Answer:
311
Step-by-step explanation:
3+13=16
16^2=16*16=256
9^3=9*9*9=81(9)=729
729*6=4374
67^2=67*67=4489
---------------------------
256-4374+4489-60=311
Answer:
The two expressions A and B are equivalent because the value of both expressions is same.
Step-by-step explanation:
Given: Expression A is 5(4+9) and expression B is 29+36.
To find: The reason why expressions A and B are equivalent.
First we solve expression A.
(using
)
⇒![5(4+9)=20+45](https://tex.z-dn.net/?f=5%284%2B9%29%3D20%2B45)
⇒![5(4+9)=65](https://tex.z-dn.net/?f=5%284%2B9%29%3D65)
Now we solve expression B.
![29+36=45](https://tex.z-dn.net/?f=29%2B36%3D45)
Clearly, the value of both the expressions is same.
Hence, the expression A is equivalent to expression B.
The total surface area of the rectangular prism is 172 cm².
Step-by-step explanation:
Step 1; To calculate the surface area of the entire prism we need to sum the areas of all the different colored sections of the prism. There are a total of 6 different sections in the prism. There are
2 green sections,
2 purple sections, and
2 red sections.
Step 2; Each square is 1 cm² so the area of each section is the length multiplied with the breadth. The sections with the same colors have the same areas.
Green sections area = length × width = 7 × 8 = 56 cm²,
Purple sections area = length × width = 2 × 8 = 16 cm²,
Red sections area = length × width = 7 × 2 = 14 cm².
Total surface area = Area of the first green section + Area of the first purple section + Area of the second green section + Area of the second purple section + Area of the first red section + Area of the second red section.
Total surface area = 56 + 16 +56 + 16 + 14 + 14 = 172 cm².
Answer:
0.7611 = 76.11% probability that the weight of a randomly selected steer is less than 1140lbs.
Step-by-step explanation:
Problems of normally distributed samples 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.
In this problem, we have that:
![\mu = 900, \sigma = 300](https://tex.z-dn.net/?f=%5Cmu%20%3D%20900%2C%20%5Csigma%20%3D%20300)
Find the probability that the weight of a randomly selected steer is less than 1140lbs.
This is the pvalue of Z when X = 1140. So
![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{1140 - 900}{300}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B1140%20-%20900%7D%7B300%7D)
![Z = 0.71](https://tex.z-dn.net/?f=Z%20%3D%200.71)
has a pvalue of 0.7611
0.7611 = 76.11% probability that the weight of a randomly selected steer is less than 1140lbs.
9514 1404 393
Answer:
276/47
Step-by-step explanation:
The fractions can be given a common denominator by multiplying the top fraction by 6/6. Then the common denominators can be cancelled.
![\dfrac{\text{ }\dfrac{46}{7}\text{ }}{\dfrac{47}{42}}=\dfrac{\text{ }\dfrac{6}{6}\cdot\dfrac{46}{7}\text{ }}{\dfrac{47}{42}}=\dfrac{\text{ }\dfrac{276}{42}\text{ }}{\dfrac{47}{42}}=\boxed{\dfrac{276}{47}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7B%20%7D%5Cdfrac%7B46%7D%7B7%7D%5Ctext%7B%20%7D%7D%7B%5Cdfrac%7B47%7D%7B42%7D%7D%3D%5Cdfrac%7B%5Ctext%7B%20%7D%5Cdfrac%7B6%7D%7B6%7D%5Ccdot%5Cdfrac%7B46%7D%7B7%7D%5Ctext%7B%20%7D%7D%7B%5Cdfrac%7B47%7D%7B42%7D%7D%3D%5Cdfrac%7B%5Ctext%7B%20%7D%5Cdfrac%7B276%7D%7B42%7D%5Ctext%7B%20%7D%7D%7B%5Cdfrac%7B47%7D%7B42%7D%7D%3D%5Cboxed%7B%5Cdfrac%7B276%7D%7B47%7D%7D)