What is the perimeter of this figure?

The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.4 mg and standard deviation 0.1

a_sh-v [17]

Answer:

Step-by-step explanation:

For this case we can define the random variable of interest as: "The nicotine content in a single cigarette " and for this case we know the following parameters:

$\mu = 0.4, \sigma = 0.1$

And for this case we select a sample size of n =100 and we want to find the following probability:

$P(\bar X$

And for this case we can use the z score formula given by:

$z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$z= \frac{0.38-0.4}{\frac{0.1}{\sqrt{100}}}= -2$

And we can find the required probability with the normal standard table and we got:

$P(z$

8 0

3 years ago

I need help pls thank you

marissa [1.9K]

Answer:

x=22°, y=50°, z=108°

Step-by-step explanation:

x=22°(alternate angles are equal)

y=50°(angle sum in triangle is 180°)

z=108°

6 0

3 years ago

A certain math teachers likes to keep a box of prizes to distribute to students. The math teacher likes to keep at least twice a

Law Incorporation [45]

Option C

Math teacher would need to buy 130 prizes

Solution:

Given that,

Math teacher currently has 109 students and the box has 88 prizes in it

The math teacher likes to keep at least twice as many prizes in the box as she has students

So, she wants the number of prizes to be twice the number of students

Therefore,

number of prizes = 2 x 109 students

number of prizes = 2 x 109 = 218 prizes

The box has 88 prizes in it

Therefore, number of prizes she would need to buy is:

⇒ 218 - 88 = 130

Thus she would need to buy 130 prizes

3 0

3 years ago

) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick

Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

3 0

3 years ago

(05.08A)Triangle ABC is transformed to similar triangle A′B′C′ below:

Romashka-Z-Leto [24]

Answer:

1st option is correct i.e., 1 over 2

Step-by-step explanation:

Given that Triangle ABC transformed to Triangle A'B'C'.

Coordinated of Triangle ABC are A(2,6) , B(2,4) and C(4,4)

Coordinated of Triangle A'B'C' are A'(1,3), B'(1,2) and C'(2,2)

Scale factor of Dilation is the no. of times coordinates of vertices of a figure increase or decrease.i.e.,

if A(a,b) ⇒ A'(c,d)

where, a.k=c & b.k=d then k is scale factor of dilation.

Value of k is same for all vertices.

For coordinates of A & A' ,we have $2.k=1\implies k=\frac{1}{2} \:\: and \:\: 6.k=3\implies k=\frac{1}{2}$

For coordinates of B & B' ,we have $2.k=1\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}$

For coordinates of C & C' ,we have $4.k=2\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}$

Therefore, the scale factor of dilation is $\:\frac{1}{2}\:$ since in all cases $k=\frac{1}{2}$

1st option is correct i.e., 1 over 2

3 0

3 years ago