Answer:
3 pennies, 9 nickels, and 6 dimes
Step-by-step explanation:
We have three conditions:
(1) p + n + d = 18
(2) 0.01p + 0.05n + 0.10d = 1.08
(3) d = 2p
Multiply (2) by 100 and rearrange (3) to get a standard array.
(4) p + n + d = 18
(5) p + 5n + 10d = 108
(6) -2p + d = 0
Subtract (4) from (5). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(6) -2p + d = 0
Multiply (4) by 2 and add to (6). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(8) 2n + 3d = 36
Double (8) and subtract from (7). This gives
(4) p + n + d = 18
(7) 4n + 9d = 90
(9) 3d = 18
Divide (9) by 3. This gives
(10) d = 6
Substitute (10) into (7). This gives
4n + 9(6) = 90
4n + 54 = 90
4n = 36
(11) n = 9
Substitute (10) and (11) into (4). This gives
p + 9 + 6 = 18
p + 15 = 18
p = 3
Sasha has 3 pennies, 9 nickels, and 6 dimes.
Answer:
a) 0.586
b) 0.846
c) We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 64.4 inches
Standard Deviation, σ =2.3 inches
We are given that the distribution of height of woman is a bell shaped distribution that is a normal distribution.
Formula:
![z_{score} = \displaystyle\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z_%7Bscore%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
a) P(selecting 1 woman with a height less than 64.9 inches)
P(x < 64.9)
Calculation the value from standard normal z table, we have,
![P(x < 64.9) = 0.586 = 58.6\%](https://tex.z-dn.net/?f=P%28x%20%3C%2064.9%29%20%3D%200.586%20%3D%2058.6%5C%25)
b) P(selecting 22 woman with a height less than 64.9 inches)
Standard error due to sampling =
![\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{2.3}{\sqrt{22}} = 0.49](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20%5Cfrac%7B2.3%7D%7B%5Csqrt%7B22%7D%7D%20%3D%200.49)
P(x < 64.9)
Calculation the value from standard normal z table, we have,
![P(x < 64.9) = 0.846 = 84.6\%](https://tex.z-dn.net/?f=P%28x%20%3C%2064.9%29%20%3D%200.846%20%3D%2084.6%5C%25)
c) Since,
P(selecting 22 woman with a height less than 64.9 inches) > P(selecting 1 woman with a height less than 64.9 inches)
We are more likely to select a sample of 22 woman with a mean height of 64.9 inches.
Due to a lack of context, I’m guessing you want the equation of this line. If you go back to the equation y = mx + b, m represents SLOPE, and b represents the y-int (0, b).
As the slope is -2 and the y intercept is (0,0), the line’s equation would be y = -2x + 0, or simply y = -2x.
Answer:
82.8
Step-by-step explanation:
24/.29
=82.75862
but you want it rounded so 82.8 is your answer
I hope this helps
Answer:
<h2>x = 2 and y = -2</h2>
Step-by-step explanation:
![\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx-y%3D4%26%5Ctext%7Badd%7D%5C%20y%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5Cx%2B2y%3D-2%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%3D4%2By%26%281%29%5C%5Cx%2B2y%3D-2%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7Bsubstitute%20%281%29%20to%20%282%29%3A%7D%5C%5C%5C%5C%284%2By%29%2B2y%3D-2%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%5C%5C4%2B%28y%2B2y%29%3D-2%5Cqquad%5Ctext%7Bsubtract%204%20from%20both%20sides%7D%5C%5C%5C%5C3y%3D-6%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5Cy%3D-2%5C%5C%5C%5C%5Ctext%7Bput%20the%20value%20of%7D%5C%20y%5C%20%5Ctext%7Bto%20%281%29%3A%7D%5C%5C%5C%5Cx%3D4%2B%28-2%29%5C%5C%5C%5Cx%3D2)