Step-by-step explanation:
We can immediately eliminate answers B and C because we have >, meaning that the circle on the number line has to be open.
-2x+7>17
subtract 7 on both sides
-2x>10
divide by -2. remember that dividing by a negative flips the greater than or less than sign.
x<-5
the answer is D
Answer:
The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.
Step-by-step explanation:
We can model this with a binomial random variable, with sample size n=20 and probability of success p=0.08.
The probability of k online retail orders that turn out to be fraudulent in the sample is:
![P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{20}{k}\cdot0.08^k\cdot0.92^{20-k}](https://tex.z-dn.net/?f=P%28x%3Dk%29%3D%5Cdbinom%7Bn%7D%7Bk%7Dp%5Ek%281-p%29%5E%7Bn-k%7D%3D%5Cdbinom%7B20%7D%7Bk%7D%5Ccdot0.08%5Ek%5Ccdot0.92%5E%7B20-k%7D)
We have to calculate the probability that 2 or more online retail orders that turn out to be fraudulent. This can be calculated as:
![P(x\geq2)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0)=\dbinom{20}{0}\cdot0.08^{0}\cdot0.92^{20}=1\cdot1\cdot0.189=0.189\\\\\\P(x=1)=\dbinom{20}{1}\cdot0.08^{1}\cdot0.92^{19}=20\cdot0.08\cdot0.205=0.328\\\\\\\\P(x\geq2)=1-[0.189+0.328]\\\\P(x\geq2)=1-0.517=0.483](https://tex.z-dn.net/?f=P%28x%5Cgeq2%29%3D1-%5BP%28x%3D0%29%2BP%28x%3D1%29%5D%5C%5C%5C%5C%5C%5CP%28x%3D0%29%3D%5Cdbinom%7B20%7D%7B0%7D%5Ccdot0.08%5E%7B0%7D%5Ccdot0.92%5E%7B20%7D%3D1%5Ccdot1%5Ccdot0.189%3D0.189%5C%5C%5C%5C%5C%5CP%28x%3D1%29%3D%5Cdbinom%7B20%7D%7B1%7D%5Ccdot0.08%5E%7B1%7D%5Ccdot0.92%5E%7B19%7D%3D20%5Ccdot0.08%5Ccdot0.205%3D0.328%5C%5C%5C%5C%5C%5C%5C%5CP%28x%5Cgeq2%29%3D1-%5B0.189%2B0.328%5D%5C%5C%5C%5CP%28x%5Cgeq2%29%3D1-0.517%3D0.483)
The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.
Answer:
7
Step-by-step explanation:
If a system decreases by 12% it's the same as multiplying it by .12-1 or .88
This means we can create the following equation
computer value=5300(.88)^n
where n is the number of years
We can then plug in the value of the computer and solve for n
2200=5300(.88)^n
Divide by 5300 and get
.415=.88^n
Then put this into log form and get
![\frac{log(.415)}{log.88}](https://tex.z-dn.net/?f=%5Cfrac%7Blog%28.415%29%7D%7Blog.88%7D)
Evaluate this into your calculator and get n=6.69 which I would probably just round to 7
The dependent variable is the cost of the pizza.
The Independent variable (or what you manipulate) is the toppings of the pizza, and the dependent variable (or what changes because you manipulated something) is the total cost of the pizza
Let's say that the value invested in the account with a rate of 8% is "x", then the amount invested in the account with a rate of 12% is:
![x+450](https://tex.z-dn.net/?f=x%2B450)
To calculate the total interest we need to calculate the interest of each individual account and sum them:
![\begin{gathered} \frac{8}{100}\cdot x=0.08\cdot x \\ \frac{12}{100}\cdot(x+450)=0.12\cdot x+54 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B8%7D%7B100%7D%5Ccdot%20x%3D0.08%5Ccdot%20x%20%5C%5C%20%5Cfrac%7B12%7D%7B100%7D%5Ccdot%28x%2B450%29%3D0.12%5Ccdot%20x%2B54%20%5Cend%7Bgathered%7D)
The total interest is the sum of the two expressions above:
![\begin{gathered} 220=(0.08\cdot x)+(0.12\cdot x+54) \\ 220=0.08\cdot x+0.12\cdot x+54 \\ 220-54=0.2\cdot x \\ 166=0.2\cdot x \\ 0.2\cdot x=166 \\ x=\frac{166}{0.2} \\ x=830 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20220%3D%280.08%5Ccdot%20x%29%2B%280.12%5Ccdot%20x%2B54%29%20%5C%5C%20220%3D0.08%5Ccdot%20x%2B0.12%5Ccdot%20x%2B54%20%5C%5C%20220-54%3D0.2%5Ccdot%20x%20%5C%5C%20166%3D0.2%5Ccdot%20x%20%5C%5C%200.2%5Ccdot%20x%3D166%20%5C%5C%20x%3D%5Cfrac%7B166%7D%7B0.2%7D%20%5C%5C%20x%3D830%20%5Cend%7Bgathered%7D)
The value invested in the account with 8% interest is 830, the one invested in the account with 12% interest is 1280.