. It contains categorical data as it lists the positions of the players - Goal, Wing, and Center. On the other hand, "Name" and "Goals" columns contain individual values and numerical data, respectively, and are not considered categorical data.
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- Please help me, I don't understand
What is the specific heat of an unknown substance if 100.0 g of it at 200.0 °C reaches an equilibrium temperature of 27.1 °C when it comes in contact with a calorimeter of water. The water weighs 75. g and had an initial temperature of 20.00 °C? (Specific heat of water is 4.18 J/g°C). Show your work
Answer:The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius (or Kelvin).
To find the specific heat of the unknown substance, we can use the following equation:
Q = m x c x ΔT
where Q is the heat gained or lost, m is the mass of the substance, c is its specific heat, and ΔT is the change in temperature.
In this problem, we know the mass and initial and final temperatures of both the unknown substance and the water, as well as the specific heat of water. We can use this information to calculate the heat gained by the water, which must be equal to the heat lost by the unknown substance:
Heat gained by water = Heat lost by unknown substance
m(water) x c(water) x ΔT(water) = m(substance) x c(substance) x ΔT(substance)
We can plug in the values we know and solve for the specific heat of the unknown substance:
m(water) = 75.0 g
c(water) = 4.18 J/g°C
ΔT(water) = 27.1 °C - 20.00 °C = 7.1 °C
m(substance) = 100.0 g
ΔT(substance) = 200.0 °C - 27.1 °C = 172.9 °C
75.0 g x 4.18 J/g°C x 7.1 °C = 100.0 g x c(substance) x 172.9 °C
Simplifying this equation, we get:
c(substance) = (75.0 g x 4.18 J/g°C x 7.1 °C) / (100.0 g x 172.9 °C)
c(substance) = 0.197 J/g°C
Therefore, the specific heat of the unknown substance is 0.197 J/g°C.
Step-by-step explanation:
Answer:
The specific heat of the unknown substance is 0.39 J/g°C.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of energy, which states that the heat lost by the unknown substance is equal to the heat gained by the water and the calorimeter. We can express this principle mathematically as:
Q_lost = Q_gained
where Q_lost is the heat lost by the unknown substance, and Q_gained is the heat gained by the water and calorimeter.
We can calculate Q_lost using the formula:
Q_lost = m × c × ΔT
where m is the mass of the unknown substance, c is its specific heat, and ΔT is the change in temperature it undergoes.
We can calculate Q_gained using the formula:
Q_gained = (m_water + m_calorimeter) × c_water × ΔT
where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat of water, and ΔT is the change in temperature of the water and calorimeter.
Since the system reaches an equilibrium temperature, we can set Q_lost equal to Q_gained and solve for the specific heat of the unknown substance (c).
Here's the calculation:
Q_lost = Q_gained
m × c × ΔT = (m_water + m_calorimeter) × c_water × ΔT
100.0 g × c × (200.0 °C - 27.1 °C) = (75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)
Simplifying:
c = [(75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)] / (100.0 g × (200.0 °C - 27.1 °C))
c = 0.39 J/g°C
Therefore, the specific heat of the unknown substance is 0.39 J/g°C.
A sports car accelerates from a stopped position (0 m/s) to 27.7 m/s in 2.4 seconds. What is the acceleration of the car?
Using simple division we know that the acceleration per second is 11.54 m/s.
What is division?Multiplication is the opposite of division.
If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The division is a mathematical process that includes dividing a sum into groups of equal size.
For instance, "12 divided by 4" translates to "12 shared into 4 equal groups," which would be 3 in our example.
So, to find the acceleration per second:
We need to perform division as follows:
= 27.7/2.4
= 11.54
Therefore, using simple division we know that the acceleration per second is 11.54 m/s.
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Find a vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the nullspace: A = [1 2 1 2 4 3 3 6 4].
A vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the null space. The orthogonal vector is :
A = [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]
The orthogonal complement of the subspace V contains any vector perpendicular to V. This orthogonal subspace is denoted V⊥. (pronounced "V perp").
By this definition, null space is the orthogonal complement of row space. Every x perpendicular to the line satisfies Ax = 0 and lies in null space.
vice versa. If v is orthogonal to null space, it must be in row space. Otherwise, we can add this v as an extra row of the matrix without changing its null space. The rice space will become larger, breaking the rule of r+(n−r) = n.
The column space extent of A. These two vectors are the basis of col(A) , but they are not normalized.
In this case, the columns of A are already orthonormal, so you don't need to use the Gram-Schmidt procedure. To normalize a vector and then divide it by its norm:
[tex]\left[\begin{array}{ccc}1&2&1\\2&4&3\\3&6&4\end{array}\right][/tex]
and the vector after orthogonal process is:
[tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]
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Fill in the missing values so that the fractions are equivalent
Step-by-step explanation:
1. 2/10
2.3/15
3.4/20
4. 5/25
5.6/30
6.7/35
What is the value of the underlined digit?
5(3)
Enter the correct answer in the box.
Answer: tens
Step-by-step explanation:
Find the sum of 67 kg 450g and 16 kg 278 g?
A special bag of Starburst candies contains 20 strawberry, 20 cherry, and 10 orange. We will select 35 pieces of candy at random from the bag. Let X = the number of strawberry candies that will be selected. a. The random variable X has a hypergeometric distribution with parameters M= , and N= n= b. What values for X are possible? c. Find PCX > 18) d. Find PX = 3) e. Determine E[X] or the expected number of strawberry candies to be selected. f. Determine Var[X]. The Binomial Distribution input parameters output The mean is The number of trials n is: The success probability p is: Binomial Probability Histogram dev. is: 1 Enter number of trials Must be a positive integer. Finding Probabilities: 0.9 0.8 Input value x fx(x) or P(X = x) Fx(x) or P(X 3x) 0.7 0.6 Input value x fx(x) or P(X = x) Fx(x) or P(X sx) 0.5 0.4 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0.3 0.2 0.1 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0 0 0 0 0 0 0 0 0 0 0
It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.
X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.
X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.
Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.
Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.
The expected value of X is E[X] = np = 35(20/50) = 14.
The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.
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the simplest form of the expression sqr3-sqr6/sqr3+sqr6?
Answer:
1 - [tex]\frac{2\sqrt{2} }{3}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3}-\sqrt{6} }{\sqrt{3}+\sqrt{6} }[/tex]
rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
the conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{6}[/tex]
= [tex]\frac{(\sqrt{3}-\sqrt{6})(\sqrt{3}-\sqrt{6}) }{(\sqrt{3}+\sqrt{6})(\sqrt{3}-\sqrt{6}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{3-\sqrt{18}-\sqrt{18}+6 }{3-\sqrt{18}+\sqrt{18}+6 }[/tex]
= [tex]\frac{9-2\sqrt{18} }{3+6}[/tex]
= [tex]\frac{9-2(3\sqrt{2}) }{9}[/tex]
= [tex]\frac{9-6\sqrt{2} }{9}[/tex]
= [tex]\frac{9}{9}[/tex] - [tex]\frac{6\sqrt{2} }{9}[/tex]
= 1 - [tex]\frac{2\sqrt{2} }{3}[/tex]
ne al Compute the derivative of the given function. TE f(x) = - 5x^pi+6.1x^5.1+pi^5.1
The derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.
The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].
Combining these terms together, the derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
This answer is the derivative of the given function. This is how the function changes as its input changes.
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The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾
To calculate the derivative of the given function, we begin by applying the power rule to each term.
The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].
The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].
The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].
Therefore, the derivative of the given function
f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].
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Question:
Compute the derivative of the given function.
f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]
Find the area of a semicircle whose diameter is 28cm
Answer:
The area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.
Step-by-step explanation:
A semicircle is a two-dimensional shape that is exactly half of a circle.
The area of a circle is given by the formula:
[tex]\sf A=\pi r^2[/tex]
where A is the area of the circle, and r is the radius of the circle.
The diameter of a circle is twice its radius.
Given the diameter of the semicircle is 28 cm, the radius is:
[tex]\sf r = \dfrac{28}{2} = 14 \; cm[/tex]
Substituting this into the formula for the area of a circle, we get:
[tex]\sf A = \pi(14)^2[/tex]
[tex]\sf A = 196 \pi[/tex]
Finally, divide this by two to get the area of the semicircle:
[tex]\sf Area\;of\;semicircle = \dfrac{1}{2} \cdot 196 \pi[/tex]
[tex]\sf Area\;of\;semicircle = 98 \pi\; cm^2[/tex]
So the area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.
