(a) Yes, we have enough information to compute Probability P(A or B).
(b) If we know P(A) and P(B), we have enough information to compute P(A or B).
(a) The probability of the union of two events (A or B) is given by the formula P(A or B) = P(A) + P(B) - P(A and B)
We know P(A) and P(B), but we don't know P(A and B) - the probability that both events occur simultaneously. Therefore, we cannot compute P(A or B) with certainty unless we are given additional information about the relationship between A and B.
(b) If we know that events A and B are mutually exclusive, then we have enough information to compute P(A or B). Mutually exclusive events are events that cannot occur simultaneously, which means that P(A and B) = 0.
In this case, the formula for the probability of the union simplifies to:
P(A or B) = P(A) + P(B)
Since we know P(A) and P(B), we can simply add them to obtain P(A or B). Therefore, in this case, we have enough information to compute P(A or B).
Learn more about Probability :
https://brainly.com/question/18882393
#SPJ4
what can be the maximum number of digits in the repeating block of digits in the decimal expansion 5/7
Answer: To find the decimal expansion of 5/7, we can perform long division as follows:
0.7│5.0
4 2
────
8 │ 30
28
───
20 │ 200
196
────
4
Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.
In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.
Step-by-step explanation:
Toshi predicted that he will perform a card trick successfully 95% of the time. He went on to perform the card trick successfully 24 out of 30 times. How did Toshi’s prediction compare with his actual results?
Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.
According to question:Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:
P(success) = 0.95
This is the probability of success for one card trick.
Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:
P(actual success) = 24/30 = 0.8
This is the proportion of successful card tricks that Toshi actually performed.
To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:
P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]
In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:
P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045
This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).
Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
in the number 425.871 which digit has the greatist value
In the number 425.871, the digit with the greatest value is 4 because it is in the hundreds place, representing a value of 400.
Explanation:In the number 425.871, each digit has a position and a value based on where it's located in the number. The position starting from the right of the decimal point we call the tenths, hundredths, and thousandths place, respectively. Similarly, the position to the left of the decimal point is called the ones, tens, hundreds place, etc., respectively. In this case, the digit with the greatest value is the one in the hundreds place, which is 4. This is because it represents 400, which is greater than any other individual digit's value in the number 425.871.
Learn more about Place Value here:
https://brainly.com/question/35447631
#SPJ11
what is the projection of u onto v with "U" having points (-9,-5) and "V" having points (-6,5)
The projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).
Explain the term projection
Projection is the process of representing a three-dimensional object or scene onto a two-dimensional surface. It involves the use of mathematical principles to create a flat image that accurately depicts the shape and position of the object or scene. Projections are widely used in fields such as engineering, architecture, and computer graphics to create visual representations of complex structures and designs.
According to the given information
The projection of a vector u onto a vector v is given by the formula proj_v(u) = (u•v)/(||v||²) * v, where u•v is the dot product of u and v, and ||v|| is the magnitude of v.
In this case, u = (-9,-5) and v = (-6,5). The dot product of u and v is u•v = (-9)(-6) + (-5)(5) = 54 - 25 = 29. The magnitude of v is ||v|| = √((-6)² + (5)²) =
√(36 + 25) = √61.
So the projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).
To know more about projection visit
brainly.com/question/17262812
#SPJ1
If events X and Y are independent, then find P(X and Y). P(X)= 2/3 and
P(Y) = 3/4
O 17/12
O 5/7
O 1/2
O 1/4
Answer:
1/2
Step-by-step explanation:
Since the events are independent, P(A and B) = P(A) * P(B)
P(X and Y) = P(X) * P(Y)
= 2/3 * 3/4
= 2/4
= 1/2
Mark Twain once said, "The secret of getting started is breaking your complex overwhelming task into small manageable tasks, and then starting on the first one. " How does this quote connect to the process you can use as a writer?
A. Divide the task into pieces and then chose just one to complete in order to write a good story. B. Find the steps a famous writer takes and follow them exactly. C. A well-written story relies on only one step and that is all you need to do as a writer. D. Breaking the story into pieces and then tackling them one at a time can help you as a writer
Mark Twain's quote about breaking down overwhelming tasks into manageable pieces is a valuable lesson for high school students, particularly when it comes to writing. (option d)
In the context of writing, this quote can be particularly helpful. Writing a story or essay can seem like a daunting task, but if you break it down into smaller pieces, it becomes much more manageable. This is where the process of outlining comes in. An outline is essentially a roadmap of your writing, breaking it down into smaller components that you can tackle one at a time.
In mathematical terms, you can think of this process as a series of equations. Each equation represents a small, manageable piece of the overall problem.
By breaking down the problem into smaller equations, you can solve each one individually, which ultimately leads to solving the larger problem. This is similar to how breaking down a writing project into smaller pieces can help you write a well-structured and coherent piece.
Hence the correct option is (d).
To know more about quote here
https://brainly.com/question/15703655
#SPJ4
The width of a rectangle is one quarter of the length of the rectangle. The perimeter of the rectangle
is 27 inches.
A. Find the width and the height of the rectangle. Show your work
B. Find the area of the rectangle. Show your work
A. The area of the rectangle is 29.16 square inches.
B. The width of the rectangle is 2.7 inches and the height (or length) is 10.8 inches
What is rectangle?A parallelogram in which each pair of adjacent sides is perpendicular is referred to as a rectangle.
We should utilize "w" to address the width and "l" to address the length of the square shape.
A. Since the width equals one quarter of the length, we are able to write:
w = (1/4)l
We also know that the perimeter of the rectangle is 27 inches, and
the formula for the perimeter of a rectangle is:
P = 2l + 2w
Substituting the first equation into the second equation, we get:
P = 2l + 2(1/4)l
27 = 2.5l
l = 10.8
Now that we know the length, we can use the first equation to find the width:
w = (1/4)l
w = (1/4)(10.8)
w = 2.7
As a result, the rectangle has a width of 2.7 inches and a height of 10.8 inches.
B. To find the area of the rectangle, we can use the formula:
Area = length *width
Substituting the values we found above, we get:
A = (2.7)*(10.8)
A = 29.16
Therefore, the area of the rectangle is 29.16 square inches.
know more about perimeter visit :
https://brainly.com/question/6465134
#SPJ1
The weight of 4 hummingbirds is recorded below. The weight of each hummingbird has been rounded to the nearest 1 /2 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. A line plot labeled weights of birds in grams shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, and five. Dots are plotted as follows: 1 dot above two and one-half; 1 dot above three; 1 dot above four and one-half, and 1 dot above five. What is the weight of all 4 hummingbirds combined? grams
Answer:
5
Step-by-step explanation:
Answer:
15 grams
Step-by-step explanation:
Based on the information provided, the weight of each hummingbird is 2.5 grams, 3 grams, 4.5 grams, and 5 grams. To find the total weight of all 4 hummingbirds combined, we can add up their individual weights: 2.5 + 3 + 4.5 + 5 = 15 grams. So, the total weight of all 4 hummingbirds combined is 15 grams.
True or False: A z-score measures how many standard deviations an individual value is from the mean.
A z-score is a statistical measurement that indicates how many standard deviations an individual value is from the mean - True.
The mean from the value of interest and dividing the result by the standard deviation.
This standardized score provides a way to compare values from different data sets or populations.
For example, if a student's score on a test is 80 and the mean score for the class is 70 with a standard deviation of 5, the student's z-score would be 2.
This means that the student's score is two standard deviations above the class mean. This information can be useful in understanding the student's performance relative to their peers.
Z-scores can also be used to identify outliers or extreme values in a data set. Values with a z-score greater than 3 or less than -3 are considered to be outliers and may warrant further investigation.
In summary, a z-score is a valuable tool in statistical analysis that measures how many standard deviations a value is from the mean. It provides a standardized way to compare values across different data sets and can help identify outliers or extreme values.
For similar question on Z-scores
https://brainly.com/question/13299273
#SPJ11
Select the correct answer.
A number is selected at random from the set (2, 3, 4.... 10). Which event, by definition, covers the entire sample space of this experiment?
O A. The number is not divisible by 5.
O B.
The number is greater than 2.
O C.
The number is neither prime nor composite.
O D.
The number is even or less than 12.
Reset
Next
G
The correct statement about the numbers is,
⇒ The number is even or less than 12.
We have to given that;
A number is selected at random from the set (2, 3, 4.... 10).
Hence, We can check all the options as;
⇒ 10 is divisible by 5
Hence, A is incorrect.
⇒ Since, 2 = 2
Hence, B is incorrect.
⇒ Since, Every numbers are less than 12 and some numbers are even.
Hence, The correct statement about the numbers is,
⇒ The number is even or less than 12.
Thus, The correct statement about the numbers is,
⇒ The number is even or less than 12.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Need help with this question!
Answer:
[tex]r = \sqrt{ {3}^{2} + {( - 7)}^{2} } = \sqrt{9 + 49} = \sqrt{58} [/tex]
[tex] {x}^{2} + {y}^{2} = 58[/tex]
What is the Hardy-Weinberg equation and what does each part mean?
The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.
It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.
The equation is expressed as: p² + 2pq + q² = 1
In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.
The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).
The sum of these terms is always equal to 1, as it represents the entire population.
This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.
In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.
For similar question on Hardy-Weinberg equation
https://brainly.com/question/29776155
#SPJ11
CAN SOMEONE PLS HELP ME WITH THIS? +35 POINTS
what order do they go in?
At sunrise, shadows are longest and point towards the west as the sun rises in the east. Therefore, the correct order would be:
Longest shadows of the day, and they point to the west → shadows gradually become shorter → very short shadows or no shadows → shadows gradually become longer → longest shadows of the day, and they point to the east.
What is the shadows about?As the sun moves across the sky, shadows change in length and direction, reaching their shortest length at noon when the sun is directly overhead. After noon, the sun starts to move towards the west, and shadows gradually become longer until sunset when they are longest again, but this time pointing towards the east as the sun sets in the west.
Therefore, correct order of descriptions of shadows during the day, from sunrise to sunset, would be:
Very short shadows or no shadows - This occurs during sunrise when the sun is low on the horizon and its rays are nearly vertical, resulting in very short shadows or no shadows at all.Shadows gradually become longer - As the sun rises higher in the sky, shadows start to lengthen gradually.Longest shadows of the day, and they point to the west - During late morning or early afternoon, shadows are at their longest and they point towards the west, opposite to the direction of the sun.Shadows gradually become shorter - As the sun starts to descend towards the horizon in the late afternoon, shadows gradually become shorter.Longest shadows of the day, and they point to the east - During sunset, shadows are again at their longest, but this time they point towards the east, following the direction of the setting sun.Read more about shadows here:
https://brainly.com/question/922673
#SPJ1
See text below
How do shadows change during the day?
Drag and drop the descriptions of shadows to show the correct order, from sunrise to sunset.
longest shadows of the day, and they point to the west
longest shadows of the day, and they point to the east
shadows gradually become shorter
very short shadows or no shadows
shadows gradually become longer
A salesman and 30% commission on all merchandise that he sells last month. He sold $700 worth of merchandise how much commission in dollars did he earn last month
What is the solution to the equation 10^x=23? a) x = log 33 b) x = log 23 c) x = log 13 d) x = log 130
Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.
Here,
Taking the logarithm of both sides of the equation 10ˣ = 23:
log(10ˣ) = log(23)
Using the power rule of logarithms, the left-hand side simplifies to:
x log(10) = x
Since log(10) = 1, we have:
x = log(23)
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
Section 2-5 Three-Dimensional Figures • Classwork
Question 1 of 15
Question 1
Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
4.0 cm
2.4 cm
2.0 cm
3.2 cm
The Surface area of the triangular prism is 26.88 cm².
The Volume of the triangular prism is 7.68 cm³.
What is the Surface Area and Volume of the Solid?The formulas we would used are:
Surface area of triangular prism = (S1 + S2 + S3)(L) + bh
Volume of triangular prism = 1/2 * base * height * length of prism
Perimeter of the triangular face = (S1 + S2 + S3) = 4.0 + 3.2 + 2.4 = 9.6 cm
Length of prism = 2.0 cm
base of triangular face (b) = 3.2 cm
height of triangular face (h) = 2.4 cm
Plug in the values:
Surface area of triangular prism = (9.6)(2.0) + (3.2)(2.4) = 26.88 cm²
Volume of triangular prism = 1/2 * 3.2 * 2.4 * 2.0 = 7.68 cm³
Learn more about Surface area on:
https://brainly.com/question/30337697
#SPJ1
What is the value for x.
The value of x is 3 unit.
The correct option is B.
We have,
P = 3√2/2
Angle= 45
Using Trigonometry
cos 45 = B /H
1/√2 = ( 3√2/2)/ x
x= 3√2/2 . √2
x = 6/2
x= 3 unit
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ1
Given a quadratic equation in vertex form, find the vertex, axis of symmetry, whether the graph
opens up or down, the maximum or minimum, and the y-intercept. Graph it!
16. y = -2(x + 2)² +4
Vertex:
Axis of symmetry:
Opens: up
Maximum
down
Minimum
X=h A must write
x=
Max/Min Value:
The key features of the given quadratic equation include the following:
Vertex = (-2, 4)
Axis of symmetry: x = -2.
Direction of opening: downward.
There is a maximum (max) at 4.
y-intercept = (0, 0).
roots: x = -4 and x = 0.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:
y = -2(x + 2)² +4
Vertex, (h, k) = (-2, 4)
Axis of symmetry, Xmax = -2.
Read more on vertex here: brainly.com/question/14946018
#SPJ1
You rolled a number cube 20 times, you get three 14 times. What is the experimental probability that you will roll a three on your next roll?
The experimental probability that you will roll a three on your next roll is 70%.
To calculate the experimental probability of rolling a number three on the next roll, we need to use the data given in the problem. Out of the 20 rolls that were performed, the number three was rolled 14 times.
The experimental probability is calculated by dividing the number of times the event occurred (in this case, rolling a number three) by the total number of trials.
So, the experimental probability of rolling a number three on the next roll is:
14/20 or 7/10
This means that based on the data from the previous 20 rolls, there is a 70% chance of rolling a number three on the next roll.
To learn more about probability click on,
https://brainly.com/question/29181048
#SPJ4
Jennifer is flying a kite. She is looking up at the kite at an angle of elevation of 39°. If the
hand that is holding the kite string is 5.5 feet above the ground, what is the kite’s vertical
distance from the ground?
It is 36 inches from the top of her head to the kite (its the triangle hypotenuse)
The kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
The kite's vertical distance from the ground is the sum of its vertical height from Jennifer's hand and the distance from the ground to the hand
we shall represent the vertical height of the kite from Jennifer's hand with the letter x so that;
x = 36 inches × sin 39°
x = 3 feet × sin 39° {36 inches = 3 feet}
x = 1.8880 feet
kite's vertical distance from the ground = 1.9 ft + 5.5 ft = 7.4 feet
Therefore, the kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.
Read more about angle of elevation here:https://brainly.com/question/2096694
#SPJ1
Solve the system using elimination -6X = 18 - Y 9 = -3X - 8Y
The solution to the system by elimination is (-2, 4).
Solving the system using eliminationTo solve the system using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by a constant.
-6X = 18 - Y
9 = -3X - 8Y
Rewrite as
-6X = 18 - Y
3X = 9 - 8Y
So, we have
-6X = 18 - Y
6X = 18 - 8Y
Now we can add this equations to the second equation to eliminate x:
0 = 36 - 9Y
This gives
9Y = 36
So, we have
Y = 4
Recall that
-6X = 18 - Y
So, we have
-6X = 18 - 4
So, we have
-6X = 12
Divide by 2
X = -2
Therefore, the solution to the system is (-2, 4).
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
29°
82°
18m
18 m
Find the perimeter
The perimeter of the figure is 38.52.
We have,
The perimeter of the figure:
Side + 18 + 18
From the figure,
82 + 90 + x = 180
172 + x = 180
x = 180 - 172
x = 8
Now,
Using trigonometric identities Sin.
Sin 8 = Side/18
0.14 = side/18
side = 0.14 x 18
side = 2.52
Now,
The perimeter of the figure.
= Side + 18 + 18
= 2.52 + 18 + 18
= 38.52
Thus,
The perimeter of the figure is 38.52.
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
#SPJ1
You spend $124.54 at Walmart but have to pay the addition 8.5% sales tax. How much sales tax do you owe?
The sales tax owed on a $124.54 purchase at Walmart with an 8.5% sales tax rate is $10.59.
Suppose you spent $124.54 at Walmart and the sales tax rate is 8.5%. To calculate how much sales tax you owe, we first need to convert the sales tax rate from a percentage to a decimal. We do this by dividing the percentage by 100. So, the sales tax rate in decimal form is:
8.5% ÷ 100 = 0.085
Next, we multiply the purchase price by the sales tax rate in decimal form to calculate the amount of sales tax owed:
$124.54 × 0.085 = $10.59
To know more about sales tax here
https://brainly.com/question/29442509
#SPJ4
i need the answers for these 2 questions plss help me
Answer:
7) 760
8) 34
Step-by-step explanation:
7) 95x8=760
8) (103-35)/2=34
URGENT - Will also give brainliest to simple answer
Answer:
160°/360° = area/(π(5^2))
area = 25π(4/9) = 100π/9 square inches
Circumference = (4/9)π(5) = 20π/9 inches
Please PLEASE HELP ME this is due in 7 minutes and it the last question PLEASE
Answer:
(3,0)
Step-by-step explanation:
the point (5,-5) a translation of 2 units left would be equivalent to x-2.
(5-2,-5)
5 units up is equivalent to y+5
therefore
(5-2,-5+5)
yields
(3,0)
3x - 24 > 54 solve the inequality?
MAKE THE FOLLOWING STATEMENTS ABOUT EXPONENTS TRUE.
--- When multiplying polynomials with the same base,
[Select]
the coefficients.
---
When dividing polynomials with the same base, [Select]
[Select]
[Select]
✓the coefficients.
--- When raising a power to a power, distribute the exponent by [Select]
and applying the exponent to the coefficient.
--- When raising anything to the Zero power, the answer will be [Select]
-- When raising anything to the 1st power, the answer will be [Select]
exponents and
exponents and
exponents
--- When trying to leave a variable without a negative exponent, you should flip the position of the variable
to the reciprocal and [Select]
✓the negative exponent.
-x² + 2x + x - 3x = -9 + 2 + 6
The solution for the equation -x² + 2x + x - 3x = -9 + 2 + 6 is derived to be x = 1
How to solve for the value of x in the equationWe shall solve for x by simplifying the equation and making x the subject as follows:
-x² + 2x + x - 3x = -9 + 2 + 6
-x² + 3x - 3x = 8 - 9
-x² = -1
multiply both sides by -1 we have;
x² = 1
take square root of both sides
x = √1
x = 1
Therefore, the equation -x² + 2x + x - 3x = -9 + 2 + 6 will have a solution for the value of x = 1
Read more about equation here:https://brainly.com/question/1214333
#SPJ1
Choose the correct graph of the given system of equations. y + 2x = −1 3y − x = 4 Group of answer choices graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1 graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1 graph of two parallel lines with positive slopes with text on the graph that reads No Solution graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions
The correct option is- A. graph of two lines with the intersecting point at (negative 1, 1).
Explain about the intersecting lines:On a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.
Given system of equations:
y + 2x = −1 ...eq 1
3y − x = 4 ..eq 2
multiply eq 2 with 2 and add to eq 1
6y − 2x = 8 ..eq 3
6y − 2x + y + 2x = 8 - 1
7y = -7
x = -1
Now,
y + 2x = −1
y + 2(-1) = −1
y = -1 + 2
y = 1
Thus, the solution of the given system of equations. y + 2x = −1 and 3y − x = 4 is found as :(-1, 1).
The graph for the equations are attached.
Know more more about the intersecting lines:
https://brainly.com/question/28744045
#SPJ1
Correct question:
Choose the correct graph of the given system of equations. y + 2x = −1 and 3y − x = 4 .
Group of answer choices :
A. graph of two lines that intersect at the point (negative 1, 1)
B. graph of two lines that intersect at the point (1, 1) < Not
C. graph of two parallel lines with positive slopes
D. None of the above