Answer:
37.50°
Step-by-step explanation:
The sum of both sides of an angle is 180°.
180° - 142.5° = 37.50°
Answer:
The probability that X is nine or more is 0.405.
Step-by-step explanation:
We have a sample of 20 random selected workers, each with a probability p=0.4 of changing jobs for "slightly higher pay".
We have a random variable X that can be modeled by the binomial distribution, with parameters n=20 (sample size) and p=0.4 (probability of success).
The probability that k workers will change jobs for slightly higher pay can be calcualted as:
![P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{20}{k} 0.4^{k} 0.6^{20-k}\\\\\\](https://tex.z-dn.net/?f=P%28x%3Dk%29%20%3D%20%5Cdbinom%7Bn%7D%7Bk%7D%20p%5E%7Bk%7D%281-p%29%5E%7Bn-k%7D%5C%5C%5C%5C%5C%5CP%28x%3Dk%29%20%3D%20%5Cdbinom%7B20%7D%7Bk%7D%200.4%5E%7Bk%7D%200.6%5E%7B20-k%7D%5C%5C%5C%5C%5C%5C)
We have to calculate the probability that the number of workers in the sample who will change jobs for slightly higher pay is 9 or higher. That is P(X≥9).
![P(x\geq9)=1-P(x](https://tex.z-dn.net/?f=P%28x%5Cgeq9%29%3D1-P%28x%3C9%29%3D1-%5Csum_%7Bi%3D0%7D%5E%7B8%7DP%28x%3Di%29%5C%5C%5C%5C%5C%5CP%28x%3D0%29%20%3D%20%5Cdbinom%7B20%7D%7B0%7D%20p%5E%7B0%7D%281-p%29%5E%7B20%7D%3D1%2A1%2A0%3D0%5C%5C%5C%5C%5C%5CP%28x%3D1%29%20%3D%20%5Cdbinom%7B20%7D%7B1%7D%20p%5E%7B1%7D%281-p%29%5E%7B19%7D%3D20%2A0.4%2A0.0001%3D0.0005%5C%5C%5C%5C%5C%5CP%28x%3D2%29%20%3D%20%5Cdbinom%7B20%7D%7B2%7D%20p%5E%7B2%7D%281-p%29%5E%7B18%7D%3D190%2A0.16%2A0.0001%3D0.0031%5C%5C%5C%5C%5C%5CP%28x%3D3%29%20%3D%20%5Cdbinom%7B20%7D%7B3%7D%20p%5E%7B3%7D%281-p%29%5E%7B17%7D%3D1140%2A0.064%2A0.0002%3D0.0123%5C%5C%5C%5C%5C%5CP%28x%3D4%29%20%3D%20%5Cdbinom%7B20%7D%7B4%7D%20p%5E%7B4%7D%281-p%29%5E%7B16%7D%3D4845%2A0.0256%2A0.0003%3D0.035%5C%5C%5C%5C%5C%5C)
![P(x=5) = \dbinom{20}{5} p^{5}(1-p)^{15}=15504*0.0102*0.0005=0.0746\\\\\\P(x=6) = \dbinom{20}{6} p^{6}(1-p)^{14}=38760*0.0041*0.0008=0.1244\\\\\\P(x=7) = \dbinom{20}{7} p^{7}(1-p)^{13}=77520*0.0016*0.0013=0.1659\\\\\\P(x=8) = \dbinom{20}{8} p^{8}(1-p)^{12}=125970*0.0007*0.0022=0.1797\\\\\\\\P(x\geq9)=1-(0+0.0005+0.0031+0.0123+0.035+0.0746+0.1244+0.1659+0.1797)\\\\P(x\geq9)=1-0.595=0.405](https://tex.z-dn.net/?f=P%28x%3D5%29%20%3D%20%5Cdbinom%7B20%7D%7B5%7D%20p%5E%7B5%7D%281-p%29%5E%7B15%7D%3D15504%2A0.0102%2A0.0005%3D0.0746%5C%5C%5C%5C%5C%5CP%28x%3D6%29%20%3D%20%5Cdbinom%7B20%7D%7B6%7D%20p%5E%7B6%7D%281-p%29%5E%7B14%7D%3D38760%2A0.0041%2A0.0008%3D0.1244%5C%5C%5C%5C%5C%5CP%28x%3D7%29%20%3D%20%5Cdbinom%7B20%7D%7B7%7D%20p%5E%7B7%7D%281-p%29%5E%7B13%7D%3D77520%2A0.0016%2A0.0013%3D0.1659%5C%5C%5C%5C%5C%5CP%28x%3D8%29%20%3D%20%5Cdbinom%7B20%7D%7B8%7D%20p%5E%7B8%7D%281-p%29%5E%7B12%7D%3D125970%2A0.0007%2A0.0022%3D0.1797%5C%5C%5C%5C%5C%5C%5C%5CP%28x%5Cgeq9%29%3D1-%280%2B0.0005%2B0.0031%2B0.0123%2B0.035%2B0.0746%2B0.1244%2B0.1659%2B0.1797%29%5C%5C%5C%5CP%28x%5Cgeq9%29%3D1-0.595%3D0.405)
Answer:
Sara should sell each bracelet at <em>$8.50</em> to make a profit of $99.
Step-by-step explanation:
We are given the following:
Total cost = $28.50
Total bracelets to be made = 15
Total profit to be made = $99
Let
be the price at which Sara sells each bracelet to make a profit of $99.
![\text{Total sales done = Number of bracelets sold }\times \text{ Sales price of each bracelet}\\](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20sales%20done%20%3D%20Number%20of%20bracelets%20sold%20%7D%5Ctimes%20%5Ctext%7B%20Sales%20price%20of%20each%20bracelet%7D%5C%5C)
![\Rightarrow 15 \times x ...... (1)](https://tex.z-dn.net/?f=%5CRightarrow%2015%20%5Ctimes%20x%20%20%20%20......%20%281%29)
Also,
![\text{Total sales price = Total Cost}+ \text{Total Profit} \\](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20sales%20price%20%3D%20Total%20Cost%7D%2B%20%5Ctext%7BTotal%20Profit%7D%20%5C%5C)
![\Rightarrow \$28.50 + \$99 ....... (2)](https://tex.z-dn.net/?f=%5CRightarrow%20%5C%2428.50%20%2B%20%5C%2499%20.......%20%282%29)
Equating (1) and (2):
![\Rightarrow 28.50 + 99 = 15x\\\Rightarrow x = \dfrac{127.5}{15}\\\Rightarrow x = $8.50](https://tex.z-dn.net/?f=%5CRightarrow%20%2028.50%20%2B%2099%20%3D%2015x%5C%5C%5CRightarrow%20x%20%3D%20%5Cdfrac%7B127.5%7D%7B15%7D%5C%5C%5CRightarrow%20x%20%3D%20%248.50)
Sara should <em>sell each bracelet at $8.50</em> to make a profit of $99.
Answer:
Depends on if you count his parent(s) if not then the answer is 5
Step-by-step explanation:
Answer:
Step-by-step explanation:
You cross multiply. So it's 14 times 250 divided by 115.
That's how much you would add to the 250 mixture.
14 times 250 is 3500, Divided by 150= 23 and a third.
It does say round to the nearest gram.
So we had to add about 23 g to 250 g of flour.