If the 2/5 of a number exceeds 1/7 of the same number by 36 then the number is

Angle between v and w ≈ 40.04 degrees ,    Angle between v and w = 90 degrees  ,   Angle between v and w ≈ 27.98 degrees    and    Angle between v and w ≈ 39.24 degrees .



(a) To find the angle between vectors v and w, we can use the dot product formula: cos(theta) = (v · w) / (|v| |w|). Here, v = (2, 1, 3) and w = (6, 3, 9).

The dot product (v · w) = 2*6 + 1*3 + 3*9 = 6 + 3 + 27 = 36. The magnitudes are |v| = sqrt(2^2 + 1^2 + 3^2) = sqrt(14), and |w| = sqrt(6^2 + 3^2 + 9^2) = sqrt(126). Plugging these values into the formula, we get cos(theta) = 36 / (sqrt(14) * sqrt(126)).Taking the inverse cosine of this value, we find the angle theta ≈ 40.04 degrees.   (b) Using the same approach, v = (2, -3) and w = (3, 2). The dot product (v · w) = 2*3 + (-3)*2 = 6 - 6 = 0. The magnitudes are |v| = sqrt(2^2 + (-3)^2) = sqrt(13), and |w| = sqrt(3^2 + 2^2) = sqrt(13).

Plugging these values into the formula, we get cos(theta) = 0 / (sqrt(13) * sqrt(13)) = 0.The angle theta is 90 degrees since the cosine is 0.

(c) For v = (4, 1) and w = (3, 2), The dot product (v · w) = 4*3 + 1*2 = 12 + 2 = 14. The magnitudes are |v| = sqrt(4^2 + 1^2) = sqrt(17), and |w| = sqrt(3^2 + 2^2) = sqrt(13). Plugging these values into the formula, we get cos(theta) = 14 / (sqrt(17) * sqrt(13)).Taking the inverse cosine of this value, we find the angle theta ≈ 27.98 degrees.   (d) For v = (-2, 3, 1) and w = (1, 2, 4),

The dot product (v · w) = (-2)*1 + 3*2 + 1*4 = -2 + 6 + 4 = 8.The magnitudes are |v| = sqrt((-2)^2 + 3^2 + 1^2) = sqrt(14), and |w| = sqrt(1^2 + 2^2 + 4^2) = sqrt(21).Plugging these values into the formula, we get cos(theta) = 8 / (sqrt(14) * sqrt(21)).Taking the inverse cosine of this value, we find the angle theta ≈ 39.24 degrees.The scalar projection of v onto w can be calculated as s = |v| * cos(theta). The vector projection of v onto w can be calculated as P = (s/|w|) * w.



Therefore, Angle between v and w ≈ 40.04 degrees ,    Angle between v and w = 90 degrees  ,   Angle between v and w ≈ 27.98 degrees    and    Angle between v and w ≈ 39.24 degrees .

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The data set contains the variable height (giving a person's height) and the variable gender (coded O=female, 1=male). Then the y-intercept of the regression equation predicting height from gender is given by: option c) the average height of females in the data set.

The y- intercept of a direct retrogression relationship represents the value of one variable when the value of the other is zero. Non-linear retrogression models also live, but are far more complex. Retrogression analysis is a important tool for uncovering the associations between variables observed in data, but can not fluently indicate occasion. The data set contains the variable height (giving a person's height) and the variable gender (enciphered O = womanish, 1 = manly). also the y- intercept of the retrogression equation prognosticating height from gender is given by option c) the average height of ladies in the data set.

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Answer:

I believe the answer is A. 4

Step-by-step explanation:

if you make a table starting with $250 and + $25 every month when you get to the 4th month Josiah has only $325 and Katie has $335. I hope this helps.

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

a) To find the probability that the television set lasts between 4 and 6 years, we need to calculate the integral of the density function f(x) over the interval [4, 6]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, we have:

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

b) To find the probability that the television set lasts at least 5 years, we need to calculate the integral of the density function f(x) over the interval [5, ∞). However, since the density function is zero for x ≥ 3, the integral over this interval is zero.

c) To find the probability that the television set lasts less than 2 years, we need to calculate the integral of the density function f(x) over the interval [0, 2]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, the integral becomes:

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

d) To find the probability that the television set lasts exactly 4.18 years, we need to evaluate the density function f(x) at x = 4.18. Plugging in the value of x into the density function, we get f(4.18) = 18(4.18) - 3.

e) To find the expected value of the number of years that the television set lasts, we need to calculate the integral of xf(x) over the entire range of x, which is [0, ∞). The expected value is given by:

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

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Answer:

Average = 2000

Step-by-step explanation:

Given numbers are:

1,000 2,300 2,600

To find:

First round off the numbers to nearest 1000 and then find Average.

Solution:

1000 is already in thousands so no need to round off.

To round off a number to nearest thousand, we need check the digit on hundred's place.

So, 2300 will be rounded off as 2000.

and 2600 will be rounded off as 3000.

Now, the numbers whose average is to be calculated are 1000, 2000, 3000.

Formula for average is given as:

\(Average = \dfrac{\text{Sum of all numbers}}{\text{Count of numbers}}\)

applying the formula:

\(Average = \dfrac{1000+2000+3000}{3}\\\Rightarrow Average = \dfrac{6000}{3}\\\Rightarrow \bold{Average = 2000}\)

So, the average after rounding off to nearest 1000 is 2000.

Answer:

Step-by-step explanation:

S(60/100)=159

60S=15900

S=265

So there are 265 total students.

Answer:

y=-3x+10

Step-by-step explanation:

Since you know that the equation of the line is perpendicular to 1/3, you have to find the inverse of 1/3. You swap the denominator and numerator and make the number negative. In this case, it will be -3. Now that you know the slope is -3, you can use the equation y-y1=m(x-x1) where m is the slope. We know that the point (2,4) is in the graph so we can plug it into the equation. y-4=m(x-2). We know that the slope is -3 so we can plug it into the equation. y-4=-3(x-2). Simplify this to get y-4=-3x+6. Simplify this to get y=-3x+10. This means that the answer is y=-3x+10.

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Answer:

Step-by-step explanation:

9+0.75x

1 metre= $9.75

2 metre= $10.50

3 metre= $11.25

4 metre= $12

5 metre= $12.75

6 metre13.50

The standard form is given by(As highest degree is 2 we will take till degree 2 i.e quadratic)

So

#1

Multiply 4

Here

#2

Already in standard form

Answer:

\(\dfrac{5}{2}x^3-\dfrac{9}{4}x^2+\dfrac{7}{2}x-\dfrac{3}{2}\)

Step-by-step explanation:

The product of the two expressions is:

\(\left(\dfrac{1}{2}x-\dfrac{1}{4}\right)(5x^2-2x+6)\)

\(=\dfrac{1}{2}x(5x^2-2x+6)-\dfrac{1}{4}(5x^2-2x+6)\)

\(=\dfrac{5}{2}x^3-\dfrac{2}{2}x^2+\dfrac{6}{2}x-\dfrac{5}{4}x^2+\dfrac{2}{4}x-\dfrac{6}{4}\)

\(=\dfrac{5}{2}x^3-x^2-\dfrac{5}{4}x^2+3x+\dfrac{1}{2}x-\dfrac{3}{2}\)

\(=\dfrac{5}{2}x^3-\dfrac{9}{4}x^2+\dfrac{7}{2}x-\dfrac{3}{2}\)

Answer: To find the excluded value in the domain of the function, equate the denominator to zero and solve for x .

Step-by-step explanation:

For example, in the problem below The domain of the function is set of real numbers except −3 . The range of the function is same as the domain of the inverse function. So, to find the range define the inverse of the function.

Answer:

Y=16

Step-by-step explanation:

Becasue if you substitute 2 in for x, you get 8 times 2=16

Answer:

y=8 and

x=2

If x=2, then

8x=8*2=16

so therefore , y=8x i.e 16

y=16

SIMPLE AS THAT !!

Step-by-step explanation:

Answer:

=> 2x²-7x+5

=> 2x²-2x-5x+5

=>2x(x-1)-5(x-1)

______________

Hope it helps

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Answer:

Step-by-step explanation:

Production: 168,500 units.

Direct materials: 337,000 pounds.

Direct labor: Calculated based on units produced.

Factory overhead: Calculated based on direct labor hours.

1. Production Budget for the Third Quarter:

BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter

Budgeted sales units: 170,000

Add: Desired ending inventory units: 5,500

Total required units: 175,500

Less: Beginning inventory units: 7,000

Units to produce: 168,500

2. Direct Materials Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter

Units to produce: 168,500

Materials needed for production (pounds): 2 pounds per snowboard

Total materials required (pounds): 337,000 pounds

Materials to purchase (pounds): Total materials required - Beginning inventory pounds - Desired ending inventory pounds

3. Direct Labor Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter

Units to produce: 168,500

Direct labor hours needed: 0.5 hour per snowboard

Cost of direct labor: Direct labor hours needed * Direct labor rate

4. Factory Overhead Budget for the Third Quarter:

BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter

Direct labor hours needed: Calculated from the direct labor budget

Budgeted variable overhead: Direct labor hours needed * Variable overhead rate

Budgeted total factory overhead: Budgeted fixed overhead + Budgeted variable overhead

Note: The specific rates for direct materials, direct labor, and variable overhead were not provided in the given information and would need to be included in the calculations based on the company's specific cost structure.

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Answer: 400 meters per minute.

Formula to find average speed: total time / total distance

Total time taken is 2+4+1+3 which is 10 minutes.

Total distance traveled is 4 kilometers.

(Unitary method)

In 10 minutes Marco runs 4 kilometers.

In 1 minute Marco will run 4/10 (0.4)kilometers.

Now to convert 0.4 kilometers to meters,multiply it by 1000.

0.4 * 1000 is 400 meters

so the final answer is he will run 400 meters in 1 minute.

5% interest is accrued on the CD (Certificate of Deposit) (or represented as .05 since percent means out of 100).  And 2976.26 is the result after rounding to the closest 10. If the rate is 5% per quarter, we could simply redo the computation with n=1 and t=24.

A = 2000*(1+.05/4)(4*8)

A = 2,976.261017

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The Certificate of Deposit (CD) accrues interest at a rate of 5%. (or represented as .05 since percent means out of 100). And the outcome, rounded to the nearest 10, is 2976.26. We could just repeat the calculation with n=1 and t=24 if the rate is 5% per quarter.

The Certificate of Deposit (CD) accrues interest at a rate of 5%. (or represented as .05 since percent means out of 100).

The rate is assumed to be 5%, which is the average yearly bank rate. It is compounded quarterly (4 times a year) throughout the period of eight years (between the ages of 6 and 14), thus a total of 24 times will be added up.

The following is the compound interest formula: A is equal to P (1 + r/n)^nt. Where P is the primary amount ($2,000),

r is the rate (.05),

n is the number of times the period was compounded (4 times each year),

and t is the length of time (8 years).

Putting the values in formula, we get,

A = 2000*(1+.05/4)(4*8)

A = 2,976.261017

And 2976.26 is the result after rounding to the closest 10. If the rate is 5% per quarter, we could simply redo the computation with n=1 and t=24.

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3√3 is not equivalent to 9³/₄

3√3 is equivalent to   \(9^\frac34\)

step-by-step:

\(9^\frac34=(3^2)^\frac34=3^{2\cdot\frac34}=3^{\frac32}=3^{1+\frac12}=3^1\cdot3^\frac12=3\cdot\sqrt3=3\sqrt3\)

The simplest form of the number \(9^\frac{3}{4}\)   is  \(3 \ \sqrt[]{3}\).

It is given that the  \(9^\frac{3}{4}\)

It is required to find the simplest value of \(9^\frac{3}{4}\)

It is defined as the number if we multiply the number by itself we get the original number it is a non-negative number.

We have:

= \(9^\frac{3}{4}\)

We can write the above number as below:

\(= (3^2)^\frac{3}{4}\)

By the property of powers:

\(\rm (x^a)^b= x^a^\times ^b\) , we get:

\(3^2^\times^\frac{3}{4} \\\\\\3^\frac{3}{2} \\\\\sqrt{3^3} \\\\\sqrt{3}\times \sqrt{3}\times\sqrt{3}\\\\3\sqrt{3}\)

Thus, the simplest form of the number \(9^\frac{3}{4}\)   is  \(3 \ \sqrt[]{3}\).

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Step-by-step explanation:

3x-6+x+90°=180°

4x+84=180

4x=96°

x=96/4

x=24°

Answer:

If you want a to be greater than 2b, then take any number in the range of real numbers that is greater than 2 times. For example, a=4, 2b=1; a=5, 2b=4.

Step-by-step explanation:

Answer:

Hello!

When solving the equation \(|2x + 2| = 10\) , your answer would be...

\(x=4,-6\)

Step-by-step explanation:

Find all solutions for x by changing the absolute value into the positive and negative components

Hope this helps!!

Answer:43.2

Step-by-step explanation:

Answer:

Vjfxfffccvvvvvv bună ziua domnule profesor

Step-by-step explanation:

Hgvjhgxxgyjjbvccjkn Hugh bună bună bună bună bună bună bună bună ziua de Emilia Caldararu de la 1 februarie bună nu gytffhgyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy bună ziua okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk vhg

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

No, there is no commutative property of subtraction for rational numbers. The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers.

The commutative property states that the order of the operands does not affect the result of an operation. For addition and multiplication, the commutative property holds true. However, for subtraction, the order of the operands does matter, and thus, the commutative property does not apply.

Let's consider an example to demonstrate this:

Take the rational numbers 3/4 and 1/2.

If we subtract 3/4 from 1/2, we have: 1/2 - 3/4 = (2/4) - (3/4)

= -1/4.

If we subtract 1/2 from 3/4, we have: 3/4 - 1/2 = (3/4) - (2/4)

= 1/4.

As you can see, the results are different when the order of subtraction is changed, indicating that subtraction does not follow the commutative property for rational numbers.

The commutative property, which states that the order of operands does not affect the result of an operation, does not apply to subtraction for rational numbers. Changing the order of subtraction changes the result, making subtraction non-commutative for rational numbers.

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The commutative property does not apply to the operation of subtraction with rational numbers. This is because changing the order of the numbers in a subtraction operation will give a different result.

In mathematics, the commutative property refers to the idea that the order in which numbers are used in an operation does not change the result of that operation. This property holds true for addition and multiplication but, unfortunately, it does not hold true for subtraction and division. For example, in subtraction, if we take two rational numbers such as 5 and 3, 5 - 3 is equal to 2, but 3 - 5 equals to -2. As you can see, changing the order of the numbers gives us different results, demonstrating that there is no commutative property of subtraction for rational numbers.

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Answer: A and D

Step-by-step explanation: A and D are the only events in which only one type of object is used.

All the situations that are independent are B. Die is thrown and a coin is flipped, C. A die is thrown and the same die is thrown again and D. Two marbles are pulled from a deck (without replacement).

The Probability of an event can be calculated through chance formulation via absolutely dividing the favorable quantity of outcomes through the overall wide variety of possible effects.

Probability is the threat that something will show up, or how probable it is that an event will occur. when we toss a coin inside the air, we use the phrase possibility to refer to how likely it's miles that the coin will land with the heads aspect up.

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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||5u - 3v||² = 25||u||² - 30(u · v) + 9||v||²

To calculate ||5u - 3v||², we can use the properties of vector norms and dot products. Let's break it down step by step.

Step 1:

Start with the expression 5u - 3v. This means we are scaling vector u by a factor of 5 and vector v by a factor of -3, and then subtracting the two resulting vectors.

Step 2:

Next, we need to calculate the norm (or magnitude) of this resulting vector. The norm of a vector ||x|| is calculated as the square root of the dot product of the vector with itself, i.e., ||x|| = √(x · x).

Step 3:

Expanding ||5u - 3v||² using the properties of norms and dot products, we get:

||5u - 3v||² = (5u - 3v) · (5u - 3v)

            = (5u) · (5u) - (5u) · (3v) - (3v) · (5u) + (3v) · (3v)

            = 25(u · u) - 15(u · v) - 15(v · u) + 9(v · v)

            = 25||u||² - 30(u · v) + 9||v||²

In this final expression, ||u||² represents the squared norm of vector u, (u · v) represents the dot product of vectors u and v, and ||v||² represents the squared norm of vector v.

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(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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