Find 14/15−1/3 . Write your answer as a fraction in simplest form.

Final answer:

To find the number of calories in 5 ounces of beef, divide 220 calories by 4 ounces to find the per ounce calorie count and then multiply by 5. The answer is 275 calories for 5 ounces of beef.

Explanation:

To determine the number of calories in 5 ounces of beef, we will first calculate the calories per ounce. Given that there are 220 calories in 4 ounces of beef, we can divide 220 calories by 4 to find the number of calories in 1 ounce.

220 calories ÷ 4 ounces = 55 calories per ounce.

Now, if one ounce of beef has 55 calories, then 5 ounces of beef would have:

55 calories/ounce × 5 ounces = 275 calories.

Therefore, 5 ounces of beef contains 275 calories.

If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.

Final answer:

Properties of vertical angles and linear pairs allow us to find unknown angles when two lines intersect by employing the facts that vertical angles are equal and linear pairs sum up to 180 degrees.

Explanation:

When two lines intersect, they form two pairs of vertical angles and two pairs of linear pairs. Vertical angles are opposite angles made by intersecting lines and are always equal. So, if one of the vertical angles is known, the opposite angle can be determined because it is congruent. Linear pairs are adjacent angles whose outer arms form a straight line. These linear pairs are supplementary, meaning their sum is 180 degrees. Therefore, if we know one angle of a linear pair, we can find the other by subtracting the known angle from 180 degrees. Understanding these properties allows us to solve for unknown angle measures around the intersection of two lines. For example, if one angle measure in a linear pair is given, we can find the measure of the adjacent angle. Knowing the measure of this adjacent angle, which is also a vertical angle, allows us to determine the measure of the angle vertical to it, as they are equal.

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:

P(Even or ODD) ( .Y .)

Step-by-step explanation:

Answer:

D is the only option that satisfies this. f(x)=-32 and f(-2)=-f(x)=32.

Step-by-step explanation:

Answer:

its 3

Step-by-step explanation:

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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:

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

To find (f of f)(0), substitute the value of f(0) into the function and evaluate.

To find (f of f)(0), we need to first find f(f(0)). Given that f(x) = 3x - 2, let's substitute f(0) into the function.

Therefore, (f of f)(0) is equal to -8.

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:

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).

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:

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.

Final answer:

The mean of this probability distribution is 2.

Explanation:

To find the mean of the probability distribution, we need to calculate the expected value. In this case, the random variable is selecting a business major as a success. So, the probability of selecting a business major is 10/25, or 0.4. The number of successes (business majors) in the group project can range from 0 to 5. Using the formula for expected value:

E(X) = p1 * x1 + p2 * x2 + ... + pn * xn,

where pi is the probability of xi occurring, we can calculate the mean as:

E(X) = (0.4 * 0) + (0.4 * 1) + (0.4 * 2) + (0.4 * 3) + (0.4 * 4) + (0.4 * 5)

E(X) = 2

Therefore, the mean of this probability distribution is 2.