Answer:

Step-by-step explanation:
Call x the amount of blinds that Manny buys.
Let's call and the amount of curtains that Manny buys
There are only 35 windows, so the number of curtains and windows can not be greater than 35.

Manny can only spend $ 2100
Then we can represent this by an inequality in the following way.

and

We can write this as a single inequality:

Finally, the set of inequalities to model this problem is:

Answer: 0.7471
Step-by-step explanation:
Given : The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of
and a population standard deviation of
.
Sample size = 50
Using formula
, the z-value corresponding to x=98 will be:-

Z-value corresponding to x=103 will be:-

Using the standard normal distribution table for z-scores, we have
P-value = 
Hence, the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103 = 0.7471
Answer:
rate = natural log (Total / Principal) / Years
We need 5,000 to become 10,000 in 10 years so,
rate = natural log (Total / Principal) / Years
rate = natural log(10,000 / 5,000) / 10
rate = natural log(2) / 10
rate = 0.69314718056 / 10
rate = .069314718056 which equals
rate = 6.9314718056 per cent
Source: https://www.1728.org/rate2.htm
(scroll to the bottom)
Step-by-step explanation:
Let the sides of the polygon (which is a triangle, by the way) be x, y and z. The sum of x, y and z is the perimeter of the original poly, and this equals 18 cm.
Letting f be the scale factor, f(18 cm) = 12 cm. Then f=2/3.
The dilation reduces the size of the polygon by a factor of 1/3, producing a similar polygon which is 2/3 the size of the original one.
In each case we have 3 side lengths but no angles. We can use Heron's formula to obtain the area in each case. Look up Heron's formula. In one version of this formula, p is half the actual perimeter, meaning that p is 18 cm / 2 for the first triangle and 12 cm / 2 for the second.
The area of the first triangle would be
A18 = sqrt( 9(9-x)(9-y)(9-z) )
whereas
A12 = sqrt( 6(6-x*a)(6-y*a)(6-z*a) ), where a represents the dilation factor 2/3.
Then the ratio of the areas of the 2 triangles is
sqrt( 6(6-x*a)(6-y*a)(6-z*a) )
---------------------------------------
sqrt( 9(9-x)(9-y)(9-z) )
2/4 and 1/2
5/10 and 1/2
1/3 and 2/6
40/90 and 4/9