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miss Akunina [59]

4 years ago

11

Solve the equation:

le="(2x+1)(5x-3)-15x^{2} =14" alt="(2x+1)(5x-3)-15x^{2} =14" align="absmiddle" class="latex-formula">

2 answers:

andrey2020 [161]4 years ago

6 0

The answer to your question is x=.71

salantis [7]4 years ago

6 0

Answer:

x=.71

Step-by-step explanation:

You might be interested in

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

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

<em>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. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection = </em>

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

5 0

3 years ago

Assume that the function f is a one-to-one function, (a) f(8) = 9, find f ^ -1 (9)

Annette [7]

(a) since we are given that f(8) = 9, the inverse of 9 is simply 8. Therefore, f^-1(9) = 8.

(b) Again, f is the inverse of f^-1, therefore, you simply switch numbers, and you get that f(-3) = -7.

8 0

4 years ago

Can someone walk me through these? I need a better understanding. Or maybe just one of them so I can understand and do the rest

Olin [163]

Step-by-step explanation:

I'll do the first one as an example.

"What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5,1) that partitions the segment into a ratio of 3 to 2?"

Let's call the point we're trying to find P. Ratio of 3 to 2 means that the distance from K to P divided by the distance from P to L is 3/2.

KP / PL = 3 / 2

Which also means the horizontal distances and vertical distances between the points have a ratio of 3:2.

KxPx / PxLx = 3 / 2

KyPy / PyLy = 3 / 2

First, let's use the x coordinates:

(x − (-5)) / (5 − x) = 3 / 2

(x + 5) / (5 − x) = 3 / 2

2 (x + 5) = 3 (5 − x)

2x + 10 = 15 − 3x

5x = 5

x = 1

And now with the y coordinates:

(y − (-4)) / (1 − y) = 3 / 2

(y + 4) / (1 − y) = 3 / 2

2 (y + 4) = 3 (1 − y)

2y + 8 = 3 − 3y

5y = -5

y = -1

So the point P is at (1,-1).

4 0

4 years ago

There are 6 puppies in a litter. Each puppy eats ½ a cup of food three times a day. How many cups of food does the litter go thr

slamgirl [31]

Answer: 9 cups of food

Step-by-step explanation:

First find out the amount of food that one puppy eats per day.

Each puppy eats 0.5 cups of food three times a day which means that in total they eat:

= 0.5 * 3

= 1.5 cups of food.

There are 6 puppies in the litter so the total amount of food they eat is:

= 1.5 * 6 puppies

= 9 cups of food

7 0

3 years ago

What is the midline equation of the function g(x)=3\sin(2x-1)+4g(x)=3sin(2x−1)+4g, (, x, ), equals, 3, sine, (, 2, x, minus, 1,

Aleksandr-060686 [28]

Answer:

Required equation of midline is x=4.

Step-by-step explanation:

Given function is,

$g(x)=3\sin (2x-1)+4\hfill (1)$

In standerd form (1) can be written as,

$a\sin (bx+c)\pm d$

where,

|a|= amplitude.

b= vertical shift.

c= horizontal shift.

Midline is the line which runs between maximum and minimum value.

In this problem,

a=3, b=2, c=-1, d=4

So amplitude a=3 and graph is shifted 4 units in positive y-axis.

Therefore,

Maximum value = d + a = 4 + 3 = 7

Minumum value = d - a = 4 - 3 = 1

Midline will be centered of the region (7, 1) that is at 4.

Hence equation of midline is x=4.

3 0

3 years ago