how many different subsets of {1,2,3,4,5,6,7,8,9,10,11,12} contain at least one element in common with each of the sets {2,4,6,8,10,12}, {3,6,9,12}, and {2,3,5,7,11}? (source: mathcounts)

Answer:

y = 5x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 9 ← is in slope- intercept form

with slope m = 5

Parallel lines have equal slopes, thus

y = 5x + c ← is the partial equation

To find c substitute (- 2, - 3) into the partial equation

- 3 = - 10 + c ⇒ c = - 3 + 10 = 7

y = 5x + 7 ← equation of parallel line

The probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls is 1/52360.

To calculate the probability of correctly choosing 4 numbers that match 4 randomly selected balls from a bucket of 35 balls with different numbers from 1 to 35, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes:

Since there are 35 balls in the bucket, the total number of possible outcomes is given by the combination formula:

nCr = n! / [(n-r)! * r!]

In this case, we need to choose 4 balls out of 35, so the total number of possible outcomes is:

35C4 = 35! / [(35-4)! * 4!]

Number of favorable outcomes:

We want to choose 4 numbers that match the 4 randomly selected balls. Since there are 4 balls that need to match, we can consider this as choosing all 4 numbers correctly.

There is only 1 way to choose all 4 numbers correctly.

Therefore, the number of favorable outcomes is 1.

Probability:

The probability of an event is given by the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is:

Probability = 1 / 35C4

Now, let's calculate the probability:

35C4 = 35! / [(35-4)! * 4!]

= (35 * 34 * 33 * 32) / (4 * 3 * 2 * 1)

= 52360

Probability = 1 / 52360

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Given the function:

Let's find the limit of the function as x approaches infinity and also as x approaches negative infinity.

We have:

The limit at infinity of a polynomial whose leading coefficient is negative is negative infinity.

• Also, the limit of the function at negative infinity:

The limit at negtaive infinity of a polynomial whose leading coefficient is negative is infinity.

ANSWER:

Answer:

210 is the rate per hour and 1,050 people in 5 hours

Step-by-step explanation:

Answer:

Step-by-step explanation:

    You need to get answer to people per hour first. 70 people could ride the ferris wheel in 20 minutes. 20 minutes is 1/3 of 60 minutes, which is an hour. So you multiply both the time and the amount of people by 3. 70 times 3 is 210. This is the amount of people that could ride the ferris wheel in 1 hour. Then, we need to multiply this number by 5, because we need the amount of people that could ride the ferris wheel in 5 hours, not 1 hour. So 210 times 5 is 1,050. 1,050 people could ride the ferris wheel in 5 hours.

    Next, we need to find the rate per hour. You already have the answer to that though. It is the amount of people that could ride the ferris wheel, so your  previous number: 210. Your rate would be 210 people per hour could ride the ferris wheel.

You're welcome, stranger :)

Answer:

.......................

Given the function:

The given function is a linear function

The rate of change of the linear function = the slope of the function

The slope = the coefficient of x = -1/4

So, from the given options, you will select the function that has a slope that is greater than (-1/4)

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

Answer:

D. 159

Step-by-step explanation:

y=13

Step-by-step explanation:

y=3x-5

y=3(6)-5

y=18-5

y=13

Therefore, the expression \(t^{(-3/4)}\) in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

What is the exponential function?

An exponential function is a mathematical function of the form:

f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

To write the expression \(t^{(-3/4)}\) in rational form, we need to eliminate the negative exponent.

Recall that a negative exponent can be rewritten as the reciprocal of the positive exponent. In this case,  \(t^{(-3/4)}\) can be written as 1/ \(t^{(-3/4)}\).

Therefore, the expression \(t^{(-3/4)}\)in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

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Answer:

C- C=0

Step-by-step explanation:

The general solution of the initial-value problem is y(x) = e^(-x/3)(c₁cos(2x) + c₂sin(2x)), where c₁ and c₂ are constants determined by the initial conditions.

To solve the initial-value problem, we first find the characteristic equation associated with the differential equation 3y'' + 7y' + 4y = 0. The characteristic equation is obtained by assuming a solution of the form y(x) = e^(rx), where r is an unknown constant. Substituting this into the differential equation, we get the characteristic equation:

3r^2 + 7r + 4 = 0.

We solve this quadratic equation to find the roots, which are r₁ = -1 and r₂ = -4/3. Since the roots are distinct, the general solution of the homogeneous equation is y(x) = c₁e^(-x) + c₂e^(-4x/3), where c₁ and c₂ are arbitrary constants.

To determine the particular solution that satisfies the initial conditions y(0) = 5 and y'(0) = -6, we substitute these values into the general solution:

y(0) = c₁e^(0) + c₂e^(0) = c₁ + c₂ = 5,

y'(0) = -c₁e^(0) - (4/3)c₂e^(0) = -c₁ - (4/3)c₂ = -6.

Solving this system of equations, we find c₁ = 1 and c₂ = 4. Therefore, the particular solution is y(x) = e^(-x)(cos(2x) + 4sin(2x)).

In summary, the solution to the initial-value problem 3y'' + 7y' + 4y = 0, y(0) = 5, y'(0) = -6 is y(x) = e^(-x/3)(c₁cos(2x) + c₂sin(2x)), where c₁ = 1 and c₂ = 4.

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Answer: See attachment (enlarge line)

Step-by-step explanation:

y = 2x

When x = -1

y = 2(-1)

y = -2

When x = 2

y = 2(2)

y = 4

Plot the points on the graph (-1, -2) and (2, 4)

Answer:

yes they both form a proportion

Answer:

multiply the numbers next to the variables by the given subtitution for the variable so 5 times 14 plus 36 and 6 times 12.5 minus 1 and 4 times 14 plus 50

Step-by-step explanation:

Answer:

The second one

The third one

Step-by-step explanation:

Answer:

the point is located at 7,0. the point is on the y-axis.

Step-by-step explanation:

The average velocity of the cat during the 62-minute period can be calculated by finding the total displacement and dividing it by the total time taken. The magnitude of the average velocity can be determined using the Pythagorean theorem, and the direction can be found using trigonometry. The average velocity is approximately 2.06 m/min in a direction of 56.3 degrees west of north.

To find the average velocity of the cat, we need to calculate the total displacement and the total time taken. The cat's displacement consists of a northward displacement of 106 m and a westward displacement of 80 m.
The total displacement is found by taking the vector sum of the individual displacements. Using the Pythagorean theorem, we can calculate the magnitude of the total displacement as follows:
Magnitude of displacement = sqrt((106 m)^2 + (80 m)^2) ≈ 130.2 m
The total time taken is the sum of the individual times, which is 47 minutes + 15 minutes = 62 minutes.
The average velocity is then obtained by dividing the total displacement by the total time taken:
Average velocity = 130.2 m / 62 min ≈ 2.10 m/min
To determine the direction of the average velocity, we can use trigonometry. The angle can be found by taking the inverse tangent of the ratio of the northward displacement to the westward displacement:
Angle = tan^(-1)((106 m) / (80 m)) ≈ 52.6 degrees
However, since the displacement is westward, the direction is the supplement of this angle:
Direction = 180 degrees - 52.6 degrees ≈ 127.4 degrees
Therefore, the magnitude of the average velocity is approximately 2.06 m/min, and it is in a direction of 56.3 degrees (180 degrees - 127.4 degrees) west of north.

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Answer:

See table below

Explanaton:

Given

Total people = 1432 people

Number of people tthat eat breakfast and take daily vitamins = 384

percentage = 384/1432 * 100%

Percentage = 38400/1432

Percentage = 21.82%

Number of people that eat breakfast with no daily vitamins = 476

percentage = 476/1432 * 100%

Percentage = 47600/1432

Percentage = 33.24%

Number of peoplewith no breakfast and take daily vitamins = 268

percentage = 268/1432 * 100%

Percentage = 26800/1432

Percentage = 18.72%

Number of peoplewith no breakfast and no daily vitamins = 304

percentage = 304/1432 * 100%

Percentage = 30400/1432

Percentage = 21.23%

Find the table below;

If each rectangle represents a room and the doors are as shown, it is not possible to pass through each door exactly once. In the given configuration, there are a total of nine doors.

To pass through each door once, we would need an even number of doors connected to each room except for two rooms that would have an odd number of doors. However, in the given layout, every room has three doors, which is an odd number. This means that there is no possible path that allows us to pass through each door exactly once. To achieve a solution, the door connections would need to be rearranged in a way that provides an even number of doors for each room except for two, allowing for a valid path.

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Answer:

17/6 or 18/6

Step-by-step explanation:

1/3        11/2        first make sure they have the same bottom number

2/6       33/6       now find the in between

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Two samples drawn from two populations are independent if the selection of one sample from a population is not related to the selection of the second sample from the same population. Option C is correct:

Independence is a fundamental concept in statistics when working with samples from different populations. It refers to the absence of any relationship or connection between the two samples. Option C correctly states that the selection of one sample from a population is not related to the selection of a second sample from the same population.

If the selection of one sample were related to the selection of the second sample from the same population (Option A), it would introduce bias and invalidate the assumption of independence. Similarly, if the two samples selected from the same population had a relationship or connection (Option B), it would violate the principle of independence.

Option D, stating that the selection of one sample from one population does not affect the selection of the second sample from the second population, is not the correct definition of independence. Independence refers to the relationship between samples drawn from the same population, rather than between samples drawn from different populations.

In summary, the independence of two samples implies that the selection of one sample from a population does not affect the selection of the second sample from the same population (Option C). This concept is crucial in statistical analysis to ensure unbiased and reliable results when working with multiple samples.

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Answer:

The mean is 24.

Step-by-step explanation:

The mean is average so add the numbers together and divide by how many you added. 24+25+23+24+24=120  120/5=24

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

The elements that Interest paid on savings accounts and interest owed on loans share are:

Interest paid on savings accounts and interest owed on loans share the following common elements:

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Answer: 420 legislators

Step-by-step explanation:

For this problem, we would have to multiply.

If Alabama has 140 legislators for 4 million people, we know the unit rate is:

\(140\) legislators for \(4\) million people.

So, we have to multiply 140 by 3 because 12 is 3 times the amount of 4, and the other state has 12 million people.

140 x 3 = 420

The answer to the question would be 420.

Answer:

420

Step-by-step explanation:

I set this up as a proportion of 140/4,000,000=x/12,000,000. Then you can cross multiply, getting 1,680,000,000=4,000,000x. Divide both sides by 4,000,000 and you get x=420. Please mark brainliest if this helped!

Step-by-step explanation:

answer criss-cross and divide by 5/8

Answer:

105/7=15

Step-by-step explanation:

equations have equal signs

Answer:

8.14 feet

Step-by-step explanation:

8.14 feet will be more precise because it measures to the hundredths place, while 13.2 feet only measures to the tenths place.

Measuring to smaller place values increases precision and accuracy because the measurements are more likely to be more exact and correct.

So, 8.14 feet is more precise

The required probability of a given case is 27.63

For the given data;

Let,

X ~ Exp(β = 12)

\(f(x) = \frac{1}{\beta } e^\frac{-x}{\beta } , 0 < x\)

\(f(x) = \frac{1}{12 } e^\frac{-x}{12} , 0 < x\) , and zero (0) otherwise.

Now,

P(X ≤ x) = 1 - \(e^\frac{-x}{\beta }\)

            = 1 - \(e^\frac{-x}{12}\) for x > 0 ⇒ P(X > x) = \(e^\frac{-x}{12 }\)

At least one call means that the probability that the next call time below this length is 0.9,

P(X < x₀) = 1 - exp(-x₀/β)

        0.9 = 1 - exp(x₀/β)

         x₀ = -ln(1 - 0.9) * β

         x₀ = 2.302 * 12

         x₀ = 27.631

P(X < x₀) = 0.9 ⇒ x₀ = 27.63

The necessary probability in a particular scenario is 27.63.

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