The circumference of the circle shown below is 42 centimeters. Which
2 answers:
You might be interested in
Answer:
Short-Term investment: 5000$
Intermediate-Term investment: 65000$
Long-Term investment: 30000$
Step-by-step explanation:
To construct our first equation lets define sort-term bond investment as x, long-term investment as y.
So the equation is:
From the equation it is found that:
Instead of y, if we put 25000+x the equation will be as following:
From the equation it is found that:
Short-Term investment is 5000$
Long-Term investment is 30000$
Rest of the money is Intermediate-Term investment 65000$
Answer:
Step-by-step explanation:
Hello!
X: length of human pregnancies from conception to birth.
X~N(μ;σ²)
μ= 264 day
σ= 16 day
If the variable of interest has a normal distribution, it's the sample mean, that it is also a variable on its own, has a normal distribution with parameters:
X[bar] ~N(μ;σ²/n)
When calculating a probability of a value of "X" happening it corresponds to use the standard normal: Z= (X[bar]-μ)/σ
When calculating the probability of the sample mean taking a given value, the variance is divided by the sample size. The standard normal distribution to use is Z= (X[bar]-μ)/(σ/√n)
a. You need to calculate the probability that the sample mean will be less than 260 for a random sample of 15 women.
P(X[bar]<260)= P(Z<(260-264)/(16/√15))= P(Z<-0.97)= 0.16602
b. P(X[bar]>b)= 0.05
You need to find the value of X[bar] that has above it 5% of the distribution and 95% below.
P(X[bar]≤b)= 0.95
P(Z≤(b-μ)/(σ/√n))= 0.95
The value of Z that accumulates 0.95 of probability is Z= 1.648
Now we reverse the standardization to reach the value of pregnancy length:
1.648= (b-264)/(16/√15)
1.648*(16/√15)= b-264
b= [1.648*(16/√15)]+264
b= 270.81 days
c. Now the sample taken is of 7 women and you need to calculate the probability of the sample mean of the length of pregnancy lies between 1800 and 1900 days.
Symbolically:
P(1800≤X[bar]≤1900) = P(X[bar]≤1900) - P(X[bar]≤1800)
P(Z≤(1900-264)/(16/√7)) - P(Z≤(1800-264)/(16/√7))
P(Z≤270.53) - P(Z≤253.99)= 1 - 1 = 0
d. P(X[bar]>270)= 0.1151
P(Z>(270-264)/(16/√n))= 0.1151
P(Z≤(270-264)/(16/√n))= 1 - 0.1151
P(Z≤6/(16/√n))= 0.8849
With the information of the cumulated probability you can reach the value of Z and clear the sample size needed:
P(Z≤1.200)= 0.8849
n= 10.24 ≅ 11 pregnant women.
I hope it helps!
Answer:
Step-by-step explanation:
A fraction can be found be taking the current amount over the total amount:
Since Darlene has only typed 23 pages out of 59, her fraction is 23 over 59. Fractions must always be in simplest form, which means that both the numerator and denominator can no longer be divided by the same factor. Since the numbers 23 and 59 are both prime and have no other factors other than 1 and themselves, the fraction 23/59 is in simplest form.