A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length
of 196196196 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the tent is 250\,\text{cm}250cm250, space, c, m long. what is the height, in centimeters, of the tent?
1 answer:
Given:
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long
I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.
I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.
a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm²
a = 169.74cm
The height of the tent is 169.74 centimeters.
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long
I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.
I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.
a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm²
a = 169.74cm
The height of the tent is 169.74 centimeters.
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Answer:
Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.
Step-by-step explanation:
Z-score
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
On which exam did Carl earn a better score with respect to his peers?
On whichever exam he had the higher z-score.
SAT
Scored 730, mean 516, standard deviation 116. So
ACT
Scored 32, mean 21, standard deviation 5.3. So
Carl's ACT grade had a higher z-score, which means that he earned a better score with respect to his peers on the ACT test.
The complete question in the attached figure
we know that
angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°
the answer is
x=147°
y=33°
we know that
angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°
the answer is
x=147°
y=33°