Answer:
The number of newborns who weighed between 1614 grams and 5182 grams was of 586.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean weight was 3398 grams with a standard deviation of 892 grams.
This means that
Proportion that weighed between 1614 and 5182 grams:
p-value of Z when X = 5182 subtracted by the p-value of Z when X = 1614.
X = 5182
has a p-value of 0.9772
X = 1614
has a p-value of 0.0228
0.9772 - 0.0228 = 0.9544.
Out of 614 babies:
0.9544*614 = 586
The number of newborns who weighed between 1614 grams and 5182 grams was of 586.
Answer: length = 24 ft
Width = 8 ft
Step-by-step explanation:
Let L represent the length of the barn.
Let W represent the width of the barn.
The area of a rectangular wall of a barn is 192 sq. Ft. This means that
LW = 192- - - - - - - - - - - - - - -1
It's length is 8 ft longer than twice it's width. This means that
L = 2W + 8
Substituting L = 2W + 8 into equation 1, it becomes
W(2W + 8) = 192
2W² + 8W = 192
2W² + 8W - 192 = 0
Dividing through by 2, it becomes
W² + 4W - 96 = 0
W² + 12W - 8W - 96 = 0
W(W + 12) - 8(W + 12) = 0
(W - 8)(W + 12) = 0
W = 8 or W = - 12
Since the width cannot be negative, then W = 8
L = 192/W = 192/8
L = 24
C, 51 because acute angles are less than 90° but together the angles create a right triangle which is 90°.
Answer:
The rug should be 15 ft wide and 28 ft long.
Step-by-step explanation:
I have attached a figure that represents the situation.
The the rug is by , the width of the strip of floor is .
We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that
<em>(this says the area of the rug must be 420 square feet)</em>
From the figure we see that
Therefore,
We expand this equation and get:
using the quadratic equation we get two solutions:
since the second solution, namely , is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take to be our solution.
Now we find the dimensions of the rug:
The rug is 15 ft wide and 28 ft long.
Answer:
approx. 24.6 ft
Step-by-step explanation:
x=the distance of the fire from the base of the tower
200ft=the height of the tower
7 degrees=the angle of depression
Using these values you can draw a diagram that highlights that you need to use trig. to work out the answer.
Using Tan:
Tan 7=x/200 ft
multiply both sides by 200 ft
200*tan 7=24.55691218
approx. 24.6 ft