In a circle with radius 6 and angle intercepts an arc of length 3pi find the angle in radians in simplest form

Answer:

13 cups

Step-by-step explanation:

If the small box has 10 cups, then:

(small)     10 cups   =   100%

(medium)    x cups     =   130%

Now, cross multiply:

10 (130) = x (100)

1300 = 100x

x = 13

Another way to solve this is by turning 30% into a decimal:

30/100 = 0.3

10 (0.3) = 3

Now you have 30% of the 10 cups, but you need 30% more than the small box, so:

10 + 3 = 13 cups

An appropriate ending to the alternative hypothesis is less than 8 hours. The alternative hypothesis would be: The average amount of sleep students at their school get per night is less than 8 hours.

The alternative hypothesis is a statement used in statistical inference experiment which is contradictory to the null hypothesis and denoted by Ha or H1. In hypothesis testing, an alternative hypothesis is a statement that a researcher is testing.

The alternative hypothesis could take one of three forms, depending on the context of the test:

Which alternative hypothesis we use (< or > or ≠) is sometimes called the direction of the test. Which direction we choose depends on the context of the test.

In this case, it is suspected that students at the school are getting less than 8 hours of sleep on average, so that is the alternative hypothesis.

Ha: The average amount of sleep students at their school get per night is less than 8 hours.

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Answer:

132

Step-by-step explanation:

$6 x 17= 102

102+$30= $132

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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The critical values of the function are x = 0 and x = 64

The critical values of a function f(x) are the values of x for which f'(x) = 0.

Given,

f(x) = \(\frac{x^{4} }{5(x-8)^{2} }\)

The derivative is found as follows, applying the quotient rule:

f'(x) = \(\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }\)

     = \(\frac{2x^{3}(x-64) }{5(x-8)^{3} }\)

The zeros of the function are the zeros of the numerator, thus:

\(2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\\)

x - 64 = 0------------->x = 64

The critical values are x = 0 and x = 64

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Suppose a certain medical test has a false positive rate of 6 out of 3,500, then during the period in which 27 false positives were obtained, the number of people tested was 15,750.

Step 1: Determine the probability of a false positive. The probability of a false positive is given as 6 out of 3500, so it can be expressed as a fraction: 6/3500

Step 2: Determine the number of false positives in the given period. The problem states that 27 false positives returned during the period, therefore: False positive rate x number of people tested = number of false positives 6/3500 x number of people tested = 27

Step 3: Solve for the number of people tested. 6/3500 x number of people tested = 27 Number of people tested = 27 / (6/3500) Number of people tested = 15,750 Therefore, during the period in which 27 false positives were obtained, the number of people analyzed was 15,750.

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Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

The degree of a polynomial function is the highest degree of any of its terms.

If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.

For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.

Thus, the term containing the highest power of the variable x is -18x¹⁴.

Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.

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Answer:

Step-by-step explanation:

Area of triangle = (1/2)bh

                          \(=\frac{1}{2}*25*21.65\\\\\)

                          = 270.625 cm²

Area of 6 triangles = 6 * 270.625

                              = 1623.75 cm²

Trapezium:

a = 25 cm

b = 25 +  12.5 +12.5 = 50 cm

h = 21.65 cm

\(Area=\frac{(a+b)*h}{2}\\\\=\frac{(25+50)*21.65}{2}\\\\=\frac{75*21.65}{2}\)

=811.875 cm²

Area of two trapezium = 2 *811.875

                                     = 1623.75 cm²

Area of star = 1623.75 +1623.75

                  = 3247.50 cm²

Answer:

3247.50 cm sq

Step-by-step explanation:

The value of x is 1 and 5/3 of the expression (4x - 4)(15x - 25)

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given expression is (4x - 4)(15x - 25)

We need to find the value of x.

Expand the expression

4x(15x - 25) -4(15x - 25)

60x²-100x-60x+100

60x²-160x+100

(4x - 4)(15x - 25)

4x-4=0

x=1 and

15x=25

Divide both sides by 15

x=25/15

As 25 and 15 are the multiples of 5 we need to divide each by 5 we get

x=5/3

Hence, the value of x is 1 and 5/3 of the expression (4x - 4)(15x - 25)

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The values for all cost is:

a. FC = 50

b. VC = 175

c. TC (Total Cost) = 225

d. AFC (Average Fixed Cost) = 10

e. Average Variable Cost = 35

f. ATC =45

g. MC (Marginal Cost) = 70

a. FC (Fixed Cost) of producing 5 units of output:

Since FC represents the cost that does not vary with the level of output,

So, the cost function at q = 0.

FC = C(0)

    = 50

b. VC (Variable Cost) of producing 5 units of output:

  VC represents the cost that varies with the level of output.

It can be calculated by subtracting FC from TC.

VC = TC - FC

     = C(5) - FC

     = (50+20 x 5+5 x 5 x 5) - 50

     = 175

c. TC (Total Cost) of producing 5 units of output:

TC = FC + VC

     = 50 + 175

     = 225

d. AFC (Average Fixed Cost) of producing 5 units of output:

AFC = FC / q

       = 50 / 5

       = 10

e. AVC (Average Variable Cost) of producing 5 units of output:

AVC = VC / q

        = 175 / 5

        = 35

f. ATC (Average Total Cost) of producing 5 units of output:

  ATC is calculated by dividing TC by the quantity produced.

ATC = TC / q

       = 225 / 5

       = 45

g. MC (Marginal Cost) when q = 5:

MC(5) = 20 + 10 x 5

          = 70

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Answer:

C

Step-by-step explanation:

Ur welcome

Answer:

You have done right but i didnt know the reason for this

Step-by-step explanation:

I think it will be the half of AA because point D falls in between the line AA

The system of equations is:

To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:

We have two equations to graph:

Comparing with the slope-intercept equation:

Where m is the slope and b is the y-intercept.

We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.

The graph of the two equations is shown in the following image:

Where the green line is the first equation, and the red line is the second equation.

There is no solution to this system of equations because the lines do not intersect each other.

Answer:

B: 1/3 × 15

Step-by-step explanation:

1/3 = 33%

Round 14 up to 15.

This will get you the closest answer

In this question the domain of the function \(\[ y=\sqrt{x-9} \]\) is {9.∞) in interval notation.

To determine the domain of the function \(y=\sqrt{x-9}\) we need to consider the values of x that make the expression under the square root non-negative.

Since the square root of a negative number is not defined in the real number system, we must have x-9\(\geq\)0 to ensure the function is valid.

Solving for x:

x-9\(\geq\)0

x\(\geq\)9

Therefore, the domain of the function is [9,∞) in interval notation, indicating that the function is defined for all values of x greater than or equal to 9.

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Answer: y=3/4x

Step-by-step explanation:

1. Find slope using slope formula

2. Find b value by plugging a point to solve for b with

Answer:

j ≥41

Step-by-step explanation:

just handle the ≥ as an equality sign and move J over

The polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\) are linear independent and span \(P_3\). So the first four Laguerre polynomials forms a basis of \(P_3\).

We have the first four Laguerre polynomials. Here \(P_3\) is the space of all polynomials of degree at most 3.

i.e., \(P_3= \{ a+bx+cx^2+dx^3| a,b,c,d \in R\}\)

So the dimension of \(P_3\) is 4. Also there are 4 Laguerre polynomials.

Now to show that the first four Laguerre polynomials forms a basis, it remains to show that they are linear independent.

Consider the polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\). Write them into a matrix with the co-efficient of 1, t, \(t^2\) and \(t^3\) in each row.

\(\left[\begin{array}{cccc}1&1&2&6\\0&-1&-4&-18\\0&0&1&9\\0&0&0&-1\end{array}\right]\)

This matrix is already in its echelon form with all its pivots occupied. The pivot of first row is 1. The pivot of 2nd row is -1. The pivot of 3rd row is 1 and the pivot of 4th row is -1.

Hence the polynomials are linearly independent since the columns of the above matrix are linearly independent.

In conclusion, the first four Laguerre polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\)  forms a basis for \(P_3\).

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Answer:

The longest side of the ΔQRS is Side RS.

Step-by-step explanation:

Given:  m∠R=65°, m∠S=35° we don't know what m∠Q is in ΔQRS.

To find m∠Q , we first need to know that all triangles have a sum of 180°. Since we are already given two angle measurements ( m∠R and  m∠S) we can add them both measurements up which gives us 100°. Then we subtract 100 from the triangle sum which is 180° (180°-100°) and we are left with 80°. Which mean that m∠Q got to be 80°.

Now we know the all the angles measurements we can immediately find out which side is the longest. To find the longest side its always lie opposite the largest angle which in this m∠Q (80°). Which mean that side RS is the longest side in the triangle.

Answer:

see explanation

Step-by-step explanation:

Since the marked angles are congruent, let them be x

(6)

The sum of the interior angles of a quadrilateral = 360°

Sum the angles and equate to 360

x + x + 120 + 90 = 360

2x + 210 = 360 ( subtract 210 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

Then ∠ X = ∠ Y = 75°

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

(7)

The sum of the interior angles of a hexagon = 720°

Sum the angles and equate to 720

x + x + 108 + 103 + 149 + 90 = 720

2x + 450 = 720 ( subtract 450 from both sides )

2x = 270 ( divide both sides by 2 )

x = 135

Then ∠ X = ∠ Y = 135°

Answer:

Step-by-step explanation:

Sum of the interior angles of a regular polygon:

Quadrilateral has sum of angles:

Sum the given angles and consider x = y as marked congruent:

Hexagon has sum of angles:

Sum the given angles and consider x = y as marked congruent:

Answer:The pool must have been the same depth at the start of the interval as it was at the end of the interval.

Step-by-step explanation:

The average rate of change is calculated as:

[final value - initial value] / time interval.

Then, the average rate of change does not take into account intermediates values, and you cannot draw any conclusion about such intermediate values.

In the given case you have:

average rate of change in depth = [final depth - initial depth] / 2 weeks.

0 = [final depth - initial depth] / 2 weeks.

⇒ 0 = final depth - initial depth

⇒ final depth = initial depth.

That is why the conclusion is the second statement of the answer choices: the pool must have been the same depth at the start of the interval as it was at the end of the interval.

In between the pool might have been deeper, more shallow, empty or change in any form, since the average rate of change does not tell the full history but only the net change.

Answer:

The pool must have been the same depth at the start of the interval as it was at the end of the interval.

Step-by-step explanation:

got it right on edge.

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

x=50

Step-by-step explanation:

1. multiply the numbers

48x25=24x

1200=24x

2. Divide both sides by the same factor

1200/24 = 24/24x

simplify the expression

x=50

Answer: i cant understand that laugaue so hopefully u do well sorry

Step-by-step explanation:

Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.

X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .

heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!

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Answer:

B)

Step-by-step explanation:

4+5*(3^2-9)/3^2=4+5*0/9=4

Answer:

the answer to your question is 4 3/8 , hope this helps have a good rest of your day :)

A study comparing one group of participants who are randomly assigned to receive a drug with another group of participants who are randomly assigned to receive a placebo is called a randomized controlled trial (RCT).

The purpose of an RCT is to evaluate the effectiveness of a treatment or intervention by comparing it to a control group that receives a placebo or alternative treatment. This design is commonly used in clinical research to establish causal relationships between treatments and outcomes.

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The probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it, and selecting another black is 9/25.

To find the probability follow these-

Determine the probability of selecting a black checker on the first draw.

There are 6 black checkers and a total of 10 checkers (6 black + 4 red).

So, the probability of selecting a black checker on the first draw is 6/10,

which can be simplified to 3/5.

Since the black checker is replaced, there are still 6 black checkers and

a total of 10 checkers in the bag. Therefore, the probability of selecting a

black checker on the second draw is also 3/5.

To find the probability of both events occurring, multiply the probabilities together: (3/5) × (3/5) = 9/25.

So, the probability of selecting a black checker from a bag of 6 black and

4 red checkers, replacing it, and selecting another black is 9/25.

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