Answer:
There are 6,296 children at the carnival
Step-by-step explanation:
The number of each group of people can be expressed as;
Number of boys (b)+number of adults (a)=7,052
b+a=7,052....equation 1
Number of girls (g)=Number of adults (a)-756
g=a-756....equation 2
But Number of girls (g)=number of boys (b)
Replacing the value of b in equation 1 with that of g in equation 2;
(a-756)+a=7,052
a+a=7,052+756
2 a=7,808
a=7,808/2
a=3,904
Replace the value of a in equation 2 with 3,904
g=3,904-756
g=3,148
But since g=b
g=b=3,148
b=3,148
Total number of children=Total number of boys (b)+total number of girls (g)
Total number of children=b+g
where;
b=3,148
g=3,148
replacing;
Total number of children=(3,148+3,148)=6,296
There are 6,296 children at the carnival
Answer:
1) 95% is the minimum
Step-by-step explanation:
If 5 tests were taken, and 100 pts each, and he received 77/100 on all 5 tests, then his grade would be 385/500 being 77%. Add another 100 pts to the denominator (for the last test) and 95 to the numerator, equaling 480/600, or 80%.
Answer: y=mx+b
Step-by-step explanation:
Answer:
x = 79°
Step-by-step explanation:
The arrows on the line segments indicate that the lines are <u>parallel</u>.
As the parallel line segments are the <u>same length</u>, the other pair of opposite line segments are also parallel and the same length. Therefore, we can apply the Alternate Interior Angles Theorem.
<u>Alternate Interior Angles Theorem</u>
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, the missing angle in the triangle including angle x is 28°.
Interior angles of a triangle sum to 180°
⇒ 73° + 28° + x = 180°
⇒ x = 180° - 73° - 28°
⇒ x = 79°
Answer:
1-i and -1+i
Step-by-step explanation:
We are to find the square roots of 
. First, convert from Cartesian to polar form:
Next, use the formula ![\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Br%7D%5Cbiggr%5B%5Ccis%5Cbiggr%28%5Cfrac%7B%5Ctheta%2B2%5Cpi%20k%7D%7Bn%7D%5Cbiggr%29%5Cbiggr%5D)
where 
to find the square roots:
<u>When k=1</u>
<u />![\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B2%5D%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%281%29%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D)
![\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%2B%5Cpi%5Cbiggr%29%5Cbiggr%5D)
<u>When k=0</u>
<u />![\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B2%5D%7B2%7D%5Cbiggr%5Bcis%5Cbiggr%28%5Cfrac%7B%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%280%29%7D%7B2%7D%5Cbiggr%29%5Cbiggr%5D)
Thus, the square roots of -2i are 1-i and -1+i
