the red line below is perpendicular to which of the following

Answer:

#3:  12 + N

Step-by-step explanation:

Adding a number n to 12 results in "a number more than 12."

Thus, the correct answer is #3.

The solutions of the given trigonometric equation are 60°, 180°, and 300°.

What is a trigonometric equation?

A trigonometric equation is an equation that contains one or multiple trigonometric ratios of unknown angles.

The given trigonometric equation is:

cos (\(\frac{x}{2}\)) - sin (x) = 0

⇒ cos (\(\frac{x}{2}\)) - 2sin (\(\frac{x}{2}\)) cos (\(\frac{x}{2}\)) = 0

⇒ cos (\(\frac{x}{2}\)) [1 - 2sin (\(\frac{x}{2}\))] = 0

Therefore,  cos (\(\frac{x}{2}\)) = 0 = cos (90°)  (\(\frac{x}{2}\) can't be 270°)

⇒ x = 180°

Again,  [1 - 2sin (\(\frac{x}{2}\))] = 0

⇒ 2sin (\(\frac{x}{2}\)) = 1

⇒ sin (\(\frac{x}{2}\)) = 1/2

⇒ (\(\frac{x}{2}\)) = 30°, 150°

⇒ x = 60°, 300°

So, The solutions of the given trigonometric equation are 60°, 180°, and 300°.

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The cheapest price for ten (10) rolls would be = £25.50. That is option B.

The wallpapers are those designed paper materials that are used in decoration of a room.

The total number of wall paper that Salima needs to buy= 10 rolls.

A single roll of wallpaper = £9.20

A pack of 3 rolls= £25:50

That is 1 roll = X

make X the subject of formula;

£x = 25.50/3

£x = £8.5

A pack of 5 rolls = £43.05

That is 1 roll = X

make X the subject of formula;

£x = 43.05/3

£x = 14.35

Therefore, the cheapest price that can be used to buy 10 rolls would be = £25.50 because one roll would be = £8.5.

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Answer:

Pack of 3 rolls (total of £85.70

Step-by-step explanation:

25.5+25.5+25.5+9.20= £85.70

The remaining two angles of the given isosceles triangle is Option(C) 40°,70° .

For an isosceles triangle, the two sides of the triangle are congruent and equal in length . Also the angles subtending the adjacent equal sides of the isosceles triangle are of same measure.  

We also know that the sum of the three interior angles of any triangle is always equal to 180° .

In the options given, in Option(C) the angles measure 40° and 70° .

Thus as one angle of the isosceles triangle is given to be 70°, the other angle of its adjacent side is also 70° .

The sum of the interior angles of the triangle is equal to -

70° + 40° + 70° = 180° which satisfies the property.

Therefore, the remaining two angles of the given isosceles triangle is Option(C) 40°,70° .

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Answer:

The equation of the parabola will be:

Step-by-step explanation:

The vertex  (h, k)  is halfway between the directrix and focus.

Find the  x  coordinate of the vertex using the formula

x = (x-coordinate of focus + directrix)/2

 = (3-3)/2

 = 0/2

 =0

The  y -coordinate will be the same as the y-coordinate of the focus.

so the vertex will be: (0, 0)

Finding the distance from the focus to the vertex

The distance from the focus to the vertex and from the vertex to the directrix is |p|.

Subtract the  x  coordinate of the vertex from the x -coordinate of the focus to find  p .

\(p=3-0\)

\(p=3\)

Substitute in the known values for the variables into the equation

\(\left(y-k\right)^2=4p\left(x-h\right)\)

\(\left(y-0\right)^2=4\left(3\right)\left(x-0\right)\)

\(\:y^2=12x\)

Therefore, the equation of the parabola will be:

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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Answer:0

Step-by-step explanation: You decreased by 4 means subtracting 4 from it.

Hope this helps!

Answer:16

Step-by-step explanation:

subtract the old number by the new number

197-181=16

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Diagram

Step 02:

a.

Big Rectangle Area = s²

= 7 cm * 5 cm

= 35 cm²

Triangle Area = (b * h) / 2

= (3 cm * 4 cm) / 2

= 12 cm² / 2 = 6 cm²

probability = Triangle Area / Big Rectangle Area

= 6 cm² / 35 cm² = 6 / 35 = 0.171

b.

Small Rectangle Area = s²

= 2 cm * 2 cm

= 4 cm²

Shaded region Area = Big Rectangle Area - Triangle Area - Small Rectangle Area

Shaded region Area = 35 cm² - 6 cm² - 4 cm² = 25 cm²

probability = Shaded region Area / Big Rectangle Area

= 25 cm² / 35 cm² = 25 / 35 = 5 / 7 = 0.714

The answer is:

a. probability = 6 / 35 = 0.171

b. probability = 5 / 7 = 0.714

Answer:

7 children

Step-by-step explanation:

$505-$115= $390

$390÷$65= 6

6+1= 7

If two samples are selected from the same population, the two samples have exactly the same t statistics if the samples are same size and have the same variance and mean

The t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers

Hence, If two samples are selected from the same population, the two samples have exactly the same t statistics if the samples are same size and have the same variance and mean

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Answer:

A. 4

B. 8

C. 3

D. 7

E. 6

F. 2

G. 3

H. 5

Step-by-step explanation:

To find the total possible collective outcomes for the first two rounds, simply multiply the possible outcomes of each round: 2^16 * 2^8 = 2^(16+8) = 2^24 possible collective outcomes.

In the first round, there are 16 pairs playing against each other, resulting in 16 winners and 16 losers. In the second round, the 16 winners are paired up again, resulting in 8 winners and 8 losers.

So, there are a total of 16 x 8 = 128 possible collective outcomes for the first two rounds. Each outcome is determined by the combination of 16 winners and 16 losers in the first round, and then the combination of 8 winners and 8 losers in the second round.
In the first round of a knockout tournament involving 32 players, there are 16 pairs playing a game. Each pair has 2 possible outcomes: either player A wins or player B wins. So, there are 2^16 possible collective outcomes for the first round.

For the second round, there are now 16 winners, forming 8 pairs. Each pair still has 2 possible outcomes: either player A wins or player B wins. So, there are 2^8 possible collective outcomes for the second round.

To find the total possible collective outcomes for the first two rounds, simply multiply the possible outcomes of each round: 2^16 * 2^8 = 2^(16+8) = 2^24 possible collective outcomes.

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Secretariat won the Belmont Stakes by a record-breaking 31 lengths.

Secretariat's victory in the 1973 Belmont Stakes is considered one of the most remarkable performances in horse racing history. The legendary racehorse won by an astonishing 31 lengths, establishing a new record that still stands today.

Secretariat's dominant performance captivated audiences as he pulled away from the rest of the field and crossed the finish line in a time of 2 minutes and 24 seconds. This extraordinary margin of victory showcased Secretariat's exceptional speed, stamina, and sheer dominance, solidifying his status as one of the greatest racehorses of all time.

His record-breaking win in the Belmont Stakes remains a defining moment in the sport of horse racing.

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Answer:

= 0.1111111... = 0.1 (repeating)

Thus, 1 is the only repeating digit that  is repeating the infinite number of times

Step-by-step explanation:

Answer:

1 is repeating

Step-by-step explanation:

I need points

Based on the altitude function h(x)=-16x²+64x+80, the parabola opens down.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = -16x² + 64x + 80 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) represent the roots or zeros.

In conclusion, the vertex is given by the ordered pair (2, 144) and it has x-intercepts at (-1, 0) and (5, 0) as shown in the image attached below.

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Answer:

let first equation be  y=x^2-14x+23

second equation be y=-3x+5

now substitute the vale of y in equation second

y=-3x+5

x^2-14x+23=-3x+5

x^2-14x+3x=5-23

x^2-11x=-18

x^2-11x+18=0

x^2-(9+2)x+18=0

x^2-9x-2x+18=0

x(x-9)-2(x-9)=0

(x-2)(x-9)=0

either x-2=0                                        Or, x-9=0

x-2=0

x=0+2

x=2

x-9=0

x=0+9

x=9

therefore x=2,9

Step-by-step explanation:

-

Answer:

(2, - 1 ) and (9, - 22 )

Step-by-step explanation:

Given the 2 equations

y = x² - 14x + 23 → (1)

y = - 3x + 5 → (2)

Substitute y = x² - 14x + 23 into (2)

x² - 14x + 23 = - 3x + 5 ( subtract - 3x + 5 from both sides )

x² - 11x + 18 = 0 ← in standard form

(x - 2)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 9 = 0 ⇒ x = 9

Substitute these values into (2) for corresponding values of y

x = 2 : y = - 3(2) + 5 = - 6 + 5 = - 1 ⇒ (2, - 1 )

x = 9 : y = - 3(9) + 5 = - 27 + 5 = - 22 ⇒ (9, - 22 )

The vector sum of u and v, u + v, can be expressed in the form ⟨a, b⟩ as ⟨1, -8⟩.

To find the vector sum of u = ⟨3, -5⟩ and v = ⟨-2, -3⟩, we add the corresponding components:

u + v = ⟨3 + (-2), -5 + (-3)⟩

Simplifying each component:

u + v = ⟨1, -8⟩

Therefore, the vector sum of u and v, u + v, can be expressed in the form ⟨a, b⟩ as ⟨1, -8⟩.

This means that the resulting vector has an x-component of 1 and a y-component of -8. The vector ⟨1, -8⟩ represents the displacement obtained by starting at the origin, moving 1 unit in the positive x-direction, and then moving 8 units in the negative y-direction.

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Answer:

1/2

Step-by-step explanation:

Answer:

He cannot save $5 when he is buying something instead of making it himself.

Step-by-step explanation:

He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.

If he made is lunch, He would have had $10 dollars.

Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.

An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.

There are a few problems with Andrew's argument.

First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).

Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.

Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.

Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.

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For the spider man the discount is of rs600, for the doll the discount is of rs1,000.

We know that the price of the spider-man is rs3,000, and we apply a discount of the 20%.

So the amount of discount for that toy is the 20% of rs3,000, which gives:

(20%/100%)*rs3,000 = rs600

So the amount discounted for the spider-man is rs600.

For the case of the doll, we know that its cost is rs5,000, the amount discounted is:

(20%/100%)*rs5,000 = rs1,000

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Answer:

Step-by-step explanation:

same thing cant see

Answer:

314cm²

Step-by-step explanation:

Surface area(sphere) =4πr²

4 * 3.14 * (5²)

4 * 3.14 * 25

Hence, Surface area is 314sq.cm

A possible name for this type of chart is Scatter Chart. James scored the most at first glance.

James tried to make his results look impressive in his first graph by drawing the graph from right to left instead of left to right.

This is a schematic of a data set showing the relationships between variable quantities. So if you look closely at the chart from left to right, you can see that Jane is the clear winner. Because James' results are not good and continue to decline.

Pie charts can be used to display percentages of the whole, representing percentages at a particular point in time.

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The rate of return on the investment for selling short 1,100 shares of Wet scope, Inc. can be calculated as approximately -36.25%.

To calculate the rate of return, we need to consider the initial margin and the final proceeds from covering the short position. The initial margin of 60 percent means that you provided 60 percent of the total value as collateral to initiate the short sale. The remaining 40 percent was borrowed.

The initial investment for short 1,100 shares at $98 per share is:

Initial Investment = 1,100 shares * $98 * (1 - initial margin) = 1,100 * $98 * 0.4 = $43,120

One year later, the shares are covered at $88.50 per share. The final proceeds from covering the short position are:

Final Proceeds = 1,100 shares * $88.50 = $97,350

The dividends paid over the period amount to:

Dividends = 1,100 shares * $0.79 = $869

The net return on the investment is:

Net Return = Final Proceeds - Initial Investment + Dividends = $97,350 - $43,120 + $869 = $55,099

The rate of return is calculated by dividing the net return by the initial investment and multiplying by 100:

Rate of Return = (Net Return / Initial Investment) * 100 = ($55,099 / $43,120) * 100 ≈ -36.25%

Therefore, the rate of return on the investment for this short sale transaction is approximately -36.25%.

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In an MDP (Markov Decision Process), the following statements are true:

The optimal policy for a given state s is unique.

The problem of determining the value of a state is solved recursively by the value iteration algorithm.

The optimal policy for a given state in an MDP refers to the best course of action to take from that state in order to maximize expected rewards or outcomes. This policy is unique because, given a specific state, there is a single action or set of actions that yields the highest expected value.

The value iteration algorithm is a dynamic programming method used to determine the value of each state in an MDP. It starts with an initial estimate of the state values and then iteratively updates them until convergence. This recursive process involves considering the immediate rewards and expected future rewards obtained by transitioning from one state to another, following the optimal policy. Through this algorithm, the values of states are refined and converge to their optimal values.

The third statement, "V* (s) = 25, T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the value function V*(s) of each state in an MDP. It states that the value of a state is determined based on the transition probabilities T(s, a, s'), immediate rewards R(s, a, s'), discount factor y, and the value of the next state V*(s'). This equation allows us to compute the value of a state by considering the expected rewards and future values.

The fourth statement, "Q* (s, a) = ∑T (s, a, s') [R (s, a, s') + yV* (s')]," represents the equation for calculating the action-value function Q*(s, a) in an MDP. It calculates the expected value of taking action a in state s, considering the transition probabilities, immediate rewards, discount factor, and the value of the next state. However, the specific notation given in the statement, with "2,," is incomplete or incorrect, making it an invalid equation.

In summary, the optimal policy for a given state in an MDP is unique, and the value of each state is determined recursively using the value iteration algorithm. The value function V*(s) and the action-value function Q*(s, a) play key roles in evaluating the expected rewards and future values in an MDP.

Answer:

1.4 is the answer i think hope this helped

Answer:

225 inches

Step-by-step explanation:

15 x 15 = 225