Which of the following gives all of the sets that contain -1/2?
the set of all rational numbers and the set of all real numbers

the set of all natural numbers and the set of all irrational numbers

the set of all integers and the set of rational numbers

the set of all natural numbers, the set of rational numbers, and the set of all real numbers

Answer:

(0, 0); (-1, -2); (1, 2) and (0, 5); (1, 6); (2, 7).

Step-by-step explanation:

The set will have a direct variation if each pair is added or subtracted by a common number in each component. You also can see it graphically, if the points form a straight growing line then the set is a direct variation. Then,

In the first set we have

(0,0), (0+2,0+4), (0+2+3, 0+4+11). The behavior is not uniform, then it is not a direct variation.

Second set: (-1, -2); (0,0); (1, 2)

(-1,-2)(-1+1,-2+2), (-1+1+1, -2+2+2). The behavior is uniform and it is increasing, then it is a direct variaton.

Third set:

(-2, 4), (-2+1,4-2), (-2+1+4, 4-2+4). The behavior is not uniform, then it is not a direct variation.

Fourth set:

(0,5), (0+1, 5+1), (0+1+1, 5+1+1). The behavior is uniform and it is increasing, then it is a direct variaton.

Final answer:

To find the probability of x successes in a binomial distribution, use the binomial probability formula. Substituting the given values into the formula will yield the probability.

Explanation:

To find the probability of x successes in a binomial distribution with n trials and probability of success p, we use the binomial probability formula. The formula is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

Using the given values n = 4, x = 3, and p = ..., we can substitute these values into the formula to calculate the probability.

For example, if p = 0.5, the probability is:

P(3) = (4C3) * 0.5^3 * (1-0.5)^(4-3) = 4 * 0.125 * 0.5 = 0.25

We are given some fractions and we need to write these fractions in terms of division problem.

a)

                  7/11

There are 7 chocolates and a total of 11 children present at a party.If the chocolates are to be distributed equally among all, then how many chocolates does each get?

b)

                    5/2

The distance traveled by Xavier is 5 km and the time taken by him is 2 hours.Then find his speed?

c)

                     9/10

If there are a total of 19 students in a class and the number of girls are 1 more than the number of boys then find the ratio of number of boys to number of girls?

d)

                     7/15

The are 7 red balls, 2 green balls and 6 yellow balls in a bag.One ball is drawn at random.What is the probability of getting a red ball?

Final answer:

Among the given options, the number 131 is a prime number, as it only has two divisors: 1 and itself.

Explanation:

The student has asked to identify which number among the given options is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Analyzing the given options:

111 is divisible by 3.

121 is divisible by 11 (11 x 11).

131 is a prime number because it has no divisors other than 1 and itself.

141 is divisible by 3.

Therefore, the correct answer is 131, which is a prime number.

 Answer:

[tex]log_5125=3[/tex]

Step-by-step explanation:

Given : [tex]log_5125[/tex]

We have to find the value of [tex]log_5125[/tex]

Consider the given expression [tex]log_5125[/tex]

Rewrite 125 in power- base form, [tex]125=5^3[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]

[tex]=3\log _5\left(5\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]

[tex]\log _5\left(5\right)=1[/tex]

[tex]3\log _5\left(5\right)=3[/tex]

Thus,  [tex]log_5125=3[/tex]

The value of log_5 125 is 3.

We have,

To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.

In other words,

What power do we need to raise 5 to in order to get 125.

So,

By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.

So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.

So,

log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.

Thus,

The value of log_5 125 is 3.

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Her mum ate 31/40 of the cake

Given the weight of the cake to 1 pound

If Carol ate 2/5 of the cake, the remaining fraction of the cake will be 1 - 2/5 = 3/5

If Dima ate 3/8 of the REMAINING cake, then the fraction of cake Dima ate will be:

Dima = 3/8 * 3/5

Dima = 9/40

Fraction of the cake that her mum ate = 1 - 9/40 = 31/40

Hence her mum ate 31/40 of the cake

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To solve this problem, set up a system of linear equations based on the total investment and profit conditions given. Solve for the variables representing investment amounts in black and white film and color film. This process demonstrates practical application of algebra in finance.

Let's find how much was invested in black and white film and color film at a film shop with a total inventory of $4000, knowing that the profit on black and white film is 12%, the profit on color film is 21%, and the profit on color film is $150 less than the profit on black and white film.

Let x represent the amount invested in black and white film, and y represent the amount invested in color film. According to the problem, we have two equations:

First, rearrange Equation 2 to isolate y: 0.12x - 150 = 0.21y. Then, convert it to y = (0.12/0.21)x - (150/0.21).

Next, substitute the value of y from Equation 2 into Equation 1: x + ((0.12/0.21)x - (150/0.21)) = 4000. Solve this equation for x to find the amount invested in black and white film, then substitute x back into either equation to find y, the amount invested in color film.

This problem involves forming and solving a system of linear equations based on the given profit percentages and the condition that profit on color film is $150 less than the profit on black and white film, demonstrating application of algebra in financial contexts.

Answer:

5 - 6i must also be a root of f(x)

Step-by-step explanation:

Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is  imaginary.

Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.

Given: if 5+ 6i is a root of the polynomial function f(x).

then,

by the conjugate root theorem;

5 - 6i is also be a root of the polynomial f(x).

It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.

To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.

Convert 18 minutes to hours.

18 minutes ÷ 60 minutes/hour = 0.3 hours

Calculate the distance Car 1 travels during the 18-minute head start.

Distance = Speed × Time

Distance = 45 mph × 0.3 hours

Distance = 13.5 miles

Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.

Calculate the relative speed of Car 2 compared to Car 1.

Relative Speed = Speed of Car 2 - Speed of Car 1

Relative Speed = 65 mph - 45 mph

Relative Speed = 20 mph

Calculate the time it takes for Car 2 to catch up.

Time = Distance ÷ Relative Speed

Time = 13.5 miles ÷ 20 mph

Time = 0.675 hours

Convert the time from hours to minutes for better understanding.

0.675 hours × 60 minutes/hour = 40.5 minutes

So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.

Answer:

The answer is 38.97 kilograms.

Step-by-step explanation:

Thirty-eight and ninety-seven hundredths kilograms in standard form is 38.97 kilograms.

Thirty eight is simply 38.

And ninety-seven hundredths means that 97 is written after decimal. This is because when there exists an 'and' in a mathematical number, this means there is a decimal.

So, the answer is 38.97 kilograms.

To calculate the cost of the turkey, multiply the weight of the turkey (1/2 pound) by the cost per pound ($6). The total cost for the turkey is $3.

Jillian bought 1/2 pound of turkey and 1 1/3 pounds of cheddar cheese at the deli, with both items on sale for $6 per pound. To find out how much the turkey costs, you need to multiply the weight of the turkey by the cost per pound. Here's how you do it:

Therefore, the cost of the turkey is $3.

Answer:

P(Even or ODD) ( .Y .)

Step-by-step explanation:

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, you can use the formula for the margin of error.

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, we can use the formula for the margin of error:

Margin of Error = Z * (Standard Deviation / √(Sample Size))

Given that we want a margin of error of ±0.0001 and a confidence level of 98%, we can find the corresponding Z-value using a standard normal distribution table.

Once we have the Z-value, we can rearrange the formula to solve for the sample size, which represents the number of measurements that must be averaged.

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