P(A∩B) = 0 (the probability of both events occurring is zero).
P(A|B) = 0.
No. The student's argument that mutually exclusive events are independent is incorrect.
How to find P(AnB) and P(AIB) of the event?If events A and B are mutually exclusive, then by definition they cannot occur at the same time.
Thus, P(A∩B) = 0 (the probability of both events occurring is zero).
Since events A and B are mutually exclusive, they cannot be independent. In fact, if two events are mutually exclusive, it means that the occurrence of one event precludes the occurrence of the other event, so they are completely dependent on each other.
To calculate P(A|B), we can use the formula:
P(A|B) = P(A∩B) / P(B)
Since P(A∩B) = 0 and P(B) = 0.70, we have:
P(A|B) = 0 / 0.70 = 0
This means that if we know event B has occurred (i.e., P(B) > 0), then the probability of event A occurring (i.e., P(A|B)) is zero. Therefore, events A and B are not independent.
The student's argument that mutually exclusive events are independent is incorrect. Mutually exclusive events are by definition dependent events.
In general, the concept of mutually exclusive events and the concept of independent events are not the same. Mutually exclusive events are dependent events, while independent events are events that do not depend on each other.
In this problem, the fact that events A and B are mutually exclusive means that they are dependent events, and this is reflected in the probability calculation for P(A|B), which is zero. Therefore, we can conclude that mutually exclusive events are not independent events.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
Marcus has 19 blueberry muffins that he wants to share equally with his two
friends. How many blueberry muffins will Marcus and his two friends receive?
Answer: 6 and 1/3
Step-by-step explanation:
Assuming that sweet generous little Marcus here wants some muffins too, he has to share 19 blueberry muffins between 3 people (Marcus + friend 1 + friend 2.)
Most unfortunately, 19 isn't divisible by 3 to create a whole number (ie. a whole muffin).
Therefore you have 2 options:
Option 1:
19/3 = 6.333....
This means that each person will get 6 and 1/3 of a muffin
Option 2:
19/3 = 6 (and 1 remainder)
This means that each person will get 6 muffins each, but there will be a leftover muffin to feed the birds or something.
(I personally prefer option 2, but I think your teacher is looking for option 1.)
The fourth term in an arithmetic sequence is 3 and the tenth term is 18. If the first term is a1, which is an equation for the nth term of this sequence?
The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)
How to determine the equation for the nth term of this sequence?From the question, we have the following parameters that can be used in our computation:
a4 = 3
a10 = 18
An arithmetic sequence is represented as
an = a + (n - 1)d
Using the above as a guide, we have the following:
a + 3d = 3
a + 9d = 18
Subtract the equations
So, we have
6d = 15
Divide
d = 2.5
So, we have
a + 3 * 2.5 = 3
This gives
a = -4.5
So, the sequence is -4.5 + 2.5(n - 1)
Read more about sequence at
https://brainly.com/question/7882626
#SPJ1
9. Liam ran 12 miles total over the weekend. He
ran 5.5 miles on Saturday. Which equation can
be used to find m, the number of miles he ran
on Sunday?
A. 12 + 5.5 = m
B. 5.5m= 12
C. m-5.5 = 12
D. 5.5+ m = 12
Answer:
x=6.5
Step-by-step explanation:
I'm not sure if it's correct
Ted made a nut mixture that contains 52%
peanuts by mixing together 9 kg of mixed
nuts that contain 20% peanuts and 16 kg
of a different brand of mixed nuts. The
second brand of mixed nuts contained
what percent peanuts?
Let's call the added amount of kg of mixed nuts that contain
40
%
peanuts
m
a
d
d
e
d
. If the new mixture contains
34
%
peanuts, then:
m
peanuts
m
total
=
0.34
The bag of
6
kg
already contained
0.3
⋅
6
=
1.8
kg
of peanuts. Furthermore,
40
%
of
m
added
will be peanuts. This means that:
m
peanuts
=
0.4
m
added
+
1.8
The total mass will be the original
6
kg
plus the added mass, so
m
total
=
m
added
+
6
.
This gives us the following equation.
0.4
m
added
+
1.8
m
added
+
6
=
0.34
Multiply both sides with
m
added
+
6
.
0.4
m
added
+
1.8
=
0.34
(
m
added
+
6
)
Multiply out the brackets.
0.4
m
added
+
1.8
=
0.34
m
added
+
2.04
Subtract
0.34
m
added
from both sides.
0.04
m
added
+
1.8
=
2.04
Subtract
1.8
from both sides.
0.06
m
added
=
0.24
Divide both sides by
0.06
.
m
added
=
4
Therefore, Jenny must add
4
kg
.
I NEED HELP ON THIS ASAP!!
The solution of both inequalities is (-1, 2).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have the inequalities
x+ y >1.........(1)
-x+ y <3.........(2)
The graph for x+ y >1 is shown by the red shaded region.
and, the graph for -x+ y <3 is shown by the blue shaded region.
Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.
Learn more about Inequality here:
brainly.com/question/30231190
#SPJ1
A car travels at an average speed of 80 km/h for 2 hours. What distance does the car travel? c) A car travels a distance of 330 km at an average speed of
I need help on this please
The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).
What is a quadratic function?Generally speaking, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
c represents the constant.
Next, we would solve the above quadratic function by using the factorization method;
x² + x - 72 = 0
x² - 8x + 9x - 72 = 0
x(x - 8) + 9(x - 8) = 0
(x + 9)(x - 8) = 0
(x + 9)(x - 8) = (x + a)(x - b).
Read more on quadratic functions here: brainly.com/question/2272989
#SPJ1
The sides of a triangle measure 32 inches, 22 inches, and 19 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is?
The area of the given triangle is approximately 204.2 square inches.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
To calculate the area of a triangle with given side lengths, we can use Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.
In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:
s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5
Now we can plug in these values into the formula and simplify:
Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16
Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.
Learn more about the triangles here:
https://brainly.com/question/17997149
#SPJ1
Which statement is true about this equation??
y = 2^x + 4
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents a function only.
D.
It represents both a relation and a function.
Answer: The correct answer is C. It represents a function only.
A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.
In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.
Step-by-step explanation:
Answer:
D. It represents both a relation and a function
Hope this helps!
Step-by-step explanation:
All functions are relations, but not all relations are functions. The equation given is an Exponential function.
The diameter of a circle is 18 millimeters. What is the circle's circumference?
Answer:
he circumference of the circle is approximately 56.52 millimeters.
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.
Substituting the given value of the diameter, we get:
C = πd = π(18) = 56.52 mm (rounded to two decimal places)
Therefore, the circumference of the circle is approximately 56.52 millimeters.
If the tire height is 5.2 in. and the rim diameter is 17 in., what is the tire diameter?
Answer:
Circumference = (3.14)(15) = 47.1 in
Step-by-step explanation:
what function is equivalent to y = 3x(x+2)^2+7?
The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.
Which function is equivalent functionally?Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.
When we add the parenthesis to the expression, we get:
[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]
If we simplify, we get:
[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]
As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.
To know more about Equivalent function visit:
brainly.com/question/30791043
#SPJ1
Please help. what is an equation of the line best fit. This is urgent
a. The line of the best fit is ŷ = -8.55485X + 118.39451.
b. The value of the correlation coefficient is -0.8619.
What is the line of best fit?A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
Sum of X = 117.4
Sum of Y = 298
Mean X = 10.6727
Mean Y = 27.0909
The sum of squares (SSX) = 0.8618
The sum of products (SP) = -7.3727
Regression Equation = ŷ = bX + a
b = SP/SSX = -7.37/0.86 = -8.55485
a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451
ŷ = -8.55485X + 118.39451
X Values
∑ = 117.4
Mean = 10.673
∑(X - Mx)² = SSx = 0.862
Y Values
∑ = 298
Mean = 27.091
∑(Y - My)² = SSy = 84.909
X and Y Combined
N = 11
∑(X - Mx)(Y - My) = -7.373
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -7.373 / √((0.862)(84.909)) = -0.8619
Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451
To learn more about the line of the best fit;
https://brainly.com/question/14279419
#SPJ1
If a vertex of a triangle is (7,-2) and the midpoints of two
sides are (3.5, -0.5) and. (3,1) find the other vertices of
the triangle.
The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
What is a triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.
Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints
Coordinates of B:
x-coordinate: (7 + 3.5)/2 = 5.25
y-coordinate: (-2 - 0.5)/2 = -1.25
So, B is (5.25, -1.25)
Coordinates of C:
x-coordinate: (7 + 3) / 2 = 5
y-coordinate: (-2 + 1)/2 = -0.5
So, C is (5, -0.5)
Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
To learn more about Triangle from given link.
https://brainly.com/question/2773823
#SPJ1
Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14
can anyone help me with this answer please.
The order from least to greatest would be as follows:
√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6
How did we get the value?To order the numbers, we need to first simplify and evaluate each expression.
1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757
2. 2√10 ÷ 5 = 1.265
3. √14 = 3.74166
4. 3√2 = 4.243
5. √19 + 1 = 5.359
6. 6 is simply 6
Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:
0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6
learn more about root order: https://brainly.com/question/28256285
#SPJ1
based on the data in the table, what is the probability that a randomly selected persons favorite restaurant is a deli?
Answer choices
8/25
2/5
1/10
9/50
The probability that a randomly selected persons favorite restaurant is a deli is 9/50
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
Total = 100
Deli = 18
So, the probability is
P = Deli/Total
Substitute the known values in the above equation, so, we have the following representation
P = 18/100
Simplify
P = 9/50
Hence, the probability is (d) 9/50
Read more about probability at
https://brainly.com/question/251701
#SPJ1
This graph represents the amount of milk in a bottle in the fridge. Tell a story of the amount of milk in the bottle.
The milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Thus, option (a) is correct.
What is passage?The term “passage” refers to the explanation and description of a sentence in relation to a topic. The passage aimed to describe those details related to the theme of the story. The different passage is to justify to the different things as to clarify. The passage is to define the important terms.
The milk bottle sat on the central shelf, as mentioned in the passage. The artifact is a completely empty milk bottle. The section gives information regarding signs. The passage was Sig's refrigerator, which had been opened. A milk bottle sat on the middle shelf, its cap missing and no milk inside.
As a result, the milk bottle, item is the best example of an artifact from the passage that reveals something about sign. Therefore, option (a) is correct.
Learn more about on passage, here;
brainly.com/question/26999874
#SPJ1
You want to save up to buy a car. You currently have $500 saved and are going to work this summer cleaning house for your grandma. She will pay you $50 every time you clean her house. Write an equation for this situation. Make sure you define your variables. (How many times will you need to clean her house to have $4,500 for the car you want to buy?
I need answer by 2/25/2023
80 times, the house should be cleaned to buy the car.
Equation for the amount is y = 50t + 500
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given,
Amount in the savings = $500
Amount to get the car = $4500
Grandma pays $50 for every time after cleaning
then, after t times, the amount will be
y = 50 t + 500
here, y is the total amount after working
t is number of times of cleaning the house
For $4500
4500 = 50t + 500
50t = 4500 - 500
50t = 4000
t = 4000/50
t = 80
Hence, we have to clean the house 80 times to have $4500.
equation for the amount is y = 50t + 500
Learn more about linear equation here:
https://brainly.com/question/11897796
#SPJ1
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
A. 2 + x = 5
B x + 1 = 4
E -5 + x = -2
Step-by-step explanation:
2 + 3 = 5
3 + 1 + 4
-5 + 3 + -2
if this correct mark me as brainliest please
You start driving west for 3 miles, turn right, and drive north for another 2 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13
L=[tex]\sqrt{13}[/tex]
drop-down menu.
An experiment is conducted in which a bead is randomly drawn from a bag, the color is recorded, and then the bead is replaced.
The results of the experiment are given in the table below.
Color
Red
Orange
Yellow
Green
Blue
Purple
Frequency
17
12
10
13
8
5
Which of the following lists would most likely have produced the given experimental results?
Color
List A
List B
Red
33
31
Orange
27
24
Yellow
22
18
Green
30
34
Blue
18
19
Purple
12
5
For the list selected above, what is the theoretical probability of selecting a red bead?
Using the experimental results, if 156 beads are drawn from a bag and returned, which color would have a frequency closest
to 24?
The theoretical probability of selecting a red bead is 0.28.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that,
Color Frequency
Red 17
Orange 12
Yellow 10
Green 9
Blue 8
Purple 5
Color List A List B
Red 33 31
Orange 27 24
Yellow 22 18
Green 30 34
Blue 18 19
Purple 12 5
Probability of selecting a red bead = 17/61
= 0.28
Orange color would have a frequency closest to 24.
Therefore, the theoretical probability of selecting a red bead is 0.28.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ9
How does the formula for the sample mean differ from the formula for the Population mean?
The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).
The sample mean is the average value for a set of observations which is derived from a population. While the population mean is the average value for the entire set of observation belonging to a particular study of interest.
The set of observation belonging to a population is denoted by 'N' ; while the sample size is denoted as 'n' :
The mean formula is written thus :
Population mean = Σx / N
Sample mean = Σx / n
Where, x = set of values.
To know more about Mean.
https://brainly.com/question/20066860
#SPJ4
Need help???!!!! Please
Answer:
+5&-2
Step-by-step explanation:
Copy each statement. Insert , -, x, + or division symbol to make each statement true.
27 3 5 2 = 19
81 11 8 4 1 = 60
The Complete statement are:
1. 27/3 + 5 x 2
2. 81 + 1 - 8 x 4 x 1 = 60
What are Arithmetic Operations?Combining operands with a single arithmetic operator specifies an arithmetic operation. The ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.
Given:
we have to apply the operation to make
27 3 5 2 = 19
81 11 8 4 1 = 60
so, first 27 3 5 2 = 19
1. 27/ 3 = 9
2. 5 x 2= 10
3. 9+ 10 = 19
For second,
1.81 + 11 = 92
2. 8 x 4 x 1 = 32
3. 92-32 = 60
Learn more about Arithmetic operation here:
https://brainly.com/question/30553381
#SPJ1
2x + 3y = 12
2x - y = 4
Answer:
The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)
Step-by-step explanation:
Please help please now help ASAP
Answer:
2
Step-by-step explanation:
Which graph represents data points that have no correlation?
Answer:
bottom-right
Step-by-step explanation:
the points on the graph are scattered and have no correlation whereas the others all remain in a relatively similar shape
Is he right explain if no explain as well and this is my last question I need to answer for my test Thank you.
Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong
How to determine if he is right or notFrom the question, we have the following parameters that can be used in our computation:
(13g + 1) + (-2 - 5g)
Remove the brackets
So, we have
13g + 1 - 2 - 5g
Evaluate the like terms
8g - 1
When factorized, we have
8/3(3g - 3/8)
This is not the same as Scott's expression
Hence, Scott is incorrect
Read more about expression at
https://brainly.com/question/15775046
#SPJ1
For the points P and Q do the following.
(a) Find the distance d(P,Q).
(b) Find the coordinates of the midpoint M of the segment PQ.
P (3√2,5√3), Q(√2,-√3)
The solution is, the distance = √116.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
here, we have,
given that,
P (3√2,5√3), Q(√2,-√3)
so, the distance d(P,Q).
by using the formula we get,
the distance = √108 + 8
= √116
Hence, The solution is, the distance = √116.
To learn more on Distance click:
brainly.com/question/15172156
#SPJ1
Write an equation in slope-intercept form for the line that passes through each pair of points.
(-7, -3) (-3, 5)
The equation of line passes through the points (- 7, -3) and (-3, 5) will be;
⇒ y = 2x + 11
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 7, -3) and (-3, 5).
Now,
Since, The equation of line passes through the points (- 7, -3) and (-3, 5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-3)) / (-3 - (-7))
m = 8 / 4
m = 2
Thus, The equation of line with slope 2 is,
⇒ y - (-3) = 2 (x - (-7))
⇒ y + 3 = 2 (x + 7)
⇒ y + 3 = 2x + 14
⇒ y = 2x + 14 - 3
⇒ y = 2x + 11
Therefore, The equation of line passes through the points (- 7, -3) and
(-3, 5) will be;
⇒ y = 2x + 11
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ9