I think the current age of the child is 16 and the father is 40. That would mean 4 years ago the father was 36 and the child was 12. This makes the father 3 times as old as his son four years ago.
Refer to the attached image,
Peter hits a ball that is 20 inch from a wall means AB=20 in
A ball travels 34 in until it hits the wall means AC=34 in
It bounces back to a position means CD = 'x' in (Say)
It bounces back to CD which is 16 in from the wall means DE=16 in
We have to calculate the value of 'x'.
Since, ball is reflected from point C. By law of reflection which states the angle of reflection is equal to the angle of incidence.
So, = y degrees (say)
Since angles BCF and FCE are right angles.
So, (equation 1)
Now, in triangle ABC and CDE
(Each angle is right angle)
(From equation 1)
Therefore, triangle ABC is similar to triangle DEC by AA similarity.
So, the ratio of corresponding sides are equal.
Substituting the values,
x = 27.2 in
Therefore, the distance, x, the ball traveled after it bounced off the wall to get to the ending position is 27.2 in
The value of x is 3. The correct option is the third option- 3
The width of the backyard is 9 yards. The correct option is the first option- 9 yards
<h3>Perimeter of a Rectangle </h3>
From the question, we are to determine the value of x
13.
Perimeter of a rectangle = 2 (l + w)
Where l is the length
and w is the width
From the given information,
Perimeter = 24 cm
In the given diagram,
l = 3x cm
w = 3 cm
Thus,
24 = 2(3x + 3)
24 = 6x + 6
6x = 24 - 6
6x = 18
x = 18/6
x = 3
Hence, the value of x is 3. The correct option is the third option- 3
14.
From the given information,
The width of the yard is 3 less than 4 times the length
That is,
w = 4l - 3 --------- (1)
Also,
Perimeter = 24 yards
∴ 24 = 2(l + w) ---------- (2)
Put equation (1) into (2)
24 = 2(l + w)
24 = 2(l + 4l - 3)
24 = 2(5l - 3)
24 = 10l - 6
10l = 24 + 6
10l = 30
l = 30/10
l = 3 yards
Substitute the value of l into equation (1) to get w
w = 4l - 3
w = 4(3) - 3
w = 12 - 3
w = 9 yards
Hence, the width of the backyard is 9 yards. The correct option is the first option- 9 yards
Learn more on Perimeter of a rectangle here: brainly.com/question/24571594
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Answer:
3
Step-by-step explanation:
3 mah fwend omg so hard my brain hurts
Answer: b. The sampling distribution of the proportion of damaged trees is approximately Normal
Step-by-step explanation:
The sample mean is an unbiased estimator of the true (unknown) population mean and The sampling distribution shows how the sample mean will vary among repeated samples. In the case above the samples are selected at random from a normally distributed population, and the number of samples selected (n=100) is a bit large therefore the sampling distribution will be approximately normal.