a) The probability of rolling a 5 or a number greater than 3 is 1/2.
b) The probability of rolling a number less than 4 or an even number is 5/6.
c) The probability of rolling a 4 or an odd number is 2/3.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
In rolling a six-sided die, the total number of outcomes is 6.
The sample space is {1,2,3,4,5,6}
The probability formula is -
Probability = Number of outcomes corresponding to events / total number of outcomes.
(a) Let A be the event of rolling a 5. Then A = {5}.
Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.
The event of rolling A or B is given by A∪B = {4,5,6}.
So, apply the probability formula -
P(A∪B) = 3/6 = 1/2
Therefore, the probability value is 1/2.
(b) Let C be the event of rolling a number less than 4. Then C = {1,2,3}.
Let D be the event of rolling an even number. Then D = {2,4,6}.
The event of rolling C or D is given by C∪D = {1,2,3,4,6}.
So, apply the probability formula -
P(C∪D) = 5/6
Therefore, the probability value is 5/6.
(c) Let E be the event of rolling a 4. Then E = {4}.
Let F be the event of rolling an odd number. Then F = {1,3,5}.
The event of rolling E or F is given by E∪F = {1,3,4,5}.
So, apply the probability formula -
P(E∪F) = 4/6 = 2/3
Therefore, the probability value is 2/3.
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Please help question below
The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)
Thus, the required equation among the option is y = -3x + 2.
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Find the sum of 4√5 and √5 in simplest form. Also, determine whether the result is
rational or irrational and explain your answer.
Answer:
See below
Step-by-step explanation:
[tex]4\sqrt{5}+\sqrt{5}=(4+1)\sqrt{5}=5\sqrt{5}[/tex]
This sum is irrational because [tex]\sqrt{5}[/tex] was irrational to begin with.
a tire of a moving bicycle has a diameter of 18 inches, if the tire is making 4 rotations per second find the bicycle's speed in miles per hour.
Speed of bicycle in miles per hour will be 12.85 mi/h.
What is the definition of speed?
The following is the definition of speed:
The rate at which the position of an item changes in any direction.
The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.
Now,
Given Diameter=18 inch
then distance covered by cycle in 4 rotation in one second =4*π*diameter
=4*22/7*18
=226.28
Then Speed=226.28 in/s
As 1 mike=63360 inch and 1 hour= 3600 seconds
then Speed in miles/hour=226.28*3600/63360
=12.85 mi/h
hence,
Speed of bicycle in miles per hour will be 12.85 mi/h.
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Can someone please help me with 83? What is A? full explanation please. Offering lots of points
Answer: A = 5
Step-by-step explanation:
So, we are given a function, with a point: we can substitute (x,y) from the coordinate into x and f(x) in the function. (recall that f(x) is just a fancy way of saying y).
so:
[tex]-1 = \frac{2(0) + 5}{0 - A}[/tex]
[tex]-1 = \frac{5}{-A}[/tex], (we can drop the negative sign from both sides here)
[tex]\frac{5}{5} = \frac{5}{A}[/tex], (recall 1 = x/x where x is literally any number)
hence we can see that A = 5
Ask questions in the comments if this doesn't make sense :)
Yusef drove 130 miles in 2.5 hours. Which equation can be used to calculater, the average
speed at which Yusef drove?
A r = 130 - 2.5
B 130 = r/2.5
C r = 130/2.5
D 130 = r + 2.5
The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5
How to determine the speed equationThe formula to calculate average speed is:
Average speed = distance traveled / time taken
In this problem, Yusef drove 130 miles in 2.5 hours.
So, we can substitute the values in the formula:
Average speed = 130 miles / 2.5 hours
Simplifying this expression, we get:
Average speed = 52 miles per hour
Therefore, the correct equation to calculate the average speed at which Yusef drove is:
r = 130/2.5 or r = 52
Option C matches this equation, so the answer is C.
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In how many ways 4-digits numbers can be formed using the digits 1,2,3,7,8,9 without repetition? How many of these are even numbers?How many of these are even numbers?
We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.
Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.
We can use the combination formula to find the total number of possible combinations:
C(4, 3) = 4! / (3! * 1!) = 4
This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.
Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:
C(6, 4) = 6! / (4! * 2!) = 15
This means that we can form a total of 15 different 4-digit numbers using the given digits.
Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.
To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:
C(3, 1) * C(5, 3) = 3 * 10 = 30
This means that we can form a total of 30 different 4-digit even numbers using the given digits.
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this problem is very confusing pls help me, I will give brainliest
The required value of the trigonometric function is sin (α - β) = - 10.96/15.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric ratios are given in the question, as follows:
sin α = -2/5 and cos β = -1/3
So cos α = √1 - (-2/5)² = √(1 - 4/25) = √21/5
And sin β = √1 - (-1/3)² = √(1 - 1/9) = √8/3
We have to determine the value of sin (α - β).
According to trigonometric identity,
sin (α - β) = sinα cos β - cos α sin β
Substitute the values of sin α = -2/5 and cos β = -1/3,
sin (α - β) = (-2/5)( -1/3) - (√21/5)(√8/3)
sin (α - β) = 2/15 - (√21×8)/15
sin (α - β) = 2/15 - (√168)/15
sin (α - β) = 2/15 - 12.96/15
sin (α - β) = - 10.96/15
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By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol. How much cholesterol is in each item? The quantity of cholesterol in an egg is.....mg, the quantity of cholesterol in a cupcake is.....mg, and the quantity of cholesterol in a slice of pizza is.....mg. (Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
The quantity of cholesterol in an egg is 272 mg
The quantity of cholesterol in a cupcake is 18 mg
The quantity of cholesterol in a slice of pizza is 9 mg
How to find the amount of cholesterol in each itemLet the amount of egg be e
Let the amount of cupcake be c
Let the amount of pizza be p
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol
e + c + p = 299
The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol
3c + 4p = 90
By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol
3e + c = 834
e + c + p = 299
3c + 4p = 90
3e + c = 834
solving the simultaneous equation gives
e = 270
c = 18
p = 9
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consider the following: Point (3,5), and Line y-1=0. Write the slope intercept form of the equation of the line through the given point an parallel to the given line.
Step-by-step explanation:
please see the attached picture
Find the slope between the two points.
(2,10) and (6,30)
Please help what’s the slope between the two points
Answer:
The slope between the two points would be 5.
Answer: The slope would be 5
Step-by-step explanation:
Proper subset is a set that contains elements contained in another set but not equal
to that set.
True or false
Answer: A proper subset of a set A is a subset of A that is not equal to A
Step-by-step explanation:
brainliest answr quick tho
Answer:
BL
Step-by-step explanation:
because it goes in both directions infintely
Hi there, here's your answer:
To find the answer to this question, let us review all the options given in the question.
a) BL
BL being two ends of a given line that extends infinitely along its axis, forms a line.
b) GK
GK being two distinct lines do not join and hence do not form an independent line.
c) EB
E being a point on the line BL and B being one end of a larger line form a ray.
d) HI
HI being two points on a line GJ form a line segment, which is finite and has definite end points.
Thus, the answer to this question is (a).
Hope it helps! Please mark as Brainliest!
Three vertices of a parallelogram are located at (-4, 3), (1, -2), and (-1,4). What are two possible locations of the fourth vertex? Explain your reasoning.
Answer:
(4, -1) and (-6, 9).
Step-by-step explanation:
To find the fourth vertex of a parallelogram, we need to find the vector that represents the displacement from one of the given vertices to another, and then add that vector to the third given vertex. Since parallelograms have opposite sides that are equal in length and parallel, adding the same displacement vector to two of the given vertices will give us the coordinates of the other two vertices.
One possible displacement vector is the difference between the first and second given vertices, or (1 - (-4), -2 - 3) = (5, -5). Adding this vector to the third given vertex, (-1, 4), gives us the fourth vertex at (4, -1).
Another possible displacement vector is the difference between the second and third given vertices, or (-1 - 1, 4 - (-2)) = (-2, 6). Adding this vector to the first given vertex, (-4, 3), gives us the fourth vertex at (-6, 9).
So the two possible locations of the fourth vertex are (4, -1) and (-6, 9).
A growing giant pumpkin weighs 40.5 pounds on day 18 and 496.3 pounds on day 50. Which equation can be
used to find the weight gain of the giant pumpkin, (pounds), from day 18 to day 50, and what is the value of x?
The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 18 , 40.5 )
Let the second point be Q ( 50 , 496.3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )
Slope m = 455.8 / 32
Slope m = 14.24375
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 40.5 = 14.24375 ( x - 18 )
On simplifying the equation , we get
y - 40.5 = 14.24375x - 256.3875
Adding 40.5 on both sides of the equation , we get
y = 14.24375x + 296.8875
where x is the number of days
Hence , the equation of line is y = 14.24375x + 296.8875
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A sign for truck drivers states that the road ahead has a constant slope of 2 in 11. This means that for every 11m horizontally its rises 2m.
a. Over what horizontal distance will the road rise 300m?
b. What is the length of the road [AB]?
Having hard tiMe finding function
The local maximums are at x = -4 and x = 4, and the value of the local maximum is f(x) = 1.
How to find the local maximums?For a function f(x), we define a local maximum as a value of x = c such that:
f(c) ≥ f(x)
for any value of x in a given interval.
Here we can see two local maximums on the graph, and we can see that these are at:
x = -4 and x = 4
b) And the local maximum value of f is the value that the function takes in the maximum, we can see that:
f(-4) = f(4) = 1
The value of the local maximum is y = 1.
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The angles of a triangle are in the ratio of 2 : 3 : 7. Find the measure of the two greatest angles of the triangle.
Answer:
Step-by-step explanation:
The measure of the two greatest angles is 105° and 45°
Let the angles be 2x, 3x and 7x ...... (i)
According to the 'Angle Sum Property' of triangle,
2x + 3x + 7x = 180°
12x = 180°
x = 15°
Now, put value of x in (i)
2x = 2 × 15 = 30°
3x = 3 × 15 = 45°
7x = 7 × 15 = 105°
so, the two greatest angles are 105° and 45°
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Graph the system of inequalities.
y> 4x-2
2y-x≤8
The solution of inequalities is (1.714 , 4.857).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary 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:
y > 4x-2
2y-x ≤ 8
Now, solving the inequalities.
y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.
The two lines of inequalities intersect at (1.714 , 4.857).
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Add a term to the expression so tha it becomes a perfect square trinomial. Y^2-13y+
The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²
What is meant by a perfect square trinomial?
By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.
Given expression y² - 13y + ?
Comparing with the general equation
a = 1
b = -13
For perfect square trinomial
b² = 4ac
(-13)² = 4 * 1 * c
169 = 4c
c = 169/4
So the expression becomes,
y² - 13y + 169/4 = (y - 13/2)²
Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.
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A recent study reported the mean body mass index (BMI) for adults in the United States was 26. 8. A researcher believes the mean BMI of marathon runners is less than 26. 8. A random sample of 35 marathon runners had a mean BMI of 22. 7 with a standard deviation of 3. 1. The researcher will conduct a one-sample t-test for a population mean. Have the conditions for inference been met
Since the samples of the study are independent, the condition for inference have been met
The body mass index for adults in the United States = 26.8
BMI stands for Body Mass Index
Body mass index of marathon runners = less than 26.8
The random samples = 35
The body mass index of the random samples = 22.7
Standard deviation = 3.1
Then the researchers will conduct a one sample t test for a population mean.
The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value
Here the samples are independent
Therefore, the condition for inference have been met
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3. Hem started to travel at 11:40 and reached to his. destination at 12:20 at the speed of 6 km/hr. Find his distance covered.
Answer:
4 km
Step-by-step explanation:
There is a period of 40 minutes between 11:40 and 12:20.
[tex]40 \: minutes \: = \frac{2}{3} \: of \: an \: hour[/tex]
[tex] \frac{2}{3} \times \frac{6}{1} kmhr \: = \frac{12}{3} = 4[/tex]
In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?
A) 1:3
B) 2:3
C) 6:13
D) 4:15
Answer:
B) 2:3
Step-by-step explanation:
If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.
RatioThe ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.
mercury : copper = 1 : 5 = 2 : 10
Then ...
mercury : tin : copper = 2 : 3 : 10
You need 2 parts mercury to 3 parts tin.
mercury : tin = 2:3 . . . . . . choice B
<95141404393>
what is v=u+at
u=17 a=4 t=8
Answer: 65
Step-by-step explanation:
17 + 48
Kate had some stickers.
She kept 2/5 of them for herself and gave 5/6 of the remaining stickers to 6 of her
friends equally.
(a) What fraction of her stickers did Kate give to her 6 friends?
(b) What fraction of Kate's stickers did each of her 6 friends receive?
a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.
b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.
What is the fraction?The fraction is the portion or part of a whole.
Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.
The total number of stickers that Kate possesses = 1/1
The fraction Kate kept for herself = 2/5
The remaining portion of Kate's stickers = 3/5 (1 - 2/5)
The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2
The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12
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3. Using the equation y = 3x - 5, what would the output be for an input of 2?
The output of the equation for input of 2 is 1.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given equation is:
y = 3x - 5
Here, x is the input value and y is the output value.
Substituting input that is x = 2.
y = 3(2) - 5
y = 6 - 5
y = 1
Hence, the output of the equation for input of 2 is 1.
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A shipping container is in the form of a right rectangular prism and it can hold 1800 cubic feet of shipped goods when it is full. Its length is 30 ft and its height is 7 ft 6 inches. Find the width of the container in feet. Round your answer to the nearest tenth if necessary.
The width of the container can be calculated by dividing the product of the length and height by the volume. The width is 28.1 ft.
[tex]30 ft x 7.5 ft = 225 ft^3[/tex]
[tex]1800 ft^3 / 225 ft^3 = 8[/tex]
[tex]225 ft^3 / 8 = 28.125 ft[/tex]
Width = 28.1 ft
To calculate the width of the shipping container, you need to divide the product of the length and height by the volume. The length of the container is given as 30 ft, and the height is given as 7 ft 6 inches or 7.5 ft. Thus, the product of the length and height is [tex]225 ft^3[/tex]. The volume of the container when it is full is given as [tex]1800 ft^3[/tex]. To find the width, divide the product of length and height by the volume. Thus,[tex]225 ft^3 / 1800 ft^3 = 8[/tex]. Then, divide the product of length and height by the result you got in the previous step, that is,[tex]225 ft^3 / 8 = 28.125 ft[/tex]. This is the width of the container. Round this value to the nearest tenth and you get 28.1 ft as the width of the container.
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Question 3
Sam built the model shown below. It is composed of two rectangular prisms. What is the volume of the figure?
Answer:
44 in^2
Step-by-step explanation:
V = L×W×H
Bottom rectangle prism
L= 6 W= 4 H= 1
V = 6×4×1
V=24
Top rectangle prism
L= 2 W= 2 H= 5
V=2×2×5
V= 20
Add both of the rectangle prisms
24+25= 44
I need help solving part b)
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
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our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
The total optimal solution based on the information will be 49 rupees.
How to calculate the valueHere, four jobs and four machines are given, with the assignment matrix.
Find out the each row minimum element and subtract it from that row
Find out the each column's minimum element and subtract it from that column.
This assignment problem is being solved using Hungerian Method as the optimal solution is:
J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:
= 11 + 13 + 14 + 11
= 49 rupees
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I barley know anything about shapes
Answer:
they all have flat sides except for the cylinder
Step-by-step explanation:
Its okay we all are bad on some things
