All categories

2 years ago

Fernando factored 45y^6 as (9y^3)(5y^3).

Mathematics

1 answer:

marishachu [46]2 years ago

4 0

Answer:

They both factored it correctly

Step-by-step explanation:

To find the one that was factored correctly, we expand the two of them and compare with $45y^6$ .

Fernando

$(9y^3)(5y^3)$

= $9 * 5 * y^3 * y^3$

= $45y^6$

Salma

$(3y)(15y^5)$

= $3 * 15 * y * y^5$

= $45y^6$

As we can see, they both factored it correctly.

You might be interested in

You need 20 pounds of grass seed to plant grass inside the baseball diamond below. About how many pounds of grass seed

taurus [48]

Answer:

13 pounds of grass.

Step-by-step explanation:

You need 20 pounds of grass seed to plant inside the baseball diamond.

The Baseball Diamond is a square of side = 90 ft

The Softball Diamond is a square of side = 60 ft

The ratio of the size of the Baseball Diamond to that of Softball Diamond is:

90: 60 = 3:2

If 3 represents 20 pounds, then 2 represents;

$\frac{2}{3}$ × 20 = 13.33333333 pounds = 13 pounds (rounded to nearest pound)

6 0

2 years ago

The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan^−1.(t/2), where t is measured in d

ira [324]

Answer:

1.21 g/day

Step-by-step explanation:

We are given that

The mass of a colony of bacteria (in (grams) is given by

$P(t)=2+5tan^{-1}(\frac{t}{2})$

Where t=Time(in days)

Differentiate w.r.t t

$P'(t)=5(\frac{1}{1+\frac{t^2}{4}}\times \frac{1}{2})$

By using the formula $\frac{d(tan^{-1}(x)}{dx}=\frac{1}{1+x^2}$

$P'(t)=\frac{5}{2}(\frac{4}{4+t^2})$

$P'(t)=\frac{10}{4+t^2}$

We are given P(t)=6

Substitute the value

$6=2+5tan^{-1}(\frac{t}{2})$

$5tan^{-1}(\frac{t}{2})=6-2=4$

$tan^}{-1}(\frac{t}{2})=\frac{4}{5}$

$\frac{t}{2}=tan(\frac{4}{5})$

$t=2tan(\frac{4}{5})$

Substitute the value of t

$P'(2tan\frac{4}{5})=\frac{10}{4+4tan^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{10}{4}\times \frac{1}{1+tan^2(\frac{4}{5})}$

We know that $1+tan^2\theta=sec^2\theta$

Using the formula

$P'(2tan(\frac{4}{5})=\frac{5}{2}\times \frac{1}{sec^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times cos^2(\frac{4}{5})$

By using $cos^2x=\frac{1}{sec^2x}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times (0.696)^2=1.21$ g/day

Hence,the instantaneous rate of change of the mass of the colony=1.21g/day

7 0

2 years ago

Read 2 more answers

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of

Gelneren [198K]

Answer:

$P(X < 24 )= 21.186\%$

$x = 19.78 \ months$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 26 \ months$

The standard deviation is $\sigma = 4 \ months$

Generally 2 year is equal to 24 months

Generally the percentage of total production will the company expect to replace is mathematically represented as

$P(X < 24 )= P(\frac{X - \mu }{ \sigma} < \frac{24 - 26}{4} )$

Generally $\frac{X - \mu}{\sigma } =Z (The \ standardized \ value \ of \ X )$

$P(X < 24 )= P(Z < -0.8 )$

Generally from the z-table

$P(Z < -0.8) = 0.21186$

$P(X < 24 )= 0.21186$

Converting to percentage

$P(X < 24 )= 0.21186 * 100$

=> $P(X < 24 )= 21.186\%$

Generally the duration that should be the guarantee period if Accrotime does not want to make refunds on more than 6% is mathematically evaluated as

$P(X < x) = P(\frac{X - \mu }{\sigma} < \frac{x - 26}{4} )= 0.06$

=> $P(X < x) = P(Z < \frac{x - 26}{4} )= 0.06$

From the normal distribution table the z-score for 0.06 at the lower tail is

$z = -1.555$

$\frac{x - 26}{4} = -1.555$

=> $x = 19.78 \ months$

6 0

2 years ago

In 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that

nirvana33 [79]

Answer:

There is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

Step-by-step explanation:

We have to answer the population proportion for Vermont.

We can only do it by a confidence interval, as we only have information from a sample.

This sample, of size n=100, has a proportion p=0.653.

The degrees of freedom are:

$df=n-1=100-1=99$

We will calculate a 95% confidence interval, which for df=99 has a critical value of t of t=1.984.

The margin of error can be calculated as:

$E=t*\sigma_p=t\sqrt{\dfrac{p(1-p)}{n}}=1.984\sqrt{\dfrac{0.653*0.347}{100}}\\\\\\E=1.984*\sqrt{0.00226}=1.984*0.0476=0.094$

Then, the upper and lower bounds of the confidence interval are:

$LL=p-E=0.653-0.094=0.559\\\\UL=p+E=0.653+0.094=0.747$

Then, we can say that there is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

7 0

2 years ago

Like charges repel and unlike charges attract. Coulomb’s law states that the force F of attraction or repulsion between two char

Artist 52 [7]

Step-by-step explanation:

The electrical force between two unlike charge is given by :

$F=\dfrac{kq_1q_2}{r^2}$