18
p.7 Central Angles and Inscribed Angles
#4 What is the measure, in degrees, of arc JKI ?
4) MJKI
80°
K
mJKI =
degrees

Answer:

16

Step-by-step explanation:

The duration of this bond is 6.5 years.

Duration is a measure of a bond's sensitivity to changes in interest rates. To calculate the duration of this bond, we need to consider the present value of the bond's cash flows and the timing of those cash flows. In this case, the bond has a face value of $1,000, a coupon rate of 10 percent, and annual coupon payments.

First, we calculate the present value of the bond's cash flows. Since the bond has a coupon rate of 10 percent, the annual coupon payment is $100 ($1,000 x 10%). The bond has a remaining maturity of seven years, so there will be seven coupon payments in total. We can calculate the present value of these cash flows using the formula for the present value of an ordinary annuity:

Present Value = Coupon Payment x [1 - (1 + interest rate)^(-number of periods)] / interest rate

Assuming an interest rate of r, we have:

Present Value = $100 x [1 - (1 + r)^(-7)] / r

Next, we need to find the yield to maturity (YTM) of the bond. YTM is the rate of return an investor would earn by holding the bond until maturity. Since the bond is currently selling for $1,104 in the market, we can set up the following equation:

$1,104 = Present Value + (Coupon Payment / (1 + r)^7)

By solving this equation for r, we can find the yield to maturity. Using a financial calculator or spreadsheet software, we can determine that the yield to maturity is approximately 7 percent.

Now, we can calculate the duration of the bond. The duration formula is the weighted average time until the bond's cash flows are received, where the weights are the present values of the cash flows. In this case, we have seven annual cash flows, so the duration can be calculated as follows:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (n x Present Value of Year n)] / Present Value of the Bond

Plugging in the values, we get:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (7 x Present Value of Year 7)] / Present Value of the Bond

Calculating the present values for each year using an interest rate of 7 percent, we find:

Present Value of Year 1 = $100 / (1 + 0.07)^1

Present Value of Year 2 = $100 / (1 + 0.07)^2

...

Present Value of Year 7 = $100 / (1 + 0.07)^7

After calculating the present values for each year and plugging them into the formula, we find that the duration of the bond is approximately 6.5 years.

Therefore, the correct answer is 6.5 years.

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Answer:

<PCH+<HCK=180-DEGREE BEING IN A STRAIGHT LINE.

3M+58+8M+155=180

11M=180-213

11M=-33

M=-3

SO,

<PCH

3M+58

=3*(-3)+58

=58-9

=49-DEGREE

Answer:

74°?

Step-by-step explanation:

180° = 7x+26

x = 22°

Answer:

0.005

Step-by-step explanation:

\(0.5 \% \: = \frac{0.5}{100} = 0.005\)

Answer:

F. (-4, oo)

Step-by-step explanation:

Start from the left side.

The arrow on the left side shows that the graph continues increasing forever as x decreases. Beginning at the highest value of y you see on the left side at point (-6, 5), as x increases, moving right along the x-axis, the y-values decrease. When you get to x = -4, y is at its lowest value which is 1.

Starting just to the right of x = -4, the y-values begin to increase from the lowest y-value of 1. The arrowhead at the right side top shows that the curve continues increasing forever to infinity.

The values of x for which y increases are all values greater than -4 and all the way to positive infinity.

This function is increasing for x > -4.

Now we need to write x > -4 in interval notation.

In interval notation, use a curved parenthesis to mean a number that is not included. The interval starts at -4, so it starts as

(-4

Then you write a comma to separate from the value where the interval ends.

(-4,

The interval in x of increasing values goes to positive infinity, so now you write the infinity symbol, and you close the interval with a curved parenthesis. By convention, infinity always gets a curved parenthesis. Also, I'll use oo for infinity below.

(-4, oo)

Answer: F. (-4, oo)

Answer:

16

Step-by-step explanation:

Let's suppose the amount of alcohol in the container after time t is x. The mixture in the container has two components, water and alcohol. The volume of the solution at any given time is y. We are given the following:  One solution is composed of alcohol and water. The container is initially filled with y gallons of a mixture of alcohol and water.

The rate at which the second solution is added is a gallons per minute. The rate at which the container is drained is b gallons per minute. The solution in the container is constantly stirred. To solve the problem, we will set up a differential equation and solve it. The differential equation is:

dy/dt = a - bAt  any given time, the amount of alcohol in the mixture is x. The percentage of alcohol in the mixture is given by:x/y * 100%Let's suppose that the concentration of the alcohol in the second solution is c%. The amount of alcohol in the second solution that is added in time t is :

c * a * t  The amount of water that is added to the container in time t is:

(1 - c) * a * t So, the total amount of alcohol in the container after time t is:

x + c * a * t The total amount of water in the container after time t is:

y + (1 - c) * a * t The total amount of solution in the container after time t is:

y + a * t - b * t Since the solution is constantly stirred, the percentage of alcohol in the mixture remains constant. Therefore:

x / (y + a * t - b * t) * 100% = x / y * 100%Solving for x, we get:

x = (y + a * t - b * t) * (x / y)The equation gives us the amount of alcohol in the container after time t. The amount of alcohol in the container after t minutes is (y + a * t - b * t) * (x / y).

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The value of r is 6.

The value of y is 509.

The given equations are:

y = (2t4 - 3)

A = 7 - (r/6)

Now, we have to find the value of y when A = 4/3

We can substitute A = 4/3 in the equation of A to find the value of r

A = 7 - (r/6)4/3 = 7 - (r/6)(4/3)4/3

= 7 - (4r/18)4/3 + (4r/18)

= 718/3 + 2r/9

= 7(9/3) + 2r/9

= 721 + 2r/9

= 21(2r/9)

= 21 - 92r/9

= 63r/9

= 9 * 2r

= 6

Therefore, the value of r is 6.

Substituting the value of r in the equation of y:

y = (2t4 - 3)

y = (2 × 4⁴ - 3)

y = (2 × 256 - 3)

y = (512 - 3)

y = 509

Therefore, the value of y is 509.

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Complete Question:

Find the values of r and y:

y = (2t4 - 3)

A = 7 - (r/6)

The closure of b, denoted by b+, is the set of all elements that can be reached from b through one or more transitions in the set F. Starting with b, we see that the transition b+c is in F, which means we can add c to our set. Then, the transition c→{de} is also in F, so we can add d and e to our set. Therefore, the closure of b is b+ = {b, c, d, e}.

Given the set F = {a+b, b+c, c→de}, the closure of b refers to the smallest set that contains b and is closed under the operations in F. In this case, the closure of b would be {b, a+b, b+c}. This is because the set includes b and is closed under the addition operation with a and c, as specified in F.

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The sample correlation coefficient would be closest to -0.9.

Here's why:

Correlation Coefficient: The correlation coefficient is a statistical measure of the degree of correlation (linear relationship) between two variables. Pearson’s correlation coefficient is the most widely used correlation coefficient to assess the correlation between variables.

Pearson’s correlation coefficient (r) ranges from -1 to 1. A value of -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation. There is a negative correlation between speed and time. As the speed of the car increases, the time needed to traverse the segment decreases. So, the sample correlation coefficient would be negative.

Since the sample size is large enough, the sample correlation coefficient should be close to the population correlation coefficient. The population correlation coefficient between speed and time should be close to -1, which implies that the sample correlation coefficient should be close to -1.

Therefore, the sample correlation coefficient would be closest to -0.9.

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Answer:

x = 17

y = 17

Step-by-step explanation:

In congruent triangles, corresponding angles are congruent.

   ΔABC ≅ ΔDEF

∠D ≅ ∠A

5x +  2 = 87

      5x = 87 - 2

      5x = 85

        x = 85 ÷ 5

        \(\sf \boxed{\bf x = 17}\)

∠B = ∠E =  42°

In triangle ABC,

     ∠A + ∠B + ∠C = 180°

     87 + 42 + 3y = 180

             129 + 3y = 180

                      3y = 180 - 129

                      3y = 51

                        y = 51 ÷ 3

                        \(\sf \boxed{y = 17}\)

Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

Answer:

Q

Step-by-step explanation:

As it's distance versus time graph

Hence Q is the answer

\(\sf \Large \boxed{\sf Q} \\\\ In \ a\ distance-time\ graph,\ the\ horizontal\ line\ represents\ an\ object\ at\ rest.\\A \ slope\ shows\ that\ it\ is\ moving.\)

Answer: It's what you believe. If you don't know what the principles are, they are listed below.

Step-by-step explanation:

1 - An offense must be committed consciously and intentionally.

2 - Must be a public act.

3 - The action must be carried out collectively.

4 - A civil disobedience act must be done using peaceful methods.

5 - Must be carried out while accepting the eventualities of a sanction.

6 - The action carried out must urge to “higher principles” to justify the violation of a norm.

Answer:

The most important element of civil disobedience is the use of nonviolence to protest against an unjust law. For such acts to be considered civil, they cannot include violent struggle. Once violence is engaged, the acts grow closer to revolution or rebellion.

Step-by-step explanation:

sample answer

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model. The optimal number of notebooks to make in each order is 590 units. The annual ordering cost (AOC) is approximately $892.20. The Annual Holding Cost (AHC) is $3540. The annual product cost (APC) is $233,460. The annual total cost of managing inventory (ATC) is approximately $237,892.20. The total number of orders in the year (N) is 33. The estimated time between each order (T) is approximately 7.58 days. The daily demand is approximately 77.82 units. The reorder point (ROP) is approximately 311 units.

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model.

To find the optimal number of notebooks to make in each order, we can use the EOQ formula:

EOQ = √[(2 * Demand * Ordering Cost) / Holding Cost]

EOQ = √[(2 * 19455 * 27) / 6]

EOQ ≈ 589.96

Since the number of notebooks must be a whole number, the optimal number to order would be 590 notebooks.

The annual ordering cost (AOC) can be calculated by dividing the annual demand by the EOQ and multiplying it by the ordering cost:

AOC = (Demand / EOQ) * Ordering Cost

AOC = (19455 / 590) * 27

AOC ≈ $892.20

The Annual Holding Cost (AHC) is calculated by multiplying the EOQ by the holding cost per unit:

AHC = EOQ * Holding Cost

AHC = 590 * 6

AHC = $3540

The annual product cost (APC) is calculated by multiplying the annual demand by the cost per unit:

APC = Demand * Cost per unit

APC = 19455 * 12

APC = $233,460

The annual total cost of managing inventory (ATC) is the sum of the annual ordering cost, annual holding cost, and annual product cost:

ATC = AOC + AHC + APC

ATC = 892.20 + 3540 + 233460

ATC ≈ $237,892.20

The total number of orders in the year (N) can be calculated by dividing the annual demand by the EOQ:

N = Demand / EOQ

N = 19455 / 590

N ≈ 33

The estimated time between each order (T) can be calculated by dividing the number of working days in a year by the total number of orders:

T = Number of working days / N

T = 250 / 33

T ≈ 7.58 days

The daily demand is calculated by dividing the annual demand by the number of working days in a year:

Daily Demand = Demand / Number of working days

Daily Demand = 19455 / 250

Daily Demand ≈ 77.82 units/day

The reorder point (ROP) is the number of units at which a new order should be placed. It can be calculated by multiplying the daily demand by the lead time (time taken for the supplier to deliver the order):

ROP = Daily Demand * Lead Time

ROP = 77.82 * 4

ROP ≈ 311.28 units

Therefore, the reorder point would be approximately 311 units.

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Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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175 miles

Hi there !

4 gallons .......... 140 miles

5 gallons ...............x miles

x = 5×140/4 = 700/4 = 175 miles

Good luck !

The variance for this population is 5.Hence, the correct option is 5.

Given that, the sum of the squared deviation scores is ss = 20 for a population of n = 5 scores. Now we have to find the variance for this population.

Variances can be found using the formula: variance = s^2 = SS / (n - 1)Here, SS = 20n = 5 We have to substitute the given values into the variance formula, which gives us: s^2 = 20 / (5 - 1)s^2 = 20 / 4s^2 = 5.

So, the variance for this population is 5. Hence, the correct option is 5.

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Answer:

\(\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}\)

\(\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

Step-by-step explanation:

Given:

\(\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi\)

\(\hrulefill\)

To determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:

\(\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}\)

Substitute the given value of sin θ into the formula:

\(\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}\)

\(\hrulefill\)

To determine the exact value of sin (θ/2), we can use the half-angle formula for sine:

\(\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}\)

First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:

\(\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}\)

As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:

\(\cos\theta&=-\dfrac{\sqrt{17}}{5}\)

Now, substitute the found value of cos θ into the half-angle formula:

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}\)

Therefore:

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}\)

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}\)

​​

​\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:

\(\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

Answer:

2600

Step-by-step explanation:

£5.20×10pens=52

52×50packs

2600

Answer:

a

Step-by-step explanation:

a because when you divide 80 by 12 you get 28, so then it is 12 x 28m. :/

Answer:

Width  W = 14 m

Length  L = 26 m

Step-by-step explanation:

Perimeter of a rectangle = 80 m = 2L + 2W

L = 12 + W

80 = 2L + 2W

80 = 2(12 + W) + 2W

80 = 24 + 2W + 2W

80 - 24 = 4W

56 = 4W

W = 56 / 4

W = 14 m

L = 12 + W

L = 12 + 14

L = 26 m

check:

80 = 2L + 2W

80 = 2(26) + 2(14)

80 = 52 + 28

80 = 80 ---- OK

With an off-course speed of 11 miles per hour, the ship will go 33 miles in 3 hours.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of same size.

Here,

speed of ship= 11 miles/hour

time given= 3 hours

distance= speed * time

=11*3

=33 miles

The ship will cover 33 miles in 3 hours while moving at the speed of 11 miles/ hour off course.

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The defect rate for your product has historically been about 1.50% For a sample size of 200, the upper and lower 3​-sigma  The upper control limit (UCL) is approximately 0.0450.

The upper control limit (UCL) for a 3-sigma control chart is given by:

\(\[UCL\) = defect rate + 3 * sqrt((defect rate * (1 - defect rate)) / sample size)

Substituting the values, where the defect rate is 1.50% (0.015) and the sample size is 200, we get:

\(\[UCL = 0.015 + 3 \times \sqrt{\frac{0.015 \times (1 - 0.015)}{200}}\]\)

Calculating this expression, we find:

\(\[UCL \approx 0.0450\]\)

Therefore, the upper control limit (UCL) is approximately 0.0450.

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Answer:

$368

Step-by-step explanation:

What is 50% of $736?

50% = \(\frac{50}{100}\) = \(\frac{1}{2}\)

We Take

736 x  \(\frac{1}{2}\) = $368

So, 50% of $736 is $368.

The interior angle of any triangle sum to 180° in measure, so that angle ACB has measure

m∠ACB = 180° - 67° - 35° = 78°

Angles ACB and BCD are supplementary because they occur on the same ray AD, which means they also sum to 180° in measure. Then angle BCD has measure

m∠BCD = 180° - 78° = 102°

Answer:

102 degrees

Step-by-step explanation:

for this problem, add the angles given to 180 degrees to find the remaining angle ACB in the triangle. Once you have that angle, you can subtract it from 180 degrees to find BCD, because side ACD is straight. By adding Angle CAB (67 degrees) and Angle ABC (35 degrees), you end up with the missing 98 degrees to reach 180 degrees. thus, when subtracting to find BCD on the straight of ACD, a value of 102 degrees remains for Angle BCD

Answer:

I think it is (0,-5) ??

Hope this helps

Step-by-step explanation:

To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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Answer:

\(\huge\boxed{x=-15}\)

Step-by-step explanation:

\(-18=-3+x\qquad|\text{add 3 to both sides}\\\\-18+3=-3+3+x\\\\-15=x\to x=-15\)