Answer:
The 95% confidence interval for the population mean daily protein intake is between 69.97g and 84.03g.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 77 - 7.03 = 69.97g.
The upper end of the interval is the sample mean added to M. So it is 77 + 7.03 = 84.03g.
The 95% confidence interval for the population mean daily protein intake is between 69.97g and 84.03g.
You want to find out how much flour she used first. In order to do that, you want to convert all your givens, into the same denominator so you can add them together.
For 2/5, multiply the top and the bottom by 2.
2/5 = 4/10 she uses for pizza.
3/10 already has the same denominator, so we can add them together.
4/10 for pizza + 3/10 for bread = 7/10 already used.
1- 7/10 = 3/10 left
Answer:
AA similarity postulate
Step-by-step explanation:
These are similar by the AA similarity postulate. There are two angles that are similar and since we know 2 angles in a triangle, we can determine the third angle. Since all three angles are similar, the triangles are similar.
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
Let's first establish that the origin is always ( 0, 0 ).
Next, as shown in the diagram attached, we can establish that there is a right-angle triangle formed when we connect the different points given from the problem. We can use this to solve the problem.
As the shape is a right-angle triangle, we can use Pythagoras' Theorem which is as follows:
a^2 + b^2 = c^2
Where c = hypotenuse of the right-angle triangle
Where a and b = other two sides of the right-angle triangle which aren't the hypotenuse
From this, we will substitute the values from the problem into Pythagoras' Theorem.
a^2 + b^2 = c^2
a = 12
b = 5
c = distance from the origin = d
THEREFORE:
( 12 )^2 + ( 5 )^2 = d^2
d^2 = 12^2 + 5^2
d^2 = 144 + 25
d^2 = 169
d = square root of ( 169 )
d = 13
FINAL ANSWER:
Therefore, the point ( 12, 5 ) is 13 units from the origin.
Hope this helps! :)
Have a lovely day! <3