Direction: Read and understand each problem and solve. Show your solution if necessary.

1. There are 3 gold medalist, 5 silver medalist and twelve bronze medalists. One student is randomly chosen for an interview. Find the probability that the student is a silver medalist.

2. A letter is chosen from the word MATHEMATICS. What is the probability that the letter is?
a. consonant?
b. vowel?
c. not a letter A?

3. Suppose the probability that a television is defective is 0.123. What is the probability that a television is not defective? ​

speed = distance/time

speed = 180/2

speed = 60km/hr

hope it helps...!!!

a) Recall the integration by parts formula:

[tex]\displaystyle \int u \, dw = uw - \int w \, du[/tex]

Then with [tex]u = x[/tex] and [tex]dw = e^x\,dx[/tex] we have

[tex]\displaystyle v = \int e^x x \, dx = xe^x - \int e^x \, dx[/tex]

[tex]\implies \boxed{v = xe^x - e^x + C}[/tex]

since [tex]w=\int e^x\,dx=e^x[/tex] and [tex]du=dx[/tex]. (C is of course an arbitrary constant that can be determined exactly if you know the velocity at some given value of x.)

b) No?

[tex]\displaystyle \int e^xx\,dx = \int xe^x\,dx[/tex]

because multiplication is commutative. I get the feeling I'm missing something here...

The system of equations of two unknowns is formulated and solved.

      [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}[/tex]

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}[/tex]

                                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}[/tex]

Possible number pairs are 4, 1 and -4, -1 .

Answer:

[tex]\dfrac{1}{64}[/tex]

Step-by-step explanation:

Hemi-, demi- and semi- are prefixes which mean half.

When applied to musical notation, each time a prefix is added it means the note's value is halved.

Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.

[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]

Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.

Answer:

(2,-4)

Step-by-step explanation:

Here, h=2 and k=-4, so the center is (2,-4)

Answer:

A

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{120}{360}[/tex]

     = 2π × 8 × [tex]\frac{1}{3}[/tex]

    = 16π × [tex]\frac{1}{3}[/tex] = [tex]\frac{16\pi }{3}[/tex] m

The expression which represents Sherly's total income is 7e + 13n.

The cost price represents the specific value that represents unit price purchased.

Here,

total pair of earrings = e

total pair of necklaces = n

Cost of 1 pair of earring = $ 7

Cost of 1 necklace = $ 13

earning from earring = 7e

earning from necklace = 13n

Total earning = earning from earring + earning from necklace

Total earning = 7e + 13n

Thus, the expression which represents Sherly's total income is 7e + 13n.

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Answer:

  x ≈ 95.6

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. Here, the hypotenuse of the triangle and the side adjacent to the given angle are marked, so the relationship of choice is ...

  Cos = Adjacent/Hypotenuse

__

Using the values shown, we have ...

  cos(15°) = x/99

Solving for x gives ...

  x = 99·cos(15°) ≈ 95.6

The length of the side marked x is about 95.6 units.

Based on the difference in the observed means given, we can infer that energy drink does indeed have an effect on performance.

First find the observed mean difference:

= 11.6 - 10.8

= 0.8 seconds

When the exercise is done only once, we see that on average, those who took the energy drink were faster and so finished earlier than those who didn't.

We can therefore infer that the energy drink has an effect on performance.

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Based on the table, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

In the first week, there's 9.5 pounds. This can be illustrated using the arithmetic progression. The formula will be:

= a + (n - 1)d

where,

a = first term

d = common difference

3rd term = a + 2d

13 = 9.5 + 2d

2d = 13 - 9.5

2d = 3.5

d = 3.5/2

d = 1.75

Therefore, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

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Answer:

Triangle ABC is not a Right Triangle

Step-by-step explanation:

The perimeter of a triangle is all of the sides added together so we can model our equation like so:

AB + BC + CA = P

or

8 + 5 + CA = 22

We first combine like terms

13 + CA = 22

Then make the variable have no numbers on its side

13 + CA = 22

-13          -13

CA = 9

So now that we know what CA is, we can determine whether or not its a right triangle

We can use the Pythagorean Theorem for this:

a^2 + b^2 = c^2   (the '^' symbol means 'to the power of')

or

5^2 + 8^2 = 9^2

Now we Solve

5^2 = 25

8^2 = 64

9^2 = 81

25 + 64 =? 81

89 does not equal 81

So Triangle ABC is not a Right Triangle

From the calculation below, the actual difference, if Robert had read the numbers correctly, is 168.

Let X represents the number from which subtrahend is subtracted.

Therefore, we can calculate X as follows:

X – 17 = 222

X = 222 + 17 = 239

If the subtrahend is read correctly as 71 and then subtracted from 239, we have:

Actual difference = 239 – 71

Actual difference = 168

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Step-by-step explanation:

un is the balance of the loan after n years.

so,

u12 is the balance of the loan after 12 years.

Answer:

y = (1/3)*x + 5

Step-by-step explanation:

Step 1: determine slope or m

m = change in y-coordinates ÷ change in x-coordinates

m = (4-7)/(-3-6) = -3/-9 = 1/3

Step 2: determine y-intercept or b

y = m*x + b

y = (1/3)*x + b

4 = (1/3)*(-3) + b

4 = -1 + b

b = 5

Step 3: substitute values for m and b into the slope intercept equation

y = (1/3)*x + 5

Using the combination formula, it is found that the number of candidates that can get a unique number sequence is given by:

b. 45.

The order of the pieces is not important, hence the combination formula is used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 2 pieces are taken from a set of 10, hence the number of sequences is given by:

[tex]C_{10,2} = \frac{10!}{2!8!} = 45[/tex]

Which means that option b is correct.

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1 year or less is at the first quartile mark in the box plot, therefore, the number of schools that participated for a year and less is: A. 6 schools.

The data point at the beginning of the edge of the rectangular box in a box plot is the first quartile mark of the data, which is 1/4 or 25% of the data.

1 year or less is at the first quartile mark in the box plot. That is 1/4 of the total number of schools.

Therefore, schools that participated for a year and less = 1/4(24) = 6 schools.

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Answer:

? = x = 12

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios. The two triangles are similar, which means that a proportion can be set up.

Givens

? = x

x + 8

9

9 + 6

Equation

x/(x + 8) = 9 / (9 + 6)       Combine

Solution

x/(x + 8) = 9/15                Cross multiply

15x = 9(x + 8)                  Remove the brackets

15x = 9x + 72                  Subtract 9x from both sides

15x - 9x = 72                   Combine

6x = 72                            Divide both sides by 6

6x/6 = 72/6

x = 12

Answer x = 12

Step-by-step explanation:

mean value is always the sum of all data divided by the number of data points.

we can see just by looking at the numbers that team B is way below team A.

mean team A : 1529/8 = 191.125

mean team B : 1141/8 = 142.625

so, clearly, team B had to make dinner.

the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.

in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :

median team A : (180+189)/2 = 184.5

median team B : (143+134)/2 = 138.5

the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.

mode team A : 212

mode team B : 99, 102, 105, 134, 143, 145, 202, 211

Answer:

21 liters

Step-by-step explanation:

14 liters + 7 liters = 21 liters

Hope this helped :)

Answer:

-12 and 2

Step-by-step explanation:

-12 × 2 is -24

and

-12 + 2 is -10

Answer:

first one

Step-by-step explanation:

because its cheap as for 1 NM it would be 10$ which is 2.5 AED so yehh

Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

Answer:

95

Step-by-step explanation:

The smallest number that divided by 6, 15, and 18 leavses 5 in each case is 95

Using the slope concept, it is found that the distance from point A to point B is of 465 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

To find the horizontal position at point A, we have that:

tan(10º) = 107/dA

dA = 107/tan(10º)

dA = 607.

For the horizontal position at point B, we have that:

tan(37º) = 107/dB

dB = 107/tan(37º)

dB = 142.

Hence the distance is given by:

D = dA - dB = 607 - 142 = 465.

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Answer:

11 hope this helps you and write

Answer:

The airplane flies 95 miles.

Step-by-step explanation:

Question:

An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.

Answer:

The plane flew 91 miles.

Step-by-step explanation:

City 1 - City 2

---------------------------------------------------------------------------------------------------------

[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]

[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]

[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]

[tex]d_1[/tex] = [tex]65[/tex]

---------------------------------------------------------------------------------------------------------

City 2 - City 3

[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]

[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]

[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]

[tex]d_2[/tex] = 26

---------------------------------------------------------------------------------------------------------

[tex]d_1 + d_2 = 65 + 26[/tex]

[tex]d_1 + d_2 = 91[/tex]

---------------------------------------------------------------------------------------------------------

Therefore, the airplane flew a total of 91 miles through every city

---------------------------------------------------------------------------------------------------------

Key words: the airplane, 91 miles, through, every, city, flies, City 1, City 2, City 3, total, number, unit, represent, mile.

<3 Lots of love!

-The Book Worm.

Answer:

the missing angle is 30 and the missing exterior angle is 150

Step-by-step explanation:

180-90=90-60=30

180-30=150

Answer: Exterior angle = 150 degrees

Step-by-step explanation:

Hope that helps!

:)

Answer:

slope = 1/3

Step-by-step explanation:

slope,m = vertical change/ horizotal change

that means (-3)-2/(-5)-10 or 2-(-3)/10-(-5)

and we got -5/-15 or 5/15.

So the answer is 1/3.

Answer:

x = (y - b)/m.

Step-by-step explanation:

y=mx+b      

Subtract b from both sides :-

y - b = mx

Divide both sides by m:-

(y - b) /m = x.