- 12x +5y = 2 -3x+3y=-3

Tristan walked for 13 1/4 hours in May and June altogether. In May, he walked 6 4/6 hours. How many hours did he walk in June?

Triss [41]

The equation that you should use to solve this is (13 + 1/4) - (6 + 2/3) = 6 and 7/12

5 0

3 years ago

Factorize: x^2 + (a^2+1)/a x+1

In-s [12.5K]

This is what I get not sure if the problem on numerator is together if it is then . X^2+(a^2+1) x^2+a^2+1. -----------------= ----------------- AX+1. Ax+1 Answer: a^2+x^2+1 ---------------- AX+1 If I wrote the actual problem wrong let me know. This is what I understood.

5 0

3 years ago

Please please help me no links

Finger [1]

Given:

In triangle ABC, AB = AC, AD is angle bisector and measure of angle C is 49 degrees.

To find:

The value of x and y.

Solution:

In triangle ABC,

$AB=AC$ (Given)

So, triangle ABC is an isosceles triangle and by the definition of base angles the base angles of isosceles triangle are congruent.

In isosceles triangle ABC,

$\angle B\cong \angle C$

$m\angle B\cong m\angle C$

$m\angle B\cong 49^\circ$

The angle bisector of an isosceles triangle is the median and altitude of the triangle. So, the angle bisector is perpendicular to the base.

$m\angle ADB=90^\circ$

$x^\circ=90^\circ$

In triangle ABD,

$m\angle DAB+m\angle ABD+m\angle ADB=180^\circ$ [Angle sum property]

$y^\circ+49^\circ+x^\circ=180^\circ$

$y^\circ+49^\circ+90^\circ=180^\circ$

$y^\circ=180^\circ-49^\circ-90^\circ$

$y^\circ=41^\circ$

Therefore, the correct option is B.

3 0

3 years ago

Please Hurry! What is the solution to log2_(9x)-log2_3=3?

brilliants [131]

Answer:

$log_{2}(9x) - log_{2}(3) = 3 \\ 3 = log_{2}(8) or log_{2}( {2}^{3} ) \\ log_{2}( \frac{9x}{3} ) = log_{2}(8) \\ \frac{9x}{3} = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x = \frac{24}{9} \\ x = \frac{8}{3} \\ x = 2 \times \frac{2}{3}$

6 0

3 years ago

Read 2 more answers

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection.

This means that,

Probability that at least one of them needs replacement at the first inspection =

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago