Number of boys=x
number of girls=y.

We can suggest this system of equations:
x/y=8/7 ⇒x=8y/7
x+y=195

this system of equations can be solve by substitution method.

(8y/7)+y=195
least common multiple=7
8y+7y=1365
15y=1365
y=1365/15
y=91

x=8y/7
x=8*91 / 7
x=728/7
x=104

Answer: there were 104 boy campers and 91 girl campers.

6 0

3 years ago

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain

noname [10]

Answer:

$Z_{H0}$ = 1.56

Step-by-step explanation:

Hello!

You have two independent samples of fertilizers from distributor A and B, and need to test if the average content of nitrogen from fertilizer distributed by A is greater than the average content of nitrogen from fertilizer distributed by B.

Sample 1

X₁: Content of nitrogen of a fertilizer batch distributed by A

n₁= 4 batches

Sample mean X₁[bar]= 23pound/batch

σ₁= 4 poundes/batch

Sample 2

X₂: Content of nitrogen of a fertilizer batch distributed by B

n₂= 4 batches

Sample mean X₂[bar]= 18pound/batch

σ₂= 5 pounds/batch

Both variables have a normal distribution. Now since you have the information on the variables distribution and the values of the population standard deviations, you could use a pooled Z-test.

Your hypothesis are:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

The statistic to use is:

Z= X₁[bar] - X₂[bar] - (μ₁ - μ₂) ~N(0;1)

√(δ²₁/n₁ + δ²₂/n₂)

$Z_{H0}$ = (23 - 18) - 0 = 1.56

√(16/4 + 25/4)

I hope this helps!

8 0

3 years ago