If an aircraft is present in a certain area, a radar correctly registers its presence with probability 0.99. if it is not present, the radar falsely registers an aircraft presence with probability 0.10. we assume that an aircraft is present with probability 0.05. what is the probability of false alarm (a false indication of aircraft presence), and the probability of missed detection (notng registers, even though an aircraft is present)? what is the probability that an aircraft is present given that the radar registers a presence?

1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

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Answer:

9

Step-by-step explanation:

If its perpendicular, it probably bisects EH, so just split it in half.

a. my opposite sides are parallel

FALSE. Only the basis sides are parallel.

b. I am a quadrilateral

TRUE. A trapezium has 4 sides.

c. I have all the sides equal

FALSE. The trapezium is a special shape in that it does not, unlike the square or rectangle, have to have any equal side lengths.

Explanation:

There are n = 5 items in set T

This means there are 2^n = 2^5 = 32 subsets

Answer:obtuse angle

Step-by-step explanation:

An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.

Answer: Option A

Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]

Step-by-step explanation:

It should be noted that, the VaR for a 3-year period with a 2.5 percent probability is Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]. Therefore, option A only is correct while other options are wrong

Answer:

A: Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]

Step-by-step explanation:

Answer:

28.05$

Step-by-step explanation:

The game got a discount of 15%.
New price is   (30$) ( 0.85 )  =  25.5$   (since the discount is 15% you only pay for the 85% of the original price)

Then an increase of 10%. this is:
New price:   25.5$ (1.10) = 28.05

New price is 28$ with 5 cents

Answer:

Angle A = 83.59° (2 d.p.)

Angle C = 56.41° (2 d.p.)

Side a = 193.25 (2 d.p.)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given:

Substitute the given values into the Sine Rule formula:

\(\implies \dfrac{\sin A}{a}=\dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}\)

Solve for angle C:

\(\implies \dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}\)

\(\implies \sin C=\dfrac{162\sin 40^{\circ}}{125}\)

\(\implies C=\sin^{-1}\left(\dfrac{162\sin 40^{\circ}}{125}\right)\)

\(\implies C=56.4136175...^{\circ}\)

Interior angles of a triangle sum to 180°. Therefore:

\(\implies A+B+C = 180^{\circ}\)

\(\implies A = 180^{\circ}-B-C\)

\(\implies A = 180^{\circ}-40^{\circ}-56.4136175...^{\circ}\)

\(\implies A = 83.5863824...^{\circ}\)

Finally, to find a, substitute the found angles and sides into the Sine Rule and solve for a:

\(\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}\)

\(\implies \dfrac{\sin 83.5863824...^{\circ}}{a}=\dfrac{\sin 40^{\circ}}{125}\)

\(\implies a=\dfrac{125\sin 83.5863824...^{\circ}}{\sin 40^{\circ}}\)

\(\implies a=193.248396...\)

Answer:

144

Step-by-step explanation:

320 ÷ 20 = 16

adults : children

11 : 9

9×16 = 144

The equivalent of 1 mile to kilometres is  approximately 1.6 km.

2.54 cm = 1 inch

5280 ft = 1 mile

100 cm = 1 m

1000 m = 1 km

Using the information let's convert 1 mile to kilometre.

1000 m = 1 km

Therefore,

1 m = 0.000621371 miles

1000 m(1 km) = ?

cross multiply

length = 1000 × 0.000621371 = 0.621371 miles

Therefore,

0.621371  miles = 1 km(1000 m)

1 miles = ?

length in km = 1.60934449789 km

Therefore,

1 miles = 1.6 km

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Answer:5 8

Step-by-step explanation:left 2 up 3

Answer:

Possibly A, cause you didn't give the first number.

The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

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Answer:

10 and -5

Step-by-step explanation:

x + y = 5

xy = -50

y = 5 - x

x(5-x) = -50

5x - x^2 = -50

x^2 - 5x - 50 = 0

from there on we can solve the classic way

\(\Delta = (-5)^2 - 4\cdot1\cdot(-50) = 25 + 200 = 225\\\sqrt{\Delta} = 15\\x_1 = \frac{5 - 15}{2} = -5\\x_2 = \frac{5+15}{2} = 10\\y_1 = 5 - x_1 = 10\\y_2 = 5 - x_2 = -5\)

Everything checks out.

Answer:

-5 × 10 = -50

-5 + 10 = 5

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

x = 9.40 cm

Step-by-step explanation:

Since it's a right triangle, we can then use pythagorean theorem to find the value of x.

Use cosine function.

\(cos \alpha = \frac{adjacent}{hypotenuse} \\cos 20 = \frac{x}{10cm} \\x = 10cos20 \\x = 9.40 cm\)

The length of the side, x in the given right-angled triangle with 10 cm length of hypotenuse is 6.82 cm.

The problem is asking us to find the length of the missing side of a right triangle. The given information is the length of one leg (10 cm) and the measure of one of the acute angles (20°).

We can use the sine function to solve for the missing side. The sine function is the ratio of the opposite side to the hypotenuse of a right triangle. In this case, the opposite side is the missing side, and the hypotenuse is the side that is opposite the right angle.

The following equation can be used to solve for x:

sin(20°) = x / 10

We can solve for x by multiplying both sides of the equation by 10 and then using a calculator to evaluate the expression. The answer is x = 6.82 cm.

To round the answer to the nearest hundredth, we can use the following steps:

Find the hundredths place of the answer, which is 2.

Look at the digit to the right of the hundredths place, which is 8.

If the digit to the right of the hundredths place is 0, 1, 2, 3, 4, or 5, then the hundredths place is rounded up.

If the digit to the right of the hundredths place is 6, 7, 8, or 9, then the hundredths place is rounded up to the next digit.

In this case, the digit to the right of the hundredths place is 8, so the hundredths place is rounded up to 9. Therefore, the rounded answer is x = 6.82 cm.

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The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

These tables represent a quadratic function with a vertex at (0,-1) what is the average rate of change for the interval from x=7 to x=8?

B.-15

Step-by-step explanation:

The average rate of change from 7 to 8 = -15

The average rate of change of a quadratic function is calculated using:

Rate = (f(b) - f(a))/(b - a)

The interval is from x = 7 to 8.

So, we have:

(a,b) = (7,8)

The equation becomes

Rate = (f(8) - f(7))/(8 - 7)

Evaluate the difference

Rate = (f(8) - f(7))/1

This gives

Rate = f(8) - f(7)

From the table, we have:

Rate from 5 to 6 = -11 where the constant is -2

So, we have:

Rate from 6 to 7 = -11 - 2

Rate from 6 to 7 = -13

Also, we have:

Rate from 7 to 8 = -13 -2

Rate from 7 to 8 = -15

Hence, the average rate of change from 7 to 8 = -15

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The equation of the parabola in vertex form is equal to the quadratic equation y - 1 = - (1 / 9) · (x + 2)².

Mathematically speaking, parabolae are represented by quadratic equations, there different forms of the equation of the parabola. In this case, we must use the vertex form, whose description is shown below:

y - k = C · (x - h)²

Where:

If we know that (x, y) = (- 5, 0) and (h, k) = (- 2, 1), then the equation of the parabola in vertex form is:

(0 - 1) = C · (- 5 + 2)²

- 1 = 9 · C

C = - 1 / 9

y - 1 = - (1 / 9) · (x + 2)²

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Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

A. In equation form: Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

B. Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

To solve this problem using E x c e l Solver, set up the revenue function and the constraints. Here's how you can do it:

a. Revenue Function:

Let's denote the number of cakes baked for each type as x1, x2, x3, x4, and x5 respectively.

The revenue function can be formulated as:

Revenue = (Selling Price of Cake 1 × Number of Cake 1) + (Selling Price of Cake 2 × Number of Cake 2) + (Selling Price of Cake 3 × Number of Cake 3) + (Selling Price of Cake 4 × Number of Cake 4) + (Selling Price of Cake 5 × Number of Cake 5)

In equation form:

Revenue = 9x1 + 12x2 + 4x3 + 5x4 + 8x5

b. Constraints:

The constraints for the availability of ingredients can be formulated as follows:

Milk constraint: 4x1 + 3x2 + x3 + 5x4 + 4x5 ≤ 280

Sugar constraint: 7x1 + 4x2 + 5x3 ≤ 300

Egg constraint: x1 + 2x2 + 3x3 + 4x4 + 5x5 ≤ 80

Flour constraint: 3x1 + 4x2 + 2x3 + 4x4 + 6x5 ≤ 250

Cream constraint: 4x1 + 5x3 + x4 + 3x5 ≤ 190

Non-negativity constraint: x1, x2, x3, x4, x5 ≥ 0

c. Solve the system of linear inequalities using E x c e l Solver:

To solve the system of linear inequalities using E x c e l Solver, follow these steps:

1. Open M i c r o s o f t E x c e l and enter the following data in a new sheet:

| | A | B |

|-----|-----------|-----------------|

| 1 | Cakes | Selling Price |

| 2 | Cake 1 | $9 |

| 3 | Cake 2 | $12 |

| 4 | Cake 3 | $4 |

| 5 | Cake 4 | $5 |

| 6 | Cake 5 | $8 |

| | | |

| | | Formula |

| 9 | Milk | 280 |

| 10 | Sugar | 300 |

| 11 | Eggs | 80 |

| 12 | Flour | 250 |

| 13 | Cream | 190 |

2. In cell B16, enter the formula for the revenue:

=B2×B7 + B3×B8 + B4×B9 + B5×B10 + B6×B11

3. In cell B18, enter the formula for the milk constraint:

=4×B2 + 3×B3 + B4 + 5×B5 + 4×B6

4. In cell B19, enter the formula for the sugar constraint:

=7×B2 + 4×B3 + 5×B4

5. In cell B20, enter the formula for the egg constraint:

=B2 + 2×B3 + 3×B4 + 4×B5 + 5×B6

6. In cell B21, enter the formula for the flour constraint:

=3×B2 + 4×B3 + 2×B4 + 4×B5 + 6×B6

7. In cell B22, enter the formula for the cream constraint:

=4×B2 + 5×B4 + B5 + 3×B6

8. In cell B24, enter the formula for the non-negativity constraint for Cake 1:

=B2

9. Repeat step 8 for the remaining cakes, entering the formulas in cells B25, B26, B27, and B28:

=B3

=B4

=B5

=B6

10. Now, select cells B16 to B28 and click on the "Solver" button in the "Data" tab.

11. In the Solver Parameters window, set the objective to maximize the cell B16 (Revenue).

12. Set the By Changing Variable Cells to B24:B28 (the number of cakes baked).

13. Click on the "Add" button in the "Subject to the Constraints" section.

14. In the Constraint window, select the range B18:B22 for the constraint cells.

15. In the Solver Parameters window, click on the "Add" button again and select the range B24:B28 for the non-negativity constraints.

16. Set the Solver options as desired, and click on the "Solve" button.

E x c e l Solver will calculate the optimal values for the number of cakes to be baked for each type that maximize the revenue, while satisfying the given constraints on ingredient availability. The solution will be displayed in cells B24:B28, indicating the number of cakes to be baked for each type.

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Answer:

the numbers are 8 and 3.

Answer:

Step-by-step explanation:

224 sq in.

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

50%

Step-by-step explanation:

There is 2 side out of 100% half is 50 :D gl and mb if its wrong!

Answer:

* Here we assume that the coin tossed is fair.

Probability of event A = # Favorable cases for event A/ # Exhaustive cases for event B

Where

Favorable cases means outcomes of an experiment that favors a particular event

Exhaustive cases means, number of total possible outcomes.

For tossing a coin one time:

# Favorable cases = 1 (getting head)

# Exhaustive cases = 2 (two outcomes, say, head and tail)

So, P(getting head in a single toss) = 1/2

For tossing a coin two times:

# Favorable cases = 1 (getting 2 heads, say, HH)

# Exhaustive cases = 2*2 or 2^2 (4 outcomes, say, HH, HT, TH, TT)

So, P(getting 2 heads in two tosses of a coin) = 1/4

Similarly, for tossing a coin five times:

# Favorable cases = 1 (getting 3 heads, say, HHHHH)

# Exhaustive cases = 2*2*2*2*2 or 2^5 (32 outcomes, say, HHHHH, THHHH, ..... etc)

So, P(getting head in 5 tosses of a coin) = 1/32

Step-by-step explanation:

With angle of depression = 48°, the horizontal distance from the base of the skyscraper to the ship is approximately 1239.8 feet.

An angle of depression is an angle formed by a horizontal line and a line of sight that is directed downward to an object or point below the horizontal line. In other words, it is the angle between a horizontal line and a line of sight that is directed downward from an observer to an object that is at a lower level than the observer.

Now,

We know that the tangent of the angle of depression A is equal to the opposite side (h) divided by the adjacent side (the distance from the observation deck to the ship). So we can set up an equation:

tan(A) = h / x

where x is the distance from the base of the skyscraper to the ship (the adjacent side).

x = h / tan(A)

A = 48 degrees (angle of depression)

h = unknown

x = unknown

tan(48) = 1.1106 (tangent of 48 degrees)

Using the equation above, we can solve for h:

h = x * tan(A)

h = 969 ft / tan(48)

h ≈ 1239.8 ft

So the horizontal distance from the base of the skyscraper to the ship is approximately 1239.8 feet.

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The angle LKN in the rhombus is 62 degrees.

A rhombus is a quadrilateral that has 4 sides equal to each other. The sum of angles in a rhombus is 360 degrees.

Opposite angles are equal in a rhombus. The diagonals bisect each other at 90 degrees. Adjacent angles add up to 180 degrees.

Therefore, let's find ∠LKN as follows:

m∠JMN = (-x + 69)

m∠LMJ = (-6x + 166)

Therefore,

1 / 2 (-6x + 166) = -x + 69

-3x + 83 = -x + 69

-3x + x = 69 - 83

-2x = -14

x = -14 / -2

x = 7

Therefore,

∠LKN = 1 / 2 (-6x + 166)

∠LKN = 1 / 2 (-6(7) + 166)

∠LKN = 1 / 2 (-42 + 166)

∠LKN = 62 degrees

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The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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