Using the concept of combinations, there are 10 ways to choose three apples from a basket, where two are rotten and one is not.
Explanation:The question is asking about the number of ways two rotten apples can be chosen from a basket, given the total apples and the number of rotten ones. This is a problem based on probability and combinations.
The total number of apples in the basket is 12, two of them are rotten. The number of ways of choosing 2 rotten apples from 2 is simply 1 way, because there are only 2 and you're choosing each one of them.
But, the student is asked to select three apples, so the last apple would be one of the other 10 (remaining good ones). The number of ways you can choose that is 10 C 1.
From combinations rules, we know nCr=n!/[r!(n-r)!], where n is the total items, r is the number chosen, and '!' refers to factorial.
So to find the number of ways to choose 1 apple from 10, we find 10! / [1!(10-1)!]. This calculates as 10! / [1!9!] = 10. So, there are 10 ways to choose three apples with two of them being rotten.
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There are 10 different ways to choose a sample of three apples from the basket such that exactly two of them are rotten.
To determine the number of ways to choose two rotten apples from a basket containing 12 apples (2 of which are rotten) when a sample of three apples is selected.
We can use combinatorics.
Step-by-Step Solution:
1. Identify the total number of apples and the rotten apples:
Total apples: [tex]\( 12 \)[/tex]
Rotten apples: [tex]\( 2 \)[/tex]
2. Determine the possible cases for choosing two rotten apples in the sample of three:
We need to choose 2 out of the 2 rotten apples.
We need to choose the remaining 1 out of the 10 good apples.
3. Calculate the number of ways to choose 2 rotten apples out of 2:
[tex]\[ \binom{2}{2} = 1 \][/tex]
4. Calculate the number of ways to choose 1 good apple out of 10:
[tex]\[ \binom{10}{1} = 10 \][/tex]
5. Multiply the results from the above steps to get the total number of ways to choose two rotten apples and one good apple:
[tex]\[ \text{Total ways} = \binom{2}{2} \times \binom{10}{1} = 1 \times 10 = 10 \][/tex].
Which is 0.54 (.54 is repeating) converted to a simplified fraction?
A) 27/50
B) 54/100
C) 6/11
D) 54/99
Answer:
B
Step-by-step explanation:
The answer above me ^^
There are 10 less trumpet and saxophone players number of saxophone players three times the number of trumpet players how many trumpet players are there?
There are 3 trumpet players.
We have,
Let's assume the number of trumpet players is represented by "x".
According to the given information, the number of saxophone players is three times the number of trumpet players, so the number of saxophone players would be 3x.
It is also stated that there are 10 less saxophone players than the total number of trumpet and saxophone players.
So, the number of saxophone players would be (x + 3x) - 10, which simplifies to 4x - 10.
Since the number of saxophone players is equal to 4x - 10, we can set up an expression to solve for x:
4x - 10 = x
To isolate x, subtract x from both sides of the expression:
4x - x - 10 = x - x
This simplifies to:
3x - 10 = 0
Next, add 10 to both sides:
3x - 10 + 10 = 0 + 10
This yields:
3x = 10
Finally, divide both sides by 3:
(3x) / 3 = 10 / 3
The solution is:
x = 10/3 or approximately 3.33
Therefore,
There are approximately 3.33 trumpet players.
Since you cannot have a fraction of a player, we can conclude that there are 3 trumpet players.
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(3y)^-2(9y)^2/3y^-4=
In the diagram, polygon ABCD is flipped over a line of reflection to form a polygon with its vertices at A′, B′, C′, and D′. Points A′, B′, and D′ are shown, but the line of reflection and point C′ are not. The line of reflection is , and the coordinates of C′ are . NextReset
A family has a monthly income of $3300 and plans to spend 11% of this amount on entertainment. How much will be spent on entertainment?
Are the fractions equivalent? 12/15 and 20/25
What are the values of the 7 in the number 17,372
A circle has a radius of 2.5 centimeters and a central angle AOB that measures 90°. What is the area of sector AOB? Use 3.14 for pi and round your answer to the nearest tenth
a carpenter goes through 2 3/5 boxes of nails finishing 3 1/2 rooves. How much would he use finishing 8 roves?
Which number is both a factor of 80 and a multiple of 4? Select three that apply.
A. 40
B. 1
C. 2
D. 8
E. 32
F. 16
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM?
The distance between the ships is changing at a rate of 39 km/hr at 4:00 PM. This is calculated using differentiation of the Pythagorean theorem relating distances between the ships.
Explanation:This is a typical
related rates problem
in calculus. Before we start, let's mark the distance between ship A and ship B as C, the distance that A traveled as X (X=35 km/hr*4 hr = 140 km), and the distance B traveled as Y (Y=20 km/hr*4 hr = 80 km). Note that X, Y, and C form a right triangle. By using the Pythagorean theorem, we get C²=X²+Y², which we can differentiate with respect to time (t) to obtain, 2C * dC/dt = 2X * dX/dt + 2Y * dY/dt. As we're solving for dC/dt (rate of change of the distance between the two ships), we get dC/dt = (X * dX/dt + Y * dY/dt) / C. Plugging in the known values (X=140 km, Y=80 km, dX/dt=35 km/hr, dY/dt=20 km/hr, and C=170 km, as it hasn't changed since they started), we get dC/dt = (140*35 + 80*20) / 170 = 39 km/hr. So, the distance between the ships is changing at a rate of 39 km/hr at 4:00 PM.
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It is claimed that in a bushel of peaches, less than 10% are defective. a sample of 400 peaches is examined and 50 are found to be defective. what is the critical value for α = 0.025?
Final answer:
To find the critical value for α = 0.025 in a one-tailed test, we look at the standard normal distribution tables; the critical value is approximately -1.96.
Explanation:
The question pertains to hypothesis testing in the context of proportion analysis. To determine the critical value for a significance level α = 0.025 in a one-tailed test about a proportion, we use the standard normal distribution (Z-distribution). Given that the sample size is large (n=400), it is appropriate to use a Z-test for this calculation. The critical value corresponds to the Z-score that has 0.025 of the distribution's area to its right (since we are checking for 'less than 10% defective').
Referring to standard normal (Z) distribution tables or using statistical software, we can find that the critical value for α = 0.025 for a one-tailed test is approximately -1.96. This is the Z-score such that the area under the normal curve to the right of this value is 0.025. If the calculated Z-score obtained from the sample proportion is less than -1.96, we would reject the null hypothesis that the proportion of defective peaches is less than 10%.
What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?
Answer:
m = (12 - 7) / (-39 - 26) = 5/(-65) = -1/13
Kathy runs a 26.2- mile marathon at an average pace of 6.2 minutes per mile how long will it take her to finish
Kathy will complete the 26.2-mile marathon in approximately 2 hours and 42 minutes by multiplying the marathon distance by her average pace and converting the result from minutes to hours and minutes.
To calculate the time it will take for Kathy to finish a 26.2-mile marathon at an average pace of 6.2 minutes per mile, we simply multiply the distance of the marathon by her average pace per mile. This is a basic mathematics problem involving multiplication to determine the total time.
Here is the calculation:
Total marathon distance = 26.2 miles
Average pace = 6.2 minutes per mile
Total time = Total marathon distance x Average pace
Total time = 26.2 miles x 6.2 minutes per mile = 162.44 minutes
To convert minutes into hours and minutes, we know that there are 60 minutes in an hour. Therefore:
Hours = Total time / 60
Hours = 162.44 minutes / 60 ≈ 2.707 hours
Since we want hours and the remaining minutes, we can take the decimal part and multiply it by 60:
Remaining minutes = 0.707 x 60 ≈ 42.42 minutes
Hence, Kathy will complete the marathon in approximately 2 hours and 42 minutes.
Find the product. Simplify if possible. −13⋅(817)
What is the thickness t of the thin film of diamond? express your answer in nanometers using three significant figures?
The thickness of a thin film of diamond can be calculated using the formula t = (m * λ) / (2 * n), where m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.
Explanation:The thickness of a thin film of diamond can be determined using the formula:
t = (m * λ) / (2 * n)
where t is the thickness, m is the number of fringes, λ is the wavelength of light used, and n is the refractive index of diamond.
In this case, the number of fringes is given as 14 per centimeter, which can be converted to 140 per meter. The wavelength of the light used is not provided, so we cannot determine the thickness without that information.
Tia cut a 4 meter 8 centimeter wire into 10 equal pieces. Marta cut a 540 centimeter wire into 9 equal pieces. how much longer is one of Marta's wires than one of Tia's?
Marta's wire is 19.2 cm longer than Tia's wire.
Further explanation
Given:
Tia 's wire is 4m 8 cm ⇒ cut into 10 equal pieces
Marta's wire 540 cm ⇒ cut into 9 equal pieces
Question:
How much longer is one of Marta's wires then one of Tia's?
1. Tia's wire is in m and cm unit, so we can not divide it straightly into its equal pieces. First step, we are going to convert meter (m) to millimeter (mm):
Tia's wire = 4 m 8 cm
[tex]\boxed {1 m = 100 cm }[/tex]
[tex]\boxed {= (4 m \times \frac{100 cm}{ 1 m}) + 8 cm ) } \\\boxed {= 400 cm + 8 cm }\\\boxed {= 408 }[/tex]
2. Second step, calculate each pieces Tia's wire:
She cut this wire into 10 equal pieces:
[tex]\boxed {= \frac{408}{10} } \\\boxed {= 40.8 cm }[/tex]
Each piece of Tia's s ribbon is is 40.8 cm long
3. Third step, we are going to calculate Marta's wire:
She has 540 cm and cut it into 9 equal pieces
[tex]\boxed {= \frac{540 cm}{9} }[/tex]
[tex]\boxed {=60 cm }[/tex]
Each pieces Marta's wire is 60 cm long
4. Last step, find the difference between Tia's wire and Marta's:
[tex]\boxed {=60 cm -40.8 cm }\\\boxed {=19.2 cm }[/tex]
So, Marta's wire is 19.2 cm longer than Tia's wire
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Keywords: converting, conversion, dividing, subtraction, find the difference, converting meter to centimeter, converting unit of length
Javier used the equivalent ratios to find the number of millimeters in 8 inches.
How many millimeters are in 8 inches?
127 mm
163.2 mm
167 mm
203.2 mm
order 56.2 56.32 56.321 from greatest you least
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply.
The domain is {x|x ≤ –2}.
The range is {y|y ≤ 6}.
The function is increasing over the interval (–∞ , –2).
The function is decreasing over the interval (−4, ∞).
The function has a positive y-intercept.
What is the 80th percentile for the average height of 10 men?
A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through?
The perimeter of a square is 32 centimeters. What is the length of one side?
A pitcher's arm rotates at a speed of 7 degrees per millisecond (degrees/ms)
At what speed does the pitcher's arm rotate in degrees/s?
To solve this problem, all we have to do is to use a conversion factor to convert millisecond into seconds. We know that there are 1000 milliseconds in a second, therefore:
pitcher’s arm rotation = 7 degrees / millisecond * (1000 milliseconds / second)
pitcher’s arm rotation = 7,000 degrees / second
Answer:
7000 Hope this helps and if it does remember to give me a like , please and thank you!
Find the value of a so that the differential equation y ' − xy − 6x = 0 has a solution of the form y(x) = a + bex2/2 for any constant
b.
Answer:
a = -6
Step-by-step explanation:
write the equation then solve to find the number:seventy four less than a number is 98
F(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (1, 2) to (2, 8) (a) find a function f such that f = ∇f.
Edmundo used a number line to show the solution for the inequality |2x-6|<4 Which number line shows the solution? HURRY PLEASE
To solve the inequality |2x-6|<4, we break it down into two inequalities and solve for the range of values. Then, we can plot the solution on a number line.
Explanation:The given inequality is |2x-6|<4. To solve this inequality, we need to break it down into two separate inequalities:
2x-6<4-(2x-6)<4Solving these inequalities will give us the range of values that satisfy the original inequality. Once we have the solution, we can plot it on a number line.
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Answer:
Step-by-step explanation:
an absolute value has two solutions, one negative and one positive.
so 2x-6<-4
2x<2
x<1
and
2x-6<4
2x<10
x<5
1>x<5
Option A is correct
James lives in San Francisco and works in Mountain View. In the morning, he has 3 transportation options (bus, cab, or train) to work, and in the evening he has the same 3 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?
How do you do it??
Answer:
1/3
Step-by-step explanation:
What is the apr of a 30 year 300000 mortage with monthly payments of 3000?