camilia saved 4/5% of her allowance. What is this percent expressed as a fraction and as a decimal

Answers

Answer 1
80% is the percentage, and .8 is the decimal

Related Questions

Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2

Answers

No, the given value of h=2 is not a solution of the equation 1/3h=6.

We are given the equation:

1/3 h = 6

We need to determine whether h = 2 is a solution of this equation. To do this, we substitute h = 2 into the equation and see if it is true or not.

1/3 (2) = 6

2/3 = 6

This is not true, since 2/3 is not equal to 6. Therefore, h = 2 is not a solution of the equation 1/3 h = 6.

There are two coins in a bin. When one of them is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3. One of these coins is to be chosen at random and then flipped. a) What is the probability that the coin lands on heads? b) The coin lands on heads. What is the probability that the chosen coin was the one that lands on heads with probability 0.6?

Answers

The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.  

a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .

Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.

Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.

So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.

Hence, the probability that the chosen coin was the one that lands on heads is 0.6 if the coin lands on heads are 2/3.

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write the hypotheses to test if the success rate for art at this clinic is significantly higher than the success rate reported by the cdc.

Answers

In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

what is null hypothesis ?

A claim or assumption that there is no statistically significant difference between two populations or sets of data is known as the null hypothesis. It serves as the beginning point for statistical hypothesis testing and is typically indicated as H0. According to the null hypothesis, any observed difference between the populations or data sets is the result of sampling error or random chance rather than a genuine difference.

given

The success rate for art at this clinic is not statistically different from the CDC's claimed success rate.

In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

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i have an assignment, its 2n + 10 = 90 our teacher is asking whats the n can someone help, with solutions is okay :)

Answers

Sure, I can help you solve this equation for n.

The equation is 2n + 10 = 90.

To isolate n, we need to get rid of the 10 on the left side of the equation. We can do this by subtracting 10 from both sides:

2n + 10 - 10 = 90 - 10
2n = 80

Now we need to isolate n by dividing both sides by 2:

2n/2 = 80/2
n = 40

Therefore, the solution to the equation 2n + 10 = 90 is n = 40.

I hope this helps! Let me know if you have any other questions.

Answer: n=40

Step-by-step explanation:

let me know if i got this right for you broski

now dance

Offering brainliest

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Answers

What are the specific answers choices?

20x50= ?
Please answer me!

Answers

The answer to the problem is 1000

Answer:

1,000

Step-by-step explanation:20*50

Hunters with dogs walked through the forest. If you count their legs, it will be 78, and if their heads, then 24. How many hunters were there and how many dogs did they have?

Answers

From the given data of hunters and do we find out there are 9 hunters and 15 dogs.

Let's assume that there were "h" hunters and "d" dogs.

Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:

2h + 4d = 78

We can simplify this equation by dividing both sides by 2:

h + 2d = 39

We also know that there were 24 heads in total, which includes the hunters and the dogs:

h + d = 24

We can now solve these two equations simultaneously to find the values of h and d.

First, we can solve for h in terms of d from the second equation:

h = 24 - d

We can substitute this expression for h in the first equation:

(24 - d) + 2d = 39

Simplifying and solving for d:

d = 15

Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:

h + d = 24

h + 15 = 24

h = 9

Therefore, there were 9 hunters and 15 dogs.

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*NEED HELP PLEASE*

Solve each radical equation for x
and check your solution. (Isolate,
solve, check)

Answers

Step-by-step explanation:

1. sqrt(x + 6)/5 = 2

sqrt(x + 6) = 10

x + 6 = 100

x = 94

sqrt(94 + 6)/5 = 2

sqrt(100)/5 = 2

10/5 = 2

2 = 2

confirmed.

2.

sqrt(9x + 2) = sqrt(11x - 12)

9x + 2 = 11x - 12

14 = 2x

x = 7

sqrt(9×7 + 2) = sqrt(11×7 - 12)

sqrt(63 + 2) = sqrt(77 - 12)

sqrt(65) = sqrt(65)

confirmed.

3.

cubic root(6x + 3) + 10 = 13

cubic root(6x + 3) = 3

6x + 3 = 27

6x = 24

x = 4

cubic root(6×4 + 3) + 10 = 13

cubic root(24 + 3) + 10 = 13

cubic root(27) + 10 = 13

3 + 10 = 13

13 = 13

confirmed.

4.

2×sqrt(5x - 4) - 24 = -6

sqrt(5x - 4) - 12 = -3

sqrt(5x - 4) = 9

5x - 4 = 81

5x = 85

x = 17

2×sqrt(5×17 - 4) - 24 = -6

2×sqrt(85 - 4) - 24 = -6

2×sqrt(81) - 24 = -6

2×9 - 24 = -6

18 - 24 = -6

-6 = -6

confirmed.

Ty worked 5 nights this week at an ice cream shop. He earned $23, $29, $25, and $16 in tips. The average amount he earned in tips for the 5 nights was $22. Is the amount he earned in tips on night 5 more or less than the average amount? Select the correct answer and explanation.

Answers

Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.

what is equation ?

A mathematical statement that demonstrates the equality of two expressions is known as an equation. Mathematical operations like addition, subtraction, multiplication, and division may be used, and it frequently involves one or more variables that are represented by letters. Equations are employed in a variety of mathematical and scientific contexts, from the solution of straightforward algebraic problems to the modeling of intricate physical systems. Finding the values of the variables that equalize both sides of the equation is necessary to solve an equation.

given

On night 5, he received the following in tips:

Total tips: ($23 + $29 + $25 + $16) multiplied by the sum of the tips from the first four nights equals $22 * 5.

Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.

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Answer:

Step-by-step explanation:

An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided. ​

Answers

Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

What is the ratio?

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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The table shows the number of hours spent studying for a history final exam and the score on that exam. Each row represents a single student. Which value is an outlier in the table below?
Exam Scores
Number of hours spent studying, x
Exam score
(out of 100), y
1.5
65
2
68
3.5
71
4.5
98
4.5
82
6
84
6.5
88
7
85
7
80
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)

Answers

Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

Learn More:

Mrs. Juarez graded ten English papers and recorded the scores. 92 ...

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If the first quartile is 142 and the semi-interquartile range is 18, find ...

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first quartile is 20 then semi-inter quartile range is

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Step-by-step explanation:

Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy

Answers

We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".

What is the correct expression?

Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".

Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".

Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.

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Which scenario shows a value of 0. 4? select all that apply

Answers

Options B and C, Utilizing basic fractions, the qualities scenario displays a result of 0. 4 Jesse completed 40 out of 100 arithmetic problems and rode his bike for 4 of the 10 kilometers.

We are seeking a scenario that corresponds to a value of 0.4 or 40% among the possibilities mentioned, which represent various sections or fractions of a total.

Jesse rode his bike 4 out of the 10 miles in option B, which is equal to 0.4 or 40%.

Similarly, Jesse completed 40 of the 100 arithmetic problems in option C, which is likewise 0.4 or 40%. The other choices don't correspond to a 0.4 value.

A fraction of 2/3, or 0.666, is represented by choice A, a fraction of 4/100, or 0.04, by option D, and a fraction of 1/2, or 0.5, by option E.

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The question is -

Which of the following scenarios shows a value of 0.4? Select all that apply.

A. Jesse sold 40 out of 60 items at a garage sale.

B. Jesse rode 4 out of 10 miles on his bike.

C. Jesse finished 40 out of 100 math problems.

D. Jesse ate 4 out of 100 jellybeans.

E. Jesse returned 4 out of 8 library books.

D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre​

Answers

Answer:

Step-by-step explanation:

Perimeter

Pls mark me brainliest

(HAZARD) Please help what graph represents Y=-2x+4 I will mark you the brainest

Answers

The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

What is intersect?

The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.

According to question:

The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To graph Y=-2x+4, follow these steps:

Plot the y-intercept at (0,4).To locate a different point on the line, use the slope of -2. To do this, move down 2 units and right 1 unit from the y-intercept. This gives you the point (1,2).Between the two points, doodle a straight line.

The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

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Fractions Questions 2

Answers

From what we are given we form the equation:

640×(1−2×3/8)

Cross out the common factor

Apply Multiplicative Distribution Law:

Cross out the common factor:

Calculate the product

Calculate the sum

Answer:
160

A-1 chemical supply pays sam sanchez a $1950 monthly salary plus a 3% commission on merchandise he sells each month. assume Sam's sales were $46,400 for last month ​

Answers

Answer:

Sam's commission for last month can be calculated as follows:

Commission = 3% of sales

Commission = 3/100 * $46,400

Commission = $1,392

Therefore, Sam's total income for last month would be his salary plus commission:

Total income = Salary + Commission

Total income = $1,950 + $1,392

Total income = $3,342

So Sam earned $3,342 in total for last month.

Step-by-step explanation:

A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?

Answers

Let's call the first ranger Ranger A and the second ranger Ranger B. We can draw a diagram of the situation:


F
|
|
|
B ----------------- A
|
|
|
We know that Ranger B is 9 miles east of Ranger A. Let's call the distance from Ranger A to the fire "x" miles. We also know that the bearing from Ranger B to the fire is S 28° W.

A bearing of S 28° W means that the direction from Ranger B to the fire is 28° west of south. We can draw a line showing this direction:


F
|
|
|
B -------28°W---- A
|
|
|
Now we can use trigonometry to find x. We have a right triangle with the following sides:

The side opposite the 28° angle is x miles (the distance from Ranger A to the fire).
The side adjacent to the 28° angle is 9 miles (the distance from Ranger B to Ranger A).
We can use the tangent function to find x:

tan(28°) = x/9

x = 9 tan(28°)

x ≈ 4.62 miles

So the first ranger is approximately 4.62 miles from the fire.

How to find the missing side of a triangle using the Law of Sines?

Answers

Step-by-step explanation:

the law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposing angles.

you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem. (Round your answer to four decimal places.) y' = x^2 + xy y(0) = 4

Answers

By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.

The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:

y_1 = y_0 + hf(x_0, y_0)

Where: y_1 is the next value of y after one iterationy

0 is the initial value of yy' = f(x, y)h is the step size

This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.

Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4

Using Euler's method with a step size of 0.2, we get:

1) When x = 0, y = 4

y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02

When x = 0.2, y = 4.02

y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523

When x = 0.4, y = 4.1052

y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144

When x = 0.6, y = 4.1994

4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545

When x = 0.8, y = 4.3033

y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496

When x = 1, y = 4.4174

y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404

Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).

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Sean pays £10 for 24 chocolate bars.

He sells all 24 chocolate bars for 50p each.

Work out Sean's percentage profit

Answers

so he got them for £10 all 24 bars, then he went and sold each for 50c, so hmmm 24 at £0.50 that's (24)(0.5) = 12, so he bought them for £10 and sold them for £12, he's got a surplus or profit of £2.

now, if we take 10(origin amount) as the 100%, what's 2 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 10 & 100\\ 2& x \end{array} \implies \cfrac{10}{2}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{5}\implies x=20[/tex]

The data in the table below shows the average temperature in Northern Latitudes:

Estimate to the nearest whole number the average temperature for a city with a latitude of 48.

[___________]

Answers

Therefore , the solution of the given problem of mean comes out to be  15 is the solution.

What is mean?

The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.

Here,

We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.

Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:

=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)

Using the numbers from the table as inputs, we obtain:

=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)

=> T(48) = 14 + 2 * 3/5

=> T(48) = 14 + 1.2

=> T(48) = 15.2

The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.

Consequently, 15 is the solution.

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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP

Answers

Answer:

The perimeter of the shape is 53km.

Answer : 53km

Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!

Can someone help me with this please??

Answers

Answer:

Angle CAB= 28°

Angle ABC= 45°

Angle DCA= 73°

Angle DCE=107°

Step-by-step explanation:

Find the magnitude of the projection

Answers

The magnitude of the projection of the two vectors is:

M =  8.73

How to find the magnitude of the projection?

If we have two vectors A and B, and we want the projection of A onto B, we need to solve:

projection = A·B/|B|

Here the vectors are <7, -6> and <5, -2>

First, the dot product between the two vectors gives:

7*5 - 6*-2 = 35 + 12 = 47

The dot product is 47.

And the module of the second vector is:

√(5² + (-2)²) = √(25 + 4) = √29

Then the magnitude of the projection is:

M = 47/√29 = 8.73

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please help me with this savvas question!

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Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

What is inequality?

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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A baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes, if any, would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point? Pick two answers.

The velocity increases.

The velocity decreases.

The velocity remains a constant value.

The acceleration increases.

The acceleration decreases.

The acceleration remains a constant value

Answers

The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.

A type of motion known as upward motion involves an item moving up against the pull of gravity.

The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.

The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.

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Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far​

Answers

Answer:

9 words

Step-by-step explanation:

We know

He has 12 words to memorize, and he is 3/4 done.

How many words has Pablo memorized so far​?

We Take

12 x 3/4 = 9 words

So, Pable has memorized 9 words.

1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x

Answers

The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z < 0.79) = Х 5 ? (b) P(Z > 0.75) (c) P(-1.06 < Z< 2.17) =

Answers

The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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