I want a way to solve such a problem​

I Want A Way To Solve Such A Problem

Answers

Answer 1
Answer: Choice A)  11.4

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

Explanation:

Refer to the table below.

The first step is to find the midpoint of each interval.

To do that, we add up the endpoints and divide by 2. The midpoint of the interval from 2 to 6 is 4 because (2+6)/2 = 8/2 = 4. Repeat these steps for the other intervals to find that the remaining midpoints are: 8, 12, 16, 20.

Overall, the midpoints from top to bottom are 4, 8, 12, 16, 20

Note how the midpoints are incrementing by 4 each time, which is the same distance between each successive left endpoint (and right endpoint endpoints as well).

Let's say m represents the set of midpoints which I'll form in the third column. Multiply the frequency column f by each corresponding midpoint m. The result fm forms the fourth column.

Add up everything in that fourth column to get 1140. We then divide that by the sum of the frequencies (100) to get 1140/100 = 11.4 which is the final answer. The average weight is 11.4 pounds.

I Want A Way To Solve Such A Problem

Related Questions

Help me answer this please!!

Help me answer this please!!

Answers

Answer:

Step-by-step explanation:

Alyssa will correctly label the numbers 48.8 48 48.09 and 48 on the number line below Which number will be located closest to 48

Answer:

the answer is (6*10^6)

Step-by-step explanation:

Multiply the beginning numbers and add the exponents.

Completing the square can be used to transform x²-6x+8=0 into the form (x - p)²= 9

What are the values of p and q?

Answers

Answer:

x² - 6x + 8 = 0

or, x² - (4+2)x + 8 = 0

or, x² - 4x - 2x + 8 = 0

or, x(x-4) -2(x -4)= 0

or , (x-4) (x-2) = 0

either,

x - 2 = 0

x = 2

OR,

x - 4 = 0

x = 4

next ,

x-p = 9

or, 2-p = 9

p= -7

either,

x-p = 9

or, 4 - p = 9

or, p= -5

hope this will help you

NO LINKS!!!

Please help me with these Venn Diagram circles

NO LINKS!!!Please help me with these Venn Diagram circles

Answers

Note1. It is considered in the answer below that polygons with more than 4 sides are all regular polygons.Note2. Only considered polygons up to octagon (8 - sided polygon).

Problem 1

Circle 1                      

Figures with more than 3 sides but with no pairs of parallel sides:

Kite,Pentagon,Heptagon

Intersection

Figures with more than 3 sides and with one or more pairs of parallel sides, almost all even sided polygons:

Square,Parallelogram,Rhombus,Trapezoid,Rectangle,Hexagon,Octagon

Circle 2

Figures with one or more pairs of parallel sides:

Empty, all included into intersection region

Problem 2

Circle 1                      

Figures with less than 4 sides:

Scalene triangle

Intersection

Figures with less than 4 sides and with at least two sides of equal length:

Equilateral triangle,Isosceles triangle

Circle 2

Figures with at least two sides of equal length:

Square,Rectangle,Rhombus,Kite,Isosceles trapezoid,Pentagon,Hexagon,Heptagon,Octagon

Problem 3

Circle 1                      

Figures with at least one curved side:

CircleIntersection

Figures with at least one curved side and with at least one obtuse angle:

Empty, not considering combination of shapes

Circle 2

Figures with at least one obtuse angle (polygons with more than 4 sides will have obtuse angles)

Trapezoid,Rhombus,Kite,Parallelogram,Pentagon,Hexagon,Heptagon,Octagon

A man's gross income is R500 000. He worked at different places throughout the year
and a total of 17% of his earnings was deducted by his employers as PAYE throughout
the tax year. He qualifies for a rebate of R13 257. Calculate how much tax he still
owes. Information taken from the tax table shows that, for a taxable income between
R393 201 and R550 100, R93 135 + 36% above R393 200 needs to be paid.
O R101 678
O R71 774
O R33 326
O R25 191
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Previou
Next >

Answers

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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How can you use the double number line diagram to find what percent 120 is of ​150?

How can you use the double number line diagram to find what percent 120 is of 150?

Answers

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.

Answers

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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The attendance at a cricket match
was 6500. At the next match the
attendance fell by 24%.
How many people attended
the second match ?

Answers

Answer:

the aswer is 4940

Step-by-step explanation:

6500-24%

=4940

Answer:

4940

Step-by-step explanation:

Find 24% of 6500

6500 * 0.24 = 1560

Then subtract the product from 6500

6500 - 1560 = 4940

I Desperately need help​

I Desperately need help

Answers

Answer:

hi

Step-by-step explanation:

Find the length of side X in simple radical form with a rational denominator

Answers

The length of side X in simple radical form with a rational denominator is 25/√3.

What is a 30-60-90 triangle?

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Find the length of side X in simple radical form with a rational denominator

) Find the average gold medal winnings of those NOCs who have been
awarded fewer than ten bronze medals.
Count the number of those NOCs that have been awarded ten or more
silver medals.

This question requires the construction and interpretation of a pie chart based
on the data throughout this task.
a) Create a suitable and fully labelled pie chart to show the total medal
winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games.
Interpret the pie chart produced in Question 8a). Discuss two probable
justifications for the behaviour of the data.

Answers

a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Find the average gold medal winnings of those NOCs who have beenawarded fewer than ten bronze medals.?

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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Logic question: 9 2 12 3 8 6 ?

Logic question: 9 2 12 3 8 6 ?

Answers

Answer:

6

Step-by-step explanation:

2 + 6 = 8

6 + 6 = 12

3 + 6 = 9

? = 6

The value of the center digit which satisfies the given scenario is 6.

What is a polygon?

A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.

Each line of the polygonal circuit's segments are referred to as its edges or sides.

If we observe the given polygon carefully every opposite side has a difference of 6 from the bigger number to the smaller number.

9 - 3 = 6.

8 - 2 = 6.

12 - 6 = 6.

So, In the center of the polygon or a hexagon, the number should be 6.

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Two trains leave a station, one headed due west and the other headed due south. How fast is the southern bound train moving if the west bound train is 15 miles from the station traveling at a constant speed of 35 mph, the distance between the trains is 24 miles, and the distance between them is increasing at a rate of 25 mph.

Answers

Answer:

dx/dt = 4 mph

Step-by-step explanation:

The two trains, with the station ( origin of the coordinates system) all, form a right triangle when we considered the distance between the two trains.

In that triangle:

distance between trains  D = 24 miles

leg (1 ) distance of train going west to origin  y = 15 miles

leg (2) distance of train going south x = ??

When d = 24 and y = 15

D² = y² + x²      ⇒   x² = D² - y²

x = √ (24)² - (15)²

x = √351

x = 18,73 miles

Now according to Pythagoras theorem

D² = x² + y²

Taking derivatives (respect to time) on both sides of the equation we get

2*D*dD/dt = 2*y*dy/dt  + 2*x*dx/dt

In this expression we are looking for dx/dt, all the rest of variables are known

2*24*25 = 2* 15*35  +  2*(18,73)* dx/dt

(1200 - 1050 )/37,46 = dx/dt

dx/dt = 4 mph

Suppose that a scarf company estimates that its monthly cost is
C(a)=500x2 + 300 and its monthly revenue is
R(x) = -0.523 +6002-200+300, where x is in thousands of
scarves sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?

Answers

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Math homework help please

Math homework help please

Answers

Answer:

answer is D

Step-by-step explanation:

(2^3)^-2= 2^(3)*(-2)
             = 2^-6
             = 1/2^6
             = 1/64

     

The expressions (a), (d), (e) and (f) have values less 1.

What are expressions?

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Solving each expression :-

1) 4¹¹ / 4¹⁴        

= 4¹¹ × 4⁻¹⁴

= (4)¹¹⁻¹⁴

= 4⁻³

= 1 / 4³

2) (3⁵)² / 3⁸

= 3¹⁰ / 3⁸

= 3¹⁰⁻⁸

= 3²

= 9

3) 4⁻¹ × 4⁵

= 4⁻¹⁺5

= 4⁴

= 64

4) (2³)⁻²

= 2⁻⁶

= 1 / 2⁶

5) (5⁴)² x 5⁻¹¹

= 5⁸ x 5⁻¹¹

= 5⁻³

= 1 / 5³

6) (6⁻⁴ x 6⁶) / 6³

= 6² / 6³

= 1 / 6

Hence, the expressions (a), (d), (e) and (f) have values less 1.

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The function g is defined below . g(x) = (x - 5)/(x ^ 2 - 36) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.

Answers

Answer:

-6, 6

Step-by-step explanation:

So we have the rational function:

\(g(x)=\frac{x-5}{x^2-36}\)

The domain of a rational function is all real numbers except for when x is a zero of the denominator.

Thus, to determine the domain restrictions, set the denominator to 0 and solve for x:

\(x^2-36=0\)

Add 36 to both sides:

\(x^2=36\)

Take the square root of both sides:

\(x=\pm 6\)

So, the values that are not in the domain of g is: -6, 6.

And we're done!

please assist with these questions thanks

please assist with these questions thanks
please assist with these questions thanks
please assist with these questions thanks

Answers

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

How to calculate the percentage total return?

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

i is the nominal interest rate.r is the real interest rate.h is the inflation rate.

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Use the table of values for
y = f(x)
to complete a table for
y = f −1(x).
(Order your answers from smallest to largest x-value.)

Answers

The table containing the values of the inverse function is given at the end of the answer.

How to find the set of points (x,y) of a inverse function?

A function will have a set of points (x,y). In the inverse function, the values of x and y are exchanged with each other, hence the rule is:

(x,y) -> (y,x).

Hence, the points are found as follows:

On the original function, when x = -4, f(x) = 10. Then, on the inverse function, when x = 10, f^-1(x) = -4.On the original function, when x = -3, f(x) = 0. Then, on the inverse function, when x = 0, f^-1(x) = -3.On the original function, when x = -2, f(x) = -10. Then, on the inverse function, when x = -10, f^-1(x) = -2.On the original function, when x = -1, f(x) = -20. Then, on the inverse function, when x = -20, f^-1(x) = -1.On the original function, when x = 0, f(x) = -30. Then, on the inverse function, when x = -30, f^-1(x) = 0.On the original function, when x = 1, f(x) = -40. Then, on the inverse function, when x = -40, f^-1(x) = 1.

The table containing these values is given at the end of the answer.

What is the missing information?

The tables are missing, and are given at the end of the answer.

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Use the table of values for y = f(x) to complete a table for y = f 1(x). (Order your answers from smallest

you have 51 coins in your pocket, all dimes and quarters. You have $10.20. How many dimes and quarters do you have?

Answers

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Simplify:
\(2 \frac{1}{4}(3.5) \)
2 1/4(3.5)​

Answers

9514 1404 393

Answer:

  7 7/8

Step-by-step explanation:

There are several ways to get there.

  2.25×3.5 = 7.875 = 7 7/8

  (2 1/4)(3 1/2) = (9/4)(7/2) = 63/8 = 7 7/8

  (2 1/4)(3.5) = 2(3.5) +(1/4)(3.5) = 7 + (2·3.5)/(2·4) = 7 +7/8 = 7 7/8

A typical graphing calculator will let you enter this problem directly, giving you a result either as a decimal, improper fraction, or a mixed number.

Simplify:[tex]2 \frac{1}{4}(3.5) [/tex]2 1/4(3.5)

you roll a fair 6 sided dice twice. what is the probability of rolling a 2 the first time and a number greater then 1 the second time?

Answers

Answer:

5/6

Step-by-step explanation:

Because there are 6 sides, and it's saying we need a greater number than 1. And there are 5 other numbers.

Which of The following system of equations is solved, what would be the value of the Y coordinate?

3x + 4y = 7
6x - 4y = 38

A)5
B)-5
C)2
D)-2

Answers

The answer would be D) -2
Answer is (-2) i hope just cheak it

Find a function rule for the line that passes through the origin (0,0) and the point (-8, -19)

Find a function rule for the line that passes through the origin (0,0) and the point (-8, -19)

Answers

Answer:

B.

\(y = \frac{19}{8} x\)

Step-by-step explanation:

Our slope is Rise over Run. In this case begin at the point (-8,-19) and find how many units up (rise) and how many units over (run) you must travel to reach the next point of (0,0).

compare: These two equations

compare: These two equations

Answers

Using translation concepts, we have that:

Function f(x) underwent a reflection over the y-axis.Function g(x) underwent a reflection over the x-axis.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For function f(x), the multiplication by -1 of the function is in the output, meaning that it was a reflection over the y-axis. For function g(x), the multiplication is in the input, the domain, hence the reflection was over the x-axis.

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PLEASE ANSWER BOTH QUESTIONS!

PLEASE ANSWER BOTH QUESTIONS!

Answers

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

Dilating a line segment can change the length.Dilating a polygon can change the area.

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?

Answers

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

i need help please and thanks

i need help please and thanks

Answers

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

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Please help!!

Complete the identity

cos^2 θ/2=?

Please help!! Complete the identity cos^2 /2=?

Answers

One identity that we can write here is:

cos²(θ/2) = - sin²(θ/2) + 1

How to complete the identity?

Here we want to find something that is equal to cos²(θ/2) for every value of theta, that will be an identity.

The general identity for trigonometric functions is:

cos²(θ) + sin²(θ) = 1

So we can rewrite this as:

cos²(θ) = - sin²(θ) + 1

If instead of theta, the argument is theta over two, we could rewrite this as:

cos²(θ/2) = - sin²(θ/2) + 1

That is the identity.

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A universitys freshman class has 7600 studends. 73% of those students are najoring in computer science. How many students in freshman clsss are computer science majors?

Answers

There are 5548 students majoring in computer science.

This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.

Given that the total number of students in the university class is =7600

Also 73% of students are majoring in computer science.

Number of students majoring in computer science is = (73/100) of 7600

                                                                                   = 73×76

                                                                                   = 5548 students

So, the total number of students majoring in computer science is 5548.

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if three apples cost 45 rupees how much with 5 apples cost? ​

Answers

if 3 apples cost 45 rupees

1 apple costs 45 : 3 = 15 rupees

how much with 5 apples cost? ​

5 x 15 = 75 rupees

Answer:

75 rupees

Step-by-step explanation:

Given:

3 apples cost 45 rupees

To Find:

How much with 5 apples cost

Solve:

if 3 apples cost 45 rupees

Since 3 apple cost 45

Thus, Find the cost of 1.

45 ÷ 3 = 15 rupees

Now,

5 x 15 = 75

Thus, 5 apples cost 75 rupees.

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differenciate the Function 1/ X3​

Answers

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

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