Answer:
see explanation
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides
(11)
given 2 sides 2, 6 , then
6 - 2 < x < 6 + 2
4 < x < 8
(12)
Given 2 sides 4, 12 , then
12 - 4 < x < 12 + 4
8 < x < 16
(13)
Given 2 sides 2, 11 , then
11 - 2 < x < 11 + 2
9 < x < 13
If f(x) = x^2 + 8x – 2 and f(0), then the result is:
-2.
0.
8.
Answer:
-2.
Step-by-step explanation:
f(0) = 0^2 + 8(0) - 2
= -2.
What do the y-coordinates on the least-squares regression line represent?
Choose the correct answer below.
O A. The y-coordinates represent the minimum expected value of the response variable for any given value of the explanatory variable.
O B. The y-coordinates represent the values of the explanatory variable.
O C. The y-coordinates represent the mean value of the response variable for any given value of the explanatory variable
O D. The y-coordinates represent the maximum expected value of the response variable for any given value of the explanatory variable.
Solve , 6x + 5 = 2y
(Hint : Use ax + by + c = 0 )
Answer:
soln;
given equation is 6x + 5 = 2y
or, 6x -2y + 5 = 0
comparing with ax + by + c = 0
a = 6, b = -2, c = 5
Halliday physics obtain Heat loss rate of douple-pane window which thikness of glass layers 3mm and thikness of air layer 3mm and outside temperture -20F and inner temperure is +72F calculate it vs (w/m^2) glass Air k₁=0.78 k₂=0.026 +72F (M.K) (x) -2 OF I کمپاس 3
The heat loss rate (Q) in units of watts per square meter (W/\(m^2\)) for the given double-pane window is approximately 35.91 * A W/\(m^2\), where A is the area of the window in square meters.
Given:
Thickness of glass layers = 3mm
Thickness of air layer = 3mm
Outside temperature = -20°F = -28.9°C
Inside temperature = +72°F = 22.2°C
To calculate the heat loss rate, we will use the formula for heat conduction:
Q = (k * A * ΔT) / d
Where:
Q is the heat loss rate
k is the thermal conductivity
A is the area of the window
ΔT is the temperature difference between the inside and outside
d is the total thickness of the window
We need to convert the thicknesses of the glass and air layers to meters:
Thickness of glass layers = 3mm = 0.003m
Thickness of air layer = 3mm = 0.003m
We can now calculate the total thickness (d) of the window:
d = 2 * thickness of glass layers + thickness of air layer
d = 2 * 0.003m + 0.003m
d = 0.009m
Assuming the dimensions of the window are provided, let's consider:
Length = L meters
Width = W meters
The area of the window (A) is given by:
A = Length * Width
The thermal conductivity values in SI units are approximately:
k_glass ≈ 0.8 W/(m·K)
k_air ≈ 0.024 W/(m·K)
Now, let's calculate the temperature difference (ΔT) in Celsius:
ΔT = 22.2°C - (-28.9°C)
ΔT = 51.1°C
Substituting the values into the heat conduction formula:
Q = (k * A * ΔT) / d
Q = (0.8 W/(m·K) * A * 51.1°C) / 0.009 m
Simplifying further, we have:
Q = 44.89 * (0.8 * A) W
Therefore, the heat loss rate (Q) in units of watts per square meter (W/\(m^2\)) for the given double-pane window is approximately 35.91 * A W/\(m^2\), where A is the area of the window in square meters.
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what is the value of x geometry PLSS HELPP
The level of the tide in a harbor changed from 9 1/4 ft to 4 1/2 ft above sea level over a period of 3 1/4 hr
Answer:
The answer is "\(\bold{- \frac{19}{13} \ / hour}\)"
Step-by-step explanation:
Please find the complete question in the attached file.
Calculating the difference of \(9 \frac{1}{4}\ and \ 4 \frac{1}{2}\) dividing the value by \(3 \frac{1}{4}\)
\(\to 4 \frac{1}{2} - 9 \frac{1}{4}\\\\ \to \frac{9}{2} - \frac{37}{4}\\\\ \to \frac{18-37}{4} \\\\ \to -\frac{19}{4}\\\\\to -\frac{19}{4} \div \frac{13}{4}= -\frac{19}{4} \times \frac{4}{13} = -\frac{19}{13}\\\)
The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function: y = 14t2. a second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 149 feet per second and can be modeled by the function: y = 149t 1200. solve the system of equations. which solution represents a viable time that the trains are side by side? a. 14 seconds b. 15 seconds c. 16 seconds d. 17 seconds
The trains are side by side after approximately 15 seconds.Option (b) is correct.
How to solve system of equation?The position of the first train is given by the function:
\($$y_1 = 14t^2$$\)
The position of the second train is given by the function:
\($$y_2 = 130t + 1200$$\)
To find the time when the trains are side by side, we need to solve for the value of t that makes y1 = y2. Thus, we can set the two equations equal to each other:
\($$14t^2 = 130t + 1200$$\)
Rearranging the terms, we get:
\($$14t^2 - 130t - 1200 = 0$$\)
Dividing both sides by 2 to simplify the coefficients, we get:
\($7t^2 - 65t - 600 = 0$$\)
We can use the quadratic formula to solve for t:
\($t = \frac{-(-65) \pm \sqrt{(-65)^2 - 4(7)(-600)}}{2(7)} = \frac{65 \pm \sqrt{4225 + 16800}}{14}$$\)
Simplifying the expression under the square root, we get:
\($$\sqrt{21025} = 145$$\)
So the solutions are:
\($t_1 = \frac{65 + 145}{14}=15$$\)
\($t_2 = \frac{65 - 145}{14} \approx -5.71$$\)
Since time cannot be negative, we discard t2 as an extraneous solution. Thus, the viable time when the trains are side by side is:
\($t = t_1 =15$$\)
Therefore, the trains are side by side after approximately 15 seconds.
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Solve the problem by writing a inequality
Answer:
first option
Step-by-step explanation:
number of shirts = x
price of shirts made = 9x+20
amount u earn by selling the shirts = 15x
profit = 15x - (9x+20)
profit of at least 150,
15x - (9x+20) ≥ 150
Quad DEFG with mZD= (12x - 4),
mZE = (18x + 4)ºmZF = (15x + 10), and
m2G= (5x)
What is the value of x?
Answer: x = 7°
Explanation:
We know that sum of angles of a quadilateral is = 360°
Therefore ATQ
⇒ (12x-4)+(18x+4)+(15x+10)+(5x) = 360
⇒ (12x + 18x + 15x + 5x) + (-4+4+10) = 360
⇒ 50x + 10 = 360
⇒ 50x = 360-10
⇒ 50x = 350
⇒ x = 350/50
⇒ x = 7
Therefore value of x is 7°
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You are given that
x^2+ ax + b = (x - 5)^2+ 7
Work out the values of a and b.
The values of a and b from the equation is -10 and 32
Given the equation expressed as \(x^2+ ax + b = (x - 5)^2+ 7\)
Expand the right side of the equation to have:
\(x^2+ ax + b = (x - 5)^2+ 7\\x^2+ ax + b = x^2 -10x + 25 + 7\)
Simplify the result to have:
\(x^2+ ax + b = x^2 -10x + 32\)
Compare both sides of the equation:
ax = -10x
a = -10
Similarly;
b = 32
Hence the values of a and b from the equation is -10 and 32
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What is the most important characteristic of a correlation coefficient?
a. number of variables included
b. absolute value
c. one tailed
d. two tailed
Answer:
The most important characteristic of a correlation coefficient is the absolute value.
The absolute value of a correlation coefficient represents the strength of the relationship between two variables, regardless of the direction of the relationship. A correlation coefficient can range from -1 to +1, where a value of -1 indicates a perfect negative correlation (i.e., as one variable increases, the other decreases), a value of +1 indicates a perfect positive correlation (i.e., as one variable increases, the other also increases), and a value of 0 indicates no correlation (i.e., there is no relationship between the variables).
The most important characteristic of a correlation coefficient is the absolute value.
The absolute value of the correlation coefficient represents the strength of the relationship between two variables, regardless of its direction. It indicates the degree to which the variables are associated with each other.
By focusing on the absolute value, we can assess the magnitude of the correlation without being influenced by whether it is positive or negative. For example, a correlation coefficient of -0.8 or +0.8 both indicate a strong relationship, while a correlation coefficient of 0 suggests no relationship.
The number of variables included is not a characteristic of the correlation coefficient itself, but rather a consideration in the analysis. One-tailed and two-tailed refer to the type of hypothesis being tested and are relevant in statistical testing. However, the absolute value of the correlation coefficient is crucial in determining the strength of the relationship between variables, making it the most important characteristic to assess in correlation analysis.
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PLEASE HELP!!
The method 100 students use to get to school and their grade level is shown below.
Find the probability a student walks, given that they are a senior.
P(walk | senior) = [?]
The probability of being a senior is the total number of seniors divided by the total number of students.
The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.
The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.
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Give an example of matrices A, B, and C (of any size), such that B does not equal C, A does not equal 0, and yet AB = AC.
An example of matrices A, B, and C that fit the given conditions are:
A = | 1 2 |
| 3 4 |
B = | 5 6 |
| 7 8 |
C = | 9 10 |
| 11 12 |
Even though B does not equal C and A does not equal 0, the product of AB and AC are the same:
AB = | 1*5 + 2*7 1*6 + 2*8 |
| 3*5 + 4*7 3*6 + 4*8 | = | 19 22 |
| 43 50 |
AC = | 1*9 + 2*11 1*10 + 2*12 |
| 3*9 + 4*11 3*10 + 4*12 | = | 31 34 |
| 69 78 |
As you can see, the product of AB and AC are the same, even though B does not equal C and A does not equal 0. This is an example of how matrices can have the same product even if they are not the same matrix.
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Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
By using slope intercept , These were the two points on the line: (0,-2) and (7,2).
Define slope intercept?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.
These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.
We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).
So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.
Graph given below:
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find the scale factor
Answer:
\(\dfrac{2}{3}\)
Step-by-step explanation:
Method 1To find the scale factor of the dilation of a figure, simply divide the x-value (or y-value) of a vertex of the dilated image Q'R'S'T' by the x-value (or y-value) of the corresponding vertex of the pre-image QRST.
\(\implies \sf Scale\;factor=\dfrac{x_{Q'}}{x_{Q}}=\dfrac{-2}{-3}=\dfrac{2}{3}\)
\(\implies \sf Scale\;factor=\dfrac{y_{T'}}{y_{T}}=\dfrac{4}{6}=\dfrac{2}{3}\)
Therefore, the scale factor is 2/3.
Method 2To find the scale factor of the dilation of a figure, first find the lengths of corresponding sides using the distance formula.
\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)
From inspection of the given diagram:
Q = (-3, 9)R = (3, 6)\(\implies QR=\sqrt{(x_R-x_Q)^2+(y_R-y_Q)^2}\)
\(\implies QR=\sqrt{(3-(-3))^2+(6-9)^2}\)
\(\implies QR=\sqrt{(6)^2+(-3)^2}\)
\(\implies QR=\sqrt{36+9}\)
\(\implies QR=\sqrt{45}\)
\(\implies QR=3\sqrt{5}\)
From inspection of the given diagram:
Q' = (-2, 6)R' = (2, 4)\(\implies Q'R'=\sqrt{(x_{R'}-x_{Q'})^2+(y_{R'}-y_{Q'})^2}\)
\(\implies Q'R'=\sqrt{(2-(-2))^2+(4-6)^2}\)
\(\implies Q'R'=\sqrt{(4)^2+(-2)^2}\)
\(\implies Q'R'=\sqrt{16+4}\)
\(\implies Q'R'=\sqrt{20}\)
\(\implies Q'R'=2\sqrt{5}\)
To find the scale factor of dilation that maps QRST onto Q'R'S'T', divide the length of Q'R' by the length of QR:
\(\implies \dfrac{Q'R'}{QR}=\dfrac{2\sqrt{5}}{3\sqrt{5}}=\dfrac{2}{3}\)
Therefore, the scale factor is 2/3.
the teacher has data representing the scores of thousands of students. for each student, the data contain the student name, the midterm exam score, the final exam score, and the result of the total points calculation. which of the following could be determined from the data? i. the average total points earned per student ii. the average increase in total points per student as a result of the score replacement policy iii. the proportion of students who improved their total points as a result of the score replacement policy a. iii only b. i and ii only c. i and iii only d. i, ii, and iii
From the data, i and iii can be determined. The solution has been obtained by using statistics.
What is statistics?
Statistics is defined as "classified facts indicating the situations of a population in a state, notably the facts that can be stated in numbers or any other tabular or classed arrangement".
We are given that a teacher has data representing the scores of thousands of students.
From this data, we can determine the average total points earned per student as we are given the total points calculation.
Also, we can determine the proportion of students who improved their total points as a result of the score replacement policy from the given data.
Hence, option C is the correct answer.
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Gary had a 40% discount for car speakers. The sale price of the speakers was $90.What was the original price of the speakers?
The original price of the speakers are found to be $150.
What is meant by the term discount?The discount is equal to the difference between both the purchase price and the par value. A discount is a reduction as well as deduction in a product's cost price. It is most commonly used in purchase and sale of products, where people are given discounts on a variety of products. The discount rate is expressed as a percentage.For the given question;
Gary had a 40% discount for car speakers.
The sales price of the speakers was $90.
Let the original price be 'x'.
Thus,
Sales price = original price - discount.
90 = x - 40% of x
90 = x - 40x/100
90 = 6x/10
x = 900/6
x = 150
Thus, the original price of the speakers are found to be $150.
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a cone-shaped water reservoir is 20 ft in diameter across the top and 15 ft deep. if the reservoir is filled to a depth of 10 ft, how much work is required to pump all the water to the top of the reservoir?
The work required to pump all the water to the top of the reservoir is equal to the volume of the water (\(πr^2h\)) multiplied by the weight of the water.
1. Calculate the surface area of the cone-shaped water reservoir:
Surface Area = π * r * (\(r + sqrt(h^2 + r^2)\))
= π * (10 ft) * (10 ft + sqrt(\(15^2 + 10^2\)))
= π * (10 ft) * (10 ft + sqrt(225 + 100))
= π * (10 ft) * (10 ft + 17.32 ft)
= π * (10 ft) * 27.32 ft
= 860.48\(ft^2\)
2. Calculate the volume of water in the reservoir when filled to a depth of 10 ft:
Volume = (1/3) * π * \(r^2\)* h
= (1/3) * π *\((10 ft)^2\) * (10 ft)
= (1/3) * π * \(100 ft^2\) * 10 ft
= 333.33 \(ft^3\)
3. Calculate the total work required to pump all the water to the top of the reservoir:
Work = Volume * Height
= 333.33 \(ft^3\) * (15 ft - 10 ft)
= 333.33\(ft^3\) * 5 ft
= 1666.65 ft lbf
The work required to pump all the water to the top of the reservoir is equal to the volume of the water multiplied by the weight of the water. The volume of the water can be calculated using the formula for the volume of a cone, which is equal to where r is the radius of the base of the reservoir (10 ft) and h is the height of the water (10 ft). The weight of the water can be calculated using the formula for the weight of a volume of water, which is equal to the volume multiplied by the density of water, which is equal to 62.4 pounds per cubic foot. So, the work required to pump all the water to the top of the reservoir is equal to multiplied by 62.4 pounds per cubic foot.
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Test test the claim that the proportion of children from the low income group that did well on the test is different than the proportion of the high income group. Test at the 0.01 significance level.
This indicates that there is a significant difference in the proportions of children from low-income and high-income groups who performed well on the test.
a) Step 1: The null hypothesis formulate
H0: p1 = p2 where p1 is the proportion of children from low-income groups that did well on the test and p2 is the proportion of children from high-income groups that did well on the test
b) Step 2: The alternate hypothesis formulate
Ha: p1 ≠ p2 where p1 is the proportion of children from low-income groups that did well on the test and p2 is the proportion of children from high-income groups that did well on the test
c) Step 3: The level of significance define
α = 0.01
d) Step 4: The test statistic select
In this case, we use the z-test statistic
\(Z = (\hat p1 -\hat p2) - 0 / \sqrt{[(\hat p1 (1 - \hat p1)) / n1 + (\hat p2 (1 - \hat p2)) / n2)] [(\hat p1 (1 - \hat p1)) / n1 + (\hat p2 (1 - \hat p2)) / n2)]}\)
where n1 is the sample size of low-income children and n2 is the sample size of high-income children,\(\hat p1\) is the sample proportion of low-income children who did well, and \(\hat p2\)is the sample proportion of high-income children who did well.
e) Step 5: The critical value determine
Since α = 0.01, the critical value at two-tailed test is zα/2 = ± 2.58.
f) Step 6: The test statistic calculate
Z = (0.25 - 0.4) - 0 / √[(0.25(1 - 0.25)) / 200 + (0.4(1 - 0.4)) / 200]
Z = - 2.72
g) Step 7: A decision make
Using the critical value, since the test statistic Z = -2.72 is less than the critical value -2.58, we reject the null hypothesis. Therefore, there is enough evidence to suggest that the proportion of children from the low-income group that did well on the test is different than the proportion of the high-income group.
In conclusion, after following the steps for hypothesis testing, we found sufficient evidence to reject the null hypothesis. This indicates that there is a significant difference in the proportions of children from low-income and high-income groups who performed well on the test.
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PLEAS HELP ASAP 50 POINTS IF RIGHT: A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image.
A rectangular prism with dimensions of 7 feet by 3 feet by 4.8 feet.
Part A: Find the total surface area of the bench. Show all work. (6 points)
Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.89 per square foot, how much will it cost to cover the bench? Show all work. (6 points)
Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.
Given dimensions:
Length = 7 feet
Width = 3 feet
Height = 4.8 feet
Surface Area of each face:
Front and back faces: Length * Height
= 7 feet * 4.8 feet
= 33.6 square feet
Top and bottom faces: Width * Length
= 3 feet * 7 feet
= 21 square feet
Side faces: Width * Height
= 3 feet * 4.8 feet
= 14.4 square feet
Total Surface Area:
2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)
= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet
= 67.2 square feet + 42 square feet + 28.8 square feet
= 137 square feet
Therefore, the total surface area of the bench is 137 square feet.
Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.
Cost per square foot = $0.89
Total Surface Area = 137 square feet
Total cost to cover the bench:
= Cost per square foot * Total Surface Area
= $0.89 * 137 square feet
= $121.93
Therefore, it will cost $121.93 to cover the bench with ceramic tiles.
[3 + 3 + 3 pts] Let (Xn)n≥1 be a sequence of independent Bernoulli random variables with success probability p. Denote by S₁ the number of failures until the first success, by S₂ the number of failures between the first and second sucess, and, in general, by Sk the number of failures between the (k-1)th and the kth success. (a) Compute the joint probability mass function of S₁,..., Sn. (b) Are the random variables S₁,..., Sn independent? Prove or disprove. (c) Compute the cdf of U = max {S₁,..., Sn}.
(a) The joint PMF of S₁, S₂, ..., Sn is: P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)
(b) The random variables S₁,..., Sn are independent.
(c) the cumulative distribution function (CDF) of U is:
\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)
To compute the joint probability mass function (PMF) of S₁, S₂, ..., Sn, we need to consider the number of failures before each success.
(a) Joint probability mass function (PMF) of S₁, S₂, ..., Sn:
Let's first define the random variable S as the sequence of failures until the first success:
S = (S₁, S₂, ..., Sn)
Now, let's calculate the PMF of S:
P(S = (s₁, s₂, ..., sₙ))
Since the random variables X₁, X₂, ..., Xₙ are independent Bernoulli random variables with success probability p.
The probability of getting s failures before the first success is given by:
\(P(S_1 = s_1) = (1 - p)^{s_1} \times p\)
The probability of getting s₂ additional failures before the second success is:
\(P(S_2 = s_2) = (1 - p)^{s_2} \times p\)
\(P(S_3 = s_3) = (1 - p)^{s_3} \times p\)
And so on, until the probability of getting sₙ additional failures before the nth success:
\(P(S= s) = (1 - p)^{s} \times p\)
Now, since the random variables S₁, S₂, ..., Sn are independent, the joint PMF is the product of the individual probabilities:
P(S = (s₁, s₂, ..., sₙ)) = P(S₁ = s₁) × P(S₂ = s₂)×... × P(Sₙ = sₙ)
Therefore, the joint PMF of S₁, S₂, ..., Sn is:
P(S₁ = s₁, S₂ = s₂, ..., Sₙ = sₙ) =\((1 - p)^{(s_1 + s_2 + ... + s_n) } \times p^n\)
(b)
To determine whether the random variables S₁, S₂, ..., Sn are independent, we need to check if the joint PMF factorizes into the product of the individual PMFs.
Let's consider three random variables, S₁, S₂, and S₃:
P(S₁ = s₁, S₂ = s₂, S₃ = s₃) = P(S₁ = s₁) ×P(S₂ = s₂) × P(S₃ = s₃)
Using the joint PMF calculated in part (a), we can rewrite this as:
\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1)} \times p \times (1 - p)^{(s_2)} \times p \times (1 - p)^{(s_3)}\times p\)
Simplifying, we have:
\((1 - p)^{(s_1 + s_2 + s_3)} p^3 = (1 - p)^{(s_1 + s_2 + s_3)} p^3\)
Since the equation holds true for any values of s₁, s₂, and s₃, we can conclude that the random variables S₁, S₂, and S₃ are indeed independent.
(c)
To compute the CDF of U, we need to determine the probability that U is less than or equal to a given value u.
CDF of U:
F(u) = P(U ≤ u) = 1 - P(U > u)
Since U represents the maximum value among S₁, S₂, ..., Sn, we have:
P(U > u) = P(S₁ > u, S₂ > u, ..., Sn > u)
Using the independence of S₁, S₂, ..., Sn, we can express this probability as:
P(U > u) = P(S₁ > u)×P(S₂ > u) × ...× P(Sn > u)
The probability that a single random variable Si is greater than u (where Si represents the number of failures between the (i-1)th and the ith success) is:
P(Si > u) = 1 - P(Si ≤ u) = 1 - ∑(k=0 to u) P(Si = k)
Using the PMF derived in part (a), we can calculate this probability:
\(P(Si > u) = 1 - \sum (1 - p)^(^k^) \times p\) (k=0 to u)
Finally, substituting this back into the expression for P(U > u), we have:
\(P(U > u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\) (k=0 to u)
Therefore, the cumulative distribution function (CDF) of U is:
\(F(u) = (1 - \sum (1 - p)^{(k)} \timesp)^n\)
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I need help with math pls help!!!
Answer:
4/3
-1/2
Step-by-step explanation:
A
company expects to receive $40,000 in 10 years time. What is the
value of this $40,000 in today's dollars if the annual discount
rate is 8%?
The value of $40,000 in today's dollars, considering an annual discount rate of 8% and a time period of 10 years, is approximately $21,589.
To calculate the present value of $40,000 in 10 years with an annual discount rate of 8%, we can use the formula for present value:
Present Value = Future Value / (1 + Discount Rate)^Number of Periods
In this case, the future value is $40,000, the discount rate is 8%, and the number of periods is 10 years. Plugging in these values into the formula, we get:
Present Value = $40,000 / (1 + 0.08)^10
Present Value = $40,000 / (1.08)^10
Present Value ≈ $21,589
This means that the value of $40,000 in today's dollars, taking into account the time value of money and the discount rate, is approximately $21,589. This is because the discount rate of 8% accounts for the decrease in the value of money over time due to factors such as inflation and the opportunity cost of investing the money elsewhere.
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The sum of two numbers is 12
and their product is 32.
What are the two numbers ?
Answer:
8 and 4
Step-by-step explanation:
8 x 4= 32
8+4 = 12
Jade fell another 660 meters during the next 12 seconds. How much greater is the unit rate of her freefall in this portion of her drop than the previous 12 seconds?
36 is the answer thats all i think this is the answer
given the equation 4x^2 − 8x + 20 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)^2 + k = 0? a. h = 4, k = −16 b. h = 4, k = −1 c. h = 1, k = −24 d. h = 1, k = 16
the values of h and k when the equation is written in vertex form a(x − h)^2 + k = 0 is (d) h = 1, k = 16.
To write the given quadratic equation \(4x^2 - 8x + 20 = 0\) in vertex form, \(a(x - h)^2 + k = 0\), we need to complete the square. The vertex form allows us to easily identify the vertex of the quadratic function.
First, let's factor out the common factor of 4 from the equation:
\(4(x^2 - 2x) + 20 = 0\)
Next, we want to complete the square for the expression inside the parentheses, x^2 - 2x. To do this, we take half of the coefficient of x (-2), square it, and add it inside the parentheses. However, since we added an extra term inside the parentheses, we need to subtract it outside the parentheses to maintain the equality:
\(4(x^2 - 2x + (-2/2)^2) - 4(1)^2 + 20 = 0\)
Simplifying further:
\(4(x^2 - 2x + 1) - 4 + 20 = 0\)
\(4(x - 1)^2 + 16 = 0\)
Comparing this to the vertex form, \(a(x - h)^2 + k\), we can identify the values of h and k. The vertex form tells us that the vertex of the parabola is at the point (h, k).
From the equation, we can see that h = 1 and k = 16.
Therefore, the correct answer is (d) h = 1, k = 16.
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Solve this quadratic equations: 10k^2-9k+2=0.
\large k=
\large k=
A Boeing 737 airplane travels about 500 miles per hour. The function d(t) = 500t represents the number
miles traveled in t hours. How far does the plane travel in 3.5 hours?
A. O 2,579.50 miles
B. 1,500.00 miles
C. 142.86 miles
D. 1,750.00 miles
Answer:
b
Step-by-step explanation:
The distance is 1,750.0 miles if a Boeing 737 airplane travels about 500 miles per hour option (D) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function d(t) = 500t represents the number of miles traveled in t hours.
Plug t = 3.5 hours in the equation of the function.
d(3.5) = 500(3.5)
d(3.5) = 1,750.0 miles
Thus, the distance is 1,750.0 miles if a Boeing 737 airplane travels about 500 miles per hour option (D) is correct.
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solve for variable y answer in simplest radical form
Answer:
option A
Step-by-step explanation:
option A y = 9√3 is the correct answer .
In∆ PQR
cos 30 = y /18
√3/2 = y / 18
y = 9√ 3
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
Evaluate the expression. −8÷−4 CLEAR CHECK −2 −12 12 2
Evaluate the expression is -10.
How should examples of expressions be evaluated?You must replace each variable with a number and carry out the arithmetic procedures to evaluate an algebraic expression. As 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can replace our variables with their values if we know what they are, then evaluate the expression after doing so.
The division can be done as follows when assessing the phrase 8 4:
−8 ÷ −4 = 2
The expression is thus reduced to:
2 - 12
12 is subtracted from 2 to yield:
-10
Thus, -10 is the correct response.
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