Find all solutions to the equation in the interval [0, 2π). (3 points) sin 2x - sin 4x = 0

pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six

0, pi divided by six , pi divided by two , five pi divided by six , π, seven pi divided by six , three pi divided by two , eleven pi divided by six

0, two pi divided by three , four pi divided by three

0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three.

6/7th of £60 to the nearest penny is £51. 43 penny

Step-by-step explanation:

The amount = £60

The fraction that needs to be decided= 6/7th part

For solving the problem, we need to find out the 6/7th part of £60 and then round off the answer to the nearest 2 digits after decimals.

Thus the amount to the nearest penny= (6/7) *60

Amount= £51.42857714285

When the above amount is rounded off to the nearest penny than the amount becomes= £51.43 meaning 51 pounds and 43 pennies.  

Three equations with a solution of x = -1/2:

(2x - 1) = 0

(-x + 3) = 1

(4x + 2) = -3

Here are three equations, each created using the digits 0 – 9, with a solution of x = -1/2:

(2x - 1) = 0

Solution: When you solve for x, you get x = -1/2.

(-x + 3) = 1

Solution: Solving for x, you find x = -1/2.

(4x + 2) = -3

Solution: Upon solving for x, the result is x = -1/2.

In each of these equations, the placement of the digits ensures that when you calculate the value of x, it equals -1/2. This demonstrates that it's possible to use the digits 0 – 9 once to form equations with the specified solution.

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Complete question below :

Using the digits 0 – 9, no more than one time each, place a digit in each box to create three equations with a solution x = -1/2.

Answer:

The size of ∠CBA is 30° ⇒ A

Step-by-step explanation:

The measure of an inscribed angle subtended by semi-circle is 90°, because the measure of the inscribed angle is one-half the measure of the subtended arc and the measure of the semi-circle is 180°, then one-half 180° is 90°

In circle O

∵ C lies on the circumference of the circle

∴ ∠ACB is an inscribed angle

∵ ∠ACB subtended by arc AB

∴ m∠ACB = [tex]\frac{1}{2}[/tex] m of arc AB

∵ AB is the diameter of the circle

- That means arc AB is a semi-circle

∵ m arc AB = 180°

∴ m∠ACB = 90°

In Δ ACB

∵ m∠CAB + m∠CBA + m∠ACB = 180° ⇒ interior angles of Δ

∵ m∠CAB = 2 m∠CBA

- Substitute m∠ACB by 90 and m∠CAB by 2 m∠CBA

∴ 2 m∠CBA + m∠CBA + 90 = 180

∴ 3 m∠CBA + 90 = 180

- Subtract 90 from both sides

∴ 3 m∠CBA = 90

- Divide both sides by 3

∴ m∠CBA = 30°

The size of ∠CBA is 30°

Answer:

The first one: 4.1 units.

Answer: 4.1 units

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the graph given,

x2 = 5

x1 = 6

y2 = 3

y1 = - 1

Therefore,

Distance = √(5 - 6)² + (3 - - 1)²

Distance = √- 1² + 4² = √1 + 16 = √17

Distance = 4.1

Answer:

10 i think

Step-by-step explanation:

The measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.

Solution:

By the property of rectangle,

Opposite sides of rectangle are parallel.

By another property of parallel lines,

If two parallel lines cut by a transversal (diagonal) then alternate interior angles are congruent.

60° and ∠1 are alternate interior angles.

Hence m∠1 = 60°.

In rectangle, all the angles are right angle.

m∠1 + m∠2 = 90°

60° + m∠2 = 90°

Subtract 60° from both sides of the equation.

m∠2 = 30°

In rectangle, all the angles are right angle.

m∠3 = 90°

Hence the measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.

Step-by-step explanation:

Start by finding when the populations become equal.

C = R

1000e^(0.1t) = 50e^(0.5t)

Divide both sides by 50.

20e^(0.1t) = e^(0.5t)

Divide both sides by e^(0.1t).

20 = e^(0.4t)

Take natural log of both sides.

ln 20 = 0.4t

Multiply both sides by 2.5

t = 2.5 ln 20

t ≈ 7.5

The population of rabbits first exceeds the population of crickets in the middle of the 7th year after 2016, or 2023.

Answer:

8th year

Step-by-step explanation:

r > C

50(e^0.5t) > 1000(e^0.1t)

(e^0.5t)/(e^0.1t) > 20

e^(0.5t-0.1t) > 20

e^0.4t > 20

ln(e^0.4t) > ln20

0.4t × lne > ln20

t > ln(20)/0.4

t > 7.489330685

Population of rabbits first exceeds the population of crickets during the 8th year

Answer:

0.00016841%

Step-by-step explanation:

The winning group of numbers consist of 6 unique number inside a pool of 30 numbers. To calculate the number of groups of 6 that can be done in a pool of 30 numbers, we do a combination of 30 chosen 6 (groups of 6 numbers in 30 numbers).

The formula of combination is:

C(n,p) = n![p!*(n-p)!]

In our case, n=30 and p=6, so we have

C(30,6)=30!/(6!24!) = 30*29*28*27*26*25/(6*5*4*3*2) = 593775

As we have 593775 numbers of different possibilities of winning ticket, the probability of winning one over this value:

p = 1/593775 = 0.0000016841 = 0.00016841%

Other way to do this question is:

We have to match all 6 numbers. The first number to match have a chance of 6 over 30 to be guessed right, as there are 6 winning number in a pool of 30.

The second number to match have a chance of 5 over 29, as we already picked one winning number, and have only 29 choices left.

Then, following this logic, we have the other 4 numbers with chance 4/28, 3/27, 2/26 and 1/25.

Multiplying all these chances, we have:

p = (6*5*4*3*2*1)/(30*29*28*27*26*25) = 0.0000016841 = 0.00016841%

Answer: 1. Pay clear attention to details of the contract

2. Negotiate

3. Hire a lawyer

Step-by-step explanation:

Pay clear attention by reading the contract agreement over and over again to be sure you are clear with terms and conditions stated.

Negotiate if need be, such that the terms are jointly agreed upon. It is essential to negotiate on the relevant terms and come to a mutual agreement so that there is no misunderstanding after the contract has been signed.

In hiring a lawyer, it is important to note that contract documentation often contains legal term that requires deep analysis. It is better to be clear and take precautions before a deal is concluded.

Answer:

The mean is 80 and the standard deviation is 20. Therefore we have

65 is 0.75 standard deviation below the mean.

Step-by-step explanation:

z = [tex]\frac{x-\mu}{\sigma}[/tex]

Since 85 is 0.25 standard deviations above the mean we have

[tex]0.25 = \frac{85-\mu}{\sigma}[/tex] or 0.25·σ  = 85 - μ......1

1.5 = [tex]\frac{\mu-50}{\sigma}[/tex] or 1.5·σ  = μ - 50..............2

From 1 we have σ = 340 - 4·μ substituting into 2 gives

1.5·(340 - 4·μ) =  μ - 50 ⇒ 510 - 6·μ = μ - 50

7·μ = 560 or μ = 80

Therefore σ = 340 - 4·μ = 340 - 4·80 = 20

A value, x, 0.75 standard deviation below the mean is given by

0.75 = [tex]\frac{80-x}{20}[/tex] which gives 15 = 80 - x or

x = 65.

Answer:

7920

Step-by-step explanation:

12C3 × 9C2

= 220×36

= 7920

The number of different ways the conference attendees be selected is 7920 ways

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

ⁿCₓ = n! / ( ( n - x )! x! )

Given data ,

The number of fresher men in sorority = 12 fresher men

The number of sophomores in sorority = 9 sophomores

In the conference ,

The number of fresher men from sorority =3 fresher men

The number of sophomores from sorority = 2 sophomores

To calculate the number of different ways the conference attendees be selected is by using combination

So , the combination will become

Selecting 3 fresher men from 12 and selecting 2 sophomores from 9

And , the equation for combination is

ⁿCₓ = n! / ( ( n - x )! x! )

The combination is ¹²C₃ x ⁹P₂

¹²C₃ x ⁹P₂ = 12! / ( 9! 3! )  x  9! / ( 7! 2! )

                = ( 12 x 11 x 10 ) / ( 3 x 2 )  x  ( 9 x 8 ) / 2

                = 1320 / 6  x  72 / 2

                = 220 x 36

                = 7920 ways

Hence , the number of different ways the conference attendees be selected is 7920 ways

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Answer:

Step-by-step explanation:

y = 3.5(10) + 3.5(5.5) + 3.5(19) - 50 + 3.5(26)

Solution:

Given that,

[tex]A(w) = -w^2 + 100w[/tex]

Where, "w" is the width

Given area is in quadratic form

To find maximum area, we need to find the vertex

[tex]w = \frac{-b}{2a}[/tex]

From given quadratic,

[tex]-w^2 + 100w[/tex]

a = - 1

b = 100

Therefore,

[tex]w = \frac{-100}{2 \times -1}\\\\w = 50[/tex]

We will get maximum area when width w = 50 meters

To find maximum are we plug in 50 for w and find A(50)

[tex]A(50) = -(50)^2 + 100(50)\\\\A(50) = -2500 + 5000\\\\A(50) = 2500[/tex]

So maximum area is 2500 square meter

Answer:50

Step-by-step explanation:

Step-by-step explanation:

open brackets by multiplying with 2

8x+6=18

8x=12

x=3/2

The solution of the quadratic equation using the discriminant formula is option C. -3 ± √18 / 4 or 0.31 and a negative of 1.81.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The quadratic expression is given as

(4x + 3)² = 18

On solving, we have

(4x + 3)² = 18

(4x + 3) = √18

  4x = - 3 ± √18

 x = -3 ± √18 / 4

Therefore, x = 0.31, -1.81

The solution of the quadratic equation using the discriminant formula is option C. -3 ± √18 / 4 or 0.31 and a negative of 1.81.

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Option D: The distance between the two points is 13 units

Explanation:

It is given that the two points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]

We need to determine the distance between the two points.

It is also given that the distance between the two points can be determined using the formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substituting the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] for the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Thus, we get,

[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]

Simplifying, we have,

[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]

Adding the terms, we get,

[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]

Squaring the terms, we have,

[tex]d=\sqrt{169+1}[/tex]

Adding the terms, we get,

[tex]d=\sqrt{170}[/tex]

Simplifying and rounding off the value to the nearest tenth, we have,

[tex]d=13.0 \ units[/tex]

Hence, the distance between the two points is 13 units.

Therefore, Option D is the correct answer.

Answer:

2 raisins.

Step-by-step explanation:

Let x represent total number of required ingredient.

We have been given that Ren finds 6 peanuts, 4 raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix. We are asked to find of which ingredient Ren will have 2 pieces for a total of 9 pieces.

First of all, we will find total number of ingredients by adding each ingredient as:

[tex]\text{Total number of ingredients}=6+4+3+5[/tex]

[tex]\text{Total number of ingredients}=18[/tex]

Now, we will use ratio to solve for our given problem as:

[tex]\frac{\text{Required ingredient}}{\text{Total ingredient}}=\frac{2}{9}[/tex]

[tex]\frac{x}{18}=\frac{2}{9}[/tex]

[tex]\frac{x}{18}\cdot 18=\frac{2}{9}\cdot 18[/tex]

[tex]x=\frac{2}{1}\cdot 2[/tex]

[tex]x=4[/tex]

Since there are 4 raisins, therefore, for  every 9 pieces in Ren's handful of trail mix there are 2 raisins.

Answer:

u

Step-by-step explanation:

Solution:-

- Claim : pizza shop deliver in 30 minutes or less or it is free.

- Alternate : People who live in on opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza.

- Sample size taken n = 50 > 30

- The sample mean = 32 mins

- The appropriate symbol for sample mean used in test statistics is (u).

The symbol for the mean delivery time found in the sample is μ, representing the population mean. To find a 90% confidence interval for this mean, identify the critical value, calculate standard error, and construct the confidence interval using the sample mean, population standard deviation, and sample size.

The appropriate symbol to represent the mean delivery time of 32 minutes for the sampled deliveries in the pizza shop scenario is μ, which stands for population mean in statistics. However, because the sample mean (μ) may differ from the actual population mean, we estimate the population mean using confidence intervals.

To find a 90 percent confidence interval estimate for the population mean delivery time, we would use the following formula:

For this problem, we do not have the value required to provide a specific confidence interval estimate. However, if the sample mean is 36 minutes, the population standard deviation is 6 minutes, and the sample size is 50 (or any other given values), we would substitute these values into the formula to calculate the confidence interval.

Answer:

the most efficient method to see the input area and summary statistics at the same time without having to scroll back and forth between sections is b) Display a Watch Window for the input section as you view the summary statistics section.

Step-by-step explanation:

A Watch Window in Excel is a window that floats in front of your workbook that lets you see selected cells from anywhere in your workbook, or even other workbooks. This can be very helpful when you want to see how changes affect cells on other tabs or that aren't within view on a large spreadsheet.

A workbook is a file that contains one or more worksheets to help you organize data. You can create a new workbook from a blank workbook or a template.

The definition of a spreadsheet is a piece of paper or a computer program used for accounting and recording data using rows and columns into which information can be entered. Microsoft Excel, a program in which you enter data into columns, is an example of a spreadsheet program.

Final answer:

The Split command is the most efficient way to view both the input data and summary statistics simultaneously in a worksheet, by allowing independent scrolling of different worksheet areas.

Explanation:

The most efficient method to see both the input area and summary statistics at the same time in a worksheet is option (d) Use the Split command and adjust one pane to see the input section and another pane to see the summary statistics. This command divides the screen into separate panes that each scroll independently, allowing you to view non-adjacent areas of your worksheet simultaneously.

Here's how you can use the Split command:

Select the row or column where you want the split to appear. For your case, you may want to select the row just below the input data or just above the summary statistics.

Go to the View tab on the Excel ribbon.

Click on the Split button within the 'Window' group of commands.

Adjust the split bars to position the panes so that one shows the input data while the other shows the summary statistics.

This will allow you to keep an eye on both the input data and the summary statistics without having to scroll up and down the worksheet.

I and III are always true: the diagonals of a rectangle are congruent, and they intersect at their midpoint.

Finally, the diagonals are perpendicular if and only if the rectangle is actually a square.

So, I and III are true for every rectangle, while II is true only for some rectangles.

The correct answer is option (c) I and  III only .

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square

Therefore we can say that The diagonals are congruent & The diagonals bisect each other i.e the correct choice is option (c)

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Answer:

5% significance level indicates the level of risk, error or exactness. It guides our conclusion on which hypothesis a data supports

Level of significance defined as the possibility, probability or chances of rejecting a null hypothesis when it's results is valid.

For every statistical hypothesis, the result has propency or likeliness to be exact or not. That is, it has chances of containing a type of error referred to as level of significance.

Now, a 5% significance level implies that, the statistical results or analysis has 95% reliability or confidence level.

In other words, a 5% significance level indicates that a result has 0.05 RISK level.

The level of significance is needed for every hypothetical test because it indicates validity of each hypothesis data. It gives confidence such that one is at peace to know the hypothesis a particular data supports

Answer:

The answer to your question is letter B

Step-by-step explanation:

Data

                     12v³  -  32v²  +  6v  - 16

- Factor the first 2 terms by common factor

                  12v³ - 32v² =   4v² (3v - 8)

- Factor the last two terms by common factor

                  6v - 16 = 2(3v - 8)

- Write the previous results

                  4v²(3v - 8) + 2(3v - 8)

- Factor again by common factor

                (3v - 8) (4v² + 2)

- Factor by common term

               2(3v - 8)(2v² + 1)

Answer:

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

2x−5y=−5

x+2y=11

In equation (1), substitution of (10,5)

2x−5y=2(10)-5(5)=20-25=-5

However in equation (2), on substitution of (10,5)

x+2y=10+2(5)=10+10=20 ≠11.

However, the solutions of the simultaneous equations

2x−5y=−5

x+2y=11

are (5,3)

The ordered pair (10, 5) is a solution to the first equation of the system but not the second, which means it is not a solution to the entire system of equations.

To determine if the ordered pair (10, 5) is a solution to the given system of equations, we need to substitute x with 10 and y with 5 into each equation and see if the equations hold true:

Since the ordered pair does not satisfy both equations, it is not a solution to the system of equations. Therefore, the correct statements are:

Answer: option C is the correct answer.

Step-by-step explanation:

The television costs $1,350. Chuy decides to save the same amount of money each week, for 27 weeks. After 8 weeks Chuy saved $440. This means that the amount that she saved per week is

440/8 = $55

If she saves $55 in 8 weeks, the number of weeks left is

27 - 8 = 19 week

Amount that she would save in 19 weeks is

19 × 55 = 1045

Total amount saved in 27 weeks is

1045 + 440 = $1485

Therefore, the conclusion that you can make about Chuy's plan is

C. Chuy will save more than he needs and will meet his goal in less than 27 weeks.

Answer:

c

Step-by-step explanation:

Answer:

a) Most frequent outcome of the experiment is 7

b) Least frequent is 2

Step-by-step explanation:

a)

x= value of dice =7  is with highest frequency = 21  

(b)

x = Value of dice = 2 is with least frequency = 1

Without a visual, it's challenging to provide exact responses to the question. However, typically the most frequent outcome when rolling two dice is 7 or 8, and the least frequent is 2 or 12.

Without a visual representation of the frequency histogram provided, it is challenging to provide exact responses to parts (a) and (b) of your question. However, in general, when two fair dice are thrown, the most likely sums are 7 and 8, while the least likely sums are 2 and 12. This is because there are more combinations of dice rolls that result in sums of 7 and 8 compared to 2 or 12. For example, for 7, the combinations could be (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

To answer your original question, in general, (a) the most frequent outcome will typically be 7 or 8, and (b) the least frequent outcome will usually be 2 or 12.

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Answer:

Probability, P(X=3)=0.05371

Step-by-step explanation:

The experiment consists of 12 Bernoulli trials,n=12

Where sucess is defined with difference between the speakers and failure is defined with no difference between the speakers

Since people are guessing,the Probability P of sucess= 1/2

Therefore P(X=3) = b(3; 12, 0.5) = (12/3) (0.5)^3× (0.5)^9

P( X=3) = 0.0537

The probability that three out of twelve people claim to have heard a difference between the two speakers is approximately 5.47%.

To find the probability that three people claim to have heard a difference between the two speakers, we can use the binomial probability formula: P(X = k) = C(n,k) * p^k * (1-p)^(n-k), where n is the total number of trials, k is the number of successes, C(n,k) is the number of combinations, and p is the probability of success. In this case, n = 12 (number of people), k = 3 (number of people claiming to have heard a difference), and p = 0.5 (probability of guessing correctly for each person). Plugging in these values, we have P(X = 3) = C(12,3) * 0.5^3 * (1-0.5)^(12-3).

Calculating C(12,3) = 220 and simplifying the equation, we get P(X = 3) = 220 * 0.5^3 * 0.5^9 = 220 * 0.125 * 0.001953125 = 0.0547, or approximately 5.47%.

Therefore, the probability that three people claim to have heard a difference between the two speakers is 0.0547, or approximately 5.47%.

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Answer:

Step-by-step explanation:

The co-ordinates of the rectangle are:

A (8, 6)

B (-4, -10)

C (-8, -7)

D (4, 9)

The Area of Rectangle is Given by: length x breadth = AB x BC

Lengths of AB and BC can be found by distance formula

length(AB) = [tex]\sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2}}[/tex] = [tex]\sqrt{(-4-8)^{2} + (-10-6)^{2}} = 20[/tex]

Similarly,

length(BC) = 5

Area of Rectangle = AB x BC = 20 x 5 = 100 square units

Answer:

y = [tex]\frac{4}{5}[/tex] x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (5, 1)

m = [tex]\frac{1+7}{5+5}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex], thus

y = [tex]\frac{4}{5}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, 1), then

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = [tex]\frac{4}{5}[/tex] x - 3 ← equation of line

Answer: the cost of a milkshake is $2.59

Step-by-step explanation:

Let x represent the cost of a banana split.

Let y represent the cost of a milkshake.

At the ice cream shop, one banana split and five milkshakes cost $16.24. This is expressed as

x + 5y = 16.24- - - - - - - - - - - - -1

If three banana splits and two milkshakes cost $15.05. This is expressed as

3x + 2y = 15.05- - - - - - - - - - - - -2

Multiplying equation 1 by 3 and equation 2 by 1, it becomes

3x + 15y = 48.72

3x + 2y = 15.05

Subtracting, it becomes

13y = 33.67

y = 33.67/13

y = 2.59

Substituting y = 2.59 into equation 1, it becomes

x + 5 × 2.59 = 16.24

x + 12.95 = 16.24

x = 16.24 - 12.95

x = 3.29

The cost of one banana split = $3.29

The cost of one milkshake is = $2.59

Let the cost of one banana split = x

the cost of one milkshake is = y.

So, according to the question:

x+5y=16.24

3x+2y=15.05

Solving the equations we get: x=3.29 and y=2.59.

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To find the zeros we have to put:

[tex]f(x)=0[/tex]

Now we have:

[tex]x^3+64=0[/tex]

[tex]x^3=-64[/tex]

[tex]x=\sqrt[3]{-64}[/tex]

[tex]x=-4[/tex]

So, the only zero is x=-4

Answer: 6m+8

m+m+8m-4m = 6m

5+12-9=8