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I am a 3-digit number. If you switch my first and last digits, I decrease by 297. Also, mymiddle digit is 6 less than my first digit, which is 2 less than 2 times my last digit. What
number am I?

Answers

Answer 1
Answer:

Answer:

  • 865

Step-by-step explanation:

Let the 3-digit number is abc = 100a + 10b + c.

We have:

  • 100a + 10b + c - 100c - 10b - a = 297
  • b = a - 6
  • a = 2c - 2

Simplify the first equation:

  • 99a - 99c = 297
  • a - c = 3
  • a = c + 3

Solve for c by substitution:

  • 2c - 2 = c + 3
  • 2c - c = 3 + 2
  • c = 5

Find a:

  • a = 3 + 5 = 8

Find b:

  • b = 8 - 2 = 6

The number is:

  • 865

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How much of a 3/4 of cup serving is in a 2/3 cup of yogurt?

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Answer:

8/9

Step-by-step explanation:

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A restaurant wants to study how well its salads sell. The circle graph shows the sales over the past few days. If 35 of the salads sold were Caesar salads, how many total salads did the restaurant​ sell?

Answers

Answer:

50

Step-by-step explanation:

From the circle graph :

Salad sold :

Caesar = 70%

Garden = 16%

Taco = 14%

If 35 of the salad sold were Caesar ;

Then ; this means

70% = 35

Total salad sold %= (70+16+14)% = 100%

Let total sales = x

70% = 35

100% = x

Cross multiply :

70% * x = 100% * 35

0.7x = 35

x = 35 / 0.7

x = 50

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 3 flights arrive late.

Answers

Answer:

There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)

In which C_(n,x) is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_(n,x) = (n!)/(x!(n-x)!)

And \pi is the probability of X happening.

In this problem, we have that:

There are 10 flights, so n = 10.

A success in this case is a flight being late.  80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that \pi = 0.2.

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

P(X < 3) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)

P(X = 0) = C_(10,0).(0.2)^(0).(0.8)^(10) = 0.1074

P(X = 1) = C_(10,1).(0.2)^(1).(0.8)^(9) = 0.2684

P(X = 2) = C_(10,2).(0.2)^(2).(0.8)^(8) = 0.3020

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778

Finally

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222

There is a 32.22% probability that at least 3 flights arrive late.

Final answer:

The problem is solved by calculating the probability of the complementary event (0,1,2 flights arriving late) using the binomial distribution, then subtracting this from 1 to find the probability of at least 3 flights arriving late.

Explanation:

This problem is typically solved by using a binomial probability formula, which is used when there are exactly two mutually exclusive outcomes of a trial, often referred to as 'success' and 'failure'.
Here, our 'success' is a flight arriving late. The probability of success, denoted as p, is thus 20% or 0.2 (since 80% arrive on time, then 100%-80% = 20% arrive late). The number of trials, denoted as n, is 10 (the number of randomly selected flights).
We want to find the probability that at least 3 flights arrive late, in other words, 3,4,...,10 flights arrive late. The problem can be solved easier by considering the complementary event: 0,1,2 flights arrive late. Then subtract the sum of these probabilities from 1.

The binomial probability of exactly k successes in n trials is given by:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where C(n, k) is the binomial coefficient, meaning choosing k successes from n trials.
We calculate like so:
P(X=0) = C(10, 0) * (0.2)^0 * (0.8)^10
P(X=1) = C(10, 1) * (0.2)^1 * (0.8)^9
P(X=2) = C(10, 2) * (0.2)^2 * (0.8)^8
Sum these up and subtract from 1 to get the probability that at least 3 flights arrive late. This gives the solution to the question.

Learn more about binomial probability here:

brainly.com/question/34083389

#SPJ3

Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?

Answers

The equation that represents an inequality in the system of inequalities shown in the graph is;

y < 2x + 2

The point that is a solution to the system is; (-1, -2)

Graph Inequalities

The image of the graph is missing and so i have attached it.

  • From the graph, we see one broken line passing through the points x = -1 and y = 2.

We also see an unbroken line passing through the points x = ½ and y = -1

Now, when we use a broken line it means greaterthan or less than but when we use a thick line which is unbroken it means y ≤ or y ≥.

Now, if we shade below the line, it is (y< or y≤) but if we shade above the line, it is (y> or y≥).

Now, we see that the solution will be in between the broken line and the thick line.

Thus, the equation is;

y < 2x + 2 with the solution as coordinates as (-1, -2)

Read more about graph inequalities at;brainly.com/question/11234618

Answer:

y<2x+2

(-1,-2)

explanation:

person above gets credit, hope it helps!

Please help, will give everything, i am stuck

Answers

Answer is probably Number 1.

if own loses weight at a rate of 2 pounds per week and after 6 weeks is 204 pounds how many weeks will he be 180

Answers

Answer:

12 weeks. 204-180=24, 24/2= 12 weeks.

Step-by-step explanation:
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