Review the proof.
Step
1
2
3
5
6
7
8
Statement
cos(2x)= 1-2sin²(x)
Let 2x = 0.
Then x =
cos() = 1-2sin²()
-1 + cos() = -2sin²)
1 + cos(e) = 2sin²)
1-cos(0) = sin²)
sin() = ±
1-cos(0)
2
Which step contains an error?
O step 2
O step 4
step 6
O step 8

The angle measures for this problem are given as follows:

θ = 150º and θ = 330º.

The trigonometric expression for this problem is given as follows:

[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]

The solution to the arctangent function is the angle which has the given tangent value.

The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:

θ = 30º.

The quadrants in which the tangent is negative are given as follows:

2nd and 4th.

Hence the equivalent angles are given as follows:

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The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13

A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.

The possible polynomial in the question is; x³ + 5·x² - 11·x + 104

The factor of the polynomial is; (x + 8)

The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.

The other steps of synthetic division can then be presented, summarily as follows;

Therefore;

-8 | 1[tex]{}[/tex]   5     -11   104

   |   [tex]{}[/tex]   -8    24  104          

     1   -3    [tex]{}[/tex] 13      0

The factors of the polynomial

The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13

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Answer:

1/4

Step-by-step explanation:

The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.

The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.

A segment bisector is defined as the line that divides a segment at the midpoint into two parts.

The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

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1. The geometric sequence is B. -1, 2, -4, 8.

2. The sixth term is 8192.

3. The next three terms are 1, 1/2 and 1/4.

4. The 10th term is 4374.

5. The eight term is 1/16.

6. The next three terms in the geometric sequence are -1/36 1/216, and - 1/1296

7. The 8th term or the sequence will be 4.

8. The 6th term of the geometric sequence is 2048.

The 6th term of the sequence is:

a₆  = -2 * 4⁵ = -2 * 1024 = -2048

The common ratio of the sequence is:

r = 8/16 = 4/8 = 2/4 = 1/2

16 * (1/2) = 8

8 * (1/2) = 4

4 * (1/2) = 2

Therefore, the next three terms in the geometric sequence are 8, 4, and 2.

The common ratio of the sequence is:

r = 6/(-36) = -1/6

-1/6 * (1/6) = 1/36

1/36 * (1/6) = 1/216

-1/216 × 1/6 = -1 /1296

Therefore, the next three terms in the geometric sequence are -1/36, 1/216 and 1/1296.

The 8th term or the sequence will be:

= 512 × 0.5 × 0.5 × 0.5 × 0.5⁴

= 4

The 6th term of the geometric sequence is:

= 2 × 4 × 4 × 4 × 4 × 4

= 2048

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The critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

To find the critical value for an 80% confidence interval, we need to determine the z-score corresponding to the level of confidence. We can use a standard normal distribution table or a calculator to find this value.

Using a standard normal distribution table, we can find the z-score that corresponds to an 80% confidence level by finding the area between the mean and the upper tail of 10%, which is (100% - 80%)/2 = 10%.

The area between the mean and 10% is 0.5 - 0.10 = 0.40. Using the standard normal distribution table, the z-score that corresponds to an area of 0.40 is approximately 1.28.

Hence, the critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

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The volume of the inside of the giant sugar cube would be = 3.375cm³

To calculate the volume of a cube, the side length should first be determined from the surface area given.

But the formula for surface area of a cube = 6a²

That is;

surface area = 13.5cm²

a = ?

13.5 = 6(a)²

13.5/6 = a²

a = √13.5/6

= √2.25

= 1.5cm

Therefore the volume of the cube = a³

= 1.5³

= 3.375cm³

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Complete question:

A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5m² of material to build the cube. What is the volume inside the giant sugar cube? Give an exact answer (do not round).

Answer: 8

Step-by-step explanation:

pemdas its not that deep

Answer:

C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.

And for the second part,

1. No solution

5x+24=5x+25

24=25

It's false

2. One solution

12p-7=-3p+8

15p=15

P=1

3. One solution.

3x+20=5x

20 = 2x

X = 10

8.69 is the length of the right angle.

Let's call the length you are trying to find x.

Using trigonometry, we know that:

cos(75) = x/9

Solving for x:

x = 9sin(75)

The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.

Using a calculator to find the cosine of 75 degrees:

x ≈ 8.69

Therefore, the length you are trying to find is approximately 8.69.

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The amount of medication should they receive per dose is,

⇒ 363.6 mg

Given that;

A patient weighs 160 pounds and needs medication with dosage instructions of 15 mg/kg/day.

And, It is to be given in 3 doses each day.

Hence, We get;

1 pounds = 1/2.2 kg

160 pounds = 160 x 1/2.2 kg

                  = 72.72 kg

Since, It is to be given in 3 doses each day.

Hence, The amount of medication should they receive per dose is,

⇒ 72.72 x 15 / 3

⇒ 363.6 mg

Thus, The amount of medication should they receive per dose is,

⇒ 363.6 mg

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In linear equation, 9 is the constant of variation k.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

given x varies inversely with y then

xy = k ← k is the constant of variation

to find k use the condition x = - 4 when y = - 9, hence

k = -4 × -9 = 36

 x = 36/y

 when x = 4 , then  y = 36/4

                                  x = 9

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Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.

Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.

Here,

A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.

For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.

You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.

You would have added

=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.

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The area of the circle is 81π. Option A.

The area of a given circle is the amount of space that the circle will cover when considered in a 2 dimensional plane. It can be determined by;

area of a circle = πr^2

where r is the radius.

The circumference of a circle is the curved boundary of a circle. It can be determined by;

circumference of a circle = 2πr

where r is its radius.

From the given information in the question, we have a circle's circumference to the circle's area;

circumference/ area = 2/ 9

But,

circumference/ area = 2πr/ πr^2

                                  = 2/ r

Then;

2/ r = 2/ 9

2r = 2*9

   = 19

r = 18/ 2

r = 9

Thus,

area of the circle = πr^2

                             = π(9)^2

                             = 81π

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Answer:

a) The population is the 1,500 employees, while the sample is the 60 female and 80 male employees selected using proportional allocation.

b) The scope of data collection is a sample survey, as only a subset of the population is being studied.

c) The variable of interest is the average monthly income of the employees.

d) The possible sources of data collection could include surveys or interviews of the selected employees, or obtaining salary data from the human resources department of the company.

e) The type of statistics used would be inferential statistics, specifically confidence interval estimation and hypothesis testing, to make inferences about the population based on the sample data.

Answer:

The distribution is symmetric

Step-by-step explanation:

Because in both sides it has the same structure, so that means that the value is the same in both sides

Therefore , the solution of the given problem of equation comes out to be the ball is 2.25 inches tall after the fifth bounce.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

a)

We are aware that the ball was dropped from a height of 6 feet, or 72 inches, and that it bounced twice, the first time for 36 inches and the second time for 18 inches. We can thus write:

=> a = 72 (the initial height)

=> B = (height of previous bounce minus height of each subsequent bounce) = 18/36 = 1/2

As a result, the following exponential equation can be used to predict the ball's height:

=> y = 72*(1/2)ˣ

b) We enter x = 5 into the equation we derived in part a) to determine the height of the ball on the fifth bounce:

=> y = 72*(1/2)⁵

=> y = 72*(1/32)

=> 2.25 inches for y.

As a result, the ball is 2.25 inches tall after the fifth bounce.

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Answer: 1/2, the same as getting tails 5 times

Step-by-step explanation:

hope this helps

Answer:

2600This is a probability conversion problem.

A graph is a visual representation of data that shows the relationship between two or more variables. It is also known as a chart or plot.Difference in S-P (sec):

The S-P difference is the interval of time between the arrival of the S wave and the P wave at a seismic station.We can observe from the accompanying diagram that the S wave begins to arrive at roughly 16 seconds, and the P wave begins to arrive at roughly 8 seconds. The S-P differential is therefore 16 – 8 = 8 seconds.(mm) Amplitude:

The amplitude of a seismic wave exhibits the greatest departure from the equilibrium position. We can observe from the provided diagram that the wave's maximum displacement is roughly 70 mm. Therefore, the wave's amplitude 70mm.

(km) Distance:

The S-P time difference and a journey time graph can be used to calculate how far the earthquake was from the seismic station.

Using the equation:

Distance is calculated as ((S-P time difference)*(km/sec))

where the travel time graph provides the km/sec value, we obtain:

distance = 56 km (8 * 7).

As a result, the quake's distance from the seismic station is 56 kilometres.

Magnitude (M):

An earthquake's magnitude is a logarithmic scale representation of the energy released by the earthquake. By measuring the greatest wave's amplitude (in mm) and applying the method below, we can determine the magnitude from the provided seismogram:

M = log(A) + 1.5 * log(S-P) - 3.2

where S-P is the S-P time difference in seconds, and A is the amplitude in millimetres. Inputting the numbers provided yields:

M = log(70) + 1.5 * log(8) - 3.2

M ≈ 4.1

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The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem

Given data ,

Let the two triangles be represented as ΔMDA and ΔMBC

Now , the measure of side MD ≅ MB ( given )

And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )

Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

So , ΔMDA ≅ ΔMBC by ASA theorem

Hence , the congruent triangles are solved

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angle1 and angle3

angle6 and angle8

angle5 and angle7

Answer:

77.53

Step-by-step explanation:

You just have to sum them up

Answer:

i think the answer is 77.53

Step-by-step explanation:

Answer:

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

Given equation to solve:

The result of the first step:

The second step:

And its result is:

The matching choice is C.

The reference angle of given angles are -6π/13 and -5π / 6

To get coterminal angles, you simply have to add or subtract 2π.

a) 32π/13 =

= -32π/13 + 2π

= -32π + 26π / 13

= -6π/13

b) -17π/6 + 2π =

= -17π + 12π / 6

= -5π / 6

Hence the reference angle of given angles are -6π/13 and -5π / 6

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The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.

To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:

B(1) = 325 - 0.005(325)

Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:

B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))

We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:

B(2) = 325(1 - 0.005)²

Generalizing this pattern, we can see that after t months, the balance will be:

B(t) = 325(1 - 0.005)ᵗ

Therefore, option A is the correct function that models the balance of Lily’s account.

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The value of amount of R4 670,00 is due to be paid back after​ 1.47 years.

We have to given that;

A discounted loan of R4 670,00 at a simple discount rate of 14% per year is offered to Mr. Mothapo.

And, The actual amount of money that Mr. Mothapo receives is R3 852,75.

Now, Let n be the loan period.

Hence, We get;

4670,00 = 385275 (1 + 0.14)ⁿ

1.212121 = (1.14)ⁿ

n log 1.14 = log 1.2121

n = 1.47

Thus, The value of amount of R4 670,00 is due to be paid back after​ 1.47 years.

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Answer:

351 cm^3

Step-by-step explanation:

The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm

ChatGPT

Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:

AC = 2x * sin(35°)

Using the sine rule in triangle ABA, we have:

AB / sin(50°) = 18 / sin(80°)

Solving for AB, we get:

AB = 18 * sin(50°) / sin(80°)

The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:

V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)

Substituting the values we have calculated, we get:

V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)

V ≈ 351 cm^3

Therefore, the volume of the prism is approximately 351 cubic centimeters.

Answer:1020 ft (squared)

Step-by-step explanation:

Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)