5 Solve the equation sin 2x = 2 cos 2x, for 0°<x< 180°​

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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Therefore, we have proven the vertical angles theorem by using congruency properties.

The intersection of two straight lines produces two sets of linear pairs with congruent angles, according to this theorem. Moreover, it indicates that the neighboring angles created by the junction of these two lines are supplementary, or 180 degrees.

Here,

THEOREM:

According to the Vertical Angles Theorem, two crossing lines' opposing (vertical) angles must be equivalent.

THE ISSUE:

Show that ∠1 ≅∠3 and ∠2 ≅ ∠4

PROOF:

(1) A straight line measures 180 degrees; m∠1 + m∠2 = 180°

(2)  m∠3 + m∠2 = 180°; the length of a straight line is 180.

(3) Since the sum of the two left-hand sides of the equation equals 180 degrees, the transitive principle of equality holds that   m∠1 + m∠2 = m∠3 + m∠2       

(4) m∠1 = m∠3       which demonstrates the equality's subtraction property ( m∠2 is subtracted from both sides).

Definition of congruent angles: (5) ∠1 ≅ ∠3 

Likewise, for ∠2 ≅∠4:

(1)   m∠3 + m∠2 = 180°  a straight line has a 180° length.

(2) m∠3 + m∠4 = 180°  a straight line has a 180° length.

(3) Since both of the equation's left-hand sides add up to 180 degrees, the expression   m∠3 + m∠2 = m∠3 + m∠4        / transitive property of equivalence.

(4)  m∠2 = m∠4    , demonstrating the equivalence of subtraction (m∠3 is subtracted from both sides).

// definition of congruent angle , ∠2 ≅ ∠4      

We have therefore established the theorem.

Therefore, we have proven the vertical angles theorem by using congruency properties.

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At the 5% significance level, a researcher conducts six separate hypothesis tests. the likelihood of finding two or fewer Type Errors.

Declare your null and alternate hypotheses in Step 1. Data collection is step two. Perform a statistical test in step three. In step four, you must choose whether to reject or not to reject your null hypothesis. Deliver your results in Step 5. Five steps make up the statistical process: design the study, assemble the data, Analyze the data, draw conclusions, and take action. In a planned experiment, the variables are under the researchers' control.

Utilizing sample data, hypothesis testing is a method used to determine whether a hypothesis is tenable. The test offers proof that, given the available data, the hypothesis is plausible. By measuring and reviewing a representative sample of the population under study, statistical analysts can evaluate a theory.Procedures for testing hypotheses Identifying the null hypothesis is the first step.

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Answer: y = 11 , x =3

Step-by-step explanation:

Since its an isosceles triangle , two angles or two side are equal.

So lets take 5y - 3 as one of the equal angles, so

5y-3+ 5y-3 + 76 = 180 (angles in a triangles should add up to 180)

10y - 6 + 76 = 180

10y = 180 - 70

10y =110

y = 110/10

y = 11

Now, since we found y we need to find x.

Lets us take 8x and 13x - 15 as the equal sides.

8x = 13x - 15

8x - 13x = -15

-5x = -15

x = -15 / -5

x = 3

so we found the values of x and y !

Answer:

Step-by-step explanation:

You want the values of x and y, given an isosceles triangle with congruent sides JK=8x and KL=13x-15, angle K=76°, and angle J=(5y-3)°.

  JK = KL

  8x = 13x -15

  15 = 5x . . . . . . add 15-8x

  3 = x . . . . . divide by 5

The sum of the angles in the triangle is 180°.

  2(∠J) +∠K = 180°

  2(5y -3) +76 = 180 . . . . substitute known values, divide by °

  10y +70 = 180 . . . . . . simplify

  y +7 = 18 . . . . . . . . divide by 10

  y = 11 . . . . . . . . . subtract 7

The values of x and y are 3 and 11, respectively.

Answer:

x=6

Step-by-step explanation:

12-6=6 or 6+6=12

An ordinary bend is a ringer molded bend that gives probabilities of irregular factors taken in a nonstop conveyance. The z score formula is used to standardize the random variables into a z score.

Using the z score formula and the z table, standardize the value of x and use it to denote the cellphone's lifetime in months.

The area under the probability density function curve in a given range is the probability that a continuous random variable fall within a given range. Because the value of a random variable must be in the sample space, the total area under the curve for any pdf is always 1.

A continuous probability distribution is the normal distribution. Probability is affected in multiple ways by this. 1 is the total area under the normal curve. A normal random variable X has a 0 chance of matching any given value.

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Full Question = A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.

The description of the proportional relationship represented by the equation y = 8 - 5x is A. The graph is a line that goes through points (0, 8) and ( 4, -12 ).

The graph is given in the form of a linear equation which is y = mx + b. In this equation, b is the y - intercept, or the point the line crosses the y - axis when x is 0. This point on y = 8 - 5x, is 8.

If the line passes through the x axis at point 4, then the y - intercept would be :

= 8 - 5 ( 4)

= 8 - 20

= - 12

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Options for this question are:

Answer:

You would have $6055.36 in 7 years.

Step-by-step explanation:

X=77

y=77by 2

answer is complete

Answer:

Step-by-step explanation:

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10.

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

  75 mg

Step-by-step explanation:

You want the dose for a 72 pound person at the rate of 2.5 mg/kg.

We multiply by conversion factors that cancel unwanted units, leaving the units we want.

At the end of the unit conversion, we need to determine if the calculated dose is closer to 75 mg or 100 mg. It is less than 87.5 mg, so is closer to 75 mg.

  [tex]\dfrac{2.5\text{ mg}}{\text{kg}}\times(72\text{ lb})\times\dfrac{0.453\text{ kg}}{\text{lb}}=2.5\times72\times0.453\text{ mg}\approx81.54\text{ mg}\\\\\approx\boxed{75\text{ mg}}[/tex]

__

Additional comment

We found the nearest 25 mg dose by dividing by 25 mg, and rounding the 3.26 dose result to 3 doses of 25 mg each.

The average rate of change between interval 5 to 11 is 4.5.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Given

Average rate of change

= Change in output/ Change in input

= 45 - 18/ 11 -5

= 27/6

4.5

The average rate of change between interval 5 to 11 is 4.5.

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L1 (Ridge Regression) regularization is better than L2( Lasso regression). A regularization term two general types of regularization L1 and L2 regularization is added to solve the overfitting problem.

Let's use a linear regression formula for this explanation, y = mx + c

This is the simplest formula, so if there is only one feature, this is the formula. But in the real world, we rarely deal with just one feature. Most of the time we have multiple functions.

y = m₁ x₁ + m₂x₂ + ----+ mₙxₙ

To create simpler (sparse) models when the dataset has a large number of features, here are some of the regularization techniques used to correct overfitting and feature selection. A regression model that uses the L1 regularization method is called a Lasso regression. Lasso regression (least absolute shrinkage and selection operator) is Add "absolute size".

∑(Yᵢ ) - ∑Xᵢβⱼ)² + λ ∑|βⱼ|

Models using L2 are called ridge regression Ridge Regression adds the "squared magnitude" of the coefficients as a penalty term to the loss function. where the highlighted part represents the L2 regularization factor and the cost function

∑(Yᵢ - ∑Xᵢβⱼ )² + λ ∑β²

The L1 regularization is more robust than the L2 regularization for fairly obvious reasons. Since we take the weights squared, the cost of outliers present in the data increases exponentially. L1 regularization takes the absolute value of the weights, so the cost increases only linearly. Both L1 and L2 can add cost penalties depending on the complexity of the model, so when calculating the cost using the loss function, an auxiliary component called the regularization term adds complexity to the model. Added for segmentation.

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To find the original price of the T-shirt before the discount, we need to divide the discount by the percentage to find the discount amount, then add the discount amount to the sale price to find the original price. In this case, the discount was $10.50 * 30% = $<<10.5030.01=3.15>>3.15. So the original price of the T-shirt before the discount was $10.50 + $3.15 = $<<10.50+3.15=13.65>>13.65. Answer: \boxed{13.65}.

Answer:

$15.00

Step-by-step explanation:

The original price is x, an unknown.

x is 100% of the original price.

The discount was 30%.

100% - 30% = 70%

The discounted price was 70% of the original price.

70% of x is $10.50

0.7x = 10.5

x = 15

Answer: $15.00

The number of right-handed players in the local little league given its percentage is 28

Based on the given task content; the number of right-handed players there can be determined by solving the percentage of right-handed players.

Number of right-handed players = Percentage of right-handed players × Total number of players in the local little league

= 40% × 70

= 40/100 × 70

= 0.4 × 70

= 28

In conclusion, the total number of right-handed players is 28

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The total cost at the peoples paper be less expensive will represent by the inequality 650 + 80w <  145w.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given that the daily info newspaper charges a fee of $650 plus $80 per week to run an ad.

Assume that after w weeks the total cost at the peoples paper be less expensive.

To run ad. for w week, the cost will be 80w.

The total cost of material of newspaper is p(w) = 650 + 80w

The peoples paper charges $145 per week.

The peoples paper charges after w week will be f(w) = 145w.

According to the question:

p(w) < f(w)

650 + 80w < 145w

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Answer:

9.1

Step-by-step explanation:

9.1 would be greater because it is basically 9 + 0.1.

The quadrilateral that has vertices (2,0), (0,-2), (-2,4) and (-4,2) is option

b. rectangle

To determine the special quadrilateral that is formed by connecting the midpoints of the sides of the quadrilateral with vertices (2,0), (0,-2), (-2,4) and (-4,2), we can find the midpoints of each side and then determine the shape formed by these points.

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. To find the midpoint of a line segment, we can take the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.

We can find the midpoint of the side between (2,0) and (0,-2) by taking the average of the x-coordinates (2 and 0) and the average of the y-coordinates (0 and -2), which gives us the point (1,-1).

We can find the midpoint of the side between (0,-2) and (-2,4) by taking the average of the x-coordinates (0 and -2) and the average of the y-coordinates (-2 and 4), which gives us the point (-1,1).

We can find the midpoint of the side between (-2,4) and (-4,2) by taking the average of the x-coordinates (-2 and -4) and the average of the y-coordinates (4 and 2), which gives us the point (-3,3).

We can find the midpoint of the side between (-4,2) and (2,0) by taking the average of the x-coordinates (-4 and 2) and the average of the y-coordinates (2 and 0), which gives us the point (-1,1).

Therefore, the special quadrilateral formed by connecting the midpoints of the sides of the given quadrilateral is a rectangle.

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The product of 0.123(overline) and 9 is equal to 149/142.

To multiply 0.123(overline) and 9, we can first rewrite 0.123(overline) as a fraction. To do this, we can express 0.123(overline) as a fraction with a denominator of 1000, which represents the number of thousandths that 0.123(overline) represents:

To find the product of 123/1000 and 9, we can use the distributive property:

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common factor, which is 7:

Therefore, the product of 0.123(overline) and 9 is equal to 149/142.

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Answer:

158 liters.

Step-by-step explanation:

G=gallons

L=Liters

Q=Quarts

42G * 4Q = 168Q

1Q = 3.785L

3.785L * 42G = 158L or another way is to go by the formula is by dividing the volume value by 1.057:

168Q divide by 1.057 = 158

The rent per unit will be $8,354.22 to have a Net Operating Income (NOI) of $100,000.

The net operating income (NOI) is the difference between the gross operating income and the operating expenses.

The net operating income excludes some fixed or period expenses.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

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The program can be broken down into four classes, each with a different percentage of instructions.

Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.

Class A consists of 20% of the instructions,

Class B consists of 30%,

Class C consists of 20%  

Class D consists of 30%.

This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.

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The program can be broken down into four classes, each with a different percentage of instructions.

Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.

Class A consists of 20% of the instructions,

Class B consists of 30%,

Class C consists of 20%  

Class D consists of 30%.

This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.

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Answer:

Step-by-step explanation:

a. To calculate the incremental income after taxes, we need to determine the incremental costs and revenues associated with extending credit to the new customers. The additional credit sales will generate $180,000 in revenue, but we need to subtract the expected uncollectible amount of 12% * $180,000 = $21,600. The net additional credit sales will be $180,000 - $21,600 = $158,400.

The production and marketing costs will be 72% * $180,000 = $129,600. The total incremental costs will be $129,600 + $16,200 (collection expense) = $145,800.

The incremental income before taxes will be $158,400 - $145,800 = $12,600. The income tax will be 34% * $12,600 = $4,284. The incremental income after taxes will be $12,600 - $4,284 = $8,316.

To calculate the return on incremental investment, we need to determine the incremental investment required to extend credit to the new customers. Since no additional investment in assets is required, the incremental investment will be equal to the incremental costs of $145,800. The return on incremental investment will be $8,316 / $145,800 = 5.7%.

Based on the return on incremental investment of 5.7%, the company should not extend credit to the new customers, as it is below the desired return of 10%.

b. If an additional investment in inventory is required to extend credit to the new customers, we will need to recalculate the incremental income after taking into account the additional investment. If the additional investment in inventory is $x, the incremental investment will be $145,800 + $x. The incremental income before taxes will be $158,400 - ($129,600 + $16,200 + $x) = $12,600 - $x. The income tax will be 34% * ($12,600 - $x) = $4,284 - $x * 0.34. The incremental income after taxes will be ($12,600 - $x) - ($4,284 - $x * 0.34) = $8,316 - $x * 0.34.

To determine whether credit should be extended, we need to compare the return on incremental investment to the desired return of 10%. The return on incremental investment will be ($8,316 - $x * 0.34) / ($145,800 + $x). Setting this equal to the desired return of 10% and solving for x, we find that the additional investment in inventory cannot exceed $24,764 for the company to meet its desired return. If the additional investment in inventory is less than or equal to $24,764, the company should extend credit to the new customers. If it is greater than $24,764, the company should not extend credit to the new customers.

Answer:

0, -12

Step-by-step explanation:

An equation in the form x = a , where a is a constant can never be a function.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

A function is generally denoted by f(x) where x is the input.

The general representation of a function is y = f(x).

According to the given question:

An equation is in the form x = a , where a is a constant.

This equation is a vertical line parallel to y axis. For a function a relation of y = f(x) is missing in the given equation since a is a constant.

Hence, x = a can never be a function.

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Answer:

x = -1.875

Step-by-step explanation:

-2 (5x + 8) = 14 + 6x

-10x - 16 = 14 + 6x

-16x = 30

x = 30/-16

x = -1.875

Answer:

Natalie arrives is Sheffield at 1:00 pm

Step-by-step explanation:

Answer:

  8/17

Step-by-step explanation:

You want the ratio of 32 mm to 6.8 cm, compared in mm.

The ratio of interest is ...

  (32 mm)/(6.8 cm) = (32 mm)/(68 mm) = (4·8)/(4·17) . . . . . mm cancels

  = 8/17

The ratio of ball diameters is 8/17.