How do you solve 2x+3=9?

The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is

x sin⁻¹x + √(1 - x²) + C.

Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as

x sin⁻¹x + √(1 - x²) + C.

where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.

Integral of Sin Reverse proof by integration by parts :

f(x) = sin⁻¹x, g(x) = 1

d(sin⁻¹x)/dx = 1/√(1 - x²)

Using these equations and facts,

∫sin⁻¹x dx = ∫sin⁻¹x.1 dx

= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx

= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx

= x sin⁻¹x - ∫x/√(1 - x²) dx

= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]

= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx

= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}

= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C

= x sin⁻¹x + (1 - x²)1/2 + C

= x sin⁻¹x + √(1 - x²) + C

Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.

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The advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

In statistics, a simple random sample is a subset of persons taken from a larger set in which a subset of individuals is chosen randomly, all with the same probability.

It is a method of choosing a sample at random.

The outcomes of the observational study can be generalized to the population.

To construct a simple random sample, there are six steps: (a) defining the population; (b) picking your sample size; (c) listing the population; (d) assigning numbers to the units; (e) discovering random numbers, and (f) selecting your sample.

Therefore, the advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

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Correct question:
Which of the following is a benefit to using a random sample for an observational study?

a. The random sample allows for different treatments to be assigned.

b. A causal relationship can be determined.

c. The results of the observational study can be generalized to the population.

d. A random sample is the easiest method of data collection.

e. The distribution of the sample will match the distribution of the population.

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer: 16

Step-by-step explanation:

32% of 50 = 16

Candice and Porter will have collected 23 signatures each in one day using a system of equations.

Equations are mathematical statements that claim that two expressions are equal or equivalent.

Equality is depicted using the equation sign (=). Candice   Porter                                                                              

The number of signatures collected for nomination     21          18

Average collection of signatures per day                       2           5

Let the total signatures collected by Candice on day x = 21 + 2x

Let the total signatures collected by Porter on day x = 18 + 5x

The day the two candidates will have collected the same signatures is set as equality:

21 + 2x = 18 + 5x

21 - 18 = 5x - 2x

3 = 3x

x = 1

Total signatures collected by on day 1:

Candice = 21 + 2x = 21 + 2(1) = 23

Porter = 18 + 5x = 18 + 5(1) = 23

Thus, using a system of equations, it will take Candice and Porter 1 day to collect the same number of signatures, and each will have 23 signatures.

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The scenario exemplifies a(n) that effect is practice effect

In experiments utilising within-subjects designs, the practise effect is especially problematic since participants' performance on the study variable may increase just by engaging in the activity again, independent of any study manipulations the researcher may have imposed.

When a test is retaken, the practise effects have an impact on the results. A practise effect, for instance, can result from taking numerous practise SAT exams; practise can raise your overall score.

Counter balancing is one strategy for limiting the effects of practise. It is possible that the trials will use randomization or will use every feasible order for administering treatments to subjects.

According to the question,

Jacob observes that the participants gain more efficiency in transferring the data with each new spreadsheet. this scenario exemplifies a(n) that this is Practice effect

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The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.

In British and other varieties of English, it is termed a trapezium.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The parallel sides are called the basis of the trapezoid.

So, we have:
The height should be 3 yards higher than the shorter base.

b₁=h+3

The height should be 3 yards higher than the shorter base.

b₂=h+7

Formula for Area of trapezoid = 1/2(b₁+b₂)h

Now, using the formula, calculate as follows:

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h should be positive:

b₁=h+3=15+3=18

b₂=h+7=15+7=22

Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

0.0076 is  the probability that the first 30 igniters tested do not fail .

What is probability in math?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

a)if the failure rate for the super igniters is 15% then the probability that each igniter fails is 0.15,and the probability that it does not fail is 0.85.Therefore the probability that the first 30 igniters tested do not fail is       (0.85)30= 0.0076.

b)given that there are no failures in the first 30 tries,the probabilities occurs on 31st try is 0.15 and the probability that it does not occur on 31st but occurs on 32nd try is (0.85)(0.15)=0.1275.therefore the probability of one or the other is 0.15+0.1275=0.2775.

c)the result of the probability calculation in part(a) provides reason to believ the failure rate of the super igniters is less than 15%.The calculated proability of 0.0076 shows that there is less than a 1% chance that 30 or more igniters in a row would not fail if the failured rate was 15%.This probability is smaller than conventional significance levels such as alpha=0.05 and 0.01 and thus is small enough to make it reasonable to believe that the failure rate of the super igniters is less than 15%.

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Answer:

[tex]$\frac{5}{8}$[/tex]

Step-by-step explanation:

1/2

what is whole number?

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

According to question,

heaviest squash than the lightest squash are,

[tex]7/8-3/8=4/8[/tex]

[tex]=1/2[/tex]

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Answer:

x=4.321928

Here’s your explanation

Let's solve your equation step-by-step.

2^x=20

Solve Exponent.

2^x=20

log(2^x)=log(20) (Take log of both sides)

x*(log(2))=log(20)
x=log(20)

log(2)

Then you get your answer x=4.321928

Step-by-step explanation:

Take the log of both sides:

log2(2^x) = log2(20)

xlog2(2) = log2(20)

x(1) = log2(20)

x = log2(20) ≈ 4.322

The inverse function of the given function y = x² + 4 will be y = √(x - 4).

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The function is given below.

y = x² + 4

The inverse function of the function y = x² + 4 is given as,

Replace x with y and y with x, then we have

x = y² + 4

Solve the equation for y, then the equation is rewritten as,

x = y² + 4

y² = x - 4

y = √(x - 4)

The inverse function of the given function y = x² + 4 will be y = √(x - 4).

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Answer:Square

Step-by-step explanation:

A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.

Answer:

D. square

Step-by-step explanation:

As an explanation, I have attached a picture of the 4 quadrilaterals and their internal angles and sides.

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Answer:

11x - 2 = 6x + 13 (corresponding angles)

5x = 15

x = 3

When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10

Sum of the two numbers = 20

First we have to find the sum of their squares is as large as possible

Consider the first number as x and second number as y

To get the largest values the value of x or the value of y should be zero

Then the two numbers are 0 and 20

To get the small as possible

x^2 + (20-x)^2 = x^2 + x^2 - 20x +400

= 2x^2 -20x + 400

= 2(x^2 - 10x + 100)

The one number will be 10 and the other number will be 10

Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10

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The number of teenagers in the game are 94.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, 4700 people attended a football game.

Here, 2% of the people who attended were teenagers

So, the number of teenagers are

2% of 4700

= 0.02×4700

= 94

Therefore, there are 94 teenagers attended the game.

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Answer: 85%

Step-by-step explanation:

Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%

If 3 appears on the first die, then the sum of the numbers on the two dice can be 8 only if 5 appears on the second die. The probability of rolling a 5 on a single die is 1/6, so the probability of rolling a 3 and a 5 on two dice is 1/6 * 1/6 = 1/36. This means that the probability of rolling a sum of 8 when 3 appears on the first die is 1/36.

√10.24 belongs to the set of rational numbers.

Here we are given the number √10.24.

Now first we see that √10.24

= 3.2

Now as we can see that there is a number other than 0 after the decimal point here. Hence the above number cannot be classified as a natural number, a whole number, or an integer.

However, on converting 3.2 into the fractional form, we see that

3.2 = 32/10

reducing this to smallest form we get

16/5

Here we could easily represent 3.2 in the form of p/q where q is not equal to 0.

Hence p/q is a rational number.

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Answer: $44

Step-by-step explanation:

Proportional functions are used to express direct variation in graphs.

The graph shows a straight difference.

How to determine the type of graph?

From the graph, we have the following ordered pairs

(x, y) = (0, 0), (2, 4) and (3, 9)

We can rewrite it as:

(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)

The above means that, the equation of the graph is:

y = x²

It means, y varies directly to the square of x

Where, the proportionality constant is equal to 1

Therefore, the graph represents a direct variation

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Shana bought  5 bags of popcorn and 2 bottles of soda.

What is an equation?

An equation is consist of two expressions. At least one of the expression contain a variable.

Given that, the cost unit bottle of soda is $3.

The cost of unit bag popcorn is $4.

Assume that she bought s number of soda bottle and p number of bags of popcorn.

Then the cost of s number of soda bottle is $3s.

The cost of p number of bags of popcorn $4p.

She spent $26 in total.

Therefore

3s + 4p = 26.....(i)

She bought 7 things from the shop.

Therefore,

s + p =7 .....(ii)

Solve equation (i) and (ii) by using elimination method:

Multiply equation (ii) by 3 and subtract it from (i)

3s + 4p = 26.

3s + 3p =21

(-)   (-)      (-)

_________

        p = 5

Putting p = 5 in equation (ii)

s + 5 = 7

s = 2

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The scale of a map is the relationship between the distance on the map and the actual distance. In this case, the scale of the map is 1:4000, which means that 1 unit on the map represents 4000 units in the actual distance. To find the actual distance that is represented by 6.4 cm on the map, we need to convert the distance on the map to the same unit as the actual distance. Since 1 cm is equal to 0.01 m, 6.4 cm is equal to 6.4 * 0.01 = 0.064 m.

Now we can use the scale of the map to convert the distance on the map to the actual distance. We can set up the following proportion:

0.064 m / 1 = x / 4000

Where x is the actual distance in metres. Solving for x, we get:

x = 0.064 m * 4000 = 256 m

Therefore, the actual distance represented by 6.4 cm on the map is 256 m.

The probability the property has oil, given that both tests report positive.

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)

P(A∩B|O) = 0.8 * 0.75 = 0.6

P(O) = 0.5

P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)

P(A|O) = 0.8, P(¬O) = 0.5

P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

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Answer:

x = 85°

Step-by-step explanation:

the angle adjacent to B inside the triangle is corresponding to 70° and are congruent.

the sum of the 3 angles in a triangle is 180° , then

x + 25° + 70° = 180°

x + 95° = 180° ( subtract 95° from both sides )

x = 85°

The second triangle pairs are not necessarily congruent.

Option 2 is true.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are some triangles is shown in figure.

Now,

We know that;

Two triangles are congruent by theorem of SAS , ASA theorem.

So, When the ''two sides and one angle'' or ''two angle and one side'' are equal to another triangle then the triangles are congruent.

Here, In second option we have;

Only angles are equal, which make them similar not congruent.

Thus, We get;

The second triangle pairs are not necessarily congruent.

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Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

For x number of lawn mows,

Total earning y = 15 + 35x

For x = 8

y = 15 + 35 x 8 = 295

Hence "The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295".

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