5. in the figure below, $overline{ab}$ is congruent to $overline{bc}$, and $overline{ae}$ intersects…

5. in the figure below, $overline{ab}$ is congruent to $overline{bc}$, and $overline{ae}$ intersects $overline{bf}$ at $c$. what is the measure of $angle b$?\na. $14^{circ}$\nb. $38^{circ}$\nc. $76^{circ}$\nd. $104^{circ}$\ne. $142^{circ}$\n6. patty, carla, shada, and ling ran a race. the bar - graph below gives each girls running time, in seconds. how many of the girls ran the race in less time than the average of the 4 running times?\npatty 81\ncarla 84\nshada 62\nling 94\nf. 0\ng. 1\nh. 2\nj. 3\nk. 4\n7. between 9:00 a.m. and 10:20 a.m., 18,000 visitors entered the family fun amusement park. between 9:00 a.m. and 10:20 a.m., an average of how many visitors per minute entered the park?\na. 20\nb. 25\nc. 150\nd. 225\ne. 300\n8. given that $mathbf{u}$ and $mathbf{v}$ are vectors such that $mathbf{u}=(-1,3)$ and $mathbf{v}=(5,8)$, what is the component form of the vector $mathbf{u}+mathbf{v}$?\nf. $(2,13)$\ng. $(4,5)$\nh. $(4,11)$\nj. $(6,5)$\nk. $(6,11)$

5. in the figure below, $overline{ab}$ is congruent to $overline{bc}$, and $overline{ae}$ intersects $overline{bf}$ at $c$. what is the measure of $angle b$?\na. $14^{circ}$\nb. $38^{circ}$\nc. $76^{circ}$\nd. $104^{circ}$\ne. $142^{circ}$\n6. patty, carla, shada, and ling ran a race. the bar - graph below gives each girls running time, in seconds. how many of the girls ran the race in less time than the average of the 4 running times?\npatty 81\ncarla 84\nshada 62\nling 94\nf. 0\ng. 1\nh. 2\nj. 3\nk. 4\n7. between 9:00 a.m. and 10:20 a.m., 18,000 visitors entered the family fun amusement park. between 9:00 a.m. and 10:20 a.m., an average of how many visitors per minute entered the park?\na. 20\nb. 25\nc. 150\nd. 225\ne. 300\n8. given that $mathbf{u}$ and $mathbf{v}$ are vectors such that $mathbf{u}=(-1,3)$ and $mathbf{v}=(5,8)$, what is the component form of the vector $mathbf{u}+mathbf{v}$?\nf. $(2,13)$\ng. $(4,5)$\nh. $(4,11)$\nj. $(6,5)$\nk. $(6,11)$

Answer

5.

Explanation:

Step1: Identify vertical - angle

$\angle ACB$ and the given $38^{\circ}$ angle are vertical angles, so $\angle ACB = 38^{\circ}$.

Step2: Use isosceles - triangle property

Since $\overline{AB}\cong\overline{BC}$, $\triangle ABC$ is isosceles and $\angle A=\angle ACB = 38^{\circ}$.

Step3: Apply angle - sum property of a triangle

In $\triangle ABC$, we know that $\angle A+\angle B+\angle ACB = 180^{\circ}$. Substitute $\angle A = 38^{\circ}$ and $\angle ACB=38^{\circ}$ into the formula: $38^{\circ}+\angle B + 38^{\circ}=180^{\circ}$. Then $\angle B=180^{\circ}-38^{\circ}-38^{\circ}=104^{\circ}$.

Answer:

D. $104^{\circ}$

6.

Explanation:

Step1: Calculate the average running time

The sum of the running times is $81 + 84+62 + 94=321$ seconds. The average running time is $\frac{321}{4}=80.25$ seconds.

Step2: Count the number of girls with less - than - average time

Patty's time is 81 seconds ($81>80.25$), Carla's time is 84 seconds ($84>80.25$), Shada's time is 62 seconds ($62<80.25$), Ling's time is 94 seconds ($94>80.25$). So only 1 girl (Shada) ran the race in less time than the average.

Answer:

G. 1

7.

Explanation:

Step1: Calculate the time interval

From 9:00 a.m. to 10:20 a.m., the time interval is 80 minutes.

Step2: Calculate the average number of visitors per minute

The number of visitors is 18000. The average number of visitors per minute is $\frac{18000}{80}=225$.

Answer:

D. 225

8.

Explanation:

Step1: Add the components of the vectors

If $\mathbf{u}=(-1,3)$ and $\mathbf{v}=(5,8)$, then $\mathbf{u}+\mathbf{v}=(-1 + 5,3 + 8)$.

Step2: Simplify the components

$-1+5 = 4$ and $3 + 8=11$, so $\mathbf{u}+\mathbf{v}=(4,11)$.

Answer:

H. $(4,11)$