The area of each triangular face is 40 square feet
<em><u>Solution:</u></em>
Given that,
Square pyramid has a base area of 64 square feet
The pyramid’s total surface area is 224 square feet
The total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base
<em><u>Therefore, total surface area of square pyramid is given as,</u></em>
Total surface area = base area + 4(Area of traingular face)
Let "x" be the area of each traingular face
Thus area of each triangular face is 40 square feet
Answer:
P(-1 < z < 1) = 0.3174
Step-by-step explanation:
Mean (μ) = 1.62 ounces
Standard Deviation (σ) = 0.05
No of balls (sample size n) = 100
X = weight of a ball
Weight of a group of 100 balls must lie in the range 162 ± 0.5 ounces i.e. weight of a single ball will be 162/100 ± 0.5/100 ounces = 1.62 ± 0.005 ounces.
So, we need to find the probability P (1.615 < X < 1.625). We will use the central limit theorem.
z = (Χ' - μ)/(σ/
)
P (1.615 < X < 1.625) = (
< (Χ - μ)/(σ/) < 
)
= (-1 < z < 1)
We need to find the probability of P (-1 < z < 1) by looking at the Normal Distribution Probability Table.
In order to make our working simpler, we need to break P (-1 < z < 1) into two parts: P(z < 1) and P(z > -1)
The probability for areas under the normal curve are given for P(z>X) so we can directly find the probability of P (z > -1) by referring to the normal probability table.
P(z > -1) = 0.1587
We can calculate P(z < 1) by subtracting P(z >1) from the total probability (i.e. 1). P(z >1) can be obtained from the normal probability table.
P(z < 1) = 1 - 0.8413 = 0.1587
By adding the two probabilities together, we get:
P(-1 < z < 1) = P(z < 1) + P (z > -1)
= 0.1587 + 0.1587
P(-1 < z < 1) = 0.3174
Answer:
Please see attached image for the sketch with the labels.
Length "x" of the ramp = 11.70 ft
Step-by-step explanation:
Notice that the geometry to represent the ramp is a right angle triangle, for which we know one of its acute angles (
), and the size of the side opposite to it (4 ft). Our unknown is the hypotenuse "x" of this right angle triangle, which is the actual ramp length we need to find.
For this, we use the the "sin" function of an angle in the triangle, which is defined as the quotient between the side opposite to the angle, divided by the hypotenuse, and then solve for the unknown "x" in the equation:
Therefore the length of the ramp rounded to the nearest hundredth as requested is: 11.70 ft
(4x20)+30=$110 taken out. if he had $96 put back in, then go $110-$96, leaving a balance of -$14, or in other words, the balance dropped $14.
Answer:
x = 7
Step-by-step explanation:
simplify 16/32
16/32 divided by 8/8=2/4
2/4 divided by 2=1/2
so
1/2 = x/14
to get to 14 from 2 you need to multiply by 7
1/2 times 2/2 = 7/14
so x = 7
