Answer:
Move all terms not containing a to the right side of the equation:
a/5 = 11
Multiply both sides of the equation by 5:
5 x a 5 = 5 x 11
Simplify both sides of the equation:
a=55
Step-by-step explanation:
Step by step-
1. Find common denominator
2. Combine fractions with common denominator
3. Multiply the numbers
4. Multiply all terms by the same value to eliminate fraction denominators
5. Cancel multiplied terms that are in the denominator
6. Multiply the numbers
7. Add 10 to both sides of the equation
8. Simplify
(THE PHOTOS SHOW YOU HOW TO DO IT STEP BY STEP IM SORRY, ITS ALOT!)
The prior probabilities for events
A1, A2, and A3
are
P(A1) = 0.20,
P(A2) = 0.30,
and
P(A3) = 0.50.
The conditional probabilities of event B given
A1,
A2,
and
A3
are
P(B | A1) = 0.50,
P(B | A2) = 0.30,
and
P(B | A3) = 0.40.
(Assume that
A1, A2, and A3
are mutually exclusive events whose union is the entire sample space.)
(a)
Compute
P(B ∩ A1), P(B ∩ A2), and P(B ∩ A3).
P(B ∩ A1)
=
P(B ∩ A2)
=
P(B ∩ A3)
=
(b)
Apply Bayes' theorem,
P(Ai | B) = P(Ai)P(B | Ai)
P(A1)P(B | A1) + P(A2)P(B | A2) + + P(An)P(B | An),
to compute the posterior probability
P(A2 | B).
(Round your answer to two decimal places.)
(c)
Use the tabular approach to applying Bayes' theorem to compute
P(A1 | B),
P(A2 | B),
and
P(A3 | B).
(Round your answers to two decimal places.)
Events P(Ai)
P(B | Ai)
P(Ai ∩ B)
P(Ai | B)
A1
0.20 0.50 A2
0.30 0.30 A3
0.50 0.40 1.00 1.00
(a) Through the conditional probability formula:\(P(B ∩ A) = P(B | A) P(A),\)
\(P(B / A1) P(A1) = 0.50 x 0.20 = 0.10A2 = 0.30 x 0.30 = 0.09A3= 0.40 x 0.50 = 0.20\)
(b)Bayes' theorem gives
\(P(A2 | B) = p(B | A2) p(A2) / [p(B | A1) P(A1) + p(B | A2) P(A2) + p(B | A3) p(A3)]= 0.26Thus, P(A2 | B) = 0.26.\)
(c)the tabular approach can show us
Events P(Ai) P(B | Ai) P(Ai ∩ B) P(Ai | B)
A1 0.2 0.5 0.1 0.167
A2 0.3 0.3 0.09 0.307
A3 0.5 0.4 0.2 0.526
Therefore,\(P(A1 | B) = 0.167, p(A2 | B) = 0.307, p(A3 | B) = 0.526.\)
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2 box plots. The number line goes from 55 to 105. For pitcher 1, the whiskers range from 55 to 105, and the box ranges from 85 to 95. A line divides the box at 94. For pitcher 2, the whiskers range from 71 to 106, and the box ranges from 78 to 102. A line divides the box at 90. The two box plots show the data of the pitches thrown by two pitchers throughout the season. Which statement is correct? Check all that apply. Pitcher 1 has a symmetric data set. Pitcher 1 does not have a symmetric data set. Pitcher 2 has a symmetric data set. Pitcher 2 does not have a symmetric data set. Pitcher 2 has the greater variation.
Answer:
its c because i got it right
Pitcher 1, because he has the lesser amount of variability in his pitches.
Answer:
B and C Are your answers :)
Step-by-step explanation: I did it on Eng.
If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)
16.67% probability = 0.1667
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Triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P'Q'R'. What are the vertices of triangle PQR
Answer:
Hope this helps!
Step-by-step explanation:
Triangle PQR has vertices P (3, 3), Q (5, -1), and R (1, -3). When triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P’Q’R’, the vertices of the new triangle are P’(-3, 3), Q’ (1, 5), and R’ (3, 1)
write a quadratic equation with -6 and 3/4 as its roots. write the equation in the form ax^2 + bx + c = 0, where a,b, and c are integers.
The quadratic equation whose roots are -6 and 3/4 is 14x²+21x-18=0
How to find quadratic equations?We should know that a quadratic equation is that whose highest power of the variable is 2
The given roots are
x=-6 and x=3/4
Let (x+6)(x-3/4)=0
Multiplying the brackets we have
\(X^{2}-\frac{3x}{4} +6x-\frac{18}{4}\) =0
Find the LCM of the denominators
\(\frac{4X^{2}+21x-18 }{4} =0\)
Cross and multiplying we have
\(4x^{2} +21x-18=0\)
Therefore, the equation is expressed in the form ax²+bx+v=0 Where a=4, b=21 and c=-18
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A bag of flour weighs 50 2/3 kg what is the total weight of 10 bag
Answer:
\(506 \frac{2}{3} kg\)
Step-by-step explanation:
50 2/3=
50×2+3/3
=152/3 kg
next 152/3 ×10
=1520/3
=506 2/3
Rosalyn has three different-shaped containers that contain marbles. She has 3 round containers, each holding 16 marbles.
She has 4 square containers, each holding 25 marbles. She has 2 rectangular containers, each holding 33 marbles.
How many marbles are in the containers altogether?
Answer:
42,996
Step-by-step explanation:
3*16+4*25+2*33=48+100+66=214
the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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suppose y varies directly as x, and y=48 when x=6. find x when y=72.
Using the constant of proportionality the value of x when y is 72 is 9.
What is a COP?
The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.
To find k, we can use the given information that y = 48 when x = 6 -
y = kx
48 = k(6)
k = 8
Now that we know k, we can use it to find x when y = 72 -
y = kx
72 = 8x
x = 9
Therefore, when x = 72, the value of x = 9.
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Write the product in simplest form: 1 2/3 x 3 4/5=
Answer:
19/3
Step-by-step explanation:
1 2/3 = (1*3 + 2)/3 = 5/3
3 4/5 = (5*3 + 4)/5 = (15 + 4)/5 = 19/5
5/3 * 19/5 = 19/3 The 5s cancel.
The simplest form is not obvious to me. I think the answer above is in simplest form, and I will put that below the answer above. But 6 1/3 is also possible.
Answer:
4 1/3
Step-by-step explanation:
1 \(\frac{2}{3}\) × 3 \(\frac{4}{5}\) =
\(\frac{5}{3}\) × \(\frac{19}{5}\) =
\(\frac{95}{15}\) = 4 \(\frac{5}{15}\) = 4 1/3
Use the following function to complete this question:
f(x)=(x-1)^3+5
Graph the function and fill in the blanks.
If the transformation listed is not applicable write none.
Fill in the blanks in the form:
4 left
5 up
Write infinity in the form: inf
Horizontal shift:
Vertical shift:
Vertical stretch factor:
Vertical compression factor:
Axis of reflection:
Domain:
Range:
Inflection Point:
Pic is attached below
The following is deduced from the equation f(x)=(x - 1)^3 + 5
Horizontal shift: 1 left
Vertical shift: 5 down
Vertical stretch factor: 1
Vertical compression factor: 1
Axis of reflection: -x + 6
Domain: all real numbers
Range: all real numbers
Inflection Point: (1, 5)
What is vertical stretch factor?The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.
The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.
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m∠AXB = this is the question
Answer:
Need a figure or more information to answer this question
THIS QUESTION IS WORTH 50 POINTSMatt and his friends hike 42 mi over a holiday weekend. they hike for 5 hours on saturday, 6 hours on sunday, and 3 hours on monday. they go hiking the following weekend. if they hike at the same rate as they hiked over the holiday weekend, how long will it take to hike 12 mi
Help would be kind :)
Kimberly had 2 times as many marshmallows as Chris. After eating 15 each, Kimberly had 3 times as many marshmallows as Chris. How many marshmallows did Kimberly have at first?
Kimberly had 2 times as many marshmallows as Chris. After eating 15 each, Kimberly had 3 times as many marshmallows as Chris. Kimberly had 60 marshmallows at first.
What is Kimberly's marshmallows count?Generally, Let's call the number of marshmallows that Kimberly had at first X.
We know that Kimberly had 2 times as many marshmallows as Chris at first, so Chris had X/2 marshmallows.
After eating 15 each, Kimberly had X - 15 marshmallows, and Chris had X/2 - 15 marshmallows.
We also know that Kimberly had 3 times as many marshmallows as Chris after eating 15 each, so
(X - 15) = 3 * (X/2 - 15).
(X - 15) - 3 * (X/2 - 15) = 0
Then, we can simplify the left side of the equation:
X - 15 - 3 * X/2 + 45 = 0
Combining like terms, we get:
-3 * X/2 + X - 15 + 45 = 0
Simplifying further:
-X/2 =-30
X = 60
Therefore, Kimberly had 60 marshmallows at first.
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what is 10x as much as 70?
9514 1404 393
Answer:
700
Step-by-step explanation:
You figure this out by multiplying 70 by 10:
10×70 = 700
Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
Name the image of p (9, 1.5) after being translated along the vector <3, -0.5>
The image for P(9, 1.5) after Translation is P'( 12, 1).
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
P(9, 1.5) with Translating Vector (3, -0.5).
So, Applying the Translation we get
P(9 + 3, 1.5 + (-0.5))
= P(12 , 1.5- 0.5)
= P(12, 1)
hence, the image is P'( 12, 1).
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To best show a possible linear trend in a scatter plot, draw a _________________.
A. regressive line
B. line of best fit
C. vertical line
D. horizontal line\
Answer:
b. line of best fit
A retailer sold a fan for ra 1800 at 10% loss what is its cost price?
How to do
Answer:
18
thả 5 sao nha.....
Step-by-step explanation:
..................
In which
situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
What is expression?Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.
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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?
On a game show, a contestant wins $200 by answering questions correctly but loses $300 for
each question answered incorrectly. How much money would a contestant win if she
answered 14 questions correct and I question incorrect?
Answer:
$2500
Step-by-step explanation:
$200×14=$2800
$2800-$300=$2500
Help.
A. RS
B. ST
C. Ut
Answer: THE ANSWER TO THAT IS B
Step-by-step explanation:
1. Rosa was hiking near the Dead Sea. She began her hike at an elevation of -600 feet and ended the hike at 92 feet. What was the change in her elevation
Change in Rosa's elevation from starting to end of her hike is 692 feet.
What is elevation in a hike?
Elevation is the height of hiker above the sea level at any point of the hike.
At the starting of the hike , Rosa was at an elevation of = -600feet
At the ending of the hike, Rosa is at an elevation of = 92 feet
Change in elevation = final elevation - initial elevation
= 92-(-600) = 692 feet
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Use the function g(x)=11 to find the following values g(-3), g(5), g(a), g(a+h)
The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11
Evaluating the function valuesA composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.
The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.
i.e. the function g(x) = 11 always returns the value 11, regardless of the input.
Therefore, we have:
g(-3) = 11
g(5) = 11
g(a) = 11
g(a+h) = 11
So, regardless of the value of a or h, the function g(x) will always return 11.
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Simplify:
1. Cos(90°-x).sin(-x)/cos² (180°+x)
2. tan² (360° + 0)/cos(90° +0).sin(180° - 0)
NB. The 0 is meant for theta
1.
cos(90-x) = sin(x)
sin(-x) = -sin(x)
cos²(180+x) = (-cos²x) = cos²(x)
Then
cos(90-x) .sin(-x)/cos²(180+x) = sin(x).(-sin(x))/cos²(x)
= -sin²(x))/cos²(x)
= −tan²(x)
2.
tan² (360° + θ)/cos(90° + θ).sin(180° - θ)
tan² (360° + θ) = tan² (θ)
cos(90° +x) = - sin(θ)
sin(180° - θ) = sin(θ)
tan² (360° + θ)/cos(90° +θ).sin(180° - θ) = tan² (θ)/- sin(θ) sin(θ)
= -tan²(θ)/sin²(θ)
= -1/cos²(θ)
= - (cos²θ + sin²θ)/cos²θ
= -1 - tan²θ
What is the
y-intercept?
Answer:
8
Step-by-step explanation:
i'm very smart and x=0 is the y intecept so
Lee put $10,000 into a stock market index mutual fund that grew at an average of 7% per year for 10 years. About how much is in Lee's mutual fund account after 10 years? Ignore compounding.
Answer:
17000
Step-by-step explanation:
we can use the equation I=PRT
I=10,000(10)(0.07)
I=100,000(0.07)
i=7000
7000+ the initial 10,000=17000
7 7/15 Write in decimal to the nearest hundredths 7 7 over 15
Answer:
.47 because 7/15 is 0.466
Step-by-step explanation:
Generalize Is a relation always a function? Is
a function always a relation? Explain.
Answer:The relation shows the relationship between INPUT and OUTPUT. Whereas, a function is a relation which derives one OUTPUT for each given INPUT. Note: All functions are relations, but not all relations are functions
Step-by-step explanation: