#13 please help explain

The length of a rectangle is 1 cm less than the width. The area of the rectangle is 12 cm². determine the dimensions of the rect

jarptica [38.1K]

Answer:

L= 3 cm

W= 4 cm

Step-by-step explanation:

Factors of 12:

1 and 12

2 and 6

3 and 4

Which of those is one number apart?

3 and 4

So the sides must be 3 by 4 cm.

6 0

2 years ago

Pick the correct answer<br> Help me please thank you :)

Andrej [43]

Answer: D
Steps: In partially legible pic below. Sorry not the best explanation

4 0

2 years ago

11.1.30<br> How many three-digit even numbers are possible if the leftmost digit cannot be zero?

Ann [662]

The total number of 3 digit even numbers is 450

Step-by-step explanation:

Step 1 :

We need to determine the number of 3 digit numbers which is even and the leftmost digit is not zero .

The 3 digits with left most digit not equal to zero starts from 100 and goes up to 998

If we consider only the even 3 digit numbers in this interval, this would form an arithmetic progression with the first number a = 100 and the common difference d = 2.

Step 2:

The last number l in this series is 998 .

So we have

a = 100

l = 998

d = 2

The nth term in the arithmetic progression is given by a + (n-1) d

so substituting the above values we get

100 + (n-1) 2 = 998

2n = 900 => n = 450

Step 3 :

Answer :

The total number of 3 digit even numbers is 450

4 0

3 years ago

Susan can mow 1/4 of a yard in 1/5 of an hour.At this rate,how many yards can she mow in one hour? Express answer as a decimal.

schepotkina [342]

Find the unit rate:

1/4 yd 1(5)
---------- = -------- = 5/4 yards, or 1 1/4 yards, in one hour. This is 1.25 yards.
1/5 hr 4(1)

3 0

2 years ago

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

2 years ago