To solve this problem, let us first assign some
variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the
following equations:
1. y + z = 30 --->
only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 --->
pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 --->
each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore
the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
Answer:
C: 23 cm
Step-by-step explanation:
This is the answer because:
1) Area of trapezoid is: (base1 + base2)/2 x height
2) In this case, it is 14 + 8 which is 22. 22/2 is 11.
3) Now we have to do 253/11 which is 23 cm.
Hope this helps! :D
Using the binomial distribution, it is found that:
The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
For each question, there are only two possible outcomes, either the guess is correct, or it is not. The guess on a question is independent of any other question, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 20 questions, hence
.
- Each question has 2 options, one of which is correct, hence

The probability is:

In which:







Then:

The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
You can learn more about the binomial distribution at brainly.com/question/24863377
Answer:
360
Step-by-step explanation:
f varies directly as g
f = kg where k is the constant of variation
f varies inversely as h
f = kg/h
We know g = 198 when h = –11 and f = –6. Substituting in
-6 = k*198/(-11)
-6 =k*(-18)
Dividing each side by -18
-6/-18 = k*-18/-18
1/3 =k
Our equation is
f = 1/3 g/h
Letting f = 12 and h = 10
12 = 1/3 g/10
Multiply each side by 10
12*10 =1/3 g/10*10
120 = 1/3 g
Multiply each side by 3
120*3 =1/3 g *3
360 =g
X - an amount

To increase an amount by 3% you can multiply the amount by 1.03.