When a number is decreased by 40 %40% of itself, the result is 6060. what is the number?

madam [21]

From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is $4^{3}$ , and $y^{3}$ .

There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.

That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are $a^{3}$ and $b^{3}$ . The difference of those two cubes is:
$a^{3} - b^{3} = (a - b)( a^{2} + ab + b^{2})$

In our problem, a = 4 (since $a^{3}$ = 64) and b = y (since $b^{3} = y^{3}$ . Plug these values into the rule to find the factor of $64 - y^3$ :
$64 - y^3 \\
= (4 - y)( 4^{2} + 4y + y^{2}) \\
= (4 - y)( 16 + 4y + y^{2})$

-----

Answer: $(4 - y)( 16 + 4y + y^{2})$

8 0

3 years ago

A unit vector lies in the xy plane, at an angle of 137 degrees from the x axis, with a positive y component. What is the unit ve

Fed [463]

Answer: ( -0.731, 0.682)

Step-by-step explanation:

The unit vector is defined as a vector that points in the same direction as our vector (137 degrees from the x-axis) and has a magnitude of 1.

Knowing the angle, is really simple to do it.

First, we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R*cos(A)

y = R*sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

x = 1*cos(137°) = -0.731

y = 1*sin(137°) = 0.682

Then the unit vector is: ( -0.731, 0.682)

8 0

3 years ago

Please help me on thissss

cupoosta [38]

Answer:No its not a function

Step-by-step explanation:

8 0

2 years ago

According to the National Vital Statistics, full-term babies' birth weights are Normally distributed with a mean of 7.5 pounds a

Sav [38]

Answer:

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 7.5, \sigma = 1.1$

What is the probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

This is the pvalue of Z when X = 8.6 subtracted by the pvalue of Z when X = 6.4. So

X = 8.6

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.6 - 7.5}{1.1}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 6.4

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6.4 - 7.5}{1.1}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

6 0

3 years ago

A particular bacterium population is found to double the in 20 minutes. If a laboratory culture

insens350 [35]

The bacteria present at t=37 minutes is found to be 8.40, with no change in growth rate.

<h3>What does population growth exponentially mean?</h3>

When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

Given:

P = 340

It has been discovered that a specific bacterial population doubles in 20 minutes.

k = 2/20 = 0.1

t = 37 minutes

We know that,

P = P₀ $e^{kt}$

340 = P₀( $e^{0.1*37}$ )

340 =P₀(40.44)

P₀ = 8.40

As a result, the bacteria that will be present in t=37 minutes is found to be 8.40 with no change in growth rate.

Learn more about exponential growth here:

brainly.com/question/13223520

#SPJ9

4 0

1 year ago

When a number is decreased by 40 %40% of​ itself, the result is 6060. what is the​ number?

When a number is decreased by 40 %40% of itself, the result is 6060. what is the number?