Given the vector u with magnitude 2 and direction 90°, and vector v with
magnitude 6 and direction 215°, find the magnitude and direction of the sum
u + v. Write the sum u + v in magnitude and direction form with the magnitude
rounded to the nearest tenth and the direction rounded to the nearest degree.
Success! Now answer the math questions below the graph.
-10-9-8 2 -6-5
u=
V =
10
(0,2)
9
-3
4
-5
-*
4
-10
2
Determine the components of each vector to at least four
decimal places:
4
3
4
5 6 7 8 9 10

The surface area of the cone is 219. 33 cm²

The formula for calculating the surface area of a cone is expressed as;

SA = πr( r + l)

Such that the parameters are given as;

Note that the formula for diameter is given as;

Radius = d/2

Substitute the values

Radius = 11/2 = 5.5cm

Substitute the values, we get;

Surface area = 3.14 × 5.5 (5.5 + 7.2)

Now, multiply the values, we have;

Surface area = 17. 27(12.7)

multiply the values

Surface area = 219. 33 cm²

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Investors seeking to assess whether they should sell, hold, or purchase a particular stock should examine its past performance, the financial health of the company, and its valuation and growth prospects.

Historical Performance: Gauge the movements of the stock's worth compared to industry peers and current market indices. This will inform one on whether purchase positions have headed in an upward direction, dropped downwardly, or basically remained still.

Financial Health: Analyze the company's accounts in detail - balance sheet, income statement and cash flow statement for instance - so as to gain insight into the organization's fiscal wellbeing. Trends relating to net income, revenue flow, and debts need to be looked at ponderously.

Valuation & Dividend Rate: Determine if the stock is priced implicitly or explicitly when almost matched against connected companies and broader market returns through ratios such as Price-to-Earnings (P/E), Price-to-Sales (P/S) and Price-to-Book (P/B). Additionally, consider any dividend yields and related payout rates should the entity offer payouts. A generally high yield may prove attractive to investors in search of a passive income while continuing solvency indicates that dividends can be sustained or possibly upped.  

Growth Prospects: Assess the firm's potential for future expansion via product introductions, broadening objectives, and regional shifts within their marketplace. Organizations with tangible upsides to their development plans are more likely to witness escalating price points as time passes.

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The triangular prism have lateral area as 144 square units, total area as 216 square units, and volume equal to 432 cubic units.

The lateral area of a triangular prism is the total surface area of all the faces of the prism except for the top and bottom faces.

the slant side length is derived using Pythagoras rule as follows:

√(6² + 8²) = 10

area of vertical face = 6 × 9 = 54

area of slant face = 9 × 10 = 90

lateral area = 54 + 90 = 144 square units

area of bottom face = 8 × 9 = 72

total area = 72 + 144 = 216 square units

volume of prism = Area of base × height

volume of the prism = 72 square units × 6 units = 432 cubic units.

Therefore, the triangular prism have lateral area as 144 square units, total area as 216 square units, and volume equal to 432 cubic units.

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The exact values of θ are θ = π/6 and θ = 11π/6.

Given that;

The expression is,

⇒ 8 cos² θ + 2 = 8

Now, We ca simplify as;

⇒ 8 cos² θ + 2 = 8

Subtracting 2 from both sides:

8cos² θ = 6

Then we divide both sides by 8:

cos² θ = 3/4

Taking the square root of both sides, we get:

cos θ = ±√(3/4)

cos θ = ±(√3)/2

Since 0 ≤ θ < 2π,

And, we know that θ is in either the first or the fourth quadrant.

Hence, In the first quadrant, cos θ is positive, and in the fourth quadrant, cos θ is negative.

Therefore, we can eliminate the negative solution and conclude that:

cos θ = (√3)/2

Using the inverse cosine function, we find:

θ = π/6 or 11π/6

So, the exact values of θ are θ = π/6 and θ = 11π/6.

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Answer: The Probability that jay will be in chorus is 11/25.

Step-by-step explanation:

The total number of students who choose extracurricular activities is:

8 + 6 = 14

Therefore, the number of students who choose chorus is:

25 - 14 = 11

The probability that Jay will be in chorus is the number of students who choose chorus divided by the total number of students:

P(Jay is in chorus) = 11/25.

This fraction cannot be simplified any further, so the final answer is:

P(Jay is in chorus) = 11/25.

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Answer:

mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra

Step-by-step explanation:

formula :

a² - b² = ( a + b )(a - b )

To determine the interest rate required for Deepa to end up with $8,100 after continuously compounding an initial investment of $6,700 for 7 years, we insert the known values into the continuous compounding formulaand solve for the unknown rate. The required rate, to the nearest tenth of a percent, is approximately 2.7%.

The question is about using the formula for continuous compound interest, which is A=P*ert, where A is the amount of money accumulated after n years, including interest; P is the principal amount (the initial amount of money); e is the mathematical constant approximately equal to 2.71828; r is the annual interest rate (decimal); and t is the time the money is invested or borrowed for, in years.

We know that Deepa wants to invest $6,700 and leave it in an account for 7 years. This will be our P and t respectively. Deepa wants to end up with $8,100, which is our A. We need to find r, the interest rate. Plugging in the numbers, we get 8100=6700*e7r. To solve for r, we first divide both sides by 6700, getting e7r=1.208955. If we take the natural logarithm of both sides, we get 7r = ln(1.208955) or r = ln(1.208955)/7.

To get r approximately equal to the nearest tenth of a percent, calculate the right-side expression to obtain r ≈ 0.027 or 2.7%.

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Answer:

8.2296 meters of fabics to make drapes.

Answer:

Therefore, the mass of the sample after six hours is approximately 339.8 grams to the nearest tenth gram.

Step-by-step explanation:

The decay of the radioactive substance can be modeled using the formula:

m(t) = m₀ * e^(-kt)

where:

m₀ = initial mass of the substance (595 grams)

t = time elapsed (6 hours)

k = decay constant (which we need to find)

m(t) = mass of the substance at time t (what we are looking for)

The relative rate of decay per hour is 11%, which means that the decay constant is:

k = ln(1 - 0.11) / 1 = -0.1178 per hour

where ln is the natural logarithm.

Substituting the given values into the formula, we get:

m(6) = 595 * e^(-0.1178 * 6) = 339.8 grams

Therefore, the mass of the sample after six hours is approximately 339.8 grams to the nearest tenth gram.

If Sirjan earned a commission of Rs 507000 at the rate of 6.5%, we can use the commission formula to find the selling price of the house. The selling price of the house is Rs 7800000.

We can use the formula for calculating commission to find the selling price of the house

commission = (rate/100) x selling price

where rate is the commission rate, and selling price is the price of the house.

We know that the commission earned by Sirjan was Rs 507000, and the commission rate was 6.5%. Substituting these values in the formula, we get

507000 = (6.5/100) x selling price

Multiplying both sides by 100/6.5, we get

selling price = (507000 x 100)/6.5

Simplifying this expression, we get

selling price = 7800000

Therefore, the selling price of the house was Rs 7800000.

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Answer:

5/1÷3 is = to 5/3

Step-by-step explanation:

I hope this helps

Answer:

7.9

Step-by-step explanation:

the formula for circumfrence

The complete table is as shown below

x         y

-2       -4

-1       -2

0        0

1        2

2       4

The similarity between y = 2x and y = x is that they are proportional relationship

The difference between y = 2x and y = x is that they are have different slopes

In mathematics, a proportional relationship is a type of relationship between two quantities where their ratio always remains the same.

How to fill the table

for x = -2, y = 2 * -2 = -4

for x = -1, y = 2 * -2 = -2

for x = 0, we solve for A; y = 2 * 0 = 0

for x = 1, y = 2 * 1 = 2

for x = 2, we solve for B; y = 2 * 2 = 4

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Answer: Area = 21/48 square feet

Step-by-step explanation:

To find the area of the tablet, we need to multiply its length and width.

Length = 3/4 foot

Width = 7/12 foot

Area = Length x Width

Area = 3/4 foot x 7/12 foot

Area = (3/4) x (7/12)

Area = 21/48 square feet

Therefore, the area of the tablet is 21/48 square feet.

Answer:

40%

Step-by-step explanation:

We Know

A bag of cotton has 10 red marbles and 15 green marbles.

10 + 15 = 25 marbles total

If you can use Lexi marble from the bag without looking, what is the probability that she will pull out a red marble?

We Take

(10 ÷ 25) x 100 = 40%

So, the probably that she will pull out a red marble is 40%

The domain of the function on the graph include the following: A. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-2, ∞}

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

y = -5x + 17 .

Step-by-step explanation:

(y - y1) = m (x - x1). m=-5 , x1 =3 , y1 =2

(y - 2) = -5 (x -3) , y-2 = -5x + 15 , collect like terms and we have y = -5x + 17 which is in form of y = MX + c

The inequality x<4 matches the graph

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

As we observe the graph , it starts at 4 which has a dot which is open and the direction of arrow is left side

The left direct indicates that it is decreasing and open dot indicates the number 4 is not included.

So the inequality x<4 matches the graph

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Answer:

a. (f+g)(-3) means we need to add the two functions f and g, and then evaluate the sum at x=-3. So, we have:

(f+g)(-3) = f(-3) + g(-3) = [(-3)² - 3(-3)] + [2 - (-3)³]

= [9 + 9] + [2 + 27]

= 46

Therefore, (f+g)(-3) = 46.

b. (g-f)(1) means we need to subtract the function f from g, and then evaluate the difference at x=1. So, we have:

(g-f)(1) = g(1) - f(1) = [2 - 1³] - [(1)² - 3(1)]

= [2 - 1] - [1 - 3]

= 3

Therefore, (g-f)(1) = 3.

c. (f•g)(-2) means we need to multiply the two functions f and g, and then evaluate the product at x=-2. So, we have:

(f•g)(-2) = f(-2) • g(-2) = [(-2)² - 3(-2)] • [2 - (-2)³]

= [4 + 6] • [2 + 8]

= 100

Therefore, (f•g)(-2) = 100.

d. (g/f)(1) means we need to divide the function g by f, and then evaluate the quotient at x=1. So, we have:

(g/f)(1) = g(1) / f(1) = [2 - 1³] / [(1)² - 3(1)]

= [2 - 1] / [-2]

= -1/2

Therefore, (g/f)(1) = -1/2.

Step-by-step explanation:

use brain

Answer:

25%

Step-by-step explanation:

[tex]\frac{45}{180}[/tex]  x 100%

.25 x 100% = 25%

Helping in the name of Jesus.

The minimum angle of rotational symmetry for the prism is 180 degrees.

If a rectangular prism has an axis of symmetry via the middle of opposite aspects, then the prism has planes of symmetry perpendicular to each other.

Let's call the length, width, and height of the rectangular prism "l", "w", and "h", respectively. The axis of symmetry via the middle of opposite aspects divides the prism into two congruent halves, each with dimensions of l x w x h/2.

To determine the minimum angle of rotational symmetry for the prism, we need to find the smallest perspective at which the prism seems the same after a rotation round its axis of symmetry.

If we rotate the prism by using 180 ranges round this axis of symmetry, it's going to end up in the exact same position as it began, due to the fact each half of the prism is congruent to the other half of.

Consequently, the minimum angle of rotational symmetry for the prism is 180 degrees.

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1. The mean of this distribution is: 27.

2. The standard deviation is:  8.2.

3. The probability that a person will be born at the exact moment that week 42 begins is P(x = 42)= 0.019.

4. 0.308

5. 0.654

6. 1

7. 0.133

8. 0.753

Cumulative distribution is a statistical measure that shows the proportion of a population that falls below a certain point on a probability distribution. It is a function that gives the probability that a random variable X is less than or equal to x.

1. The mean of this distribution is:

The mean of the Uniform distribution is calculated by taking the average of the lower and upper bounds of the distribution (1 + 53) / 2 = 27.

2. The standard deviation is:

The standard deviation of a Uniform distribution is calculated by taking the square root of the variance, which is (b - a)² / 12, where b is the upper bound and a is the lower bound of the distribution. In this case, the standard deviation is √(53 - 1)² / 12 = 8.2

3. The probability that a person will be born at the exact moment that week 42 begins is P(x = 42)

The probability of a person being born at the exact moment that week 42 begins is given by the probability density function of a Uniform distribution, which is 1 / (b - a). In this case, P(x = 42) = 1 / (53 - 1) ≈ 0.019

4. The probability that a person will be born between weeks 15 and 22 is

The probability that a person will be born between weeks 15 and 22 is given by the cumulative distribution function of a Uniform distribution, which is (x - a) / (b - a).

In this case, P(15 < x < 22) = (22 - 15) / (53 - 1) ≈ 0.308

5. The probability that a person will be born after week 33 is P(x > 33) =

The probability that a person will be born after week 33 is given by the cumulative distribution function of a Uniform distribution, which is (x - a) / (b - a).

In this case, P(x > 33) = (53 - 33) / (53 - 1) ≈ 0.654

6. P(x > 15 | x < 19) =

The probability that a person will be born after week 15 and before week 19 is given by the conditional probability P(x > 15 | x < 19), which can be calculated by dividing the probability of the event occurring by the probability of the condition being true.

In this case, P(x > 15 | x < 19)

= (19 - 15) / (19 - 15)

= 1

7. Find the 8th percentile.

The 8th percentile is calculated by taking the cumulative distribution function of a Uniform distribution, which is (x - a) / (b - a).

In this case, the 8th percentile is (8 - 1) / (53 - 1) ≈ 0.133.

8. Find the minimum for the upper quartile.

The minimum for the upper quartile is found by taking the cumulative distribution function of a Uniform distribution, which is (x - a) / (b - a).

In this case, the minimum for the upper quartile is (40 - 1) / (53 - 1) ≈ 0.753.

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The solution of percentage problem is the new deferred tax liability of Teal Corporation after the enactment of the new tax law will be 50,760. This represents a decrease of 321,480 (372,240 - 50,760) from the previous deferred tax liability of 372,240

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%".

The increase in the tax rate from 22% to 25% will affect the deferred tax liability of Teal Corporation.

To calculate the new deferred tax liability, we need to recalculate the deferred tax liability using the new tax rate of 25%. We can use the following formula:

New deferred tax liability = Future taxable amounts x (New tax rate - Old tax rate)

New future taxable amounts = 1,692,000

New tax rate = 25%

Old tax rate = 22%

Therefore, the new deferred tax liability can be calculated as follows:

New deferred tax liability = 1,692,000 x (25% - 22%) = 50,760

Thus, the new deferred tax liability of Teal Corporation after the enactment of the new tax law will be 50,760. This represents a decrease of 321,480 (372,240 - 50,760) from the previous deferred tax liability of 372,240.

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A large box weighs 15.5 kilograms and a small box weighs 13 kilograms.

Let x = the weight of a large box in kilograms

Let y = the weight of a small box in kilograms.

Based on the parameters given in the question, we can write two equations out like this:8x + 3y = 163 ------ (1)2x + 5y = 96 ------- (2)

We can solve for x and y simultaneously using algebra.8x + 3y = 163 (multiply equation (1) by 2)8x + 20y = 384 (multiply equation (2) by 4)-17y = -221Solving for y, we get:y = 13

Now we can substitute this value of y into either of the two equations to find x.

Let's use equation (1):8x + 3y = 1638x + 3(13) = 1638x + 39 = 1638x = 124x = 15.5

Therefore, a large box weighs 15.5 kilograms and a small box weighs 13 kilograms.

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The zeros of the quadratic equation 10e²+69e = 0 are 0 and -6

The zeros of the quadratic polynomial are the x coordinates of the points where the graph of polynomial intersects the x -axis. They can also be called the root of quadratic equation.

A quadratic equation is an equation whose highest power of it's variable is 2.

10e²+60e = 0

10e( e+6) = 0

therefore;

10e = 0 or e+6 = 0

e = 0 or -6

therefore the zeros of the equation are 0 and -6.

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Answer:

[tex](-2.9)^{8}[/tex]

Step-by-step explanation:

[tex](-2.9)[/tex] · [tex](-2.9)^{7}[/tex]

We add the power of the two numbers. 1 + 7 = 8

So, the answer is [tex](-2.9)^{8}[/tex]

The roots of the given quadratic equation -2x² + 2x - 56 are 7 and 4.

Given quadratic equation =  -2x² + 2x - 56

To find out the roots of the above quadratic equation, we have to use the factorization method where we separate the equation into two multiples by equaling to the zero and find the roots as shown below:

-2x² + 2x - 56 = 0    

2x² - 2x + 56 = 0

Let's take 2 as common,

2(x² - x + 28 ) = 0

x² - x + 28 = 0     [ 2 becomes zero when we send it to RHS ]

28 = -7 x -4

x² - 7x -4x + 28 = 0

Now, take x and 4 as common.

x (x-7) - 4(x-7) = 0

(x-4) (x-7) = 0

x= 4 and x=7

From the above analysis, we can conclude that the roots of the given quadratic equation are 4 and 7.

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Given question is incomplete, the correct form of the question is "Obtain the roots by solving the following quadratic equation  -2x² + 2x - 56".

Answer:

Step-by-step explanation:

A triangle has a sum of angle measurements equal to 180 degrees.

For number 1, x is equal to 180-(82+49) = 49 degrees.

For number 2, 3x = 180, x = 60 degrees

For number 3, x = 180-(90+45) = 45 degrees

For number 4, x = 180-(60+30) = 90 degrees

For number 5, x = 180-(53+48) = 79 degrees

For number 6, x = 180-(110+41) = 29 degrees

For number 7, x = 180-(62+48) = 70 degrees

For number 8, x = 180-(80+24) = 76 degrees

For number 9, 180 - 120 = 2x, x = 30 degrees

For number 10, x = 180-(98+27) = 55 degrees