Which 3d vector in rectangular form below has the greatest magnitude?
(12,-14,13)
(17,2,11)
(15,12,-7)
(19,4,-8)

The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangle:

Area = 1/6 cm²

Length = 1.5 cm

Width = w

Now,

Area = length x width

Perimeter = 2 (length + width)

So,

1/6 = 1.5 x w

w = 1/(6 x 1.5)

w = 1/9 cm

And,

Perimeter.

= 2 (1.5 + 1/9)

= 2 x (13.5 + 1)/9

= 29/9

= 3.2 cm

Thus,

The width of the rectangle is 1/9 cm.

The perimeter of the rectangle is 3.2 cm.

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The nuts left with Pablo after using 840 g of nuts to make 7 packets is 392 g.

We are given that:

Pablo has

Cashew nuts = 638 g

Peanuts = 594 g

He now has mixed the nuts.

Total amount of nuts will be calculated by using addition.

Total amount of nuts = T = 638 g + 594 g

T = 1232 g

He has made a total of 7 packets and in each packet, he has put 120 g of nuts.

Total nuts used = 7 × 120 g = 840 g

Nuts left with Pablo = 1232 g - 840 g

Nuts left = 392 g

Therefore, we get that the nuts left with Pablo after using 840 g of nuts to make 7 packets is 392 g.

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Answer:

1/16

Step-by-step explanation:

2^-4 = 1/16 and 4^0 = 1

1/16 over 1 is just 1/16

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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So, we're going to simplify:

For this, we could sum the fractions in the numerator, and the denominator, first:

We could rewrite the previous fraction as:

And, finally:

Answer: $5400

Step-by-step explanation:

x =  amount raised so far

13500 - x = amt. still needed

x/3 = (13500 - x)/2

2x = 3(13500 - x)

2x = 40500 - 3x

5x = 40500

x = 40500/5 = 8100 (amt. raised so far)

13500 - 8100 = 5400 (amt. still needed)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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The value of expression after subtraction is, 2,226.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The expression is,

⇒ three hundred fifty - two thousand five hundred seventy-six

Now, We can write the expression as;

⇒ three hundred fifty - two thousand five hundred seventy-six

⇒ 350 - 2,576

After subtraction we get;

⇒ - 2,226

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Simply plug 3 into the equation.

\(f(3) = 3(3)^2+2(3) = 3(9) + 6 = 27 + 6 = 33\\\\\\f(3) = 33\)

Answer:

Step-by-step explanation:

Plugin x = 3 in the function

f(x) = 3x² + 2x

f(3) = 3*(3)² + 2*3               {3² = 3*3 = 9}

     = 3*9 + 6

     = 27 + 6

f(3) = 33

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer:

2048ft^3

Step-by-step explanation:

First, we find the radius. We get this by dividing the diameter by 2.

16 / 2 = 8

Then we solve the volume equation, using 3 for pi.

4/3 * 3 * 8^3

4/3 * 3 * 512

12/3 * 512

4 * 512 = 2048

Answer:

2048ft^3

Step-by-step explanation:

Answer:

(a) To find the probability that a household views television between 3 and 11 hours a day, we need to calculate the z-scores for 3 and 11 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 3 hours is (3 - 8.35) / 2.5 = -2.14 and the z-score for 11 hours is (11 - 8.35) / 2.5 = 1.06. Using a standard normal distribution table, we find that the probability of a z-score being between -2.14 and 1.06 is approximately 0.8209.

(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television viewing households, we need to find the z-score that corresponds to the top 3% of the standard normal distribution. Using a standard normal distribution table, we find that this z-score is approximately 1.88. Using the formula x = μ + zσ, we can calculate that a household must view television for approximately 8.35 + (1.88 * 2.5) = 12.75 hours to be in the top 3% of all television viewing households.

(c) To find the probability that a household views television more than 5 hours a day, we need to calculate the z-score for 5 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 5 hours is (5 - 8.35) / 2.5 = -1.34. Using a standard normal distribution table, we find that the probability of a z-score being greater than -1.34 is approximately 0.9099.

Answer:

Step-by-step explanation:

The mean daily viewing time of television is 8.35 hours and the standard deviation is 2.5 hours. We can use a normal probability distribution to answer the following questions about daily television viewing per household:

(a) The probability that a household views television between 3 and 11 hours a day is 0.9772 (rounded to four decimal places).

(b) To be in the top 3% of all television viewing households, a household must have 15.68 hours of television viewing per day (rounded to two decimal places).

The probability that a household views television more than 5 hours a day is 0.8944 (rounded to four decimal places).

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

the answer is D

Answer:

63 m/s

Step-by-step explanation:

h(3) = 3(3)² + 36(3) + 300 = 435

h(6) = 3(6)² + 36(6) + 300 = 624

v = Δh/Δt = (624m - 435m) / (6s - 3s) = 63 m/s

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer: 14%

Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.

- Lizzy ˚ʚ♡ɞ˚

The polynomial after simplification is obtained as \(5 x^{2}\) + 9x + 3.

What is simplification?

In mathematics, reducing an expression, fraction, or problem to a simpler form is referred to as simplification. With calculations and solution, the problem is made simple. Make something simpler by simplifying it.

We are given a polynomial as

5x - 5 + \(11 x^{2}\) + 4x - \(6 x^{2}\) + 8

Now, in order to simplify the given polynomial, we will combine the like terms of the polynomial.

On combining the like terms, we get

\(5 x^{2}\) + 9x + 3

Hence, the polynomial after simplification is obtained as \(5 x^{2}\) + 9x + 3.

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The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Fundamental Theorem of Arithmetic is not a method for solving a system of equations.

A system of equations is a collection of two or more equations with a same set of unknowns.

The system of equation can be solved using the following method.

The graphing involves using graph to find the intersection of the system of equation.

Substitution method involves substituting one variable to another.

Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations

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Answer:

\(P(x > 0.28) = 1\)

Step-by-step explanation:

Given

\(p = 33\%\) --- orders from first time customer

\(n =163\) --- samples

Required

\(P(x >0.28)\)

First, calculate the mean

\(\bar x = np\)

\(\bar x = 163 * 33\%\)

\(\bar x = 53.79\)

Next, the standard deviation

\(\sigma = \sqrt{\bar x * (1 - p)\)

\(\sigma = \sqrt{53.79* (1 - 33\%)\)

\(\sigma = \sqrt{53.79* (1 - 0.33)\)

\(\sigma = \sqrt{53.79* 0.67\)

\(\sigma = 6.00\)

For \(P(x >0.28)\),

The z score is:

\(z = \frac{x - \bar x}{\sigma}\)

\(z = \frac{0.28 - 53.79}{6}\)

\(z = \frac{-53.51}{6}\)

\(z = -8.92\)

So:

\(P(x > 0.28) = P(z > -8.92)\)

From z probability:

\(P(z > -8.92) =1\)

Hence:

\(P(x > 0.28) = 1\)

Answer:

the first easy assignment for aii the students

the first day of school is go in to be in a while

Step-by-step explanation:

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

400 litres

Step-by-step explanation:

It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

To find x using the sine rule, we need to solve the equation:

sine(45) / x = sine(30) / (2x + 2√3)

Simplifying this equation, we have:

(2x - 1) / x = 1 / (2x + 2√3)

Cross-multiplying and simplifying further, we get:

(2x - 1)(2x + 2√3) = x

Expanding the brackets, we have:

\(4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x\)

Rearranging the terms and simplifying, we get:

\(4x^2 - 3x - 2\sqrt3 = 0\)

Using the quadratic formula, we can solve for x:

x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))

x = (3 ± √(9 + 32√3)) / 8

Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

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Answer:

5.93

Step-by-step explanation:

\(Average= \frac{9+5/9+7+2/9+2+7/36+4+3/4}{4} = 5.930555\) or \(\frac{427}{72}\)

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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