The length of the diagonal of the square is the square root of 32 which equals approximately 5.6569.
The length from the corner to the center of the square is half of the diagonal which is 2.8284. I hope this helps!
Answer:
lateral area = 2320 m²
Step-by-step explanation:
The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.
Half of the square base is 40/2 = 20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.
Using Pythagoras's theorem
c² = a² + b²
c² = 20² + 21²
c² = 400 + 441
c² = 841
square root both sides
c = √841
c = 29 meters
The slant height of the pyramid is 29 meters.
The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.
area of triangle = 1/2 × base × height
base = 40 meters
height = 29 meters
area = 1/2 × 40 × 29
area = 580
area of one triangle = 580 m²
Lateral area = 4(580)
lateral area = 2320 m²
Answer:
4x+5 ft
Step-by-step explanation:
1/2(4x²+29x+30) = 1/2 (x+6) * Height
Height = (4x²+29x+30) / (x+6) = (x+6) (4x+5) / (x+6) = 4x+5
The amount of calvin’s starting balance for the next month will be C. $625.91.
<h3>How to calculate the amount?</h3>
From the information given, the monthly percentage rate will be:
= 14.75/12
= 1.22%
Therefore, the amount of calvin’s starting balance for the next month will be $625.91.
In conclusion, the correct option is C.
Learn more about amount on:
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Answer:
Step-by-step explanation:
Hello!
The objective of this experiment is to test if two different foam-expanding agents have the same foam expansion capacity
Sample 1 (aqueous film forming foam)
n₁= 5
X[bar]₁= 4.7
S₁= 0.6
Sample 2 (alcohol-type concentrates )
n₂= 5
X[bar]₂= 6.8
S₂= 0.8
Both variables have a normal distribution and σ₁²= σ₂²= σ²= ?
The statistic to use to make the estimation and the hypothesis test is the t-statistic for independent samples.:
t= ![\frac{(X[bar]_1 - X[bar]_2) - (mu_1 - mu_2)}{Sa*\sqrt{\frac{1}{n_1} + \frac{1}{n_2 } } }](https://tex.z-dn.net/?f=%5Cfrac%7B%28X%5Bbar%5D_1%20-%20X%5Bbar%5D_2%29%20-%20%28mu_1%20-%20mu_2%29%7D%7BSa%2A%5Csqrt%7B%5Cfrac%7B1%7D%7Bn_1%7D%20%2B%20%5Cfrac%7B1%7D%7Bn_2%20%7D%20%7D%20%7D)
a) 95% CI
(X[bar]_1 - X[bar]_2) ± 
*
Sa²= 
= 
= 0.5
Sa= 0.707ç
(4.7-6.9) ± 2.306* 
[-4.78; 0.38]
With a 95% confidence level you expect that the interval [-4.78; 0.38] will contain the population mean of the expansion capacity of both agents.
b.
The hypothesis is:
H₀: μ₁ - μ₂= 0
H₁: μ₁ - μ₂≠ 0
α: 0.05
The interval contains the cero, so the decision is to reject the null hypothesis.
<u>Complete question</u>
a. Find a 95% confidence interval on the difference in mean foam expansion of these two agents.
b. Based on the confidence interval, is there evidence to support the claim that there is no difference in mean foam expansion of these two agents?
