Answer:
The area of a rhombus is
square units.
Step-by-step explanation:
Side length of rhombus = 6 units.
Interior angle of rhombus = 120°
another Interior angle of rhombus = 180°-120° = 60°.
Draw an altitude.
In a right angled triangle
![\sin \theta=\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
![\sin (60)=\frac{h}{6}](https://tex.z-dn.net/?f=%5Csin%20%2860%29%3D%5Cfrac%7Bh%7D%7B6%7D)
![\frac{\sqrt{3}}{2}=\frac{h}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D%5Cfrac%7Bh%7D%7B6%7D)
Multiply both sides by 6.
![3\sqrt{3}=h](https://tex.z-dn.net/?f=3%5Csqrt%7B3%7D%3Dh)
The height of the rhombus is
.
Area of a rhombus is
![Area=base\times height](https://tex.z-dn.net/?f=Area%3Dbase%5Ctimes%20height)
![Area=6\times 3\sqrt{3}](https://tex.z-dn.net/?f=Area%3D6%5Ctimes%203%5Csqrt%7B3%7D)
![Area=18\sqrt{3}](https://tex.z-dn.net/?f=Area%3D18%5Csqrt%7B3%7D)
Therefore, the area of a rhombus is
square units.
Answer:
87 sq in
Step-by-step explanation:
Surface area of the net
![= 3(8) + 3(6) + (2) \frac{1}{2} (6)(5) + (5)(3) \\ \\ = 24 + 18 + 30 + 15 \\ \\ = 87 \: {in}^{2}](https://tex.z-dn.net/?f=%20%3D%203%288%29%20%2B%203%286%29%20%2B%20%282%29%20%5Cfrac%7B1%7D%7B2%7D%20%286%29%285%29%20%2B%20%285%29%283%29%20%5C%5C%20%20%5C%5C%20%20%3D%2024%20%2B%2018%20%2B%2030%20%2B%2015%20%5C%5C%20%20%5C%5C%20%20%3D%2087%20%5C%3A%20%20%7Bin%7D%5E%7B2%7D%20)
The correct answer would be (-6, 0).
Answer:
4
Step-by-step explanation:
count up from -5 to -1
so -5,-4,-3,-2,-1 and there are four numbers excluding-5
Answer:
The probability that X is between 1.48 and 15.56 is ![P(1.48 \leq X \leq 15.56) = 0.919](https://tex.z-dn.net/?f=P%281.48%20%5Cleq%20X%20%5Cleq%2015.56%29%20%3D%200.919)
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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.
X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.
This means that ![\mu = 8, \sigma = 4](https://tex.z-dn.net/?f=%5Cmu%20%3D%208%2C%20%5Csigma%20%3D%204)
The probability that X is between 1.48 and 15.56
This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So
X = 15.56
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{15.56 - 8}{4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B15.56%20-%208%7D%7B4%7D)
![Z = 1.89](https://tex.z-dn.net/?f=Z%20%3D%201.89)
has a pvalue of 0.9706
X = 1.48
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{1.48 - 8}{4}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B1.48%20-%208%7D%7B4%7D)
![Z = -1.63](https://tex.z-dn.net/?f=Z%20%3D%20-1.63)
has a pvalue of 0.0516
0.9706 - 0.0516 = 0.919
Write out the probability notation for this question.
![P(1.48 \leq X \leq 15.56) = 0.919](https://tex.z-dn.net/?f=P%281.48%20%5Cleq%20X%20%5Cleq%2015.56%29%20%3D%200.919)
The probability that X is between 1.48 and 15.56 is ![P(1.48 \leq X \leq 15.56) = 0.919](https://tex.z-dn.net/?f=P%281.48%20%5Cleq%20X%20%5Cleq%2015.56%29%20%3D%200.919)