Please find the answer everything you need is in the photo

The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

9.02 B .......

Step-by-step explanation:

because I'm not really sure but that's an answer

Answer:

example of compound interest with solution

The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.

To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.

Given:

Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.

Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.

No information is provided about the defect rate of the third plant.

To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.

Let's calculate the overall probability:

Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)

Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)

To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:

Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)

Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)

Overall probability of selecting a defective MP3 player is given by:

Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)

Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%

Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.

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Answer:

NO solution, this statement is not true.

Step-by-step explanation:

Distribute

1.5x-12=3/2x-1.2

Combine Like terms

1.5x=3/2x+10.8

Combine like terms

0=10.8

NO solution! 0 is NOT equal to 10.8!

Answer:

The answer is c because if you multiply 3/5 and 3/10 by doing butterfligt

Answer:

i.24

Ii.48

Step-by-step explanation:

if Gokul gets 6 correct and each answer is 4 marks it becomes

4×6=24

and same for neena

12×4=48

Answer:

Half

Step-by-step explanation:

by dividing in half, it shows both sides are equal/symmetric

hope this helps:)

Answer:

\(\huge\boxed{\textbf{Two\ identical\ halves}}\)

Step-by-step explanation:

Symmetry:

Line of symmetry:

\(\rule[225]{225}{2}\)

The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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For the matrix

the determinant using the method of expansion by minors, expanding on the third row is:

Answer:

First, we compute the determinants of the minors:

Therefore:

The amount of mango juice you need is 8 litres

From the question, we have the following parameters that can be used in our computation:

Orange juice = 3 parts

Mango juice = 6 parts

When these parameters are represented as ratio, we have the following expression

Ratio = Orange : Mango

This is then represented as

Orange : Mango = 3 : 6

When the litres of orange juice is 4, we have

4: Mango = 3 : 6

Express as fraction

Mango/4 = 6/3

Multiply through by 4

Mango = 4 * 6/3

Evaluate

Mango = 8

Hence, the mango juice is 8 litres

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When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Answer:

Go to an online grapher called desmos . com where you can graph and get the answer! The website is used in khan academy

Step-by-step explanation:

Answer:

37/24

Step-by-step explanation:

You have to find the common denominator.

Answer:

2 ( -2 ) -8 = -12

3 ( -3 ) -18 = -27

Step-by-step explanation:

Answer:

(h°f)(n) = 32n - 9

Step-by-step explanation:

h(f(n)) = h(-8n+4)

h(-8n+4) = -4(-8n+4) + 7

h(-8n+4) = 32n - 9

(h°f)(n) = 32n - 9

The restrictions on the width is that it must be between 14.1 yards and 17.3 yards

From the question, we have the following parameters that can be used in our computation:

Area = between 240 yd² and 360 yd²

Also, we have

Length = 1.2 times the width

This means that

l = 1.2w

The area is then calculated as

Area = lw

So, we have

Area = 1.2w²

This means that

240 < 1.2w² < 360

Divide through by 1.2

200 < w² < 300

Take the square roots

14.14 < w < 17.32

Approximate

14.1 < w < 17.3

Hence, the width must be between 14.1 yards and 17.3 yards

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Answer:

50 yards

Step-by-step explanation:

This is a 3-4-5 triangle. You can use this shortcut to find the hypotenuse. (Multiply the3, 4, 5 by 10) OR

You could also use Pythagorean Theorem.

30^2 + 40^2 = h^2

900+1600=h^2

2500 = h^2

Squareroot.

50 = h

Answer:

9: tens place

4: tenths place

Step-by-step explanation:

HCF of the algebraic terms 3xy and 4x = x

Answer:

x

Step-by-step explanation:

HCF of the algebraic terms 3xy and 4x is x because x is common in both the terms.

Answer:

Step-by-step explanation:

7 - (6x + 3)

7 - 6x - 3 = 4 - 6x

The simplified Stirling's approximation of the expression is  Ω ≈ (Ne/N↓)^N ↓ ​  

Stirling's approximation is a method to approximate factorials of large numbers. It is given by the formula:

n! ≈ (√2πn) (n/e)ⁿ, where e is the mathematical constant approximately equal to 2.71828.

The two-state paramagnet has N spins, each of which can be either up or down. The number of possible arrangements of the N spins is 2ⁿ. However, we need to account for the fact that the energy of the system is dependent on the number of spins in the up state.

Let M be the number of spins in the up state. The energy of the system is given by E = -μBM, where μB is the Bohr magneton, and B is the magnetic field. The multiplicity of the system is given by the number of ways we can arrange the N spins such that M spins are in the up state.

Using Stirling's approximation, we can approximate the factorials involved in the multiplicity expression as follows:

Ω = (N!/(M!(N-M)!)) ≈ \(((N/e)^N / ((M/e)^M ((N-M)/e)^{N-M}))^{1/2}\)

We can simplify this expression in the limit N↓​≪N, which means that the number of spins is much smaller than the total number of particles in the system. In this limit, we can make the approximation that (N-M) ≈ N.

Ω ≈ \(((N/e)^N / ((M/e)^M ((N-M)/e)^{N-M}))^{1/2}\)

Ω ≈ \(((N/e)^{N-M} / (M/e)^M)^{1/2}\)

Ω ≈ ((Ne/N↓​)^ⁿ↓​)

This is similar to the result obtained in Problem 2.17, which was for a system of N distinguishable particles distributed among g energy levels. In the limit where the number of particles in each energy level is much smaller than the total number of particles in the system, we obtain a similar formula for the multiplicity.

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