12x−3y=, when x=−1/4 and y=3

Answer:

a = -6

Step-by-step explanation:

Using the concept of combinations, there are 10 ways to choose three apples from a basket, where two are rotten and one is not.

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].

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.

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.

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.

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.

Learn more about expressions here:

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You diver begin at -150 feet and then descend at 5 feet/minute for 3.5 minutes, which could be represented by (-5)(3.5). you then go up 122.2 feet. The expression is -150 + (-5)(3.5) + 122.2. You then get that the diver’s depth is 45.3 feet below sea level, or -45.3.

Answer:

B

Step-by-step explanation:

The answer above me ^^

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.

The given inequality is |2x-6|<4. To solve this inequality, we need to break it down into two separate inequalities:

Solving 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

The Second train will catch up with the first train after 15 hours which is 8a.m the following morning.

First train :

Departure time = 2 pm

Speed = 50 mph

Second train :

Departure time = 2 pm + 3 hours = 5 pm

Speed = 60 mph

Distance = speed × time

Distance already covered by first train before the departure of the second = 50 mph × 3 hpird = 150 miles

The number of hours needed for second train to catch up will be h;

(60 × h) = (50 × h) + 150

60h = 50h + 150

60h - 50h = 150

10h = 150

h = 150/ 10

h = 15

Second train will catch up after 15 hours :

Hence, time will be : (5pm + 15 hours) = 8 a.m the following morning.

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Answer: 8:00 am

Step-by-step explanation:

(5pm + 15 hours) = 8 a.m the following morning.

60h = 50h + 150

60h - 50h = 150

10h = 150

h = 150/ 10

h = 15

Answer: Segment BC of image is parallel to  segment AD of image.

Step-by-step explanation:

Given: Quadrilateral ABCD is the result of a translation of quadrilateral EFGH.

Segment EF is parallel to segment HG in the pre-image.

Since translation is a rigid transformation which preserves the side-lengths and angles of the original figures.

Therefore, all the segments of the image figure are parallel to correspondent segments of the original figure.

Segment AD of image is parallel to segment HG  in the pre-image.

Segment BC of image is parallel to  segment  EF in the pre-image.

Hence, if Segment EF is parallel to segment HG in the pre-image.

⇒ Segment BC of image is parallel to segment AD in image.

To calculate the total time it takes to run 2 miles uphill at 4 mph and then 3 miles downhill at a speed that takes the same time as running 2 miles uphill, we find that the time for each is 0.5 hours, or 30 minutes, totaling 1 hour

The main question asks how long it would take for the runner to run 2 miles uphill and then 3 miles downhill, knowing that he jogs at a rate of 4 miles per hour uphill, and he can run 3 miles downhill in the same time it takes to run 2 miles uphill

First, let's find the time it takes to run 2 miles uphill. Since he runs at 4 miles per hour uphill, the time for 2 miles uphill is 2 miles divided by 4 miles per hour, which equals 0.5 hours or 30 minutes. Now, since it takes the same time to run 3 miles downhill, we know the downhill time is also 30 minutes

The total time taken for 2 miles uphill and 3 miles downhill is the sum of both, which is 30 minutes + 30 minutes = 60 minutes, or 1 hour. Thus, the answer to the student's question is 1 hour

Answer:

12

Step-by-step explanation:

The formula given is [tex]a_n=84+(n-1)(-6)[/tex]

Where [tex]a_n[/tex] gives the nth term

Since we want 13th term, we can say we want [tex]a_{13}[/tex] and we plug in 13 in [tex]n[/tex] into the formula. So we get:

[tex]a_n=84+(n-1)(-6)\\a_{13}=84+(13-1)(-6)\\a_{13}=84+(12)(-6)\\a_{13}=84-72\\a_{13}=12[/tex]

So, the 13th term of the sequence is 12

To express the given ratio as a unit rate, divide the miles by the gallons to obtain 18.8 miles per gallon.

To express the given ratio as a unit rate, divide the miles by the gallons. So, the unit rate would be:

325.4 miles ÷ 17.3 gallons = 18.8 miles per gallon

Therefore, the unit rate for the given ratio is 18.8 miles per gallon.

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