Factor the expression r^2+19rs+90s^2

What is the surface area of a box that is 20.1 m long, 6.8 m wide and 7.4 m high?

blsea [12.9K]

Answer:

Surface area of the box is $=671.48m^2$

Step-by-step explanation:

The box is in the shape of a cuboid:

Surface area of the cuboid = 2(L*W+W*H+H*L)

Length(L)=20.1 m

Width(W)=6.8 m

Height(H)=7.4 m

Surface area:

$2((20.1*6.8)+(6.8*7.4)+(7.4*20.1))\\\\=2(136.68+50.32+148.74)\\\\=2(335.74)\\\\\=671.48m^2\\\\$

The surface area of the box is $=671.48m^2$

6 0

4 years ago

John and Annie have two distinguishable ponds. Initially, each of the ponds contains four ducks and five geese. John first picks

Sladkaya [172]

Answer: 4/9

Step-by-step explanation:

The probability that annie picks a duck Pt= the probability of picking a duck without accounting for the added one (Po)+ probability of picking the added bird and it's a duck(Pi)

Pt = Po+Pi

Since the total number of birds in the right pond is 10 after the addition of one by john

Po= 4/10

Pi= the of john adding a duck × the probability of annie picking the added bird

Pi= 4/9 × 1/10

Pi = 4/90

Pt= 4/10 + 4/90

Pt = (36+4)/90

Pt=40/90

Pt= 4/9

(This implies that the probability of picking a duck remain the same even after the addition of one bird from the left ponds because they both have equal proportions of duck and geese i.e the initial number of duck and geese in both right and left ponds are 4 and 5 respectively)

Thanks.

4 0

3 years ago

Solve each problem. Round to the nearest tenth if necessary. Use 3.14 for π. What is the radius of a circle with a circumference

KiRa [710]

Answer:

2.3

Step-by-step explanation:

First off, you start with the circumference formula which is 2(pi)r. Since we know our circumference, we can create the equation solving for r. so we have 15=2(pi)r. Now in order to solve for r, we need to transfer everything to the other side, meaning dividing by 2(pi). So 15/2(pi)=2(pi)r/2(pi). Since we are using 3.14 for pi, 3.14*2 is 6.28. 15/6.28 which is about 2.388 So the radius of the circle is 2.3 (rounded to the nearest tenth)

4 0

3 years ago

5x times 1509y what is the answer

alisha [4.7K]

Answer:

7545xy

Step-by-step explanation:

i hope this helps

5 0

3 years ago

In a random sample of 25 people, the mean commute time to work was 33.9 minutes and the standard deviation was 7.2 minutes. Ass

Phoenix [80]

Answer:

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=33.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.2 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,24)".And we see that $t_{\alpha/2}=1.32$

Now we have everything in order to replace into formula (1):

$33.9-1.32\frac{7.2}{\sqrt{25}}=31.999$

$33.9+1.32\frac{7.2}{\sqrt{25}}=35.801$

So on this case the 80% confidence interval would be given by (31.999;35.801)

And the margin of error is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}}$

And replacing we got:

$ME = 1.32\frac{7.2}{\sqrt{25}} =1.9008$

7 0

4 years ago