Given v=5l+4j and w=6l-J, What is the angle between v and w? (Type your answer in degrees)

Tan(3/4 - \(\pi\) ) = 1, which is the ratio of a right triangle with a 45° angle's opposite side to its adjacent side. This is different from value of \(tan(3\pi /4)\), which is -1, it corresponds to a different angle.

The tangent of the angle 3/4 (or 135 degrees) is equal to -1 because \(tan(3/4)\)has a value of -1. The ratio of the opposite side to the adjacent side can be calculated by drawing a right triangle with an angle of 135 degrees.

To obtain the value of\(tan(3\pi /4 - \pi )\), we first need to simplify the phrase \(3\pi /4 - \pi\), which gives us\(\pi /4\) (or 45 degrees). Therefore, we need to find the tangent of the angle 45 degrees.

The ratio of the opposite side to the adjacent side of a right triangle with a 45-degree angle has the value of \(tan(45)\), which is equal to 1.

So, \(tan(3\pi /4 – \pi ) = tan(\pi /4) = 1.\)

In summary, the value of\(tan(3\pi/4 - \pi)\)) is equal to 1, which is the ratio of the opposite side to the adjacent side of a right triangle with an angle of 45 degrees. This is distinct from the value of \(tan(3\pi /4)\), which is -1, as it corresponds to a different angle.

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Answer:

b = 7

Step-by-step explanation:

We know that the three interior angles of a triangle add up to 180 degrees.

The missing angle is 45 degrees (since 180 = 45 + 45 + 90).  Since we have two angles equal opposite the sides of length 7 and b, we know that b = 7.

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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100 ml of the first solution and 200 ml of the second are required.

The t-statistic for testing H0: μ = 100 against Ha: μ < 100 with an SRS of 9 observations, X-hat = 98, and s = 3 is -2.

To calculate the t-statistic, follow these steps:

1. Determine the null hypothesis (H0) and alternative hypothesis (Ha): H0: μ = 100, Ha: μ < 100
2. Identify the sample size (n), sample mean (X-hat), and sample standard deviation (s): n = 9, X-hat = 98, s = 3
3. Calculate the standard error (SE): SE = s / √n = 3 / √9 = 1
4. Compute the t-statistic: t = (X-hat - μ) / SE = (98 - 100) / 1 = -2

The t-statistic of -2 indicates that the sample mean is 2 standard errors below the hypothesized population mean. This value helps you determine the significance of your test and whether to reject the null hypothesis.

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Answer:

QS=SR ( being PS median of triangle PQR,psㅗQR)

<QPS=<SPR (Median PS bisects the angle P)

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The height of the actual building, given the height of the model, can be found to be 1, 455 feet

The model is such that every inch of the building on the model is 75 feet of the actual building.

This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:

= Height of building in model x Scale factor per inch

= 19 ² / ₅  x 75

= 97 / 5 x 75

= 1, 455 feet

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15% of $30 is $4.50 because​ of the​ concept of pe​rce​ntage​ which is a chapter from mathematics.

Give​n: 15% of $30

Find: You need to find the 15% rate of $30.

Solution: A percentage can be defined as a number or ratio expressed as a fraction of 100. It is often denoted by the percent sign (%), but the abbreviation percent, percent, and in some cases percent is also used. Percentages are dimensionless numbers (pure). There are no units of measurement.

Example: If 25% of the total number of students in a class are male, 25 out of 100 are male. He has 500 students, 125 of whom are male.

So 15% of $30 = (15/100) x $30 = 0.15 x $30 = $4.50.

So using the percentage gives the answer  as $4.50.

 Therefore, percentages are very  useful in our daily life.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I hope this helped you out

Answer:

6x+3=5x-8

6x-5x= -8-3(match the like terms)

x= -11

Answer:

330 television set

Step-by-step explanation:

Last month production = 880 television sets

This month production = 1,210 television sets

The increase in production from last month to this month = This month production - Last month production

= 1,210 - 880

= 330

The increase in production from last month to this month = 330 television set

As per linear equation, the increase in production of television of the factory is 330.

A linear equation is an equation where the variable has the highest power of 1.

Given, a factory produced 880 television sets last month.

This month, the same factory produced 1,210 television sets.

Therefore, the increase in production of television of the factory is

\(= (1210-880)\\= 330\)

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Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.

If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.

Option A: (2, 1)

Substituting x = 2 and y = 1 into the equation, we get:

1 = 4 * 2 - 7

1 = 8 - 7

1 = 1

Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.

Option B: (4, 9)

Substituting x = 4 and y = 9 into the equation, we get:

9 = 4 * 4 - 7

9 = 16 - 7

9 = 9

Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.

Option C: Both (2, 10) and (4, 9)

Substituting x = 2 and y = 10 into the equation, we get:

10 = 4 * 2 - 7

10 = 8 - 7

10 = 3

Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.

So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).

Step-by-step explanation:

Answer:

30 Mins

Step-by-step explanation:

9 mins for 3 waffles is 3 mins per waffle. 9÷3=3

3 mins for each of 10 waffles is 30 mins. 3×10=30.

This is the simplified form of the expression.

2x^2 + 4x - 9y^2 - 4y

Simplifying:

3x^2 + 2y^2 - x^2 + 4x - 5y^2 - 4y

The process of simplifying an expression involves combining like terms and eliminating any unnecessary terms. In the given expression, we have multiple terms that have the same variable and exponent, these are called like terms. Like terms can be combined by adding or subtracting their coefficients.

In this case, we have 3x^2 and -x^2, the x^2 terms have the same exponent and variable so they can be added together by combining their coefficients (3-1) = 2x^2.

3x^2 - x^2 + 4x - 5y^2 - 4y + 2y^2

Similarly, we have -5y^2 and 2y^2, the y^2 terms have the same exponent and variable so they can be added together by combining their coefficients (-5+2) = -3y^2.

The x terms and y terms are separated and not interacting with each other, so we can't combine them. Finally, we have -4y and 4x, they are not like terms and can't be combined.

So, we have 2x^2 + 4x - 3y^2 - 4y as the simplified form of the expression.

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Answer:

62.8 cm²

Step-by-step explanation:

The formula for SA of a cylinder is:

\(SA=2\pi rh+2\pi r^{2}\)

with r being the radius and h being the height.

Let's substitute:

SA=2(2)(3)+22²

simplify

SA=26+24

SA=12+8

SA=20

SA=62.831

The surface area of this cylinder is 62.8 cm² (rounded to nearest tenth)

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Answer:

$37,396

Step-by-step explanation:

take 2388.5x4 since there are 4 weeks = $9554

then you subtrct since the portfolio fell.

So $46,950-9554 = $37,396

The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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Answer:

Area = 51 square units

Step-by-step explanation:

Area of the figure given in the attachment = Area of a parallelogram ABEF + Area of a rectangle BCDE

Area of the parallelogram = Base × Height

                                           = AB × GE

                                           = 4 × 3

                                           = 12 square unit

Area of rectangle BCDE = Length × Height

                                        = BC ×  CD

                                        = \((\sqrt{9^2+6^2})\times (\sqrt{2^2+3^2} )\) [By Pythagoras theorem]

                                        = (√117) × (√13)

                                        = √1521

                                        = 39 square units

Now total area of the figure = 12 + 39 = 51 units²

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Step-by-step explanation:

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Thank You!

Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor

The amount of radioactive dye remaining in your system after t minutes can be modeled as:

A(t) = 11 * (1/2)^(t/20)

where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.

A(t) = 11 * (1/2)^(t/20) = 2

Solving for t:

(1/2)^(t/20) = 2/11

Taking the natural logarithm of both sides:

(t/20) = ln(2/11) / ln(1/2)

Multiplying both sides by 20:

t = 20 * ln(2/11) / ln(1/2)

Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.

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The correct matches are =

Proxy voting- Allowing someone else to vote one's shares

Board of Directors- the committee that hires, evaluates and monitors the senior managers of the firm

Preemptive right- The right to firstly buy any additional shares that the firm may issue before they are sold to the public

Straight-line voting- each candidate for the board of directors is elected by a majority vote

Cumulative voting- board seats are awarded in proportion to the votes received.

Definitions =

Proxy voting = Proxy voting is when a shareholder delegates their voting rights to another person or entity, known as a proxy, to vote on their behalf. This can be done for various reasons, such as when a shareholder is unable to attend a meeting or wants to entrust their voting decisions to someone else. It does not directly relate to board seats being awarded in proportion to the votes received.

Board of Directors = The Board of Directors is a group of individuals elected or appointed to represent the shareholders and oversee the management of a company. They are responsible for making major decisions, setting company policies, and appointing senior executives. Each candidate for the board of directors is typically elected by a majority vote of the shareholders.

Preemptive right = Preemptive right, also known as the right of first refusal, is a privilege granted to existing shareholders of a company. It allows them to have the first opportunity to purchase additional shares before they are offered to the public. This right helps protect the ownership interests of existing shareholders by giving them the chance to maintain their proportional ownership in the company.

Straight-line voting = Straight-line voting is not a commonly used term in corporate governance. However, based on the given options, it seems to be referring to a voting system where each shareholder is entitled to one vote per share they own. This is the standard method of voting in most corporate elections, where each shareholder's voting power is directly proportional to their shareholding.

Cumulative voting = Cumulative voting is a voting method that allows shareholders to pool their votes and allocate them as they see fit among the candidates for the board of directors. It gives minority shareholders the opportunity to concentrate their votes on fewer candidates and increase their chances of electing a representative to the board. This mechanism helps to ensure a more proportional representation of shareholders on the board.

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The complete question =

Match the following concepts Group of answer choices

Proxy voting [ Choose ] board seats are awarded in proportion to the votes received.

Board of Directors [ Choose ] each candidate for the board of directors is elected by a majority vote

Preemptive right [ Choose ] The right to firstly buy any additional shares that the firm may issue before they are sold to the public

straight-line voting [ Choose ] the committee that hires, evaluates and monitors the senior managers of the firm

cumulative voting [ Choose ] Allowing someone else to vote one's shares

The equation of the circle with center (5,-8) containing the point (14,-17) is (x - 5)² + (y + 8)² = 162.

The general equation of a circle with center (h,k) and radius r is given by:

(x - h)² + (y - k)² = r²

Given that:  the center of the circle is (5, -8) and the circle contains the point (14, -17).

We can use these values to find the radius, r, and then substitute them into the equation of a circle to obtain the final answer.

The radius r is simply the distance between the center (5,-8) and the point (14,-17). We can use the distance formula to calculate it:

r = √[ (14 - 5)² + (-17 + 8)²]

r = √[ 81 + 81 ]

r = √162

r = 9√2

Now that we have the value of the radius, we can substitute it into the equation of a circle to obtain the final answer:

(x - 5)² + (y + 8) = (  9√2 )²

(x - 5)² + (y + 8)² = 162

Therefore, the equation of the circle is (x - 5)² + (y + 8)² = 162.

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To find the cost of one bottle of water, we need to divide the total cost of the case by the number of bottles in the case, which is 24.

So,

Cost of one bottle of water = Total cost of case / Number of bottles in case

= $2.99 / 24

= $0.1246

Rounding this to two decimal places, we get:

Cost of one bottle of water = $0.12

Therefore, one bottle of water costs $0.12.

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I'm going to assume the 2 shapes are both squares. ABCD has side of 4, BPQR has side of 5.

BP=5 AB=4 We can use Pythagorean theorem to see easily that AR= sqrt(5^2-4^2)=3.

Next step, we can see that angle A and angle D are both equal to 90 degrees. And angle DRS = <A+<ABR-<BRQ (exterior angles theorem) and <BRQ - <A= 90 degrees. Therefore...

triangle DRS is similar to triangle ABR so RD/SD=AB/AR=4/3

and RD=5-3=2 So SD is 3/2 because 2/ 3/2= 2*2/3 = 4/3 like above.

Now we can find shaded area by subtraction from square ABCD.

16-3*4/2-2*(3/2) /2=16-6-3/2=10-3/2=17/2.

I hope this answer helped if you have any question just ask in the comment!

Answer:

x=1

Step-by-step explanation:

First you distribute the 3 to 5x and 1 to get 15x+3=18x

Then you subtract 15x from 18x and get 3x

Lastly you divide 3 by 3 to separate the 3 and x and get x=1.

Answer:

x=30

Step-by-step explanation:

          3

Simplify   —

           5

 3          

 (— • x) -  18  = 0  

  5          

STEP

  Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         18     18 • 5

   18 =  ——  =  ——————

         1        5    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x - (18 • 5)     3x - 90

—————————————  =  ———————

      5              5  

Pull out like factors :

  3x - 90  =   3 • (x - 30)

 3 • (x - 30)

 ————————————  = 0  

      5      

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 3•(x-30)

 ———————— • 5 = 0 • 5

    5    

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  3  •  (x-30)  = 0

Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

  Solve  :    x-30 = 0  

Add  30  to both sides of the equation :  

                     x = 30

One solution was found :

x = 30

Answer:

58.17 seconds

Step-by-step explanation:

48.47 + 9.7 = 58.17

Answer:

38.77 seconds

Step-by-step explanation:

Given that,

Kim finished a race in 48.47 seconds.

This is 9.7 seconds faster than her practice time.

We need to find Kim's practice time.

Finished time =  9.7 + (practice time)

i.e.

Practice time = (Finished time-9.7)

= 48.47 - 9.7

= 38.77 seconds

Hence, the practice time is 38.77 seconds.

=======================================================

Work Shown:

A = old value = 360

B = new value = 270

C = percent change

C = (B-A)/A

C = (270-360)/360

C = -90/360

C = -0.25

C = -25%

The negative C value indicates we have a percent decrease.

Note how 25% of 360 = 0.25*360 = 90, meaning that the price has dropped by 90 galleons. And also note that 360-270 = 90 is that same figure of 90. This helps confirm the answer.

Answer: The answer is 10

Step-by-step explanation:

The centroid of any triangle has the following property:
The distance between the centroid and one of the extremities is two times longer than the distance between the opposite side.  
In this case AG = 20 should be twice the distance then GK.
If 20 is twice the distance then that distance that we are  searching for is:
20/2 = 10