Answer:
(-2, -3)
Step-by-step explanation:
If a segment having extreme ends as 
and 
is divided by a point (x, y) in the ratio of m:n,
x = 
y = 
Since, a line RT has extreme ends as R(-5, 3) and T(-1, -5) then a point S(x, y) which divides RT in the ratio of 3 : 1 will be,
x = 
= 
= -2
y = 
= 
= -3
Therefore, coordinates of the point S will be (-2, -3).
Answer:
25
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 175cm
Standard deviation = 6 cm
Percentage of students below 163 cm
163 = 175 - 2*6
So 163 is two standard deviations below the mean.
By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.
2.5% of the students have heights less than 163cm.
Out of 1000
0.025*1000 = 25
25 is the answer
<h2>
Answer with explanation:</h2>
As per given , we have
, n=331
Critical value for 90% Confidence interval : 
a) Confidence interval :
Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : 
b) Margin of error : E=1.5%=0.015
Formula for sample size : 
For p =0.48 , we have
Hence, the required sample size to survey = 3002
If the adjusted ratio was 2:7, then
2x is the number of pull-ups
and
7x is the number of box jumps.
You can state that since he completed 63 box jumps at the end of his training, then
7x=63,
x=9
and
2x=18.
The total number of exercises performed is 2x+9x=18+63=81.
As at start the ratio was 5:4, then
5y was the number of pull-ups
and
4y was the number of box jumps.
Therefore, 5y+4y=81,
9y=81,
y=9
and 5y=45, 4y=36.
Answer: Initially: 45 pull-ups and 36 box jumps. At the end: 18 pull-ups and 63 box jumps.
Let us say that:
x = is the number of ads that Nadia sold every week
P = payment or amount that she receives every week
So the equations we can formulate for choice A and B are:
choice A: P = 110 x
choice B: P = 150 + 85 x
The amount that she receives for A must be greater than
she receives for choice B, so:
110 x > 150 + 85 x (inequality equation)
Calculate for x:
110 x – 85 x > 150
25 x > 150
x > 6
Therefore Nadia must sell more than 6 ads every week so
that Choice A would be the better choice.
