a) The probability that a hand will contain exactly 2 wild cards is 0.0246.
b) The probability of choosing a hand with seven yellow cards is 0.00056.
a) To find the probability that a hand will contain exactly 2 wild cards, we need to consider the number of ways we can choose 2 wild cards from 8 and the number of ways we can choose 5 non-wild cards from the remaining 100 cards. The total number of ways to choose 7 cards from 108 is:
C(108, 7) = 85,900,584
The number of ways to choose 2 wild cards from 8 is:
C(8, 2) = 28
The number of ways to choose 5 non-wild cards from the remaining 100 cards is:
C(100, 5) = 75,287,520
Therefore, the total number of ways to choose a hand with exactly 2 wild cards is:
28 * 75,287,520 = 2,108,196,160
The probability of choosing a hand with exactly 2 wild cards is:
2,108,196,160 / 85,900,584 ≈ 0.0246, or about 2.46%
b) To find the probability that a hand contains seven yellow cards, we need to calculate the number of ways we can choose 7 yellow cards from the 25 available, and divide this by the total number of ways to choose 7 cards from the 108 available. The number of ways to choose 7 yellow cards from 25 is:
C(25, 7) = 48,048
The total number of ways to choose 7 cards from 108 is:
C(108, 7) = 85,900,584
Therefore, the probability of choosing a hand with seven yellow cards is:
48,048 / 85,900,584 ≈ 0.00056, or about 0.056%
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Leo Gandolfi takes out a short-term loan of $1,800 at 12 percent
for 6 months. The monthly payment is $310.50. The balance of the loan after 4 payments is
$612.34. How much does he save by paying off the loan when the next payment is due?
A. $6.12 B. $18.00 C. $2.54 D. $618.46
Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To find out how much Leo Gandolfi saves by paying off the loan early, we need to first calculate how much interest he would pay if he were to continue making payments for the full 6-month term of the loan.
The total interest on the loan for the full 6 months can be calculated as:
Total interest = Total payments - Loan amount
We know the loan amount is $1,800, and the monthly payment is $310.50, so the total payments for the full 6 months would be:
Total payments = Monthly payment x Number of payments
Total payments = $310.50 x 6 = $1,863
Therefore, the total interest paid over the 6-month term of the loan would be:
Total interest = $1,863 - $1,800 = $63
Now, we need to calculate how much interest Leo Gandolfi would pay if he were to pay off the loan after making 4 payments.
The remaining balance on the loan after 4 payments is $612.34, so if Leo were to make one more payment, the remaining balance would be:
Remaining balance = $612.34 - $310.50 = $301.84
To calculate the interest paid on this remaining balance, we need to calculate the interest for one month:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 12% / 12 = 1%
Monthly interest = Monthly interest rate x Remaining balance
Monthly interest = 1% x $301.84 = $3.02
Therefore, if Leo were to make one more payment, he would pay $310.50, which includes both the principal and the interest. So, the amount of interest he would pay if he were to pay off the loan after 4 payments is:
Interest paid = Total payment - Remaining balance
Interest paid = $310.50 - $301.84 = $8.66
So, by paying off the loan early, Leo Gandolfi would save:
Savings = Total interest - Interest paid
Savings = $63 - $8.66 = $54.34
Therefore, Leo Gandolfi would save $54.34 by paying off the loan when the next payment is due.
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For a game you roll a dice. If you get a 1-3 you get nothing.
If you get 4 or 5 you break even and if you roll a 6 you win
$20. If the game costs $5 to play what is the expected value
For a game you have a 15% chance to get nothing a 25%
Is that all of the question?
In a group of 62 people 27 like cold tea while 42 like hot tea how many people like neither of the two
Can some one help sovle this?
-
By using the graph of the piecewise function we can see that:
f(0) = 0.
How to find the value of f(0)?Here we have the graph of a piecewise function, and we want to find the function when x = 0.
Remember that on a graph, an open circle means that the value does not belong to the graph, while a closed circle means taht the value belongs to the graph.
Here we can see that the closed circle at x = 0 is on the line at the middle, then we can conclude that f(0) = 0.
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3. find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
The lower and upper bounds of the given confidence interval of 95% with sample size= 1,555 , sample mean = 2.938 and standard deviation 2.837 is equal to ( 2.797 , 3.079 ).
Upper and lower bounds of the confidence interval is :
= Sample mean ± Margin of error
And Margin of error is :
= Z-critical × ( σ/√(n ) )
Standard deviation 'σ ' = 2.837
Sample size 'n' = 1,555
Sample mean 'μ' = 2.938
Z-critical for 95% confidence interval
= Zα/2
= 1.96
Margin of error
= 1.96 × (2.837/√1,555)
= 1.96 × (2.837/ 39.43 )
= 0.1410
Confidence interval:
Upper boundary
= 2.938 + 0.1410
= 3.079
Lower boundary
= 2.938 - 0.1410
= 2.797
Therefore, for the given confidence interval of 95% the lower and upper bounds of the interval are ( 2.797 , 3.079 ).
The above question is incomplete , the complete question is:
find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
Sample size Sample mean Standard deviation
1,555 2.938 2.837
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3. The scatter plot represents the age x of a driver in years and the monthly cost of insurance y
in dollars for a specific car model. The equation of the line of best fit for this data is
y=474.34-7.445x
Cost (dollars)
A
350
300
250
200
150
100
50
increases
decreases
0
5
10
Monthly Auto Insurance Costs
Write the values that complete each sentence.
Part A
The slope of the line of best fit is
The y-intercept of the line of best fit is
Part B
Circle an answer choice in each box to make each statement true.
The slope of the line of best fit means that as the age of the driver (A), the predicted monthly
cost of insurance (B)
B
15
20
Age of Driver (years)
The value of the y-intercept (C) make sense in this context. The predicted monthly cost of
surance for a driver who is 0 years old (D) possible for this situation.
25
decreases
30
increases
stays the same
35
does
40
does not
D
is
is not
NEED HELP NOWWWWW
Hence, or otherwise, find the two consecutive integers whose squares have a difference of 279
The two consecutive integers whose squares have a difference of 279 is 140 and 139.
What are consecutive integers?The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.
Let us suppose a number = x.
The consecutive number is given as (x - 1)
Two consecutive integers whose squares have a difference of 279, is given as:
x² - (x - 1)² = 279
x² - x² + 2x - 1 = 279
2x - 1 = 279
2x = 280
x = 140
x - 1 = 140 - 1 = 139
Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.
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If a = 6 and B = 40 degrees,
find c.
Answer: My guess is 90 degrees if we're looking at the uppercase C
Step-by-step explanation: Because of the square in the corner
A new image that is formed after a transformation is called an ________
A new image that is formed after a transformation is called reflection.
What is a reflection?A sort of symmetry known as reflective symmetry occurs when one half of an object mirrors the other half. For instance, both the left and right sides of a human face are typically the same. Most butterflies have identical wings on their left and right sides.
From the question, it is asked what we call a new image that is formed after a transformation. Reflection is the name given to the new picture that results from a change.
Therefore, the new image will be called a reflection after transformation.
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A picture 6 1/2 feet long is to be centered on a wall that is 21 feet long. How much space is there from edge of the wall to the picture
On solving the provided question, we can say that by fractions, the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Simply subtract the length of the image from the length of the wall to get the total area below and above the picture from the edge of the wall. So.
[tex]14\frac{1}{2} - 10\frac{1}{4}[/tex]
29/2 - 41/2
17/2
the space from the edge of the wall to the picture = 17/4*1/2 = 17/8
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Newington Town Manager Tanya Lane proposed a $124.2 million budget Monday night -- a 4.7 percent increase over the previous year." [R141] What was Newington's budget in the "previous year"?
Newington's budget in the "previous year" is $119.2 million
The term "budget" refers to a financial plan for a given period that outlines expected expenses and revenues. The previous year's budget for Newington is the financial plan that the town had for the previous fiscal year.
Assuming the previous year's budget refers to the fiscal year that ended just before the current fiscal year, we can find the amount by looking at the town's financial statements for that period. These statements will show the town's revenues and expenses for that fiscal year, and the difference between the two will be the budget.
If the town had $100 million in revenues and $95 million in expenses in the previous fiscal year, then the budget for that year would be $5 million. This means that the proposed $124.2 million budget for the upcoming year is a 4.7% increase from the $119.2 million budget of the previous year.
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pls help will give brainliest??
which statement best describes the association between variable X and Y?
you do not give the answer choice in this picture, but I assume it is along the lines of this
The scatter plot shows a negative association between variable X and Y
Find a polynomial function of degree 3 such that f(10)=17 and the zeros of f are 0, 5 and 8
Please help giving brainliest answer
To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of the polynomial. The polynomial can be written as f(x) = (17/20)x(x - 5)(x - 8).
If the zeros of a polynomial function are 0, 5, and 8, then the factored form of the polynomial can be written as: f(x) = k(x - 0)(x - 5)(x - 8)
To find a polynomial function of degree 3 such that f(10) = 17 and the zeros of f are 0, 5, and 8, we can use the factored form of a polynomial. The factored form of a polynomial is the product of its factors, which are its linear binomials that correspond to its zeros.
For example, if a polynomial has zeros of 1, 2, and 3, then its factored form can be written as (x - 1)(x - 2)(x - 3). We can use this concept to find the factored form of the polynomial with zeros of 0, 5, and 8, which is:
f(x) = k(x - 0)(x - 5)(x - 8)
where k is a constant coefficient that we need to determine. We can use the given condition that f(10) = 17 to solve for k. When we plug in x = 10, we get:
f(10) = k(10 - 0)(10 - 5)(10 - 8) = 2k * 5 * 2 = 20k
Since f(10) = 17, we can set 20k = 17 and solve for k:
k = 17/20
Therefore, the polynomial function of degree 3 with the given conditions is:f(x) = (17/20)x(x - 5)(x - 8)
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For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]A =1 2 11 1 1
We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix
Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.
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If an 8-pound turkey takes 150
minutes to cook, how long would
it take a 16-pound turkey to cook?
_____ minutes
Answer:
just 150x2 = 300 minutes or just 150 minutes to cook
Step-by-step explanation:
The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.
question 10
What is the length of segment LN?
21.93
27.57
30.36
55.14
Frodo ran 2 4/5 in 7/12 of an hour. How many miles can Frodo run in one hour?
Answer:
In 1 hour run:
4 4/5 miles
Step-by-step explanation:
2 4/5 = 2 + 4/5 = 10/5 + 4/5 = (10+4)/5 = 14/5
Proportions:
14/5 miles ⇒ 7/12 hour
A miles ⇒ 1 hour
A = (14/5 miles)(1hour) / (7/12 hour)
A = (14/5)/(7/12)
A = (14*12) / (5*7)
A = 168 / 35
A = 140/35 + 28/35
A = 4 + 28/35
A = 4 + 4/5
A = 4 4/5 Miles
One angle of an isosceles triangle measures 140°. What measures are possible for the other two angles? 28? 22? 26? 20?
The measures of angle possible for of an isosceles triangle when one angle given is 140° then other two angles is 20°.
In an isosceles triangle, two of the angles have the same measure. Let's call this measure x. Since the sum of the angles of a triangle is 180 degrees, we can set up an equation:
x + x + 140° = 180°
Simplifying the equation, we get:
2x + 140° = 180°
Subtracting 140° from both sides, we get:
2x = 40°
Dividing both sides by 2, we get:
x = 20°
So the other two angles in the isosceles triangle each measure:
x = 20°
Therefore, the measures 28°, 22°, 26° are not possible for the other two angles of the isosceles triangle, but the measure 20° degrees is possible.
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There are 9 times as many strawberries as plums in a fruit basket. What is the ratio of the number of plums to the total number of strawberries and plums.
Answer:
Below
Step-by-step explanation:
strawberries to plums 9:1 then total would be 10 parts of which 1 is plums so 1 : 10
A 6
6
-foot ribbon is cut into 4
4
equal pieces.
Which equation shows how to find the length of each piece?
The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.
To find the length of each piece, we can use the following equation:
Length of each piece = Total length of the ribbon / Number of pieces
In mathematical terms, we can represent this equation as:
L = R / N
Where,
L is the length of each piece
R is the total length of the ribbon (66 feet in this case)
N is the number of pieces (44 in this case)
In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.
Using this equation, we can easily find the length of each piece:
L = 66 / 44
L = 1.5 feet
Therefore, each piece of the ribbon is 1.5 feet long.
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Solve: s=4+sqrrt s+2
s = 2
s = 7
s = 2 or s = 7
no real solution
There is no real solution to the given equation s = 4 + sqrt(s+2) with value of s = 2, s = 7, s = 2 or s = 7.
To solve the equation:
s = 4 + sqrt(s+2)
We can start by isolating the square root term on one side:
s - 4 = sqrt(s+2)
Then, we can square both sides to eliminate the square root:
(s - 4)^2 = s + 2
Expanding the left side:
s^2 - 8s + 16 = s + 2
Bringing all terms to one side:
s^2 - 9s + 14 = 0
We can solve for s using the quadratic formula:
s = (9 ± sqrt(9^2 - 4(1)(14))) / 2(1)
s = (9 ± sqrt(49)) / 2
s = (9 ± 7) / 2
So the two possible solutions are:
s = 8/2 = 4
s = 2/2 = 1
However, we need to check if these solutions satisfy the original equation.
If we plug s=4 into the equation, we get:
4 = 4 + sqrt(4+2)
4 = 4 + sqrt(6)
This is not true, since the right-hand side is greater than the left-hand side.
If we plug s=1 into the equation, we get:
1 = 4 + sqrt(1+2)
1 = 4 + sqrt(3)
This is also not true.
Therefore, there is no real solution to the equation s = 4 + sqrt(s+2).
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Answer:
B
Step-by-step explanation:
a farmer, cole, who is 6 feet tall, wants to determine the height of his barn. cole notices that his shadow is 14 feet long. the shadow cast by his barn is 70 feet long. how tall is the barn?
The barn with shadow height, 70 feet, having the the height which is equals to the 30 feet, that is barn is 30 feet tall.
The height of farmer Cole = 6 feet
The height of shadow of farmer Cole = 14 feet
The height of shadow of barn = 70 feet
Let the height of barn be ' x feet '. We have to determine the value of x. Now, we the above figure, AB and CD represents height of barn and Cole respectively. Similarly BE and CE represent the shadow height of barn and Cole respectively.
Let angle BAE made here be equals to θ. Also angle BAE = angle CDE = θ. Now, consider right angled triangle, CDE with sides. Using triganomertric functions, tanθ = height/base
=> tanθ = CE/CD = 14/6
simplify, tanθ = 7/3 --(1)
Also, consider right angled triangle ABE,
tanθ = height/base = BE/AB
=> tanθ = 70 / x
=> x tanθ = 70
from equation (1), x (7/3) = 70
=> 7x/3 = 70
=> 7x = 210
=> x = 210/7
=> x = 30
Hence, required value of x is 30 feet.
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In Exercises 1-4, tell whether the ordered pair is a solution of the inequality.
1. x - y > 2; (5, 4)
2. x + y ≤ -3; (−1, −4)
3. 5x + y ≤ 12; (2, 2)
4. x-3y > 6; (3, −1)
(5×-1)(6×2+3×+8) box method
The final result is: 30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8
What is the Box method?The box method, also known as the FOIL method, is a way of multiplying two polynomials by using the distributive property.
Given the expression (5x - 1)(6x^2 + 3x + 8), we can use the box method to multiply the terms as follows:
First terms: (5x - 1) * 6x^2 = 30x^3 - 6x^2Outer terms: (5x - 1) * 3x = 15x^2 - 3xInner terms: (5x - 1) * 8 = 40x - 8Last terms: (5x - 1) * 8 = 8Therefore., the final result is:
30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8
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A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
Answer:
hope this helps!
Step-by-step explanation:
Four friends plan to rent a car to go on a camping trip. At the campground the friends sign up to go on a mountain bike tour
The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.
In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.
To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.
G = Total Distance Traveled / MPG
To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.
T = G x C
Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:
=> T = G x C
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Complete Question:
Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.
Write an algebraic expression for the total cost of the gasoline.
Cameron has a bag of 24 letter tiles. Some are vowles and some are consonants. He randomly chooses a letter tile and places it back in the bag. He chose 4 vowels and 2 consonants. How many vowels are likely in the bag?
In all, Cameron removed 6 tiles (3 consonant vowels and 4 vowel consonants). Take that amount, 6, then divide it by the 24 vowels in total. 24/6=4. It provides you four. Then you multiply that number, 4, by the number of consonant vowels he removed, which is 3, for a total of 6, or 4*2. your response is six vowels.
The five distinct vowel letters are A, E, I, O, and U. The English language has vowels in practically every word and phrase, making them incredibly prevalent. Any letter of the alphabet that isn't a vowel is referred to as a consonant (a, e, i, o, u).All of the non-vowel sounds in the English alphabet are consonants. Vowels, the loud sounds that make up each syllable's core and are separated by consonants. Letters A and O stand in for vowels, whereas B, C, D, F, J, K, M, N, P, Q, S, T, V, X, and Z stand in for consonants.
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What is the number 9.88 x 10-5 in standard notation?
€-grade10
mathematics
Answer:
29/5
Step-by-step explanation:
hope this helps
Why the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
The statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.
What is meant by probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
The given statement is:
"the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring."
This is a false statement.
The probability of the union of two events is the probability of individual events without considering the probability of the intersection of the events.
When the events do not have an intersection, then the probability of a union of events is greater than the probability of an intersection of events.
The chance of both occurrences occurring together is given by the union of two events, but the probability of both events occurring simultaneously is given by the intersection of two events, which is smaller than probability of union of events.
Therefore the statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.
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