There are six possible ways a person can choose two balls at random from an urn containing five balls numbered 1, 2, 2, 6, and 6.
To understand how to calculate the number of combinations, let's break it down into two parts: selecting the first ball, and then selecting the second ball. Since there are five balls in the urn, the first ball can be chosen in five possible ways. Then, when selecting the second ball, the number of possible selections is reduced to four because one ball has already been selected. This can be expressed mathematically as: n(A)=5x4.
To calculate the total number of combinations, we then multiply the two numbers: 5x4=20. This result is then divided by two because the order of selection does not matter. As a result, 20/2=10, which means that there are ten possible combinations when choosing two balls at random from the urn. In conclusion, if an urn contains five balls numbered 1, 2, 2, 6, and 6, there are six possible ways a person can choose two balls at random. This can be expressed mathematically as n(A)=6 or n(A)=5x4/2.
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if atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, how many of each coin does he have?
If Atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, then he has 1 nickels and 4 dimes.
Let x be the number of nickels and y be the number of dimes. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, we can write two equations:
x + y = 10 (since he has 10 coins in total)
5x + 10y = 70 (since the combined value of the coins is 70 cents)
We can simplify the second equation by dividing both sides by 5:
x + 2y = 14
Now we can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:
x + y = 10x = 10 - y
Now we can substitute this expression for x into the second equation:
x + 2y = 14(10 - y) + 2y = 14
Simplifying, we get:
10 + y = 14
y = 4
Therefore, Atharv has 5 - 4 = 1 nickel and 5 - 1 = 4 dimes.
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all the edges of a cube are expanding at a rate of 4 4 in. per second. how fast is the volume changing when each edge is 10in. 10 in. long?
Answer:
Step-by-step explanation:
every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get
85.184in^3 per second
Lydia uses 6. 2 pints of blue paint and white paint to paint her bedroom walls. 3
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Lydia used a total of approximately 16.33 pints of paint to paint her bedroom walls, with 6.2 pints being blue and 10.33 pints being white.
We know that 3/5 of the total paint used is blue, and the remaining 2/5 must be white.
Let x be the total amount of paint used in pints. Then, we can write:
3/5 x = 6.2 (pints of blue paint used)
2/5 x = ? (pints of white paint used)
To solve for the pints of white paint used, we need to isolate the variable x in the second equation:
2/5 x = (2/3) * 3/5 x (multiply both sides by 2/3 to simplify)
2/5 x = 6.2 * 2/3
2/5 x = 4.1333...
Now we can solve for x by multiplying both sides by 5/2:
x = (5/2) * (2/5) x = (5/2) * 4.1333... = 10.3333...
Therefore, Lydia used approximately 10.33 pints of white paint and 6.2 pints of blue to paint her bedroom walls.
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which number is absent in the first 31 digits of π
The number which is absent in the first 31 digits of the pi is 9
The digit that is absent in the first 31 digits of pi is the digit 9. Pi is an irrational number with an infinite number of decimal places, and it is believed to be a random sequence of digits. However, the absence of the digit 9 in the first 31 digits of pi is just a coincidence and has no special mathematical significance.
It is important to note that the digits of pi are not random in the strict sense of the word, but they appear to be so, and they follow a pattern that has yet to be fully understood by mathematicians. The quest to discover the properties of pi has been ongoing for centuries, and it continues to be a fascinating and important area of research in mathematics.
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The given question is incomplete, the complete question is:
Which number is absent in the first 31 digits of pi
a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?
A total of 5 glove prices meet the condition of having an absolute deviation from the mean of $8 or less.
To find the mean price, we need to sum up all the glove prices and divide by the total number of gloves.
Sum of glove prices = $55 + $42 + $28 + $39 + $82 + $25 + $40 + $32 + $45 + $38 + $52 + $34 = $512
Total number of gloves = 12
Mean price = Sum of glove prices / Total number of gloves = $512 / 12 = $42.67
To find the absolute deviation of each glove price from the mean, we subtract the mean from each price and take the absolute value.
Absolute deviation from mean for each glove = |Price - Mean price|
For example, for the first glove price of $55, the absolute deviation from the mean is |$55 - $42.67| = $12.33
We want the absolute deviation to be at most $8, so we need to find how many glove prices have an absolute deviation from the mean of $8 or less.
We can calculate the absolute deviation for each glove price and count how many are less than or equal to $8.
First row:
|$55 - $42.67| = $12.33
|$42 - $42.67| = $0.67
|$28 - $42.67| = $14.67
|$39 - $42.67| = $3.67
|$82 - $42.67| = $39.33
|$25 - $42.67| = $17.67
Out of the 6 glove prices in the first row, 2 have an absolute deviation from the mean of $8 or less.
Second row:
|$40 - $42.67| = $2.67
|$32 - $42.67| = $10.67
|$45 - $42.67| = $2.33
|$38 - $42.67| = $4.67
|$52 - $42.67| = $9.33
|$34 - $42.67| = $8.67
Out of the 6 glove prices in the second row, 3 have an absolute deviation from the mean of $8 or less.
Therefore, a total of 5 glove prices meet the condition
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The given condition is incomplete, the complete question is:
a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?
suppose you have a set of normally distribution data where the mean is 120 and the standard deviation is 15. what score is located at -3sx?
The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.
To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.
Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.
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Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot.
A number line goes from 1 to 12. 1 dot is above 2. 2 dots are above 7. 3 dots are above 8. 1 dot is above 9. 3 dots are above 11. 4 dots are above 12.
Which statement must be true according to the dot plot?
The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed left and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
The data is skewed right and shows that on half of the days, Darren received 7 to 9 e-mails from the customer.
A statement that must be true according to the dot plot include the following: A. the data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
By critically observing the given dot plots which is used to illustrate the number of e-mails that Darren received from one of his customers each day for 14 days, we can reasonably infer and logically deduce that the data set is skewed left, which ultimately implies that that on half of the days (7 days), Darren received a total of 11 or 12 e-mails from this customer.
In conclusion, the dot plot is skewed left because it has a long tail on its left side and 7 days is the half of 14 days.
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the probability that the splices in a rope splicing shop are weak is 1/1000 and the probability that the splices are ugly is 1/20. the probability that the weak splices are ugly is 2/3. find the probability that an ugly splice is weak.
The probability that an ugly splice is weak is 2/3.
This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).
In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).
The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.
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the number of students who seek assistance with their statistics assignments is poisson distributed with a mean of 0.24 per day. what is the probability that at least three students seek assistance in 10 days?
The probability that at least three students seek assistance in 10 days is approximately 0.117.
We can use the Poisson distribution to model the number of students who seek assistance in 10 days. Let X be the number of students who seek assistance in 10 days.
Then X follows a Poisson distribution with parameter λ=2.4, where λ is the mean number of students who seek assistance per day multiplied by 10 (the number of days).
Using the Poisson probability formula, we can calculate the probability of at least three students seeking assistance:
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]
We can find that:
P(X ≥ 3) = 0.117
Therefore, the probability that at least three students seek assistance in 10 days is approximately 0.117.
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Suppose we have a solid with volume 10 cubic units.
It's dilated, and the volume of the image is 40 cubic
units.
How can you find the scale factor that was used?
Answer:
Step-by-step explanation:
We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:
(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3
(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3
4 = (linear dimension of image / linear dimension of original)^3
Taking the cube root of both sides, we get:
(cube root of 4) = (linear dimension of image / linear dimension of original)
Simplifying, we have:
2 = (linear dimension of image / linear dimension of original)
Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.
Which value represents |-50|?
Answer:50
Step-by-step
Answer:
Answer is D
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50
excel a university found that 5% of its students who enroll in an introductory statistics class withdraw. assume 90 students have registered for an introductory statistics course this semester. (a) what is the probability that no student will withdraw from the course?
The probability that no student will withdraw from the course is approximately 0.008 or 0.8%, assuming a binomial distribution with n=90 and p=0.05.
Since each student's decision to withdraw or not is independent of others, we can model the number of students who withdraw as a binomial random variable with n=90 and p=0.05.
To find the probability that no student will withdraw from the course, we want to find P(X=0), where X is the number of students who withdraw. This is given by the binomial probability mass function:
P(X=0) = (n choose 0) * p^0 * (1-p)^(n-0) = (90 choose 0) * 0.05^0 * 0.95^90
Using a calculator or software, we find:
P(X=0) ≈ 0.008
Therefore, the probability that no student will withdraw from the course is approximately 0.008 or 0.8%.
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Rename 1 foot with an equivelint fraction in yards
Renaming 1 foot to equivalent fraction in yards as 1/3 yards
We multiply the number of feet by 1/3 to convert this to yards, and then we need to identify the two elements of this equation that have a functional relationship.
As we are aware,
1 foot equals 3 yards.
As a result, we must multiply the unknown numbers, denoted by the letter x, by 1/3 in order to get the feet.
Let's say that the variables in this situation are x and y, where x stands for feet and y for yards.
To get the unit in yards, multiply the unit in feet by a factor of three-quarters. x = 1/3y
Hence, the renaming of 1 feet as 1/3 yards, where the fraction is 1/3.
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What is 50. 7 / 7 bc im not sure I understand
The value of 50.7 / 7 is approximately equal to 7.24285714.
The given expression is 50.7 / 7.
Creating equal groupings or determining how many individuals are in each group after a fair distribution is the basic objective of division.
To simplify the expression, we need to perform the division operation.
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
To solve this, we can perform the following steps:
First, we can write the given expression as:
50.7 ÷ 7
Then, we can perform the division operation as shown below:
50.7 ÷ 7
= 7.24285714 (rounded to 8 decimal places)
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Describe and correct the error a student made in identifying the growth or decay factor for the
function y = 2.55(0.7)
Step 1 The base of the function
is 0.7, so it represents
exponential decay.
Step 2 The function in the form
y = a(1-r)* is
y = 2.55(1-0,7)*
Step 3 The decay factor is 0.3.
X
The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.
Explain function?
A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.
The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]
To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]
So, the corrected version of the solution is:
Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.
Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]
Step 3: The decay factor is [tex]0.3.[/tex]
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(+8) - (+3) = (+8) + (-3)
solve for x (Please leave an explanation)
The value of x for the angle 100 + x under the top parallel line is equal to -10.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.
The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:
100 + x = 90
subtract 100 from both sides
x = 90 - 100
x = -10.
Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.
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ILL GIVE THE BRAINLIEST
Answer:1, -.66 repeating, 1.25
Step-by-step explanation i turned them into decimals
24/8x-1/3= -1
-2/5x5/3= -.66 repeating
-5/6x-3/2= 1.25
Help, need to finish this class asap
A medical equipment industry manufacturers x-ray machines. The unit cost C (the cost in dollars to make each x-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C(x)=0.6x^2-372x+63,308. How many machines must be made to minimize the unit cost? Do not round
To find the number of machines that minimize the unit cost, we need to find the value of x that minimizes the function C(x). We can do this by finding the critical points of C(x) and determining which one corresponds to a minimum.
First, we take the derivative of C(x) with respect to x:
C'(x) = 1.2x - 372
Then, we set C'(x) equal to zero and solve for x:
1.2x - 372 = 0
1.2x = 372
x = 310
So the critical point is x = 310.
To determine whether this critical point corresponds to a minimum or a maximum, we need to examine the second derivative of C(x):
C''(x) = 1.2
Since C''(x) is positive for all values of x, we know that the critical point x = 310 corresponds to a minimum.
Therefore, the number of machines that must be made to minimize the unit cost is 310.
Whats the highest degree x^4-3x^2+9x
Answer:
4th degree
Step-by-step explanation:
When you are looking for the degree of an expression or equation, you just look for the biggest exponent.
Here, there is an
"x to the 4th power",
a "minus3 to the second power" and
a "9x" (which is a power of 1)
So the biggest exponent is 4...4th degree. That's it!
What is the distance from −12 to −5 on a number line?
A -17
B -7
C 17
D 7
Can someone pls help me with this
A. The equation of the line is expressed as: y = (-5/2)x + 13.
B. The x-intercept of the equation is calculated as: 26/5.
How to Find the Equation of a Line?A. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to find the equation of a line passing through the point (4,3) with a slope of -5/2.
Substituting the values, we get y - 3 = (-5/2)(x - 4), which simplifies to y = (-5/2)x + 13 by expanding and adding 3 to both sides.
B. To find the x-intercept of the equation y = (-5/2)x + 13, we set y to 0 and solve for x. 0 = (-5/2)x + 13, which simplifies to x = 26/5 by multiplying both sides by -2/5 and adding (26/5) to both sides.
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what is the measure of angle 1 in degrees?
Answer:
54 degrees
Step-by-step explanation:
180-126=54
Question
A ribbon is 20 feet long. You cut the ribbon into strips that are 14 inches long.
How many 14-inch strips do you cut from the ribbon?
How many inches of ribbon are remaining?
in.
Answer:
17 strips, 2 inches remain
Step-by-step explanation:
20(12)/14=17
17x14=238
240-238=2
A 20-foot ribbon converts to 240 inches. It can be cut into 17 strips of 14 inches each, leaving 2 inches of ribbon leftover.
Explanation:To solve this problem, we need to first convert the length of the ribbon from feet to inches, since the length of the strips is given in inches. One foot equals 12 inches, so a 20-foot ribbon is 20*12 = 240 inches long.
Now, to find out how many 14-inch strips can be cut from the ribbon, we do the division: 240 divided by 14 equals 17 strips with a remainder. This means 17 full strips can be cut from the ribbon.
To find how many inches are left, we need to multiply the number of strips by the length of each strip and then subtract the result from the total length of the ribbon. So it's 240 - (17 * 14) = 2 inches.
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-1/5+2/15 what is the answer the answer to that
Answer:
-0.06666666666
hope it helps :)
Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. If she spends 3x-7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which
value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s)
She spends
(Simplify your answer.)
dollars on electricity.
The values of x is [tex]x < 39.5[/tex].
Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]
Spending of shopkeeper on rent [tex]= 3x-7[/tex]
So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
[tex]2x+21 < 100[/tex]
[tex]2x < 100-21[/tex]
[tex]2x < 79[/tex]
[tex]x < 39.5[/tex]
All the values of [tex]x < 39.5[/tex].
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the spirit club buys shirts in bulk for $8 each. they mark up the shirts 25% to sell in the school store. at the end of the year, they sell the shirts for 25% off. how much profit does the spirit club make on each shirt sold at the end of the year?
Answer:
The cost price of each shirt is $8.
They mark up the shirts 25%, which means they increase the price by (25/100) * $8 = $2.
So, the selling price of each shirt becomes $8 + $2 = $10.
At the end of the year, they sell the shirts for 25% off, which means they reduce the price by (25/100) * $10 = $2.50.
Therefore, the selling price of each shirt after the discount becomes $10 - $2.50 = $7.50.
The profit made on each shirt sold at the end of the year is the difference between the selling price and the cost price, which is $7.50 - $8 = -$0.50.
Since the profit is negative, it means that the Spirit Club is making a loss of $0.50 on each shirt sold at the end of the year.
t-test is used when you have two samples or data coming from 2 groups, and you want to compare whether or not they're distinct (in other words, is the data coming from 2 separate populations, or not?)
The result is the t-statistic, which is used to compare the two samples.
The t-test is used to compare the means of two independent samples. The formula for the t-test is:
[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],
where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.
To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.
Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).
Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.
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hi what is 2x -9x =5x so x = ?
Answer:
-3x
Step-by-step explanation:
FIrst you subract 2 from both sides then eliminate the x's
what is the future value of 6000 earning 18% interest, compounded monthly for 8 years
Answer:
To calculate the future value of an investment earning compound interest, we can use the formula:
FV = P(1 + r/n)^(nt)
where:
FV is the future value
P is the principal (starting amount)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
P = 6000
r = 0.18 (18% annual interest rate)
n = 12 (compounded monthly)
t = 8
Substituting these values into the formula, we get:
FV = 6000(1 + 0.18/12)^(12*8)
FV = 6000(1.015)^96
FV = 6000(3.045)
FV = 18270
Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.