Answer: All Real Numbers Are Solutions
81x - 126x ÷ 3x + 1
45x / 3x + 1
15x / x + 1
Answer: After 7 years the population will be one-half the initial amount.
Step-by-step explanation:
Given: Initial population = 500,000
The population declines according to the equation:
, where P is the population in t years later.
One-half the initial amount = 0.5 x 500,000
= 250,000
Put P(t)=250,000, we get
![250000=500000e^{-0.099t}\\\\\Rightarrow\ \frac{500000e^{-0.099t}}{500000}=\frac{250000}{500000}\\\\\Rightarrow\ e^{-0.099t}=\frac12\\\\\Rightarrow\ -0.099t=\ln \left(\frac{1}{2}\right)\\\\\Rightarrow\ t=\frac{1000\ln \left(2\right)}{99}=\frac{1000(0.69314)}{99}\\\\\Rightarrow\ t=7.00148\approx7](https://tex.z-dn.net/?f=250000%3D500000e%5E%7B-0.099t%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Cfrac%7B500000e%5E%7B-0.099t%7D%7D%7B500000%7D%3D%5Cfrac%7B250000%7D%7B500000%7D%5C%5C%5C%5C%5CRightarrow%5C%20e%5E%7B-0.099t%7D%3D%5Cfrac12%5C%5C%5C%5C%5CRightarrow%5C%20-0.099t%3D%5Cln%20%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5C%5C%5C%5C%5CRightarrow%5C%20t%3D%5Cfrac%7B1000%5Cln%20%5Cleft%282%5Cright%29%7D%7B99%7D%3D%5Cfrac%7B1000%280.69314%29%7D%7B99%7D%5C%5C%5C%5C%5CRightarrow%5C%20t%3D7.00148%5Capprox7)
Hence, After 7 years the population will be one-half the initial amount.
Answer:
x = - 7
Step-by-step explanation:
Using the rule of exponents
×
= ![a^{(m+n)}](https://tex.z-dn.net/?f=a%5E%7B%28m%2Bn%29%7D)
Given
×
= 6², then
= 6²
Since the bases on both sides are equal then equate the exponents
9 + x = 2 ( subtract 9 from both sides )
x = - 7
Answer:
The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.
Let X = <em>t</em><u><em>he blood platelet counts of a group of women</em></u>
The z-score probability distribution for the normal distribution is given by;
Z =
~ N(0,1)
where,
= population mean = 247.3
= standard deviation = 60.7
Now, according to the empirical rule;
- 68% of the data values lie within one standard deviation of the mean.
- 95% of the data values lie within two standard deviations of the mean.
- 99.7% of the data values lie within three standard deviations of the mean.
Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;
z-score for 65.2 = ![\frac{X-\mu}{\sigma}](https://tex.z-dn.net/?f=%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D)
=
= -3
z-score for 429.4 = ![\frac{X-\mu}{\sigma}](https://tex.z-dn.net/?f=%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D)
=
= 3
So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.