PLEASE HELP !! 51 POINTS !!
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given.

Student A

Step 1: cosecant theta over cosecant theta minus sine theta over cosecant theta

Step 2: 1 minus sine theta over the quantity 1 over sine theta end quantity

Step 3: 1 − sin2 θ

Step 4: cos2 θ

Student B

Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta

Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta

Step 3: cosine squared theta over sine squared theta

Step 4: cot2 θ

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

The value of x is 3 and  -3 respectively.

Given that;

From equation (1)

4x+60 < 72  

First, collect like terms

4x < 72 - 60

subtract like terms

4x < 12

Make 'x' the subject

x < 12/ 4

x < 3

For equation (2)

14x +11 <-31

collect like terms

14x < -31 - 11

14x < -42

Make 'x' the subject

x < -42/ 14

x < -3

Thus. the value of x is 3 and  -3 respectively.

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As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

As given,

Regular working hours =40 hours

Overtime at the rate of (1.5 of regular hours) = 6 hours

Gross pay =$650

Let 'h' be the hourly rate

Required equation

40h + 6(1.5h) =650

⇒ 40h +9h=650

⇒49h=650

⇒h=$13.27(approximately)

Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).

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plss give your self a answer

Answer:

What do you need help with?

Step-by-step explanation:

Answer:

hello

Step-by-step explanation:

hi

MSA

my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours

Answers:

Length = 45 feet

Width = 9 feet

=========================================================

Work Shown:

x = width

5x = five times the width = length

P = perimeter of the rectangle

P = 2*(length + width)

P = 2*(5x+x)

P = 2*(6x)

P = 12x

Set this equal to the stated perimeter (108) and solve for x.

12x = 108

x = 108/12

x = 9 feet is the width

5x = 5*9 = 45 feet is the length

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

Check:

P = 2*(9+45) = 108

or you could add up the four sides like this

P = 9+45+9+45 = 108

Either way the answers are confirmed.

The price of the jacket is $23.75

Let m be the price of a jacket and n be the price of pair of pants.

The total cost of a jacket and a pair of pants was $52.37

So, we get an equation,

m + n = 52.37              ................(1)

Also, the price of the jacket was $4.87 less than the pair of pants

So, we get an equation,

m = n - 4.87               .............(2)

Substitute above value of m in equation (1)

⇒ (n - 4.87) + n = 52.37

⇒ 2n - 4.87 = 52.37

⇒ 2n = 52.37 + 4.87

⇒ 2n = 57.24

⇒ n = 28.62

This means, the cost of a pair of pants is $28.62

Substitute above value of n in equation (2)

⇒ m = n - 4.87

⇒ m = 28.62 - 4.87

⇒ m = 23.75

This means, the cost of a jacket is $23.75

Therefore, the price of the jacket is $23.75

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Rewrite the function as

[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]

Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).

We have

[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]

[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]

In the first case, we have

[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]

where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.

In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].

This means [tex]x=4[/tex] is not an asymptote. (C)

Answer:

Step-by-step explanation:

You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.

For the same distance, speed is inversely proportional to time.

  speed multiplier = (speed B)/(speed A) = (time A)/(time B)

  speed multiplier = ((2 h)/(1/2))/(5 min)

  speed multiplier = (240 min)/(5 min) = 48

The speed of Jet B is 48 times that of Jet A:

  48(417 mph) = 20016 mph . . . . speed of Jet B

__

Additional comment

The time for the full trip by Jet A can be found using the proportion ...

  partial time/partial distance = total time/total distance

If the total distance is "1 unit", then this proportion is ...

  (2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A

You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.

From the given scatter plot, finding a line of best fit, the estimate of the amount of prize money in year 10 of the contest is of $11,790.

To find the equation of the line of best fit, we need to insert the points (x,y) from the scatter plot in the calculator.

From the scatter plot, the points are given as follows:

(1, 9.5), (2,9), (3,7), (4,10), (5,11), (6, 10), (7, 10.5).

Inserting these points into a calculator, the line of best fit for the prize in year x is given as follows:

P(x) = 0.32143x + 8.28571

For year 10, we have that x = 10, hence:

P(10) = 0.32143(10) + 8.28571 = $11,500.

The closest option is $11,790, and the difference is due to rounding of coefficients or points in the table.

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we end up paying 41.25 % of the original price after the addition sale on the clearance.

Let the original price of the good be x

Now, there is a sale of 25 %.

So the price will become

Price = x - 25 % of x

Price = x - 25 / 100 x

Price = x - 0.25 x

Price = 0.75 x

Now, there is an addition 45 % sale on the price.

so the price become:

New price = P = 0.75 x - 45 % of 0.75 x

P = 0.75 x - 45 / 100 (0.75 x)

P = 0.75 x - 0.45( 0.75 x)

P = 0.75 x - 0.3375 x

P = 0.4125 x

percentage of original price is:

P = 41.25 % of x

Therefore, we get that, we end up paying 41.25 % of the original price after the addition sale on the clearance.

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Answer: Joe's book has 1248 Pages.

Step-by-step explanation:

468 * 2 2/3

Multiply 2 and 3 to get 6.

468×( 6+2/3)

Add 6 and 2 to get 8.

468x(8/3)

Express 468×(8/3) as a single fraction

468x8/3

Multiply 468 and 8 to get 3744.

3722/3

Divide 3744 by 3 to get 1248.

1248

So Joe's Book has 1248 pages

The number of oranges that will fit in the box is 235 oranges.

The dimensions of the box are 13 inches by 16 inches by 13 inches.

Therefore,

volume of the box = lwh

where

Hence,

volume of the box = 13 × 16 × 13

volume of the box = 2704 inches³

volume of the spherical orange = 4 / 3 πr³

where

volume of the spherical orange = 4 / 3 × 3.14 × 1.4³

volume of the spherical orange = 34.46464 / 3

volume of the spherical orange = 11.4882133333 inches cube = 11.5 inches³

number of oranges in the box = 2704  / 11.5

number of oranges in the box = 235.130434783

number of oranges in the box = 235 oranges

Therefore, the number of oranges that will fit in the box is 235 oranges.

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((9×7)÷9−6)+13

(63÷9−6)+13

(7−6)+13

1+13

14

Answer:

9 X 7 / 9 - 6 + 13

we can cut 9

=7-6 + 13

=1+13

=14

3(n-10)=-7

Solve the equation in 2 step equation.

n=18.5

Given that 3(n-10)=7

step1: multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

3n-30=7

step2: adding 30 on both sides of the equation.

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

2n-30+30=7+30

2n=37

step3: divide the equation by 2.

Basically, dividing is the act of dividing anything into equal sections or groups.

[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]

Therefore, n=18.5

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Answer:

500

Step-by-step explanation:

3+6=9
10-9=1

They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left

Answer: 500 balloons

Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000

Answer:

One could be: 8*8 times 4*4

Another could be: 8 to the second power times 4 to the second power

A third way to write this could also be: 8*4*8*4

Step-by-step explanation:

Hope its helpful

The cardinal number of (2, 4, 6, ..., 106) is 53.

The cardinal number of a set is the number of elements in the particular set.

We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).

Hence, let the number of elements or the cardinal number of the set be n.

Hence, according to the formula of AP, we can write,

2 + (n-1)(2) = 106

2(n-1) = 106 - 2

2(n-1) = 104

n - 1 = 104/2

n - 1 = 52

n = 52 + 1

n = 53

Hence, the cardinal number of the set is 53.

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Answer:

3×a-3×2=3a-6

3a-6=3a-6 proved

The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].

As per the question statement, we are to flip or toss a fair coin thrice consecutively.

We are required to calculate the probability that no Tails is achieved during the above mentioned event.

To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]

The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.

Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].

These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]

And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.

Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].

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Answer:

Hello,

Step-by-step explanation:

a)

[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]

b)

[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]

a dot plot can easily show all the data.

Step-by-step explanation:

In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.

Answer:it's the second option

Step-by-step explanation:

-x is already -1 so why would factoring it make it -1 again

The nth term of the given sequence is 4n - 1.

So,

Therefore, the nth term of the given sequence is 4n - 1.

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There are 5 possible arrangements to make seat all 22 children.

The smallest number of tables Ms. Francis is 10 tables.

Total number of children at the party = 22

When we picturize the scenario, each child need to get a side of the table.

So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.

It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.

For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.

Similarly, for 3 rows, a total of 24 square tables are required.

For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.

We cannot make a 6 row because it will be same as a 5 row.

So 5 different arrangements can be made to seat all 22 children.

They are:

1 row → 1 x 10 = 10 tables

2 rows → 2 x 9 = 18 tables

3 rows → 3 x 8 = 24 tables

4 rows → 4 x 7 = 28 tables

5 rows → 5 x 6 = 30 tables

The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.

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The term containing b^6 is -210 a^6 b^6

The given expansion can be solved by using the Binomial expansion

The binomial expansion for two terms (a + b)  raised to the power n is given by

(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!

To find term contain b^6 we use the formula

Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]

Putting n=10,

we get 10-r=6

             r=4

Therefore,

it is the fourth term ,

T = (-1)^3  10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]

   = -1  x   10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]

Hence the term containing b^6 is -210 a^6 b^6

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Answer:

I think Dessicant

Step-by-step explanation:

i hope it helped you if I'm right :D