Let A and B be two disjoint events such that P(A) = 0.47 and P(B) = 0.3.
What is P(A or B)?
Answers
Work Shown:
P(A or B) = P(A) + P(B)
P(A or B) = 0.47 + 0.30
P(A or B) = 0.77
Notes:
The formula only works if A and B are disjoint, aka mutually exclusiveIf A and B are not disjoint, then use this formula: P(A or B) = P(A) + P(B) - P(A and B)Answer:
P(A or B) = 0.77
Step-by-step explanation:
Related Questions
What is the product of 5 x 5 1/3
Answers
Answer:
26\(\frac{2}{3}\)
Step-by-step explanation:
The required product of expression 5 × 5 1/3 is given as 80/3 or 26 1/3.
Given that, to determine the product of 5 x 5 1/3.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
According to the question,
= 5 × 5 1/3,
= 5 × 5 + 1 / 3
= 5 × 16 / 3
= [5 × 16]
= 80 / 3
= 26 1 /3
Thus, The required product of 5 × 5 1/3 is given as 80/3 or 26 1/3.
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7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
Answers
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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Anne had seven times as many stickers as Jasminka. Anne then lost 13 stickers at school. If x represents the number of stickers that Jasminka has, which expression below represents the number of stickers Anne has left?
A. 7(x - 13)
B. 7x - (x - 13)
C. 7x - 13
D. (7x + 13) - x
Answers
How to factor 3x^3 - 48x
Answers
Given the expression:
\(3x^3-48x\)First, we use common factor:
\(3x(x^2-16)\)Now, we use difference of squares:
\(3x(x+4)(x-4)\)ANSWER
3x(x - 4)(x + 4)
A skier IS skiing down a slope on the mountain.
Is the mechanical energy conserved? Why or why not?
Answers
Answer:
The mechanical energy isn't conserved.
Step-by-step explanation:
Honeslty I think you should Start cheatin on your Hw
Answer:
The mechanical energy is not conserved
Step-by-step explanation:
Recall that the law of conservation of energy states that in an isolated system (no external forces acting on it), the mechanical energy is conserved.
A skier skiing down a slope is not an isolated system in this case because the friction of the snow causes some of the mechanical energy to convert to thermal energy.
Optimal Chapter-Flight Fare If exactly 212 people sign up for a charter flight, Leisure World Travel Agency charges $292/person. However, if
more than 212 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how
many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 212. Show that the
revenue function R is given by R(x) = (212+x)(292-x).
passengers
What is the maximum revenue?
$
What would be the fare per passenger in this case?
dollars per passenger
Answers
Answer:
Dollars per passenger would be $252.
The maximum revenue is $63,404.
Step-by-step explanation:
Let's define the number of passengers above 212 as x.
The revenue function is given by R(x) = (212 + x)(292 - x).
We can expand and simplify the revenue function:
\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)
= \(61804 - 212x + 292x - x^2\)
= \(-x^2 + 80x + 61804\)
The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.
To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).
\(x=\frac{-80}{2*(-1)}\)
\(= \frac{80}{2}\)
\(= 40\)
Therefore, the number of passengers above 212 for maximum revenue is 40.
Substitute x = 40 into the revenue function to find the maximum revenue:
\(R(x) = -(40)^2 + 80(40) + 61804\)
\(= -1600 + 3200 + 61804\)
\(= 61804 + 1600\)
\(= 63404\)
Hence, the maximum revenue is $63,404.
To determine the fare per passenger, subtract x from the base fare of $292:
Fare per passenger = Base fare - x
\(= 292 - 40\)
\(= 252\) Dollars per passenger.
2a+c=162.97
how do you use the elimination method for this
Answers
When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation
To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.
The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.
In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':
2a + c = 162.97
Rearrange the equation to isolate 'c':
c = 162.97 - 2a
Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.
For example, let's say we choose 'a' = 10:
c = 162.97 - 2(10)
c = 162.97 - 20
c = 142.97
So, when 'a' is 10, 'c' is approximately 142.97.
You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.
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Felica is trying to simplify the expression 9 + (8 x 9) - (18\3
Answers
Answer:
The answer is 75.
Step-by-step explanation:
First, we apply the rule of PEMDAS (or whatever order of operations rule you have learned). In this equation, we first solve inside the parentheses.
8 x 9 = 72
18/3 = 6
Now, our equation has become 9 + 72 - 6. We can solve this left to right:
9 + 72 = 81
81 - 6 = 75
What other pair of corresponding congruent parts is needed to prove that the two triangles are congruent by ASA congruence postulate?
Answers
By another pair of sides along with pair of angles we can prove that two triangles are congruent by ASA congruence postulate.
What is ASA Congruence Postulate?
A set of triangles can be proven to be congruent using the angle-side-angle rule.
According to the ASA rule, two triangles are congruent if their two included sides and two angles are the same as those of another triangle.
Using the ASA Congruence Postulate and by considering the following image,
∠ B = ∠ Q, ∠ C = ∠ R and sides between ∠B and ∠C , ∠Q and ∠ R are equal to each other.
i.e. BC= QR.
Hence, Δ ABC ≅ Δ PQR.
Therefore, By another pair of sides along with pair of angles we can prove that two triangles are congruent by ASA congruence postulate.
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A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle. The subtended arc is how many times as long as the circle's radius? 07 _ 15 = 8 O15 _ 7 = 8 7 0.467 15 15 0.341 2T0 15 2.143
Answers
The subtended arc is 2.14 times as long as the circle's radius.
What is radius of circle?
A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of those line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
Given:
A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle.
The radius of the circle is 7 and length of the subtend are is 15 cm. The required value is given by:
Subtended arc / Radius = 15 / 7 = 2.14
Therefore, option (e) is the correct answer.
Hence, the subtended arc is 2.14 times as long as the circle's radius.
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A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answers
Answer:
Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)
Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2
Answers
There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.
Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.
Denote this path as P. Let x be the vertex on path P that is closest to v.
By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.
Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.
Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
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For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
Answers
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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Question in the attachment
Answers
Answer:
Step-by-step explanation:
this is really tricky
so the first pick will make sense
P(m1) 26/46 for pick on.. but that removed one male from the population and also one from the total
P(m2) 25/45
now multiply those two fractions together to get the total probability
26/46 * 25/45 = 650/2070 obviously reduce fraction
65/207= .3140096618
They don't say if you are supposed to use a percent or not
so just try 0.314 :/
A satellite 200 miles above the earth is orbiting the earth once every 6 hours. How far does the satellite travel in 1 hour?
(Assume the radius of the earth is 4,000 miles.) Give your answer as both an exact value and an approximation to three significant digits
Answers
Answer:
The answer is below
Step-by-step explanation:
Speed is the ratio of total distance travelled to total time taken to cover distance.
The radius of the orbit = radius of earth + height of satellite from earth = 4000 miles + 200 miles = 4200 miles
The total distance around the orbit = perimeter of orbit = 2π(radius of orbit) = 2π(4200) = 8400π miles
\(Speed=\frac{distance \ traveled}{time\ taken} =\frac{8400\pi\ miles}{6\ hours} =1400\pi\ miles/hour\\\\Distance \ traveled\ in \ 1\ hour=1400\pi\ miles/hour*1\ hour=1400\pi\ miles=4398.23\ miles\\\\Distance=4398\ miles\)
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
Answers
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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3. An investor plans to invest $500/year and expects to get a 10.5% return. If the investor makes these contributions at the end of the next 20 years, what is the present value (PV) of this investment today?
Answers
The present value (PV) of the investment today is approximately $2,965.05.
To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.
The formula for the present value of an annuity is given by:
PV = C * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.
Let's plug in these values into the formula and calculate the present value (PV):
PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]
Using a calculator, we can evaluate the expression inside the brackets:
PV = $500 * [(1 - 0.376889) / 0.105]
Simplifying further:
PV = $500 * [0.623111 / 0.105]
PV = $500 * 5.930105
PV = $2,965.05
Therefore, the present value (PV) of the investment today is approximately $2,965.05.
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3
Which number line shows a number equivalent to
1 Sume
Choose 1 answer:
ctions
++
wat tract
>
2
0
1
A
U
HHH
iz 1
X 8 min
>
2
0
1
N
ctions
FE
4HHHH
0
>
2
1
iz 2
6 3 mor
Answers
Answer: B
Step-by-step explanation:
2/3 means 1.5
what does 7,124 ÷ 26 equal to?
Answers
274
hope that helps
:D
btw i used long division
Part B A constant of proportionality is the same as a unit rate. The point (1/3, 1) represents the unit rate In kilograms per inch. Which point represents the unit rate in inches per kilogram?
Answers
Answer:
x: weight in kilograms
y: distance stretched in inches
proportionality constant:
Step-by-step explanation:
Answer:
The point (1, 3) represents the unit rate in inches per kilogram.
Step-by-step explanation:
Got it form the assignment
PLZ I WILL GIVE BRAINLEST
Bobby has 38 dolar and his siter had 92 dolar how much more money sister have?
Answers
Answer:
54
Step-by-step explanation:
92 (how much his sister has) - 38 (how much he has) = 54 (how much more money his sister has then him)
Answer: His sister had 54 more dollars than him.
Step-by-step explanation: 92 (sister's amount) -38 (Bobby's amount) = 54 (total difference).
The scatterplot below shows a data set
and an approximate trend line for the
data.
7
6
5
3
1
0 10 20 30 40 50 60 70
Which is the best estimate of the value of
x that corresponds to y = 3? (8.18, 8.10,
SIE, SIF)
Where does
F 35
the line y = 3
G 25
intersect the
trend ine?
H 50
10
Answers
Ayuda porfa es para ahora
Answers
Answer:
i really dont know this is hard hm
Step-by-step explanation:
chance paid $15.52 for stamps so he could mail thank you notes for wedding gifts. the number of $0.05 stamps was 26 more than twice the number of $0.39 stamps. How many $0.39 stamps, and $0.05 stamps were purchased?
Answers
Answer:
I'm pretty sure the number of stamps purchase is about 132 stamps
I’ll give BRAINLIEST if correct need ASAP pls
Answers
Explanation :
which choice is equivalent to the expression below? The square root of -81.
A:-9
B:-/sqrt/9
C:i/sqrt/9
D:9i
E:sqrt/9i
Answers
Answer:
D: 9 i
Step-by-step explanation:
The square root of -81 is 9 i.
What is the value of csc 47° to the nearest thousandth?
Answers
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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Find the area and perimeter of ABC. A(-2,-4)B(1,5)C(2,2)
Answers
The area of triangle ABC is 23.5 square units and the perimeter is 20.4174 units.
To find the area and perimeter of the given triangle ABC, we need to apply the following formulas:Formula for Distance between two points:
The distance between two points (x1, y1) and (x2, y2) is given by:
AB = √(x2-x1)²+(y2-y1)²BC = √(x3-x2)²+(y3-y2)²AC = √(x3-x1)²+(y3-y1)²
Formula for Area of Triangle: If we know the length of the three sides of a triangle then,
using Heron's formula, we can calculate the area of the triangle as:
area = √s(s-a)(s-b)(s-c)where a, b, and c are the lengths of the sides of the triangle and s is the semi-perimeter of the triangle, which is given as s = (a+b+c)/2
Formula for Perimeter of Triangle: The perimeter of the triangle is the sum of the lengths of its sides.
That is: perimeter = AB + BC + ACArea of ΔABCAB
= √(1 - (-2))² + (5 - (-4))²AB
= √3²+9² = √90BC
= √(2 - 1)² + (2 - 5)²BC
= √1²+3² = √10AC
= √(2 - (-2))² + (2 - (-4))²AC
= √4²+6²
= √52Semi-Perimeter (s)
= (AB + BC + AC)/2
= (√90 + √10 + √52)/2
= 12.8572Area of ΔABC
= √s(s-a)(s-b)(s-c)
= √12.8572(12.8572-√90)(12.8572-√10)(12.8572-√52)
= 23.5
Perimeter of ΔABC = AB + BC + AC = √90 + √10 + √52 = 20.4174
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Solve the following polynomial:
(
x
−
2
)
2
(
x
+
2
)
4
(
x
−
5
)
2
Answers
Answer: 16 • (x - 2) • (x + 2) • (x - 5)
Step-by-step explanation: 1
(((2•(x-2)•(x+2))•4)•(x-5))•2
STEP
2
:
Equation at the end of step 2
((2•(x-2)•(x+2)•4)•(x-5))•2
STEP
3
:
Equation at the end of step 3
(8 • (x - 2) • (x + 2) • (x - 5)) • 2
STEP
4
:
Equation at the end of step 4
8 • (x - 2) • (x + 2) • (x - 5) • 2
STEP
5
:
Final result :
16 • (x - 2) • (x + 2) • (x - 5)
Find the center and radius! In standard form! ( Type an ordered pair)
Answers
Step-by-step explanation:
The center of the circle is (-2,-3)
The radius is 2 since the distance from the center to the point on the circle is 2
Therefore the standard equation is
\((x + 2) {}^{2} + (y + 3) {}^{2} = 4\)