If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) =
a. 0.10
b. 0.90
c. 0.00
d. 0.20
The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.
In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.
Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.
To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.
In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.
Therefore, the correct answer is: c. 0.00
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what percent of 56.25$ is 11.25$
Answer:
3%percent of $375 is $11.25 and 20% of $56.25 is $11.25 .
Step-by-step explanation:
3 Factorise 5y - 6py
Step-by-step explanation:
5y-6py
y(5-6p)
Answer
hope it helps
Answer:
5y - 6py
y(5-6p)
is the answer
How many times does 22 go into 53?
Answer:
It only goes into it twice.
The decimal form is 2.40909091
Answer:
2 times
Step-by-step explanation:
53 ÷ 22 = 2.41
You can multiply 22 by 2 which equals 44
If you multiply 22 by 3 you get 66 which is too big to fit in 53
Scientists have increased their ability to make observations beyond their own senses through the invention of specialized equipment such as xray telescopes. which best explains how such technology has affected society?
The human understanding of the cosmos beyond Earth has grown after inventing specialized equipment such as x-ray telescopes.
What is x-ray telescopes?X-ray telescope, a device made to find and focus X-rays from sources beyond the atmosphere of Earth.
Some key features regarding the x-ray telescope are-
X-ray telescopes have to be launched into orbit outside of the atmosphere or propelled to great heights by rockets and balloons due to atmospheric absorption. While telescopes carried aloft using rockets or satellites serve to detect softer radiation, balloon-borne telescopes may catch the more piercing (harder) X-rays.That sort of telescope must have a completely different design from a typical optical telescope. Since X-ray photons are so energetic, a typical reflector's mirror wouldn't be able to stop them from passing through. If X-rays are to be collected, they must bounce off a reflector at an extremely low angle.To know more about x-ray telescope, here
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what percent of flights are expected to meet the 20 minute "time to carousel"?
that it is difficult to determine an exact percentage of flights that are expected to meet the 20 minute "time to carousel" as it can vary depending on factors such as airport size, number of passengers, and baggage handling procedures. However, according to the Department of Transportation, the average wait time for baggage retrieval at major airports in the United States is around 30 minutes.
In explanation, the time it takes for baggage to reach the carousel after a flight lands is affected by several factors. These include the size of the airport, the number of passengers on the flight, the efficiency of baggage handlers, and any delays or issues that may occur during the transportation of the luggage from the plane to the carousel.
while it is difficult to provide an exact percentage of flights that meet the 20 minute "time to carousel" goal, it is clear that wait times for baggage retrieval can vary and can sometimes exceed 30 minutes. Factors such as airport size and efficiency of baggage handling can contribute to this variation.
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An object is dropped from the top of Pittsburgh's USX Towers, which is 841 feet tall. The
height of the object after t seconds is given by the function h(t) = 841 - 16t?
To the nearest whole number, estimate how many seconds until the object hits the ground.
Answer:
Step-by-step explanation:
h(t) = 841 - 16t
[Is this written correctly? The time is usually t^2, not t. I'll solve with the written equation, but check the equation]
The height at ground level is 0, so we want the value of t when h(t) = 0:
0 = 841 - 16t
-16t = -841
t = 53 seconds
One can also graph this formula and find the time to hit the ground at the point the line intersects the x axis (x = 0).
====
If the equation should have read h(t) = 841 - 16t^2, solve it as above, setting h(t) = 0.
t = (29/4) seconds
This can also be graphed.
The sum of a number and 12 squared
Answer:
x = the unknown number. Its square is x2. The sum of a number and its square is 12:
x + x²= 12
Putting the quadratic into standard form:
x2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 and 3
Let's check x=-4:
x + x2 = 12
(-4) + (-4)2 = 12
-4 + 16 = 12
12 = 12
Now let's check x= 3:
x + x2 = 12
3 + 32 = 12
3 + 9 = 12
12 = 12
Yup, they both work. There are two answers, x = -4 and x = 3
Four friends all five each other presents
The total cost of presents is £80.52
Work out the mean cost of presents in pounds
Step-by-step explanation:
Four friends all give each other presents. The total cost of the presents is £80.52. We need to find the mean cost of a present in pounds. So, the mean cost of a present is equal to 20.13 .
Jackie has two new puppies. One weights 5 9/16 pounds, and the other weighs 6 1/4 pounds. Find the difference in their weights.
Answer:big brrrrrrd
Step-by-step explanation:
yes
Answer:
11/16 pounds
Step-by-step explanation:
The difference between their weights can be found by subtracting 6 1/4 pounds from 5 9/16 pounds to find the difference. To do this we must transfer it from 1/4 to sixteenths which is 4 sixteenths. Then we subtract.
6 4/16
- 5 9/16
11/16
brainliest please . . . uwu
what is x? please help!
Answer:
x is 10x-33
Step-by-step explanation:
pls help I am terrible at math
1. 9(k+3)=27 combine like terms
Answer:
1.9k=21.3
Step-by-step explanation:
1.9k+5.7=27 then subtract 5.7 from 27 and have 1.9k=21.3
Answer:
k = 15
Step-by-step explanation:
A data flow diagram (DFD) does not provide any information about process timing. T/F
Answer:
Step-by-step explanation:
True.
A Data Flow Diagram (DFD) is a graphical representation of a system or a process that shows how data flows through different components of the system. It provides a visual representation of the system's inputs, processes, and outputs.
While a DFD can provide information on the data that flows between the different components of a system, it does not provide any information about the timing or sequence of those processes. A DFD is a static diagram that only depicts the flow of data in a system and does not provide any indication of when or how frequently processes occur
The area of a rectangle is 114 square meters. The length is 13 m longer than the width. Find the length and width of the rectangle.
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
Salary Education
44 3 49 2 ⋮ ⋮ 34 0 Click here for the Excel Data File
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round your answers to 2 decimal places.)
b. Interpret the coefficient for Education.
multiple choice
As Education increases by 1 year, an individual’s annual salary is predicted to increase by $6,430.
As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590.
As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590.
As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $6,430.
The sample regression is Salary = 23.62 + 6.43*Education
The sample regression equation tells us that as Education increases by 1 year, an individual’s annual salary is predicted to increase by $6,430, holding all other factors constant.
To find the sample regression equation, we need to estimate the values of β0 and β1. This can be done using a technique called least squares regression, which minimizes the sum of the squared errors between the observed values of Salary and the predicted values based on Education.
Using the data provided, we can estimate the sample regression equation as:
Salary = 23.62 + 6.43*Education
This equation tells us that for every additional year of education, an individual's annual salary is predicted to increase by $6,430. The intercept of 23.62 represents the predicted salary for an individual with zero years of education.
The coefficient for Education, which is 6.43 in this case, is a measure of the relationship between Education and Salary. It tells us how much the dependent variable (Salary) is expected to change for a one-unit increase in the independent variable (Education), all other things being equal.
In other words, as Education increases by 1 year, an individual’s annual salary is predicted to increase by $6,430, holding all other factors constant.
This coefficient is positive, indicating a positive relationship between Education and Salary. As individuals acquire more education, they are expected to earn higher salaries.
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What is the domain of g?
Answer: The domain of G is 4
Step-by-step explanation:
The domain is the set of all inputs that makes the function definable. The domain is always represented on the x axis.So looking at g on its x axis you see 4. So the domain is 4.
Answer:
4
Step-by-step explanation:
Can someone show me how to solve this
(-12)+7
Answer:
-5
Step-by-step explanation:
negative 12 + positive 7 = 5
so....
it is basically -12 + 7
Greta uses 3 ounces of pasta to make 3/4 of a serving of pasta.
How many ounces of pasta are there per serving?
Answer:
3 oz / 3/4
3*4/3=12/3=4
4 oz/1
4oz per serving
What do I do I am confused please help
Answer:
this is the answer of your question
Answer:
Step-by-step explanation:
1. \(\frac{2}{t}=\frac{12}{18}\) you have to cross multiply for you to get a value of t
2t=2x18
2t=36
t=3
note: you have to do the same with the other problems to find the value of the other.
Evaluate 5x – 2 when X = 3
Answer:
The answer is 13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
5(3)-2
15-2
13
Sketch the region corresponding to the statement P(z > 2. 3) Shade: Left of a value. Click and drag the arrows to adjust the values. -2 Sketch the region corresponding to the statement P(z > c) = 0. 1. Shade: Left of a value Click and drag the arrows to adjust the values
The region corresponding to the statement P(z > 2.3) is the area shaded to the right of the value 2.3 on a standard normal distribution curve.
To understand the region corresponding to the statement P(z > 2.3), we need to consider the standard normal distribution, also known as the z-distribution. The z-distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1.
The value 2.3 represents the number of standard deviations away from the mean. Since the statement is P(z > 2.3), we are interested in finding the probability of obtaining a z-score greater than 2.3.
To visualize this, we draw a standard normal distribution curve and shade the area to the right of 2.3. The shaded region represents the probability of observing a z-score greater than 2.3.
In this case, the region shaded to the right of 2.3 indicates the probability of observing a value that is more than 2.3 standard deviations above the mean. This can be interpreted as the likelihood of an event occurring that is more extreme than 2.3 standard deviations from the mean.
By shading the region to the right of 2.3, we are focusing on the upper tail of the distribution and finding the probability associated with that specific range.
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please help i have to get this all done by tommorw
Find the constant a, P and Q such
that 3x²-12x+16=a(x+p) +q
Answer:
Step-by-step explanation:
Rewrite 3x²-12x+16 as follows:
3(x^2 - 4x) + 16
Complete the square of x^2 - 4x; it is (x - 2)^2 - 4. We then have:
3( (x - 2)^2 - 4) + 16, or:
3(x - 2)^2 - 12 + 16, or
3(x - 2)^2 + 4
Then a = 3, p = -2 and q = 4
********************************************************************
Completing the square of x^2 - 4x is done as follows:
1. Identify the coefficient of x: It is -4.
2. Take half of this result: It is -2
3. Square this, and then add the square to x^2 - 4x, and then subtract it:
x^2 - 4x = x^2 - 4x + 4 - 4
4. Rewrite this result in the form (x - a)^2 - c:
(x - 2)^2 - 4
5. Now follow the remainder of the problem solution (given above)
Select all the points that are on the graph of the function defined by y = 2x + 3
a. (-4,3)
b. (-1,1)
C. (0,0)
d. (2,7)
e. (3,9)
f. (3,12)
g. (4.5, 12)
Answer:
b, d, e, g are the points
The coordinates (-, 1), (2, 7), (3, 9) and (4.5, 12) are the points that are on the graph of the function. Therefore, the options B, D, E and G are the correct answers.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=2x+3.
A) Substitute (x, y)=(-4, 3) in y=2x+3, we get
3=2(-4)+3
3≠-5
B) Substitute (x, y)=(-1, 1) in y=2x+3, we get
1=2(-1)+3
1=1
C) Substitute (x, y)=(0, 0) in y=2x+3, we get
0≠3
D) Substitute (x, y)=(2, 7) in y=2x+3, we get
7=2(2)+3
7=7
E) Substitute (x, y)=(3, 9) in y=2x+3, we get
9=2(3)+3
9=9
F) Substitute (x, y)=(3 12) in y=2x+3, we get
12=2(3)+3
12≠9
G) Substitute (x, y)=(4.5, 12) in y=2x+3, we get
12=2(4.5)+3
12=12
Therefore, the options B, D, E and G are the correct answers.
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Find -1 1/8 - 3/4.
First write the expression with a common denominator
-1 1/8 - 3/4 = -1 1/8 - ?/8
The value of the unknown is 6
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
the expression -1 1/8 - 3/4 = -1 1/8 - ?/8 shows that
-3/4=-?/8
the LCM of the denominator of two fractions is 8
multiply both sides by 8
-3/4×8=-?/8×8
therefore,. -? = -3×2
?= 6
Therefore the value if the unknown is 6
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The fraction is expressed with a common denominator as - 15/ 8
What is a fraction?A fraction is simply described as the part of a whole, element or number.
There are several types of fractions, which includes;
Simple fractionsComplex fractionsProper fractionsImproper fractionsMixed fractionsFrom the information given, we have the fractions;
-1 1/8 - 3/4.
Convert the mixed fraction to improper fraction
- 9/ 8 - 3/4
Find the Lowest common multiple
-9 - 6 /8
Subtract the numerators
-15/ 8
Hence, the value of the expression is -15/8
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Whole milk containing 10% fat enters the skimming process which cream containing 75% fat and skimmed milk containing 1% fat. All percentages are by weight. For every metric ton of skimmed milk produced, how much whole milk is needed in the process. Give your answer in metric tons in three decimal places.
Skimmed milk requires 1.099 metric tons of whole milk, based on 10% fat, 75% fat, and 1% fat ingredients in the skimming process.
To determine the amount of whole milk needed to produce one metric ton of skimmed milk, we need to consider the fat content of the ingredients involved. Whole milk typically contains 10% fat, while cream has a fat content of 75% and skimmed milk contains only 1% fat.
In the skimming process, cream is separated from whole milk to obtain skimmed milk. Since the fat content in skimmed milk is significantly lower (1%) than that in whole milk (10%), it implies that a larger quantity of whole milk is needed to obtain the same amount of skimmed milk.
By using the principle of conservation of mass, we can set up an equation to determine the amount of whole milk required. Let's assume that x metric tons of whole milk are needed to produce one metric ton of skimmed milk. The fat content in the whole milk portion would then be 0.1x metric tons. Since the fat content in the skimmed milk portion is 0.01 metric tons (1% of 1 metric ton), the fat content in the cream portion would be 0.1x - 0.01 metric tons.
Considering the cream's fat content of 75% (0.75 metric tons), we can set up the equation: 0.75 = (0.1x - 0.01) / x. Solving this equation, we find that x ≈ 1.099 metric tons of whole milk are required to produce one metric ton of skimmed milk.
To produce one metric ton of skimmed milk, approximately 1.099 metric tons of whole milk is needed. This calculation is based on the fat content of the ingredients involved in the skimming process, considering the percentages of fat in whole milk, cream, and skimmed milk.
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Sergio poured 45/ of the soda from a 2-liter bottle for his guests. how much soda in liters is still left in the bottle?
The soda left in the bottle is 0.4 liters in a 2-liter bottle.
Let’s understand this with the concept of Ratio.
How does ratio work?
When two objects are related using numbers or amounts, the relationship is known as a ratio.
Initially, we are given that the bottle is 2 liters. From that, Sergio poured ⅘ of the soda.
So, the soda left is the initial quantity- the final quantity
= 2(initial quantity) - ⅘*2(final quantity)
=2 - 1.6= 0.4 liter
So finally, the soda left in the 2-liter bottle is 0.4 liter.
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Simplify the expression 2(3+d-1)=
Answer:
4+2d
Step-by-step explanation:
2(3+d-1)
6+2d-2=6+(-2)+2d
=4+2d
Mean of a data setOn a survey, 7 students reported how many minutes it takes them to travel to school. Here are their responses.16, 11, 10, 12, 16, 13,9Find the mean travel time for these students.If necessary, round your answer to the nearest tenth.minutes
The total number of students is 7.
To find the mean you must add all the numbers in the list given and then divide the sum by the total of the numbers.
The sum of all the numbers.
\(\begin{gathered} 16+11+10+12+16+13+9 \\ 87 \end{gathered}\)Next divide 87 by 7.
\(\frac{87}{7}=12.42\)So, the mean of their travel time is 12.4 (rounded to the nearest tenth)
find value of test statistic Claim: Most adults would erase all of their personal information online if they could. A GFI Software survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could
The value of the test statistic for this problem is given as follows:
z = 4.28.
How to calculate the test statistic?As we are working with a proportion, the z-distribution is used, and the equation for the test statistic is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters for this problem are given as follows:
\(\overline{p} = 0.59, p = 0.5, n = 565\)
(p = 0.5 because the most word states that we are testing if the proportion is greater than 0.5).
Hence the test statistic is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{565}}}\)
z = 4.28.
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