A bag contains eight batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected without replacement.

Answer:

Lateral areas have ratio of 4:1

Volumes have ratio of 8:1

Step-by-step explanation:

There is a rule in 3D geometry that when two solids are similar, and their edges are in the ratio of [tex]a:b[/tex], the ratio of any surface area type measure is always [tex]a^2:b^2[/tex] this includes the lateral area, which is just a surface area minus the base, which is not important for this problem. The ratio of volumes of those similar solids is in the ratio of [tex]a^3:b^3\\[/tex].

Now, to solve this, we need to find the ratio of any corresponding length of these similar pyramids. We have both the heights, so if we form a ratio of [tex]\frac{5\frac{1}{2} }{2\frac{3}{4} }[/tex] which if you simplify it, it is [tex]\frac{5.5}{2.75}[/tex], which is [tex]2[/tex]. The ratio of the heights are [tex]2:1[/tex].

Now we can apply those rules to this ratio, the ratio of lateral areas would then be [tex]2^2:1^2[/tex], which is [tex]4:1[/tex]. the ratio of volumes would be [tex]2^3:1^3[/tex], which is [tex]8:1[/tex]

Answer:

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with a mean of 118 centimeters and a standard deviation of 8 centimeters.

This means that [tex]\mu = 118, \sigma = 8[/tex]

Sample of 16 shells

This means that [tex]n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

What is the probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

This is the pvalue of Z when X = 120 subtracted by the pvalue of Z when X = 116.

X = 120

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{120 - 118}{2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.841

X = 116

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{116 - 118}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.159

0.841 - 0.159 = 0.682

0.682 = 68.2% probability that the average length of these 16 shells will be between 116 and 120 centimeters when the machine is operating "properly".

Answer:

4 sq. un

Step-by-step explanation:

Answer:

it's a yes

Step-by-step explanation:

X/6 ≤ 30

to find the value of X we have to move the numerical to the other side

in this case the number is 1/6

X * 1/6 ≤ 30

so to balance the both side and get rid of the number on the left side we multiple with 6.

1/6*6 = 1 on the left side

30*6 = 180 on the right side

so the full equation will be

X * 1/6 * 6 ≤ 30 * 6

X * 1 ≤ 180

X ≤ 180

Answer:

Hello~

Llamalover here!

Skew lines are never parallel.

Skew lines are non-coplanar lines that do not intersect,

and parallel lines are coplanar lines that do intersect.

Step-by-step explanation:

I hope this helps!

Brainly?

In 3D geometry, diagonal lines are two lines that do not intersect and are not parallel. A simple example of a pair of diagonal lines is a pair of lines that pass through the opposite edge of a regular tetrahedron.

Some pairs of diagonal lines are also parallel. This is incorrect. By definition, diagonal lines are on different planes and parallel lines are on the same plane. The two lines can be diagonal or parallel (or both), but not both.

The position of the twist is two lines that do not intersect and are not parallel to each other. Diagonal lines can only exist in dimensions higher than 2D space. They do not have to be coplanar. That is, such lines are in different planes. In a two-dimensional space, two straight lines can intersect or run parallel to each other.

Learn more about skew lines here: https://brainly.com/question/2099645

#SPJ2

Answer:

i dont see the angles but heres how to solve for X

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's in the same order, from broker 1 down to broker 5. Straight up

Answer:
Broker E
|
V
Broker C
|
V
Broker D
|
V
Broker B
|
V
Broker A

Question

( 10 + 5x )7

Lets solve this easily.

So, basically, 10 + 5x is 15 but we still didn't

get rid of the x so therefore it's still 15x and then there's 7 so we multiply 15 x 7 giving us 105x.

Hence, the answer is.

(C), 70 + 35x is the answer.

Answer:

-5 degrees! If you did 20-25 it would get you -5! Hope this helps :)

Step-by-step explanation:

x = 95°

The angles are vertically opposite so they are equal.

Answer:

Around 5.5 or 5 1/2

Step-by-step explanation:

Answer:

y=-7x+9

Step-by-step explanation:

Answer:

F=(-1, -2)

G=(-3, -5)

H=(-3, -2)

Step-by-step explanation:

Answer:

your answer will be -1.2

Step-by-step explanation:

hope it helps you

have a great day

Answer:

Arc RP is 125 degrees, arc QS is also 125 degrees, and I think the ast one would be 110 degrees

Step-by-step explanation:

Answer:

X》55

Step-by-step explanation:

hope it helps u

have a great day!!

The number in question is 7.5

Step-by-step explanation:

15 ÷ 2 = 7.5

Why divide by 2? Because dividing by 2 is the inverse of multiplying by 2. To double-check our solution, just multiply 7.5 by 2... and 15!!

Answer:

equivalent

Step-by-step explanation:

when you divide the second one by 2 you'll get the first one

Answer:

86

Step-by-step explanation:

Answer:

(17-5)x

Step-by-step explanation:

the x next to the parenthesis means multiplication

Answer:

17 - 5s

Step-by-step explanation:

difference = minus sign

5 times = 5s

Answer:

t - 4 ≤ 4

Step-by-step explanation:

Hi I really need help with this

The number line represents t ≤ 8

Since the line is on 8 and moving towards the negative part of the number like (less than)

The equivalent equation will be;

t - 4 ≤ 4

Ads 4 to both sides

t-4+4≤4+4

t ≤ 8

Since the solution is similar to the expression above hence t - 4 ≤ 4 is correct

Answer:

x = 8.92 units

Step-by-step explanation:

From the triangle given in the picture,

Missing side of the triangle is the opposite side of the angle measuring 28°

And hypotenuse measuring 19 units has been given.

So, we will use sine ratio for the given angle.

sin(28°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

sin(28°) = [tex]\frac{x}{19}[/tex]

x = 19sin(28°)

x = 8.92 units

Answer:

The vertex is at [tex](0, -9)[/tex]

The axis of symmetry [tex]x = 0[/tex]

Step-by-step explanation:

Note: You can answer all the questions looking at the graph

We have the function [tex]f: \mathbb{R} \rightarrow\mathbb{R}[/tex](I am assuming this) such that [tex]f(x) = y = (x-3)(x+3)[/tex]

We note that

[tex](x-3)(x+3) = x^2-9[/tex] once we have a difference of squares

Therefore, we have a quadratic function.

So

[tex]y = x^2-9[/tex]

The vertex [tex](h, k)[/tex] is

[tex]h = \dfrac{-b}{2a} = \dfrac{-0}{2 \cdot 1} = 0[/tex]

[tex]k= h^2 - 9 = 0^2 - 9 =-9[/tex]

Therefore, the vertex is at [tex](0, -9)[/tex]

As we know the vertex, we conclude that the axis of symmetry [tex]x = 0[/tex]

The x-intercepts occur at [tex]y = 0[/tex]

[tex]y = (x-3)(x+3) \implies x = -3, x=3[/tex]

So, the left x-intercept is [tex](-3, 0)[/tex] and the right x-intercept is [tex](3, 0)[/tex]

As I stated in the beginning, the domain is the set of all real numbers. Precisely,

[tex]Dom(f) = \mathbb{R} = (-\infty, \infty)[/tex]  

Once, we know the vertex, we also conclude that the Range is

[tex]Ran(f)= [-9,\infty)[/tex]

Greater than or equal to -9

Answer:

with these number it is impossible to use the correct equation to solve this

I've already tried multiple times the best guess I can give you is B.

Answer:

B

Step-by-step explanation:

Becaus e that wahta is said

Answer:

Sample space is the collection of all possible events.

So, sample space of tossing two coins, S=(H,T),(T,T),(T,H),(H,H)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6 * 1/2 = 3

Answer:

None.

Step-by-step explanation:

let's check it

- 2a + 2a + 7 = 8

7≠ 8

So there's no solution for the given equation.