This is for one person (you know who you are) lol

By the definition of inverse functions, we will get:

[tex]arcsin(-1) = -pi/2[/tex]

The function arcsin(x) is the inverse of the sine function, such that, if:

[tex]sin(x) = y\\\\arcsin(y) = x[/tex]

Now, we know that:

[tex]sin( -pi/2) = -1[/tex]

Where pi = 3.14

Then, using the above rule:

[tex]arcsin(-1) = -pi/2[/tex]

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Answer:

Step-by-step explanation:

Similar Triangle:

Triangle ABC has angles of 53 and 62 degrees....the sum is 115 degrees.  The third angle must be 180 - 115 = 65 degrees.

A triangle with one angle = 61 degrees cannot be similar

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Answer: The triangles are not similar; no expression for x can be found.

The derivative and domain of the function f(x) = x²-2x³  is :[tex](-\infty, \infty)[/tex].

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]

       [tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]

       [tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      [tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :[tex](-\infty, \infty)[/tex].

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The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

If  function 'f' is defined by f(x)=2-x and 2f(p)=8 then the value of f(2p) is 6.

Given, f(x) = 2-x

Solve this problem by making a series of substitutions.

First, find the value of p.

Then use the definition of the function f to find the value of f(2p).

We are given

f(x) = 2 - x

Multiply both sides by 2, and simplify.

2f(x) = 2(-x +2)

2f(x) = -2x + 4

Let x = p.

2f(p) = -2(p) + 4

We are given that 2f(p) = 8.

Substitute 20 for 2f(p).

8 = -2p + 4

2p = -4

p = -2

Now we know that p = -2, so we can find f(2p).

f(x) = -x + 2

f(2p) = -2p + 2

Substitute -2 for p.

f(2p) = -2(-2) + 2

f(2p) = 4 +2

f(2p) = 6

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Answer:

V≈113.1in³.

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Quarts of detergent 1208

First, we convert each unit to its pint equivalent.

1 gallon =eight US Pint

114 gallons =114 X eight =912 Pint

34 gallon =34 X 8 =272 Pint

further, 1 quart =2 Pint

12 quart = 12 X 2 Pint =24 Pint

including the three values

912+272+24=1208 Pint

therefore, Meredith will want 1,208 Pint boxes.

The unitary technique is a way of solving trouble by way of first finding the fee of a single unit, and then finding the essential value with the aid of multiplying the unmarried unit price.

The system of the unitary technique is to locate the fee of an unmarried unit after which multiply the fee of a single unit to a wide variety of devices to get the vital fee.

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Answer:

your picture is blank if you can fix it i will be glad to help you

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

The line corresponds to the f(x).

Hope this helps

Answer:

C is correct

Step-by-step explanation:

I'm not sure what the substituting part has to do anything, but here is how I got the answer

4(x+x+7)-2x+8-4

4(2x+7)-2x+4

8x+28-2x+4

6x+32

Factor and you get

2(3x+16), which is answer choice C

You can check that the answer is right by plugging in x=1 and x=2 into the original equation and the answer choice, which may be what that is asking.

The values of b and c are -4 and 4 respectively

The function is given as:

f(x) = x^2 + bx + c

Differentiate f(x)

f'(x) = 2x + b

Set to 0

2x + b = 0

Solve for b

b = -2x

The minimum is (2, 0).

So, we have:

b = -2 * 2

b = -4

Substitute b = -4 in f(x) = x^2 + bx + c

f(x) = x^2 - 4x + c

Substitute (2, 0)

0 = (2)^2 - 4(2) + c

This gives

0 = 4 - 8 + c

Evaluate

c = 4

Hence, the values of b and c are -4 and 4 respectively

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The distance between the bottom of the lighthouse and the boat is 77.6m.

The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The  distance between the top of the lighthouse and boat would be the hypotenuse. The  distance between the bottom of the lighthouse and the boat would be the base.

In order to determine the required distance, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

125²  = 98²  + b²

b² = 125²  - 98²

b = √(25²  - 98² )

b = 77.6m

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Answer:

d

Step-by-step explanation:

there is a common difference between consecutive terms in the series, that is

4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 9 , then

S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]

      = 14.4(26 + (- 252))

      = 14.5(26 - 252)

      = 14.5 × - 226

      = - 3,277

Answer:

x= 10 y=14 : 10 3 point, 14 5 point

Step-by-step explanation:

Write your equation down vertically,

3x + 5y = 100

 x + y   =  24

Next find multiply bottom equation by one number from the tops opposite,

3x + 5y = 100

(-3)x +(-3)y = (-3)24

3x + 5y = 100

-3x - 3y= -72

Add the two functions to isolate y

2y= 28 y=14

Plug y back into original and solve

3x +5(14) =100 --> 3x + 70 =100 --> 3x = 30 x=10

Answer:

answer is 121/9

Step-by-step explanation:

13.4444444444 (decimal form)

121/9 (improper fraction form)

13 4/9 (mixed fraction form)

There are 430 non square numbers that lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

Given two numbers [tex]215^{2}[/tex] and [tex]216^{2}[/tex] and we are require to find non square numbers that lie between them.

Numbers can be consecutive numbers or non consecutive numbers. In our question we will find the consecutive numbers.

Square numbers are those numbers whos square is in a proper number means decimal should not be there.

First number=[tex]215^{2}[/tex]

Second number=[tex]216^{2}[/tex]

First we have to find the exact value of numbers by finding the square of these numbers.

First number=215*215=46225

Second number=216*216=46656

Numbers that  lie between them=(46656-46225)-1

=431-1

=430

Hence 430 numbers lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

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Answer:

The second choice.

Step-by-step explanation:

Correspond sides are in the same ratio

12/4 =  x/8

.

The citizens of a state may only register to vote after proving to have submitted their census survey is a "false" statement.

In order to create statistics that define populations and their characteristics, such as age, education, housing, and income, the U.S. Census Bureau compiles data from households.

The purpose of census survey are-

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The complete question is-

The citizens of a state may only register to vote after proving to have submitted their census survey.(True/False)

If two cans hold 750ml ,then their voLume is 0.3 liters less than 1.8 liters.

Given volume of two cans being 750 ml each.

We are required to calculate the quantity in liters of how much the volume of two cans less than 1.8 liters.

Volume is the quantity of substance a container can hold in its capacity.

So volume of cone means quantity of liquid cone can hold if fully filled.

Volume of first cone=750 ml

Volume of second cone=750 ml

Total volume=750+750

=1500 ml

1 liter= 1000 ml

so 1500 ml will be equal to 1500/1000

=1.5 liter

We are required to do comparison with 1.8 liters.

Difference =1.8-1.5

=0.3 liters.

Hence two cans have 0.3 liters less than 1.8 liters.

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The probability that at least one of them is a kindergartner; 0.643.

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

Calculation for the probability of the one of them is a kindergarden;

The total number of children is 8.

The total number of kindergarden are 3.

The total number of first graders are 5.

Let 'P' be the probability that at least one of them is kindergarden.

P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)

The probability that all are first-graders = (5/8)×(4/7)

                                                                  = 5/14

Therefore, P(at least one kindergartner) = 1 - (5/14)

                                                                   = 9/14

                                                                   = 0.643

Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.

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The correct question is-

A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.

Answer: y=-(1)/(3)x-3

Please mark brainiest

Answer: A

Step-by-step explanation:

[tex]P(x) Q(x)=R(x)\\\\(x+1)Q(x)=2x^3 + 2x^2 - 3x-3\\\\Q(x)=\frac{2x^3 + 2x^2 - 3x-3}{x+1}\\\\Q(x)=\frac{2x^2 (x+1)-3(x+1)}{x+1}\\\\Q(x)=2x^2 - 3[/tex]

Answer:

The 3rd answer down

Step-by-step explanation:

If I broke apart the initial answer, I would see that x is equal to or greater than 8 and x is less than 9.5

To test the value of the mean in a population when only sample mean and sample deviation are known to perform the test then it is appropriate to use z-test procedure.

What is a Z-test?

A statistical method of testing a hypothesis is the z-test where either:

Additional prerequisites for using the z-test include the following:

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The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.

According to the central limit theorem,

Sample mean = Population mean = μ

Sample standard deviation = (Population standard deviation)/√n = σ/√n

where n is at least 30.

It is given that,

The overall population mean = 20,500

Population standard deviation σ = 2180

Sample size n = 30

Since n = 30, the central limit theorem can be applied.

According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.

So, the interval is calculated by

Sample mean = Population mean = μ = 20500

Standard deviation(sample) = σ/√n

⇒ S = 2180/√30 =398.011 ≅ 398

Thus,

The lower bound  = 20500 - 3 × 398 = 19,306

The upper bound = 20500 + 3 × 398 = 21,694

Therefore, the required interval is from 19,306 to 21,694.

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Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit

From the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks

In the graph, we have a scatterplot.

The line drawn is the line of best fit

Hence,

Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.

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It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

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Answer:

Cos (3pi/4) =0.999154554

Sin (3pi/4)=0.041111762

Step-by-step explanation:

On your calculator there should be SIN and COS next to each other

#1 tap COS

#2 put your given numbers, in this case

COS(3pi/4) = 0.999154554

same goes for SIN

SIN (3pi/4)=0.041111762

Answer:

c) 58x2

Step-by-step explanation:

Twice the number 29 is 58

So, 29 is related to 58

Therefore 29*4 = 58*2

Applying the angle of intersecting chords theorem, the value of x is: 40º.

According to the angle of intersecting chords theorem the following equation is true:

x = 1/2(a + b).

Given the following:

a = 35º

b = 45º

Plug in the values

x = 1/2(35 + 45)

x = 1/2(80)

x = 40º

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