Find the values of x and y in the diagram.

Answer:

A² = 9

Step-by-step explanation:

substitute A = - 3 into A² , that is

A² = (- 3)² = - 3 × - 3 = 9

Answers for different section are given below;

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

   f(x) = -x² - 4x + 6

1.    If we take -1 common from the given function, we get

                      f(x) = -1 (x² + 4x - 6)

                      f(x) = -1 (x² + 4x) + 6

      Thus, first block contains -1 and second block contains 4.

2.   Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².

                 f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6

                 f(x) = -1 ( x² + 4x + 2²) +4 + 6

Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.

3. Then we factorize the bracket and simplify outside the bracket;

                 f(x) = -1 (x + 2)² + 10

Thus, first block contains -1, second block contains 2 and third block contains 10.

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Answer:

48

Step-by-step explanation:

40% of 120

40  x     120   = 4800 / 100 = 48

100      

Answer:

A- 48

Step-by-step explanation:

You divide your percentage by 100. So, 40% would be 40 divided by 100 or . 40. Once you have the decimal version of your percentage, simply multiply it by the given number.

We will improve the argument by stating that two intersecting lines have vertically opposite angles equal in magnitude.

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Answer:

x = 4

Step-by-step explanation:

Given: 190x + 700 = 1,460

1. Subtract 700 from both sides:

190x + 700 - 700 = 1,460 - 700

190x = 760

2. Divide both sides by 190 to isolate x:

190x ÷ 190 = 760 ÷ 190

x = 4

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Answer:

b

Step-by-step explanation:

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Answer:

1. yes

2. No

Step-by-step explanation:

1. The triangles are congruent

2. It's not matching

If event A occurs, it does not necessarily mean that its complement will also occur. The occurrence of one event has no effect on the occurrence of its complement.

If two events are complementary, then we know that the sum of their probabilities is equal to 1.Regarding the rules of probability, the statement "If event A occurs, then its complement will also occur" is incorrect. Two events are said to be complementary if they are mutually exclusive and together they make up the entire sample space. This means that the probability of either event occurring is equal to the sum of their probabilities, which is equal to 1. So, if the probability of event A occurring is p(A), then the probability of its complement, denoted by A', occurring is 1 - p(A).

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The expected profit at node 0 (value of the game) is $1.50. The player can receive a maximum of $2.52 by drawing all four cards successfully, which occurs with a probability of 1/12. The player can lose a maximum of $0.50 by drawing a second card, which happens with a probability of 11/12.

Using backward induction, we start from the final node (node 12) and work our way back to node 0. At each node, we calculate the expected value of the game based on the probabilities of reaching the subsequent nodes. Node 12 represents drawing the 52-card, which has a value of $2.52. Node 7 represents drawing the 4-card, which is the desired outcome with a value between $0.50 and $2.52.

Moving back to node 8, the player has the option to stop or continue playing. If the player stops, the cash in hand is compared to the expected value calculated at node 7 ($0.50 to $2.52). If the player decides to continue, they move to node 3, where they can draw either the 2-card or the 4-card. Here, rational expectations come into play as the player evaluates the potential outcomes and compares them to the cash in hand.

Moving further back, node 4 represents drawing the 4-card, which has a value of $2.50. Node 5 represents drawing the 2-card, which has a value of $0.50. At node 1, the player can choose to stop or continue. If they stop, the cash in hand is compared to the expected value calculated at node 4 or node 5. Finally, at node 2, the player can draw either the 2-card or the 4-card.

Throughout the process, iterated expectations were used to calculate the probabilities of each path, considering the choices made at each node. Rational expectations were employed to compare the cash in hand to the expected values and make decisions accordingly. The maximum amount you would be willing to pay to play this game depends on your risk appetite and how much you value the potential profit.

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Answer:

First, here we must use the decimal notation for the percentages.

if we have a percentage x%, the decimal notation will be:

x%/100%.

Then for example, if x% = 90%.

the decimal notation will be:

90%/100% = 0.90

Data that we have:

90% order a meat entree, and 80% of these, order a drink.

So the percentage here that orders a drink is:

(0.9*0.8)*100% = 0.72*100% = 72%

10% order a vegetarian entree, and 40% of those order a drink, so the percentage here that orders a drink is:

0.1*0.4*100% = 0.04*100% = 4%.

Then the total percentage that orders drinks is 72% + 4% = 76%

76% of the customers that order an entree (meat or vegetarian) also order a drink.

We know that (A) odd integers represent the universal set.

So, we have:

Now, give logic as follows:

Therefore, we know that (A) odd integers represent the universal set.

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Answer:

C) \(n^3+4n^2+8n-16\)

Step-by-step explanation:

\(2n^3+4n^2-7+(-n^3)+8n-9=\\n^3+4n^2-7+8n-9=\\n^3+4n^2+8n-9-7=\\n^3+4n^2+8n-16\)

(Just combine like terms)

Only C) \(n^3+4n^2+8n-16\) fits our answer.

Answer:

\( {n}^{3} + 4 {n}^{2} + 8n - 16\)

Option C is the right option

Solution,

\(2 {n}^{3} + 4 {n}^{2} - 7 + ( - {n}^{3} + 8n - 9) \\ = 2 {n}^{3} + 4 {n}^{2} - 7 - {n}^{3} + 8n - 9 \\ \)

combine like terms

\(2 {n}^{3} - {n}^{3} + 4 {n}^{2} + 8n - 7 - 9 \\simplify \\ = {n}^{3} + 4 {n}^{2} + 8n - 16\)

hope this helps...

Good luck on your assignment..

The distance from Alain to Bernadette is approximately 245.9 meters. The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

To find the distance from Alain to Bernadette, we'll use the angle of depression and the given height of 300 m above the ground.

Step 1: Draw a horizontal line from Pierre to points A and B on the ground, and connect the points vertically. Now we have two right triangles.

Step 2: Calculate the distance from Pierre to Alain (PA) using the angle of depression of 40°.
tan(40°) = opposite/adjacent = 300/PA
PA = 300 / tan(40°) ≈ 358.4 m

Step 3: Calculate the distance from Pierre to Bernadette (PB) using the total angle of depression of 40° + 32° = 72°.
tan(72°) = opposite/adjacent = 300/PB
PB = 300 / tan(72°) ≈ 112.5 m

Step 4: Subtract the distance from Pierre to Alain (PA) from the distance from Pierre to Bernadette (PB) to find the distance from Alain to Bernadette (AB).
AB = PA - PB = 358.4 - 112.5 ≈ 245.9 m

The distance from Alain to Bernadette is approximately 245.9 meters.

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No, the method of equivalent pipes cannot be used to find a single hypothetical pipe that is equivalent to the pipe system of problem 3.12.6.

This is because the method of equivalent pipes is used to combine two or more pipes into one pipe to simplify a system. In problem 3.12.6, the given system already consists of only one pipe. Therefore, it is not possible to use the method of equivalent pipes to determine an equivalent pipe.The method of equivalent pipes is used to calculate the head losses for a system of pipes with multiple branches and junctions, using the Loss Coefficient Method and Hazen-Williams Equation. The method of equivalent pipes allows us to convert a complex pipe network into an equivalent pipe with a single diameter and length. However, this method cannot be used for a pipe system with no branches and junctions, such as the one in problem 3.12.6.

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Answer:

451/20

Step-by-step explanation:

22.55/1

To get rid of the decimal point in the numerator, you count the numbers after the decimal in 22.55, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on. Therefore, in this case you multiply the numerator and denominator by 100 to get the following fraction: 2255/100. Then you need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction. The GCD of 2255 and 100 is 5. When you divide the numerator and denominator by 5, we get the following: 451/20.

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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Answer: rise over run

Step-by-step explanation: i think the slope is 0/2

because 9-7=2 and 8-8=0. btw rise/run= y1-y2/x1-x2

which is 8-8/9-7=0/2

Answer:

x = 0.2

Step-by-step explanation:

-7.8x = -1.56

-1.56/-7.8 = 0.2

x = 0.2

Answer:

\(x =\frac{1}{5}\) or \(0.2\) (they're the same)

Step-by-step explanation:

Answer:

10584 inches of paper

Step-by-step explanation:

to find the surface area of a cone the formula you use is A= πr(r+h2+r2)  *you need to divide 16 by two to find the radius 16 is the diameter*

and this subsituted is π8(8+9(2)+8(2)) and this equals 504 inches and you then multiply by 21 to get enough paper to cover all 21 cones and that equals 10584 inches

The values of "a" and "b" that satisfy the equation are: a = -4 and b = 5

To find the values of "a" and "b" in the equation:

−3(2x² + ax + b) = −6x² + 12x − 15

Start by expanding and simplifying the left side of the equation:

−6x² - 3ax - 3b = −6x² + 12x − 15

Now, group the like terms:

(-6x²) + (-3ax) + (-3b) = (-6x²) + (12x) - 15

Comparing the coefficients of each degree term, we have:

-6x² = -6x² (coefficients of x² on both sides are the same)

-3ax = 12x (coefficients of x on both sides are the same)

-3b = -15 (constants on both sides are the same)

From the first equation, we can see that the coefficient of x² on both sides is -6. This means that the equation is satisfied for any value of "a" as long as the other equations are also satisfied.

From the second equation, equate the coefficients of x:

-3ax = 12x

This implies that -3a = 12, so we can solve for "a":

-3a = 12

a = -12/3

a = -4

Finally, from the third equation, solve for "b":

-3b = -15

Dividing both sides by -3:

b = (-15)/(-3)

b = 5

Therefore, the values of "a" and "b" that satisfy the equation are:

a = -4

b = 5

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Answer:

abe = ebc

Step-by-step explanation:

bcos both the seperate angels have the same degree

Answer:

H

Step-by-step explanation:

every "|" is equal to 0.1

so you count 5 points which will get you to H which is 0.5

Answer:

because the answer is 6.601 not 6.501

Step-by-step explanation:

you must have done the work wrong

The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207

finding the percentage of 65 of 330 individuals

65 / 330 * 100 = 19.697% = 0.19697

number of samples, n = 330

standard deviation, σ   is calculated from

= √{(p(1 - p)) / n}

= √{(0.197 * (1 - 19.7)) / 330}

= √{(0.197 * (0.803)) / 330}

= 0.022

Margin of error, E

= Z(0.95) * σ/√(n)

= 0.171 * 0.022/√(330)

= 0.171 * √(0.022²/330)

= 0.000207

= 0.021%

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The perimeter of a rectangle is the sum of all sides of the rectangle. Then the width of the city block is 100 units.

Given,

Bijan will cover the neighborhood block 20 times and runs a total of 8 miles.

Now,

Perimeter of rectangle,

Perimeter of rectangle = 2 (Length + Width)

Length = 3/20

Width = w

To find the width of a city block,

So for one time he runs will be,

= 8/20 = 0.4

Perimeter = 0.4 mile

Then width will be,

Perimeter of rectangle = 2 (Length + Width)

0.4 = 2(3/20 + w)

w = 0.05

Then the width of a city block will be

width = 1/w = 20

width = 20 units

Thus, the width of the city block is 20 units.

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The function represents the height of the plant in centimetres after n days, so n cannot be negative.

Part A:

To find a reasonable domain to plot the growth function, we need to consider the practical limitations of the growth of the plant. Also, since the function represents the growth of a particular species of plant, there may be an upper limit to how many days the plant can grow.

Assuming that the plant is not a perennial plant and has a limited lifespan, we can choose a reasonable domain for the function as [0, t], where t is the expected lifespan of the plant in days.

Since we do not have information about the expected lifespan of the plant, we can choose a reasonable value such as \(t = 365\)  (assuming it is an annual plant). So the domain for the function can be  \([0, 365]\)  .

Part B:

The y-intercept of the graph of the function f(n) represents the height of the plant when it was planted or started growing, that is, at n = 0. To find the y-intercept, we can substitute n = 0 in the equation:

\(f(0) = 15(1.02)^0 = 15\)

Therefore, the y-intercept of the graph of the function f(n) is \(15\) cm.

Part C:

The average rate of change of the function f(n) from n = 1 to n = 4 can be calculated using the formula:

average rate of change \(= [f(4) - f(1)] / (4 - 1)\)

Substituting the values in the equation, we get:

average rate of change \(= [15(1.02)^4 - 15(1.02)^1] / 3\)

average rate of change \(≈ 1.42 cm/day\)

Therefore, The average rate of change of the function f(n) from n = 1 to n = 4 represents the average daily growth rate of the plant during this period.

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Answer:

5/24

Step-by-step explanation:

Multiply across

2 x 3 = 5

3 x 8 = 24

Hope this helps, I really don't know any other way to explain it!

Answer:

Bond Price​= 1,892.73

Step-by-step explanation:

Giving the following information:

Par value= 1,600

Cuopon= 1,600*0.045= 72

YTM= 3.2%

Number of years (n)= 19

To calculate the price of the bond, we need to use the following formula:

Bond Price​= cupon*{[1 - (1+i)^-n] / i} + [face value/(1+i)^n]

Bond Price​= 72*{[1 - (1.032^-19)] / 0.032} + [1,600 / (1.032^19)]

Bond Price​= 1,013.29 + 879.44

Bond Price​= 1,892.73