Answer:
90°
Step-by-step explanation:
All circles are equal to 360°. Since the pie chart is a circle, if you added all of the central angles for all three sections, it would total to 360°.
Since the circle is not divided into 360 parts for each degree, but 100 parts for each percent %.
You can <u>solve using an equivalent</u>. Write each fraction in the form "Lemonade" over "total". The left side is percentage, the right side is degrees.
Let x be the central angle for lemonade
Solve for the central angle of lemonade by <u>isolating 'x'</u>. To isolate x, move 360 over to the other side. When moving numbers in an equivalent, you do the opposite operation to both sides. Since 'x' divides by 360, multiply 360 on both sides.
360 cancels out on the right
Combined multiplication in numerator
When dividing, 0s cancel out
Simplify fraction over 1
Answer
Therefore the central angle in the Lemonade section is 90°.
You can choose to answer this with fractions or decimals. I'll choose fractions because we won't need calculators. 22 1/2 miles "in" 1/3 hour, means 22 1/2 mi divided by 1/3 hour.
22 1/2 = [(22×2) + 1] ÷ 2 = 45/2
So (45/2)mi ÷ (1/3)hr is the same as (45/2) × (3/1), or (45×3)/2 = 135/2, which is 67 1/2, or 67.5 mi/hr (mph).
Because it wouldn't matter which direction you go in first. For example would it matter if you took two steps left then three forward or if you took three forward and then two left. It wouldn't because you would end up in the exact same place.
Answer:
The answer to your question is the third histogram
Step-by-step explanation:
What we must check in a histogram is that the x-axis is represented the intervals and in the y-axis is represented the frequency.
The first histogram is incorrect just by observing the first bar, we notice that the correct frequency from 0 to 4 is 3, not 14. This histogram is incorrect.
Also, the second histogram is incorrect, the frequency of the first category is 3, not 12. This histogram is wrong.
The third histogram is correct because all the bars are in agreement with their frequencies.
The last histogram is incorrect, for example, the last frequency is 12, not 3.
This looks complicated
lets simplify both sides
By multiplying top and bottom by the conjugate:-
left side = (5-3i)(x + iy) (4+5i) (5-3i)(x + iy) (4+5i)
------------------------ = ------------------------
(4-5i)(4+5i) 41
right side = (2 + i + 3-4)(2+i - 3 + 4i) (by Difference of 2 squares)
= 5-3i)(-1 + 4i)
so as left side = right side
(5-3i)(x+yi)(4+5i) = 41 (5-3i)(-1+5i)
5-3i is common so:-
(x + iy)(4+5i) = 41(-1+5i)
4x +5xi + 4yi - 5y = -41 + 205i
4x - 5y + (5x + 4y)i = -41 + 205i
EQuating coefficients we are left with the system of equations
4x - 5y = -41
5x + 4y = 205
solving this gives x = 21 and y = 25
