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3 years ago

The graph of y=x^3 is transformed as shown in the graph below. With. Equation represents the transformed function

Mathematics

1 answer:

taurus [48]3 years ago

8 0

Answer: y' = (-x)^3 - 4

Step-by-step explanation:

The graph y = f(x) = x^3 passes trough the point (0,0)

because when x = 0

f(0) = y = 0^3 = 0

in the graph of the image, we can see that the graph intersects the y-axis in the point (0, -4)

This means that we have a vertical displacement of 4 units downwards.

When we have a graph y = f(x), a vertical translation of A units can be written as

y' = f(x) + A

If A is positive, the displacement is upwards, if A is negative, the displacement is downwards.

So if the displacement is of 4 units down, A = -4

We also have that when x is negative, the value of y is positive.

But in our original function, we have that for x = -1, y = (-1)^3 = -1

so in our original function, when x is negative also does y.

Then we also did a reflection around the y-axis, this means that we now evaluate the function in -x instead of x.

So the equation of the graph is:

y' = (-x)^3 - 4

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HELP!!!<br><br><br> -1/2(b-6)=5

notsponge [240]

Answer:

Step-by-step explanation:

5 0

3 years ago

A 1200 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pair

julia-pushkina [17]

Using it's concept, the range of the function is given as follows:

0 ≤ m ≤ 1200.

<h3>What is the range of a function?</h3>

The range of a function is the set that contains all possible output values for the function.

For this problem, we have to consider these two bullet points next, considering the mass is the output value of the function.

The smallest possible mass for the substance is of 0 grams, as after the substance decays to 0 grams, it will not assume a negative value, it will just disappear.

The greatest possible mass for the substance is the initial mass of 1200 grams, as the substance does not adquire mass with time, it just loses it.

Considering these masses, the range of the function is given as follows:

0 ≤ m ≤ 1200.

More can be learned about the range of a function at brainly.com/question/10197594

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3 0

1 year ago

Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 64% of vehi

ira [324]

Answer:

a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

b) 0.996 is the probability that more than half of the vehicles carry just one person.

Step-by-step explanation:

We are given the following information:

A) Binomial distribution

We treat vehicle on road with one passenger as a success.

P(success) = 64% = 0.64

Then the number of vehicles follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

$P(x \geq 6) = P(x =6) +...+ P(x = 10) \\= \binom{10}{6}(0.64)^6(1-0.64)^4 +...+ \binom{10}{10}(0.64)^{10}(1-0.79)^0\\=0.7291$

0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

B) By normal approximation

Sample size, n = 92

p = 0.64

$\mu = np = 92(0.64) = 58.88$

$\sigma = \sqrt{np(1-p)} = \sqrt{92(0.64)(1-0.64)} = 4.60$

We have to evaluate the probability that more than 47 cars carry just one person.

$P(x \geq 47)$

After continuity correction, we will evaluate

$P( x \geq 46.5) = P( z > \displaystyle\frac{46.5 - 58.88}{4.60}) = P(z > -2.6913)$

$= 1 - P(z \leq -2.6913)$

Calculation the value from standard normal z table, we have,

$P(x > 46.5) = 1 - 0.004 = 0.996 = 99.6\%$

0.996 is the probability that more than half out of 92 vehicles carry just one person.

5 0

3 years ago

Which established actor stared in The Godfather as Don Vito? a. Marlon Brando b. John Wayne c. Henry Fonda d. None of the above

Harman [31]

Answer:

a) Marlon Brando

Step-by-step explanation:

Don Vito Corleone was played by Marlon Brando in the film Godfather released in the year 1972 directed by Francis Ford Coppola based on the 1969 book by Mario Puzo. Paramount studios was against the casting of Marlon Brando but the director insisted on giving him a screen test. The screen test convinced the studio to cast him in the role.

5 0

3 years ago

Help<br><br> Answer <br><br> Help <br><br> Help

lana66690 [7]

Answer:

5x+5y=15

Step-by-step explanation:

6 0

3 years ago