13x = 15x - 8

What is the value of X?

Using continuity concepts, it is found that the function is left-continuous at x = 1.

-------------------------------

A function f(x) is said to be continuous at x = a if:

• If only , the function is left-continuous.

• If only , the function is right-continuous.

-------------------------------

The piece-wise definition of the function is:

We have to check the continuity at the points in which the definitions change, that is, x = 0 and x = 1.

-------------------------------

At x = 0:

• The definition at 0 is
• Approaching x = 0 from the left, we have values less than 0, thus:

• Approaching x = 0 from the right, we have values greater than 0, thus:

Since the limits are equal, and also equal to the definition at the point, the function is continuous at x = 0.

-------------------------------

At x = 1:

• The definition at 1 is

• Approaching x = 1 from the left, we have values less than 1, thus:

• Approaching x = 1 from the right, we have values greater than 1, thus:

To the right, the limit is different, thus, the function is only left continuous at x = 1.

A similar problem is given at brainly.com/question/21447009

Answer:

the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right , when

when x→a⁺ lim f(x)=f(a)

and from the left when

when x→a⁻ lim f(x)=f(a)

then since the functions presented are continuous , we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f(x)=lim  e^x = e^0 = 1

when x→0⁻ lim f(x)=lim  (x+4) = (0+4) = 4

then since f(0) = e^0=1 , the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f(x)=lim  (8-x) = (8-0) = 8

when x→1⁻ lim f(x)=lim e^x = e^1 = e

then since f(1) = e^1=e , the function is continuous from the left at x=1

Answer:

a. The rock's velocity is  and the acceleration is

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

• Velocity is defined as the rate of change of position or the rate of displacement.
• Acceleration is defined as the rate of change of velocity.

a.

The rock's velocity is the derivative of the height function

The rock's acceleration is the derivative of the velocity function

b. The rock will reach its highest point when the velocity becomes zero.

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height =

To find the time it reach half its maximum height, we need to solve

For a quadratic equation of the form the solutions are

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

The rock is aloft for 45 seconds.

The question is incomplete. Here is the complete question.

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 or 5 of them germinate. Do not round your intermiediate computations, and round your answer to three decimal places.

Answer: P(4<X<5) = 0.624

Step-by-step explanation: The probability of a seed germinate is a BinomialDistribution, i.e., a discrete probability distribution of the number of successes in a sequence of n independents experiments.

This distribution can be approximated to normal distribution by determining the values of mean and standard deviation population:

where

n is the sample quantity

p is proportion of successes

For the spinach seeds:

Mean is

5.85

Standard deviation is

1.431

Now, use

to convert into a standard normal distribution.

The probability we want is between 2 values: P(4<X<5).

Therefore, we have to convert those two values:

For X = 4:

z = -1.29

For X = 5:

z = -0.59

Using z-table:

P(X>4) = 1 - P(z< -1.29) = 0.9015

P(X<5) = P(z< -0.59) = 0.2776

The probability will be

P(4<X<5) = P(X>4) - P(X<5)

P(4<X<5) = 0.9015 - 0.2776

P(4<X<5) = 0.624

The probability of 4 or 5 seeds germinate is0.624.

Answer:

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Step-by-step explanation:

Given the data :

City A :

Reordered data:

0, 0.2, 0.2, 0.3, 0.4, 1, 1.3, 1.5, 2.5, 3

City B :

Reordered data:

0, 0, 0.1, 0.1, 0.2, 0.3, 0.4, 1, 1, 1

Using a calculator :

Mean Rainfall for City A = 1.04

Mean rainfall for city B = 0.41

Range : maximum - minimum

City A = 3 - 0 = 3

City B = 1 - 0 = 1

Mode (most occurring) :

City A = 0.2

City B = 1

Median :

City A = 0.7

City B = 0.25

The only true conclusion in the options given that can be drawn from the data is that ;During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Answer:

the Answer is C.

Step-by-step explanation:

I just took the test

Answer:

6 and 7

Step-by-step explanation:

I think you mean 'the sq rt of 48 lies between what 2 integers.'

The answer is 6 and 7.