Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².
<h3>What is volume?</h3>
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,
Area of triangle = 0.5 × 4cm × 11cm
Area of triangle = 22 cm²
Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,
Volume of the triangular prism = 22cm² × 3cm = 66cm³
Hence, the volume of the triangular prism is 66cm².
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Digit in ones place- 6
Digit in tenths place- 5
The equation in spherical coordinates will be a constant, as we are describing a spherical shell.
r(φ, θ) = 8 units.
<h3>
How to rewrite the equation in spherical coordinates?</h3>
The equation:
x^2 + y^2 + z^2 = R^2
Defines a sphere of radius R.
Then the equation:
x^2 + y^2 + z^2 = 64
Defines a sphere of radius √64 = 8.
Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:
r(φ, θ) = 8 units.
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Answer:
B. $840
Step-by-step explanation:
Given that
Rate of simple interest = 3.5%
Principal amount = $12,000
Time = 2 year
To find:
Interest earned = ?
Solution:
Formula for Simple Interest is given as:

Where P is the principal amount
R is the annual Rate of interest
T is the time for which principal was invested.
Here, we are given that:
P = $12,000
R = 3.5%
T = 2 years
Putting all the values in the formula:

So, answer is:
B. $840
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean