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3 years ago

This cuboid is made from cm squares

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

3 0

Answer:

Step-by-step explanation:

Each signal unit cubes are 1 cm to each side

the dimensions of the large cube is 4 by 6 by 3 width height and depth

a) volume of the cube Vol = area of the base times height

area of the base = the width times the depth

Volume = Base Depth

= Width x Depth x Height

= 4 x 3 x 6

= 12 x 6

Vol = 72 cm ³

b ) the volume of the smaller cuboid has different dimensions

the smaller cube is 2 by 2 by 1 width height and depth

Volume = Base Depth

= Width x Depth x Heigh

= 2 x 2 x 1

Vol smaller cuboid = 4

How many smaller cubes can be made?

The obvious answer might be to straight up divide the large cube volume by the smaler cuboid volume. That might work IF all of the cuboid dimensions divide evenly into the cube dimensions.

Number of cuboid = Volume of the cube / Volume of the cuboid

= 72 / 4

= 18

Check this answer by dividing the dimension of the cube by the cuboid

4 by 6 by 3

2 by 2 by 1

(4/2) by (6/2) by (3/1)

2 by 3 by 3 = 2 x 3 x 3 = 18

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An honest die is rolled. If the roll comes out even (2, 4, or 6), you will win $1; if the roll comes out odd (1,3, or 5), you wi

jenyasd209 [6]

Answer:

(a) 50%

(b) 47.5%

Step-by-step explanation:

According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, $\mu=\frac{n}{2}$ and standard deviation, $\sigma=\frac{\sqrt{n}}{2}$ .

Here the number of tosses is, n = 2500.

Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.

The mean and standard deviation are:

$\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25$

(a)

To not lose any money the even rolls has to be 1250 or more.

Since, μ = 1250 it implies that the 50th percentile is also 1250.

Thus, the probability that by the end of the evening you will not have lost any money is 50%.

(b)

If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.

Then for number of "even rolls" as 1300,

1300 = 1250 + 2 × 25

= μ + 2σ

Then P (μ + 2σ) for a normally distributed data is 0.975.

⇒ 1300 is at the 97.5th percentile.

Then the area between 1250 and 1300 is:

Area = 97.5% - 50%

= 47.5%

Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.

(c)

To win $100 or more the number of even rolls has to at least 1300.

From part (b) we now 1300 is the 97.5th percentile.

Then the probability that you will win $100 or more is:

P (Win $100 or more) = 100% - 97.5%

= 2.5%.

Thus, the probability that you will win $100 or more is 2.5%.

7 0

3 years ago

Evaluate log(-13) Correct answer will get brainliest

Sedaia [141]

if given log(a)=b, where no base is stated, we assume base 10, or $log(a)=log_{10}(a)$

also, $log_a(b)=c$ translates to/can be written equivilently as $a^c=b$

therefore, given

$log(-13)=?$ where we want to find ?

assume base 10 and translate

$10^?=-13$

since we cannot raise a positive number to any real power and give a negative number, ? is not a real number and therefore, there are no real solutions

if we do want to find a solution, we can use Euler's idendity

$e^{\pi i}=-1$ where i is the complex number i=√-1 and e is euler's number

we can try to change bases to find the value of ?

$e^{\pi i}=-1$

$13e^{\pi i}=-13$

$13e^{\pi i}=10^?$

taking ln of both sides

$ln(13e^{\pi i})=ln(10^?)$

using log rules

$ln(13)+(\pi i)ln(e)=(?)ln(10)$

$ln(13)+\pi i=?ln(10)$

divie both side by ln(10)

$\frac{ln(13)+\pi i}{ln(10)}=?$

in a+bi form

$?=\frac{ln(13)}{ln(10)}+\frac{\pi}{ln(10)}i$

there are no real numbers that it evaluates to

however, it does evaluate to a complex number which is $\frac{ln(13)}{ln(10)}+\frac{\pi}{ln(10)}i$ or aproximately 1.11394+1.36438i

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3 years ago

A telescope is regularly priced at $180, but is on sale for 25% off. What is the price after the discount and 5% sales tax??????

sashaice [31]

100-25=75
100+5=105

180*0.75*1.05=141.75

final price is $141.75

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What is the mass of aluminum?

garik1379 [7]

Answer:

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Step-by-step explanation:

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Nataly_w [17]

Answer:

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