The probability of needing fewer than 4 rolls to get doubles is 13/25.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.
This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).
Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:
P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4
P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4
The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.
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Complete questions as follows-
Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.
Simplify using law of exponents. (3^4)^8
Step-by-step explanation:
[tex] {( ({3})^{4} })^{8} \\ = {3}^{32} [/tex]
Identify the converse of the statement "A → B: If x = 3, then x + 8 = 11."
A) ∼A → ∼B: If x ≠ 3, then x + 8 ≠ 11.
B) ∼A → B: If x ≠ 3, then x + 8 = 11.
C) B → A: If x + 8 = 11, then x = 3.
The converse of the statement "A → B: If x = 3, then x + 8 = 11" is Option(c) which is "B → A: If x + 8 = 11, then x = 3."
The "Converse" of a "conditional-statement" can be expressed by interchanging the hypothesis and the conclusion of "original-statement".
In this case, The "conditional-statement" is given to be "A → B: If x = 3, then x+8=11", which is read-as that if "x" is equal to 3, then expression "x + 8" is equal to 11.
So, The converse statement would say that if "x + 8" is equal to 11, then x must be equal to 3.
Therefore, the correct option is (c).
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Explain by using an example why you need to multiply when converting from a larger unit to a smaller unit
Multiplying is necessary because each larger unit contains a certain number of the smaller units and we need to account for that conversion factor.
Why is multiplication necessary with examples?For example, when converting from meters to centimeters where we know that 1 meter is equal to 100 centimeters.
To convert 3 meters to centimeters, we need to multiply by the conversion factor of 100 which gives us:
= 3 meters * 100 centimeters/meter
= 300 centimeters
So, without the multiplication, we would not account for the fact that each meter contains 100 centimeters. This principle applies to all conversions from larger units to smaller units and it is important to remember to ensure accurate conversions.
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Mo is running the tracks where one lap is 400m. After completing some laps, he found that he has completed 40% of the total distance. After another 2, 50% is done. What is the total distance that he needs to cover in meters?
I REALLY NEED THE ANSWER SOON,
IF YOU CAN DO IT WELL THANK YOU.
Answer:
Total distance is 8000 m------------------
According to the problem, 2 laps make a difference of 10% as:
50% - 40% = 10%Hence the total distance in terms of laps is:
100% / 10% = 10 times the 2 laps:Find the total distance:
Total distance = 10*2 = 20 lapsTotal distance = 20*400 m = 8000 mThe distance between Kingston and Sunny Place is 35 km. At 8.30 a.m. , Joel cycles from Kingstown towards Sunny place at an average speed of 12 Km/h. At the same time, Ryan cycles from Sunny place towards Kingstown, along the same route, at an average speed of 8 Km/h.
a) At what time will the cyclists meet on the way?
b)How far will each cyclist have travelled when they meet?
Answer:
Distance = Speed × Time.
Let's break down the problem into two parts:
a) At what time will the cyclists meet on the way?
Let's assume t represents the time in hours when the cyclists meet.
The distance Joel travels in t hours is given by: Distance = Speed × Time = 12t km.
The distance Ryan travels in t hours is given by: Distance = Speed × Time = 8t km.
Since they are cycling towards each other, the sum of their distances should equal the total distance between Kingston and Sunny Place, which is 35 km.
So, we can set up the equation: 12t + 8t = 35.
Simplifying the equation, we have: 20t = 35.
Dividing both sides of the equation by 20, we get: t = 35/20 = 1.75 hours.
Therefore, the cyclists will meet on the way after 1.75 hours, which is equivalent to 1 hour and 45 minutes.
b) How far will each cyclist have traveled when they meet?
To find the distance traveled by each cyclist, we can substitute the value of t into their respective equations:
Distance traveled by Joel = 12t = 12 × 1.75 = 21 km.
Distance traveled by Ryan = 8t = 8 × 1.75 = 14 km.
Therefore, when the cyclists meet, Joel would have traveled 21 km and Ryan would have traveled 14 km.
Need answer asap. Thank you for helping me.
The estimate of the cost for a 20-ft cord is given as follows:
$74.66.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points in the context of the problem are given as follows:
(3, 12.75), (5, 16), (6, 25.99), (50, 185).
Inserting these points into a calculator, the regression equation is given as follows:
y = 3.6794x + 1.06462.
Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:
y = 3.6794(20) + 1.06462
y = $74.66.
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Solve for x, in terms of y: 23 x + 15 y = 2
MAKE BRAINLYST AND 100
To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.
Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.
Therefore, the solution for x in terms of y is x = (2 - 15y)/23.
Solve for x. Round to the nearest tenth, if necessary.
50 points
Answer: 8.7
Step-by-step explanation:
Given:
hypotenuse = 9
Angle x =75
opposite of angle = x
Solution:
From SOH CAH TOA, use SOH
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] > substitute
sin 75 = [tex]\frac{x}{9}[/tex] > multiply both sides by 9
9*sin 75 =x
x=8.7
Help please
Expand the logarithm as much as possible
logy^10
Using some logarithm properties we will get the expanded expression:
log(y^10) = 10*ln(y)/ln(10)
How to expand the logarithm?So there are two logarithm properties that we can use here, these are:
logₙ(x) = ln(x)/ln(n)
and:
logₙ(x^a) = a*logⁿ(x)
Now let's go to our expression, it is:
log(y^10)
Using the second property we can remove the exponent, then we will get:
log(y^10) = 10*log(y)
Now we can use the first rule, remember that log(x) has a base of 10, then we can write:
10*log(y) = 10*ln(y)/ln(10)
That is the expession expanded.
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Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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Find the inequality represented by the graph.
The inequality represented by the given graph as required to be determined in the task content is; y ≥ 0.5x.
Which inequality is represented by the given graph?It follows from the task content that the inequality which is represented by the given graph is required to be determined.
By observation; the slope of the border line is; 0.5 and the y-intercept is; 0.
Ultimately, the corresponding equation to the border line is; y = 0.5x.
Hence, since the region above the line is shaded and the line is a solid line; the required inequality is; y ≥ 0.5x.
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9. What is the volume of a rectangular prism with a length of 11 meters, width of 26 meters, and height of 38 meters?
Answer:
10868
Step-by-step explanation:
11x26=286
286x38=10868
Look at this pictograph:
Library books checked out
December
January
February
March
April
Each = 5 books
How many more books were checked out in March than in April?
books
There were no more books checked out in March than in April.
What is the pictograph about?The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.
The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.
To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:
5 books (March) - 5 books (April) = 0 books
Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.
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Which of the following is the graph of the quadratic function y = x² - 4x+4?
A. Graph C
B. Graph B
C. Graph D
D. Graph A
Answer:
The correct answer is C, Graph D.
x^2 - 4x + 4 = (x - 2)^2.
Girish left his home at 7 45 and travelled to Muar, which was 120 km away. He arrived
at Muar 2 h later. After staying 1 2/3 hours in Muar, he travelled from Muar back to his home
along the same route at a speed which was 20 Km/h slower than his previous speed.
At what time did Girish reach home?
Answer:
2:35
Step-by-step explanation:
it takes 2 hours to get to Muar so 9:45
he spends 1 hour 40 in muar so 11:35
he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35
Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these?
Spinner B is the spinner that has a probability of 1/3 of spinning orange.
How to find the he probability of spinning orange is more than 40%a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.
From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.
b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).
From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.
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Helppppppp pleaseee
The loudness of sound in decibels perceived by the human ear depends on the intensity levels according to
D=10log(I/lo)
Find the decibel level when I is 63, 096 times Io.
The decibel is -------------- dB when I is 63, 096 times Io.
Round your answer to the nearest whole number.
Answer:
We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:
D = 10log(I/lo)
Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.
So, substituting the values, we get:
D = 10log(63,096*Io/Io) = 10log(63,096)
Using a calculator, we find:
D ≈ 47.1 dB
Rounding this to the nearest whole number, we get:
The decibel level is 47 dB when I is 63,096 times Io.
I hope this helps mate.
A glass jug can hold (p+6) quarts less water than a plastic container. 2 glass jugs and 2 plastic containers contain 6p quarts of water in all.
How much water can the plastic container hold? Give your answer im terms of p.
The amount of water that the plastic container can hold is -p + 3.
How to determine the amount of water that can be heldTo determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.
So, the glass jug can hold:
p + 6 - x
2 glass jugs and 2 plastic containers can hold 6p quarts of water.
= 2(p + 6 - x) - 2x = 6p
2p + 12 - 2x -2x = 6p
2p + 12 -4x = 6p
12 - 4x = 6p - 2p
-4x = 6p -2p - 12
-4x = 4p -12
x = 4p - 12/-4
x = -p - 3
or -p + 3
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b/8 < 8 help me please I also need the graphic
The solution of the inequality given is b < 64
the graph is attached
How to solve for bIn the equation, let us replace b with x
To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.
We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:
Therefore, the solution to the inequality x/8 < 8 is x < 64.
This means that any value of x that is less than 64 will make the inequality true.
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what principal will earn $67.14 interest at 6.25% for 82 days?
Answer:
I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1
Step-by-step explanation:
The pic
Type the correct answer in each box.
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of its square base. Nathan
uses the formula for the volume of a pyramid to determine the dimensions of the sculpture
V= }ah
Here, a is the side length of the pyramid's square base and h is its height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x? +
= O can be used to find that the length of
the sculpture's base is
centimeters.
The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.
Explain about the pyramid:The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.
volume of a pyramid = V=1/3 a²h Given volume V = 162 cm³Let 'x' be the side length.Then , (x - 3) be the height of sculpture.Put the values and find the length.
162 = 1/3 (x)² (x-3)
162 * (3) = (x)² (x-3)
486 = x²(x-3)
486 = x³ - 3x²
x³ - 3x² - 486 = 0
(use a graphing tool or calculator equation mode).
x = 9
Thus,
side length of sculpture = 9 cm
height of sculpture = 9 - 3 = 6cm
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Correct question:
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.
V=1/3 a^2h
Here, a is the side length of the pyramids square base and h is it’s height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures. base is _ centimeters.
If g(q) = 2q-4 / q-A
and g(-3) = 2, what is the value of A?
Answer:
To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.
g(q) = (2q-4) / (q-A)
2 = (2(-3)-4) / (-3-A)
Multiplying both sides by (-3-A), we get:
2(-3-A) = -10 - 2A
Expanding the left side, we get:
-6 - 2A = -10 - 2A
Adding 2A to both sides, we get:
-6 = -10
This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:
There is no value of A that satisfies the given conditions.
What is the value of X? (Thx for any help!)
Answer:
x=109 y=100
Step-by-step explanation:
Answer:
x=100
y=109
Step-by-step explanation:
For any quadrilateral (4-sided shape) inscribed in a circle (all 4 vertices of the quadrilateral are on the edge of the circle), there is a special relationship between certain pairs of angles within the quadrilateral.
Specifically, opposite angles (angles across from each other) must sum (add) to 180 degrees.
The angle measuring 80 degrees is opposite the angle measuring x degrees, so x + 80 = 180, implying x = 100.
In this case, the angle measuring 71 degrees is opposite the angle measuring y degrees. So, 71 + y = 180, which implies y = 109.
Mateo produces a street sign graphic on his computer that is 4 inches by 5 inches. He enlarges the graphic by a scale factor of 3 to print. Then Mateo enlarges the image by a scale factor of 4 before sending it to the machinist.
What are the dimensions of the sign? Write the smaller dimension first and the larger dimension second.
The dimensions of the sign are as follows, using an overall scale factor of 12 on the original graphic:
Smaller Dimensions = 12 inches by 15 inchesLarger Dimensions = 48 inches by 60 inches.What is the scale factor?The scale factor refers to the ratio of an original scale, object, or drawing to its model or final version.
The scale factor may enlarge or reduce the original dimensions.
The dimensions of the street sign graphic on computer = 4 inches by 5 inches
Scale factor of the graphic on print = 3
The first smaller dimensions:
4 x 3 inches and 5 x 3 inches
= 12 inches by 15 inches
The second larger dimensions:
Scale factor = 4
12 x 4 inches by 15 x 4 inches60 i
= 48 inches by 60 inches
Overall scale factor of the original graphic to the last model = 12 (3 x 4)
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Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound=0.640, upper bound=0.910, n=1200
The point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample are:
margin of error = 0. 135point estimate = 0. 775 x = 930 peopleHow to find the parameters ?The point estimate of the population proportion:
= (lower bound + upper bound) / 2
= (0.640 + 0.910) / 2
= 0. 775
The margin of error for the confidence level :
= p - hat - lower bound
= 0. 775 - 0. 640
= 0. 135
The number of individuals in the sample with the specified characteristic (x ) :
= n x p - hat
= 1, 200 x 0. 775
= 930 people
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Ashley made 4 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 4 necklaces was $29.20 . If the beads cost a total of $13.60 , how much did each pendant cost?
$3.90
29.20-13.60=15.6
15.6/4= 3.90
Help with math problems
The surd forms are simplified to give;
21. 10√6 - 12√10
23. -56a - 5√2a - 25
25. -4√15x - 25x + 3
What are surds?Surds are described as values in square root that can no longer be simplified into whole numbers or integers
They are also seen as irrational numbers.
From the information given, we have that;
√15(2√10 - 4√6)
Expand the bracket and multiply the surd forms
2√150 - 4√90
Factorize the forms
2√25 ×√6 - 4√9 × √10
find the square root
10√6 - 12√10
23. (√2a - 5)(7√2a - 5)
expand the bracket
7√4a² - 5√2a - 35√4a² + 25
find the square root, we have;
7×2a - 5√2a - 35×2a + 25
collect the like terms
14a - 70a - 5√2a - 25
-56a - 5√2a - 25
25. (√3 + √5x)(√3 - 5√5x)
expand the bracket
3 - 5√15x + √15x - 5√25x²
find the square root
3 - 5√15x + √15x - 25x
collect the like terms
-4√15x - 25x + 3
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Which expression is equivalent to 6^2/7 ?
Answer: A
Step-by-step explanation:
well i did alll of them and got A
A gas station sells regular gas for $2.20 per gallon and premium gas for $2.75 a gallon. At the end of a business day 340 gallons of gas had been sold, and receipts totaled $803. How many gallons of each type of gas had been sold?
Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:
Regular Gas = 240 gallonsPremium Gas = 100 gallons.What is a system of equations?A system of equations refers to two or more equations solved concurrently.
A system of equations is also known as simultaneous equations because they can be solved at the same time.
Regular Premium
Price per gallon $2.20 $2.75
Total number of gallons of gas sold = 340
The total receipts for the 340 gallons = $803.
Let the number of gallons of the regular gas = x
Let the number of gallons of the premium gas = y
Equations:x + y = 340 ...Equation 1
2.2x + 2.75y = 803 ...Equation 2
Multiply Equation 1 by 2.2:
2.2x + 2.2y = 748 ...Equation 3
Subtract Equation 3 from Equation 2:
2.2x + 2.75y = 803
-
2.2x + 2.2y = 748
0.55y = 55
y = 100
x = 240 (340 - 100)
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The sequence is geometric.
1, 6, 30, 60, . . .
The sequence 1, 6, 30, 60, . . . is not a geometric sequence
Checking if the sequence is geometricFrom the question, we have the following parameters that can be used in our computation:
1, 6, 30, 60, . . .
To check if the sequence is geometric, we calculae the common ratio of the sequence using
r = next term/previous term
Using the above as a guide, we have the following:
r = 6/1 = 6
r = 30/6 = 5
r = 60/30 = 2
The common ratios of the sequence calculated above are different
This means that the sequence is not geometric
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