Can you please help me with number 16

[tex]\text{Given that,}\\\\\cot A = -\dfrac{9}{\sqrt{40}}\\\\\\\implies \tan A = -\dfrac{\sqrt{40}}9\\\\\\\implies \tan^2 A = \dfrac{40}{81}\\\\\\\implies \sec^2 A -1 = \dfrac{40}{81}\\\\\implies \sec^2 A = 1 + \dfrac{40}{81}\\\\\implies \sec^2 A = \dfrac{121}{81}\\\\\implies \sec A = \pm \sqrt{\dfrac{121}{81}}= \pm\dfrac{11}{9}\\\\\\\text{Since the angle A is in quadrant II, the value of sec A will be negative.}\\\\\\\text{Hence,}~ \sec A=-\dfrac{11}{9}[/tex]

Answer:

52.4

Step-by-step explanation:

% change = 100 x final initial/initial

Answer:

Step-by-step explanation:

The supplement of 102 = 180 - 102 = 78

It is the interior angle of the given exterior angle.

It is also the enclosed angle of the isosceles triangle

Each of the other two angles = y

180 = 2*y + 78              Subtract 78 from both sides

180 - 78 = 2y                Combine

102 = 2y                       Divide by 2

102 / 2 = y    

51 = y

The smaller triangle on your right has  2 equal sides that are marked.

The angle you just found = <2 and the vertically opposite angle of the 51

So <2 = 51

Based on the information given the  percent of Jon's total income did he spend for food is 25%.

Using this formula

Percent of total income=Amount spent for food/Total income last year

Where:

Amount spent for food=$7,900

Total income last year=$31,300

Let plug in the formula

Percent of total income=$7,900/$31,300

Percent of total income=25%

Inconclusion the  percent of Jon's total income did he spend for food is 25%.

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Answer:

Wind speed = 40 km/hr

Speed of the plane in still air = 280km/hr

Step-by-step explanation:

Formula to use

Distance = Rate multiplied by Time

D = R × T

Speed of the plane in still air = a

Speed of the wind = b

Plane with the wind (tailwind) is a + b where the time = 3hours

Plane against the wind is a - b, where the time = 4hours

This would give us 2 equations

3 × (a+ b) = 960

3a + 3b = 960 ...... Equation 1

4 × (a- b) = 960

4a - 4b = 960 ........ Equation 2

Solve this like you would with system of equations:

We solve the equation using elimination method.

Mulitply equation 1 by 4 and equation 2 by -3

4 × (3a + 3b = 960)

12a + 12b = 3840 ..... Equation 4

-3 × (4a- 4b = 960)

-12a + 12b= -2880 ........ Equation 5

Therefore we have

12a + 12b = 3840 ..... Equation 4

-12a + 12b= -2880 ........ Equation 5

24b = 960

b = 960÷ 24

b = 40

Wind Speed = 40km/hr

To find the speed of air, we use equation 2

4a - 4b = 960 ........ Equation 2

Substituting 40 which is wind of speed for b in equation 2 we would have

4a - 4(40) = 960

4a - 160 = 960

4a = 960 + 160

4a = 1120

a = 1120 ÷ 4

a = 280

The speed of the small plane in still air is 280 km/hr

Answer:

Having enough to retire.

Step-by-step explanation:

The biggest long-term financial goal for most people is saving enough money to retire. The common rule of thumb that you should save 10% to 15% of every paycheck in a tax-advantaged retirement account like a 401(k) or 403(b), if you have access to one, or a traditional IRA or Roth IRA.

Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters are:

In this problem:

The probability that fewer that 5 in a sample of 20 pills will be acceptable is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]

[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]

[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]

[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]

[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]

0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

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The point-slope equation of the line as described by the points is; y + 5 = -4(x - 2).

The equation of the line given in the task content in the point-slope form can be determined as follows;

Slope = (-5-3)/(2-0) = -8/2 = -4.

Hence, it follows that point-slope form of the equation of the line is; Choice A; A. y + 5 = -4(x - 2).

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Answer: 0.1(1000 + 300m)

Use the distributive property: a x (b + c) = a x b + a x c

0.1 x 1000 + 0.1 x 300m

Evaluate both products: 100 + 30m (1)

Note: Multiplying a number by 0.1 is the same as dividing the number by 10.

We need to determine the profit when 50 pieces are sold.

Substitute m with 50 in equation (1).

100+30(50)

Evaluate product: 100 + 1500

Evaluate sum" 1600

Thus the profit is $1600.

Step-by-step explanation: I hope this helps you on any other problem! :)

Good Luck!

Answer:

well, all you need to do is 8 x 3.14 so then you shall get your answer!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 65. You just add the number of computer towers that fall into that category. So your sum would look like this:

Divisor: 5+ 12 + 21 + 15 + 12 = 65

The question does not ask you to do any more than figure out what you will be dividing by. Thank goodness it does not ask what you will be dividing into which is a whole lot more complicated problem.

Answer: neither statement is correct

Step-by-step explanation:

on Khan Academy

The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept.

According to the question

Tom and Rosie are designing a game.

In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn.  

let X represent the sum in a given turn

the expected value of X is E(X)=17.5

As

expected value is also called mean value  

i.e

highest value of sum = 6+6+6+6+6

                                   = 30

Lowest value of sum = 1+1+1+1+1

                                   = 5

Therefore,

Mean = [tex]\frac{30+5}{2}[/tex]

          = 17.5

Now,

Tom says, "A player will most likely get 17.5

This statement is correct as per expected value which is mean value and it is 17.5 .

Rosie says, "Over 100 turns, we can expect a total of about 175

This statement is incorrect as per expected value as

expected value = 17.5

when 100 turn will happen it will

17.5 * 100

= 1750

Hence, The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

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Answer is below in the picture:-

(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')

I hope it helps.

It is proved that the ray BC is the angle bisector of angle ABA'.

Angle bisectors are lines who bisect the considered angle. Bisect refers to splitting in two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if it in a mirror.

We will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

From the given problem, we know Triangle A'B'C' is a reflection of triangle ABC across line BC.

Therefore, <A'B'C' = <ABC

By the properties of congruent triangles. Means if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Hence, the ray BC is the angle, bisector of angle ABA'.

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Answer:

x=33

Step-by-step explanation:

you move the 4 to the other side

x=7-4

so

x=3

Answer:

x=3

Step-by-step explanation:

This should be easy.

4+x=7

-4    -4

x=7-4

x=3

Word explanation:

Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.

Factors of 36 are the list of integers that we can split evenly into 36. There are overall 9 factors of 36 among which 36 is the biggest factor and its positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Pair Factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6) and its Prime Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36

Negative Factors of 36: -1, -2, -3, -4, -6, -9, -12, -18 and -36

Prime Factors of 36: 2, 3

Prime Factorization of 36: 2 × 2 × 3 × 3 = 22 × 32

Sum of Factors of 36: 91

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, factors of 36 are those numbers that exactly divide 36 leaving no remainder. In other words, we can say if two numbers are multiplied and the product is 36, then the numbers are factors of 36.

Let us do a hit and trial method to find factors of 36.

Divide 36 ÷ 2 = 18

Quotient = 18, remainder = 0

Now multiply 18 × 2 = 36

Hence, 18 and 2 are the factors of 18.

36 is a composite number as it has factors other than 1 and itself.

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 36.

The most common method we use to find factors is the prime factorization method.

In prime factorization, we express 36 as a product of its prime factors.

In the division method, we see which numbers divide 36 exactly without a remainder.

Let us calculate factors of 36 using the following two methods:

Factors of 36 by prime factorization factor tree method

Factors of 36 by upside-down division method

Prime Factorization of 36 by Upside-Down Division Method

Now as discussed above, in the prime factorization method we show factors of 36 as a product of prime factors of 36. Follow the steps to find the prime factors of 36 by the prime factorization method.

With the help of divisibility rules, find out the smallest factor of the given number. Here, 36 is an even number. So it is clearly divisible by 2. In other words, 2 divides 36 with no remainder. Therefore, 2 is the smallest prime factor of 36.

36 ÷ 2 = 18.  Now find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 18 is the quotient.

18 ÷ 2 = 9. Here, 9 is the quotient. Now find the prime factors of the 9.

9 ÷ 3 = 3. Here 3 is the prime number. So we can stop the process.

Prime factorization of 36 using upside-down division method is 2 × 2 × 3 × 3 = 2² × 3².

Prime Factorization of 36 by Factor Tree Method

The factor tree method is another visualization method to represent factors of 36. It also helps in determining prime factors of 36. A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6.

Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².

Explore factors using illustrations and interactive examples

Factors of 33: The factors of 33 are 1, 3, 11, and 33.

Factors of 34: The factors of 34 are 1, 2, 17, and 34.

Factors of 38:  The factors of 38 are 1, 2, 19, and 38.

Factors of 30: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Factors of 35: The factors of 35 are 1, 5, 7, and 35.

Factors of 37: The factors of 37 are 1 and 37.

Factors of 36 in Pairs

Factor pairs are the two numbers that, when multiplied, give the number 36. Find all of the factors of the number 36 using the steps below:

Step I: Start with 1 and the number itself.

Step II: Count up by ones to see if you can multiply two numbers together to get your target number.

Step III: Stop when you can’t get any more numbers in between.

Step IV: Connect the factor pairs.

Factor pairs of 36 are given below:

36 = 1 × 36

36 = 4 × 9

36 = 6 × 6

36 =12 × 3

36 = 18 × 2

Let us club the numbers in pairs.

The factors of 36 in pairs are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).

There are a total of 5 pairs of factors of 36.

We can have negative factors also for a given number.  

Since the product of two negative numbers is positive [(-) × (-) = +].

The negative pair factors of 36 are (-1, -36), (-4, -9), (-6, -6), (-12, -3), and (-18, -2)

There are a total of 5 negative pairs of factors of 36.

Important Notes:

36 is a composite number as it has factors other than 1 and itself.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Pair factors of 36 are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).

1 is a factor of every number.

Prime factorization of 36 is 2 × 2 × 3 × 3 = 2² × 3².

Challenging Questions:

Find the factors of 3600 with the help of techniques used in finding factors of 36.

Prove that the factor of a number is always less than or equal to the number itself?

he must buy 24 jackets to get atheist 260 dollars

Answer:

18-3(n-1)

Step-by-step explanation:

The Distributive Property shows that 6(p + q) is equivalent to 6p + 6q

The distributive property tells us how to solve expressions in the form of a(b + c).  The distributive property is sometimes called the distributive law of multiplication and division. It is given by:

a(b + c) = ab + ac

Given the expression:

6(p + q)

Using the distributive property:

= 6p + 6q

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Answer:

18mph

Step-by-step explanation:

We convert this to solve! 1 mile equals 1760 yards,1 yard equals 3 feet, 60 seconds equals a minute, and 1 hour equals 60 minutes.

[tex]\frac{88yd}{10sec} times \frac{3ft}{1yd} times\frac{1mi}{5280ft} times\frac{60sec}{1min} times\frac{60}{1hr}[/tex]

When you multiply all that you get 18 mph

Answer:

C 136

Step-by-step explanation:

2×68= 136

...........

....

Step-by-step explanation:

Shop charges =13

Many left for renting bike = 45-13 =$32

If renting for 1hr cost $8

then renting for X Hrs will cost $32

1/X =8/32 cross multiplying

8X= 32

X= 32÷8= 4hrs

Answer:

Change the sign

Step-by-step explanation:

Asumming you are talking about the keep change flip method for dividing fraction, you would 1) keep 3/1, 2) flip the / symbol into * and 3) flip the 2nd fraction

Answer:

6z+12

Step-by-step explanation:

you distribute it

Answer:

Grows by 2.4 million each year

Step-by-step explanation: