Final answer:
The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.
Explanation:
The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.
If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:
P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...
This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:
P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.
In a certain town 22 of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure
Answer:
4.6
Step-by-step explanation:
Allow me to revise your question and hope it will be the same as the original one:
In a certain town 22% of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure
a. 1.9
b. 13
c. 4.6
d. 3.6
Here is my answer:
Given:
22% of voters favor a given ballot = 0.22 Groups of 21 votersSo the variance is: 21*0.22 = 4.6
We choose B
In a set of integers between 18 and 95, inclusive, how many are divisible by 6 but not 12?
find cosx if tanx cscx=2
A)2
B)square root 2
C)square root 2/2
D)1/2
The value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2
What is Trigonometry?From the question, we are to determine the value of cosx
From the given information,
tanx cscx=2
Recall that,
[tex]tan(x )= \frac{sin (x)}{cos(x)}[/tex]
and
[tex]csc(x) = \frac{1}{sin(x)}[/tex]
Then,
Substitute these values into the given equation
tanx cscx = 2 becomes
[tex]\frac{sin (x)}{cos(x)} \times \frac{1}{sin(x)} = 2[/tex]
[tex]\frac{1}{cos(x)} = 2[/tex]
∴ [tex]cos(x) = \frac{1}{2}[/tex]
Hence, the value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2
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If f(x)=-4x^2+15,then f(-3)=??
The value of f(-3) for the given function f(x) = -4x² + 15 will be -21.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
f(x) = -4x² + 15
Put x = -3
f(-3) = -4(-3)² + 15
⇒ -4 x 9 + 15
⇒ -36 + 15 = -21
Hence "The value of f(-3) for the given function f(x) = -4x² + 15 will be -21".
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Which of the following types of data are likely to be normally distributed? Check all that apply.
A. The time it takes for an airliner to fly from Los Angeles to New York
B. The distance of an archer's shots from the center of a target
C. The driving distances of American commuters
D. The outcomes of flipping a coin fifty times
E. The amount of popcorn that pops per bag
The answer is A. the time it takes for an airliner to fly from Los Angeles to New York city and B. the distance of an archer's shot from the centre of a target.
What is a normal distribution?A normal distribution is a symmetrical continuous probability distribution in which values are usually clustered around the mean.
A & B should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.
Therefore, The answer is A the time it takes for an airliner to fly from Los Angeles to New York City and B the distance of an archer's shot from the centre of a target.
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One bag of Glizard wood chips covers a 215 square foot area. How many total bags of wood chips must be purchased to cover an area that is 42 feet by 61 feet?
42 x 61 = 2562
2562/215 = 11.92
12 total bags are needed
-7=7d-8
help me with the equation for that problem
What is the greatest number of triangular sections, each with a base of 5 inches and a height of 8 inches, that can be cut from a rectangular piece of paper measuring 30 inches by 40 inches?
What is the simplified form of the expression? (2 – 9c)(–8)
EASY 5 POINTS!! Which expression gives the correct volume of the figure?
Answer : The correct option is, [(10 × 4 × 5) + (5 × 5 × 5)] cubic inches.
Step-by-step explanation :
As we know that,
Formula used for volume of cube is:
[tex]V=(a)^3[/tex]
or,
[tex]V=a\times a\times a[/tex]
where,
V = volume of cube
a = side of cube
Formula used for volume of cuboid is:
[tex]V=l\times b\times h[/tex]
where,
V = volume of cuboid
l = length of cuboid
b = breadth of cuboid
h = height of cuboid
The given figure is formed by the combination of two figure that is cube and cuboid.
Volume of cube = [tex](a)^3[/tex]
Given :
a = side of cube = 5 inch
Volume of cube = [tex]5\times 5\times 5[/tex] cubic inches
and,
Volume of cuboid = [tex]l\times b\times h[/tex]
Given :
l = length of cuboid = 10 inch
b = breadth of cuboid =5 inch
h = height of cuboid = 4 inch
Volume of cuboid = [tex]10\times 5\times 4[/tex] cubic inches
Total volume of figure = Volume of cuboid + Volume of cube
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Thus, the correct volume of the figure will be,
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Jack was 11 years older than Pricilla. Together their ages totaled 151 years.what are their ages?
a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text message.Plan b charges $31 for unlimited cell phone minutes plus $0.15 per text message.How many text messages must a customer send in order for the cost of plan a to be equal to cost of plan b
41+0.10x = 31+0.15x
10 +0.10x=0.15x
10=0.05x
x=10/.05
x= 200 text messages
check 200*0.10 = 20 +41 =61
200*0.15 = 30+31 = 61
they equal each other so number of texts is 200
A customer must send 200 text messages for the cost of Plan A ($41 plus $0.10 per text) to be equal to the cost of Plan B ($31 plus $0.15 per text).
To find out how many text messages a customer must send for the cost of Plan A to be equal to the cost of Plan B, we can set up an equation based on the cost structures given. Let x be the number of text messages sent.
Cost of Plan A: $41 + $0.10x
Cost of Plan B: $31 + $0.15x
To find the point where both plans cost the same, we set the costs equal to each other:
41 + 0.10x = 31 + 0.15x
Solving the equation:
0.05x = 10
x = 10 / 0.05
x = 200
The customer must send 200 text messages for the costs of Plan A and Plan B to be equal.
Use a triple integral to find the volume of the given solid. the solid enclosed by the cylinder x2 + y2 = 9 and the planes y + z = 14 and z = 2.
To find the volume of the solid enclosed by the given cylinder and planes, you convert to cylindrical coordinates. Then, you set up a triple integral with respect to these coordinates as ∫∫∫ dz dr dθ where the bounds of integration are 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.
Explanation:The volume of the solid can be found using a triple integral in cylindrical coordinates. First, we need to identify the boundaries of the solid. From the cylinder equation, we see that x² + y² = 9, which in cylindrical coordinates converts to r^2 = 9, so 0<=r<=3. Then, from the plane equations y + z = 14 and z=2, we can determine that in cylindrical coordinates, 2<=z<=14-r.
Therefore, the volume V can be found by:
V = ∫∫∫ dz dr dθ
with bounds for integration being 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.
Running this triple integral will provide the volume of the solid.
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$765.13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. Find the amount of the account. Round your answer to the nearest cent.
The final amount is = $ 959.779
What is compound interest?
Compound interest is when you earn a hobby on both the cash we've got stored and the hobby we earn.
calculation:-
principal amount = $765.13
rate if interest = 12%
for 1st year:-
interest amount= $765.13*12/100
= $ 91.8156
final amount = $765.13 + $ 91.8156
= $ 856.9456
for 2nd year:-
principal amount = $ 856.9456
12% interest on $ 856.9456 = $ 102.833472
final amount = $ 856.9456+$ 102.833472
= $ 959.779 answer
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An isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 15 inches each. Find the height of the triangle. (Round your answer to the nearest tenth of an inch.)
Final answer:
By using the Pythagorean theorem on one of the right triangles formed by dividing the isosceles triangle, we find the height to be approximately 13.0 inches when rounded to the nearest tenth.
Explanation:
To find the height of an isosceles triangle with a base of 15 inches and congruent sides each 15 inches, we can use the Pythagorean theorem or note that the triangle can be split into two right triangles by a height dropping from the vertex opposite the base to the midpoint of the base.
The midpoint will divide the 15-inch base into two segments, each 7.5 inches. The height of the isosceles triangle is the same as the height of the right triangle.
Using the Pythagorean theorem (a² + b² = c²), we can find the height (h) knowing that the hypotenuse (c) is one of the congruent sides (15 inches) and one leg (a, half of the base) is 7.5 inches:
h² + (7.5 inches)² = (15 inches)²
h² + 56.25 inches sup>2 = 225 inches²
h² = 225 inches² - 56.25 inches²
h² = 168.75 inches²
h = sqrt{168.75 inches²}
h approx 12.99 inches, which rounds to 13.0 inches to the nearest tenth.
Therefore, the height of the isosceles triangle rounds to 13.0 inches.
the following data values represents a population. What is the variance of the values? 6, 10, 14, 2
Answer:20 !
Step-by-step explanation:
2.8 meters linen divided into 45 cm pieces = # of pieces and waste
What percent of 645 is 187.05?
To find what percent 187.05 is of 645, one can use the following formula:
[tex]\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \][/tex]
In this case, the Part is 187.05 and the Whole is 645. Plugging these values into the formula gives:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 \][/tex]
Now, calculate the fraction:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 = \left( 0.29155 \right) \times 100 \][/tex]
[tex]\[ \text{Percentage} = 29.155 \][/tex]
Therefore, 187.05 is approximately 29.155% of 645. To express this as a fraction, one can write:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \approx 29.155\% \][/tex]
To get the exact fraction, we can simplify:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \times \frac{20}{20} = \frac{374100}{12900} \][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 300, we get:
[tex]\[ \text{Percentage} = \frac{374100 \div 300}{12900 \div 300} = \frac{1247}{430} \][/tex]
So, the exact fraction representing the percentage is:
[tex]\[ \text{Percentage} = \frac{1247}{430} \times 100 \][/tex]
[tex]\[ \text{Percentage} = \frac{1247}{4.3} \][/tex]
[tex]\[ \text{Percentage} = 29.00 \% \][/tex]
Thus, 187.05 is exactly 29% of 645.
6/5 × 25/24 multiple
eliminate the parameter. x = 5 cos t, y = 5 sin t help please!
Final answer:
To eliminate the parameter 't' from the equations x = 5 cos t and y = 5 sin t, use the Pythagorean identity which leads to the non-parametric equation of a circle: x^2 + y^2 = 25.
Explanation:
To eliminate the parameter 't' from the parametric equations x = 5 cos t, y = 5 sin t, we can use the Pythagorean identity sin^2(t) + cos^2(t) = 1. Plugging in the given expressions for x and y:
(x/5) = cos(t)
(y/5) = sin(t)
We can square both sides of these equations and then add them together:
(x/5)^2 + (y/5)^2 = cos^2(t) + sin^2(t)
As cos^2(t) + sin^2(t) equals 1, the equation simplifies to:
(x/5)^2 + (y/5)^2 = 1
Thus, the eliminated parameter equation representing the same curve without the parameter 't' is:
x^2 + y^2 = 25
This is the equation of a circle with a radius of 5, centered at the origin.
Inez waters her plants every two days. She trims them every 15 days. She did both today. When will she do them both again?
The answer is 30 days.
The solution for this is to find the least common multiple. By getting the multiple of both numbers.
Multiples of 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40…..
Multiples of 15: 15,30,45,60,75……..
The Least Common Multiples of 2 and 15 is 30. So, Inez will do them both again in 30 days.
The least common multiple (LCM) of two numbers is the smallest number that is multiple by the both number.
What is the next number in the series? 83 79 75 71 67
83-79 =4
79-75 = 4
the numbers are decreasing by 4
so the next number would be 67-4 = 63
If point A lies on the line of reflection, where does the reflected image, point A', lie?
Write the phrase as an algebraic expression 6 less than a number times 11
A set of data with a mean of 62 and a standard deviation of 5.7 is normally distributed. what is the value that is −1 standard deviation from the mean
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?
60t – 55t = 0
60t + 55t = 1
60t + 55t = 150
60t – 55t = 150
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Here,
60t represents the distance covered by the first car in time t, and 55t represents the distance covered by the second car in time t.
When they meet, the sum of their distances would be equal to the total distance between them, which is 150 miles.
Therefore,
We can add their distances and set them equal to 150 miles to solve for t.
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Round 1.136 to the nearest hundredth
(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the volume of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. The a, b, and c are positive constants.
A store has a $43.89 item on sale. The total discount of the sale is $9.66. What is the sale percentage off on this item?
Question part points submissions used give two sets of five numbers that have the same mean but different standard deviations. set 1: 2, 3, 7, 11, 12 set 2: 5, 6, 7, 8, 9 set 1: 2, 4, 6, 8, 10 set 2: 3, 4, 5, 7, 11 set 1: 4, 5, 7, 8, 11 set 2: 3, 6, 7, 9, 10 set 1: 3, 4, 6, 9, 13 set 2: 2, 5, 7, 8, 13 set 1: 4, 6, 7, 8, 15 set 2: 3, 6, 7, 10, 14 give two sets of five numbers that have the same standard deviation but different means.