Answer:
<h2>
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Step-by-step explanation:
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.
The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in
The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³
The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³
Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³
<span>If the company, hewerrtt, would like to make letter codes using all of the letters in the word hewerrtt, they would be able to make five codes. Altogether, there are eight letters in the word, but there are duplicates of the letter e, the letter r, and the letter t, so that takes out three possibilities. Three subtracted from eight is equal to five, therefore the company can make five codes using the company name.</span>
Answer:
There are 8 true/false questions and 26 fill-in-the-blank questions.
Step-by-step explanation:
Let "t" be the number of 2-point true/false questions and "f" the number of 5-point fill-in-the-blank questions.
Mrs. Simmons gave a history test worth 92 points. Symbollically,
2 t + 5 f = 92 [1]
There were a total of 34 questions in the test. Symbollicaly,
t + f = 34
t = 34 - f [2]
If we replace [2] in 1, we get
2 (34 - f) + 5 f = 92
68 - 2 f + 5 f = 92
3 f = 24
f = 8
We replace f = 8 in [2],
t = 34 - 8 = 26
There are 8 true/false questions and 26 fill-in-the-blank questions.
