Let x be the width of the playground, then 3x is the length of the
<span>playground
х * 3х = 75
3x</span>² = 75
x² = 25
x = 5 m (width)
5*3=15 m (length)
Perimeter = 2(5+15) = 2*20 = 40 meters.
Answer: Each friend will get 3 gumballs.
Step-by-step explanation:
Given: Pete has 4 packs of gumballs. Each pack has 5 gumballs.
Total gumballs he has = 4 x 5 = 20
Now , if he needs to divide them into 6 friends , then each friend will get (20 ÷ 6) gumballs

So each friend will get 3 gumballs.
Answer:
There is no enough evidence to claim that there is a difference between the two population proportions.
Step-by-step explanation:
We have to perform an hypothesis testing for a difference between two population proportions.
The null hypothesis will state that both proportions are the same, and the alternative hypothesis will state that they differ. This would be than a two-side hypothesis test.
We can write this as:

The significance level for this test is 0.05.
The sample of city residents with school-age children has a sample size n1=230 and a sample proportion p1=0.41

The sample of city residents without school-age children has a sample size n2=341 and a sample proportion p2=0.51

The weighted p, needed to calculate the standard error, is the weighted average of both sample proportions:

The standard error of the difference of proportions can now be calculated as:

The test statistic z is:

The P-value for this two side test and this value of the z-statistic is:

The P-value is bigger than the significance level, so the effect is not significant. The null hypothesis failed to be rejected.
There is no enough evidence to claim that there is a difference between the two population proportions.
Answer:
see below
Step-by-step explanation:
If we let X represent the number of bagels produced, and Y the number of croissants, then we want ...
(a) Max Profit = 20X +30Y
(b) Subject to ...
6X +3Y ≤ 6600 . . . . . . available flour
X + Y ≤ 1400 . . . . . . . . available yeast
2X +4Y ≤ 4800 . . . . . . available sugar
_____
Production of 400 bagels and 1000 croissants will produce a maximum profit of $380.
__
In the attached graph, we have shaded the areas that are NOT part of the solution set. (X and Y less than 0 are also not part of the solution set, but are left unshaded.) This approach can sometimes make the solution space easier to understand, since it is white.
The vertex of the solution space that moves the profit function farthest from the origin is the one we are seeking. The point that does that is (X, Y) = (400, 1000).