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2 years ago

An angle bisector always creates two acute angles. find a counterexample to show that the conjecture is false.

1 answer:

5 0

An acute angle is an angle that is less than 90°. An angle bisector is a ray drawn along an angle that bisects it into two equal and adjacent parts. Now, if the total angle is, say 270°, which is more than a half circle, it would result to two 135-degree angles. In this case, the angle is no longer acute, but obtuse.

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Ayuda es para mañana El estudiante 1 y el estudiante 2 están a 53 metros, uno del otro. El estudiante 1, desde su posición, ve u

hram777 [196]

Answer:

La opción correcta es;

Estudiante 2, ya que está aproximadamente a 32,39 metros de distancia

Step-by-step explanation:

Los parámetros dados son;

La distancia entre los dos estudiantes = 53 metros

El ángulo medido entre la línea del Estudiante 1 a la caja fuerte y el Estudiante 1 y el Estudiante 2 = 37 °

El ángulo medido entre la línea del Estudiante 2 a la caja fuerte y el Estudiante 2 y el Estudiante 1 = 43 °

Dado que los dos estudiantes y la caja fuerte forman los vértices de un triángulo, tenemos;

Sea θ el ángulo del triángulo opuesto a la distancia entre los dos estudiantes

Por lo tanto;

θ + 43 ° + 37 ° = 180 ° (teorema de suma de ángulos)

θ = 180 ° - (43 ° + 37 °) = 100 °

Por regla del seno, tenemos;

a / (sin (A) = b / sin (B)

Por lo tanto;

53 / (sin (100 °)) = b / (sin (37 °)) = c / (sin (43 °))

Lo que da;

b = (sin (37 °)) × 53 / (sin (100 °)) = 32,39 metros

c = (sin (43 grados)) × 53 / (sin (100 grados)) = 36,7 metros

Por lo tanto, el Estudiante 2 está más cerca, ya que está aproximadamente a 32,39 metros de distancia.

6 0

2 years ago

Margie divided 24 by 3

Levart [38]

Answer:

24 divided by 3 is 8

Step-by-step explanation:

3 goes into 24, 8 times

3 0

2 years ago

Read 2 more answers

Suppose that the Department of Transportation would like to test the hypothesis that the average age of cars on the road is less

dimulka [17.4K]

Answer:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

$z_{critc}= -1.64$

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

Step-by-step explanation:

Data given and notation

$\bar X=10.6$ represent the sample mean

$\sigma=4.1$ represent the population standard deviation

$n=45$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 12, the system of hypothesis would be:

Null hypothesis: $\mu \geq 12$

Alternative hypothesis: $\mu < 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

Critical value

For this case since w ehave a left tailed distribution we need to find a value who accumulates 0.05 of the area on th left in the normal standard distribution, and we can use the following excel code:

"=NORM.INV(0.05,0,1)"

$z_{critc}= -1.64$

Conclusion

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

3 0

2 years ago

You use index cards to play a homemade game. The object is to be the first to get rid on all your cards. How many cards are in y

pav-90 [236]

the number of cards in my friends stack is 20 total cards

3 0

2 years ago

Read 2 more answers

Betsy started a business 2 years ago. She had 8 customers in the first year. She added 18

Tatiana [17]

Answer:

Betsy isn't correct. Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Step-by-step explanation:

- Betsy started her business 2 years ago.

- In the first year, Betsy has 8 customers.

- In the second year, Betsy added 18 customers,

- So, her customers are now 8+18 = 26

- Betsy's goal is that in each of the next 4 years, she will have three times as many customers as the year before.

If the base number of customers is truly 26 this year,

Next year, Betsy would have 26 × 3 = 78 customers.

In 2 years, she would have 78 × 3 = 234

Thus indicating that in t years from now, the number of her customers will be

N(t) = N₀ × 3ᵗ

where

N(t) = number of customers t time from now

N₀ = number of customers at the moment = 26

t = number of years from now.

N(t) = 26 × 3ᵗ

In 4 years from now, Betsy will have

N(t=4) = 26 × 3⁴ = 2,106

So, it is evident that Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

Hope this Helps!!!

5 0

2 years ago