Which of the following statements is true?(1 point)
Responses
19−−√
is equal to 4.358
square root of 19 is equal to 4 point 3 5 8
913
is an irrational number
9 over 13 is an irrational number
3.6¯¯¯
is equal to 113
3 point repeating 6 is equal to 11 thirds
44−−√
is a rational number
The statement "44−−√ is a rational number" is true.
A typical red blood cell in the human body is 0.000008 m
in diameter. What is this number expressed in scientific notation?(1 point)
Responses
8×10−5
8 times 10 to the negative 5 power
8×10−7
8 times 10 to the negative 7 power
8×10−4
8 times 10 to the negative 4 power
8 ×10−6
8 ×10−6
The number expressed in scientific notation is 8×10−6.
Lines P and Q are parallel. Which of the following pairs of angles have the same measure?
To determine which pairs of angles have the same measure, we need more information about the angles. Please provide the angles that are given or any other relevant information about the angles.
Nicholas places his 30-foot ladder against a house he is painting. If the foot of the ladder is 8 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?(1 point)
Responses
28.9 ft.
28.9 ft.
22.0 ft.
22.0 ft.
27.8 ft.
27.8 ft.
31.0 ft.
31.0 ft.
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To find the height the ladder reaches on the house, we can use the Pythagorean theorem.
According to the theorem, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance from the foot of the ladder to the base of the house and the height above the ground).
So, we have:
(8 ft)^2 + (height)^2 = (30 ft)^2
Simplifying, we have:
64 + (height)^2 = 900
Subtracting 64 from both sides, we get:
(height)^2 = 836
Taking the square root of both sides, we find:
height = √836 ≈ 28.9 ft
Therefore, the height above the ground that the top of the ladder touches the house is approximately 28.9 ft.
Question
The frozen yogurt cone shown is made from a cone and a hemisphere. The radius is 6 cm. The total height of the cone is 24 cm. The cone is completely packed with frozen yogurt.
What is the exact volume of the frozen yogurt in the cone and hemisphere? Leave your answer in terms of pi.
(1 point)
Responses
288π cm3
288π cm3
216π cm3
216π cm3
360π cm3
360π cm3
144π cm3
144π cm3
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To find the volume of the frozen yogurt in the cone and hemisphere, we need to find the volumes of the cone and the hemisphere separately and then add them together.
Volume of cone = (1/3) * π * (radius)^2 * height
Volume of cone = (1/3) * π * (6 cm)^2 * (24 cm)
Volume of cone = (1/3) * π * 36 cm^2 * 24 cm
Volume of cone = 288π cm^3
Volume of hemisphere = (2/3) * π * (radius)^3
Volume of hemisphere = (2/3) * π * (6 cm)^3
Volume of hemisphere = (2/3) * π * 216 cm^3
Volume of hemisphere = 144π cm^3
Total volume = Volume of cone + Volume of hemisphere
Total volume = 288π cm^3 + 144π cm^3
Total volume = 432π cm^3
Therefore, the exact volume of the frozen yogurt in the cone and hemisphere is 432π cm^3.