In the figure below, circle O has a central ángel of 120 degrees. what is the area shaded of the circle in terms of ,r, the radius? Leave your answer in terms of pi.
​

Answer:

L ≈ 1023.0562

Step-by-step explanation:

We are given;

x = t² - 2t

dx/dt = 2t - 2

Also, y = t^(5)

dy/dt = 5t⁴

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt

L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt

L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt

Using online integral calculator, we have;

L ≈ 1023.0562

The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.

Given :

First, differentiate x and y with respect to 't'.

[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]

[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]

Now, determine the length of the curve using the below formula:

[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]

Now, substitute the value of the known terms in the above formula and then integrate it.

[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]

[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]

Now, simplify the above integration using the calculator.

L = 1023.0562

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[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]

Answer:

√32

Step-by-step explanation:

Explanation:

The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).

Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.

Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.

You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.

Answer:

Point D is located at (5, -2)

Step-by-step explanation:

The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2

Answer: 45

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 99 - 54 or 45. So the range of this data set is 45.

Answer:

Step-by-step explanation:

Given data:

83 , 71 , 62 , 86 , 90 , 95 , 61 , 60 , 87 , 72 , 95 , 74 , 82 , 54 , 99 , 62 , 78 , 76 , 84 , 92

largest value = 99

Smallest value = 54

Let's find the range:

Range = Largest value - smallest value

= 99 - 54

= 45

Extra information:

Range

It is the simple method of measuring the variations. A range is defined as the difference between the largest and the smallest value of distribution. If the data are arranged in ascending or descending order, then the difference between the largest and smallest value is called the range.

The range is defined by

Range = Largest value - smallest value i.e ( highest value - lowest value )

= L - S

Range is the absolute measure of dispersion = L - S

Thus, if a₁ , a₂ , a₃ ...............aₙ are n term in a sequence arranged in ascending order, the range is given by

R = aₙ - a₁ where a₁ is the smallest value and aₙ is the highest value or R = L - S , where L is the largest value and S is the smallest value.

Hope I helped!

Best regards!

Work Shown:

(f+g)(x) = f(x) + g(x)

(f+g)(x) = 2x+6 + 4x^2

(f+g)(x) = 4x^2+2x+6

Answer:

Step-by-step explanation:

This is a bit ambiguous. I will answer it as (-4) - 3 = - 4 - 3 = - 7

However it could be (-4)(-3) = 12

Moral, with this editor use brackets.

Answer:

-54 is a integer and rational number

Step-by-step explanation:

Answer:

D question,somewhat confusing, itsit's like simultaneous equation,but values are different

Answer:

x = 4 + 2y/3

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

From the picture attached,

Bar graph sketched shows the grades earned by the students in an exam.

Number of students who achieved the grade A = 17

Number of students who achieved grade B = 14

Number of students with grade C = 5

Number of students with grade D = 9

Total students who took the exam = 17 + 14 + 5 + 9 = 45

Option (1)

"[tex]\frac{1}{5}[/tex] of the students earned a C"

Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]

                                                          = [tex]\frac{5}{45}[/tex]

                                                          = [tex]\frac{1}{9}[/tex]

Therefore, this option is incorrect.

Option (2)

"3% more students earned an A then B"

Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                = [tex]\frac{17}{45}\times 100[/tex]

                                                                = 37.78%

Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                = [tex]\frac{14}{45}\times 100[/tex]

                                                                = 31.11%

Difference in percentage = 37.78 - 31.11

                                          = 6.67%

Therefore, this option is not correct.

Option (3)

"20% of the students earned a D"

Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                 = [tex]\frac{9}{45}\times 100[/tex]

                                                                 = 20%

Option (3) is the correct option.

Option (4)

" [tex]\frac{1}{4}[/tex] of the class earned a B"

Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]

                                                    = [tex]\frac{14}{45}[/tex]

Therefore, Option (4) is not correct.                                        

Answer:

174 cm²

Step-by-step explanation:

The figure given is a prism with isosceles trapezoid as base.

Its surface area can be calculating the area of each face that makes up the prism, and summing all together.

There are 6 faces. Their dimensions and areas can be calculated as follows:

2 isosceles trapezium:

It has 2 parallel bases, (a and b), of 4cm and 6cm,

Height (h) = 2.8cm

Area = ½(a+b)*h

Area = ½(4+6)*2.8

Area = ½(10)*2.8 = 5*2.8 = 14 cm²

4 rectangles of different dimensions:

Rectangle 1 (down face): l = 10cm, b = 4cm

Area = 10*4 = 40 cm²

Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm

Area = 2(l*b) = 2(10*3) = 60cm²

Rectangle 4 (top face) = l = 10cm, b = 6cm

Area = 10*6 = 60cm²

Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²

Answer:

C. -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.

A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.

B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.

C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.

Hope this helps!

Answer:

Whatever is raised to the power of 0 is 1

SO the answer is 1

Answer:

A. -f(1/2 x)

Step-by-step explanation:

Reflextion about the x-axis is

f(x) -> -f(x)

and horizontal dilation is

f(x) -> f(-x/b) where b is the factor of dilation.

so the proper answwer is

A. -f(1/2 x)

Answer:

D

Step-by-step explanation:

-3, 3, 6, 9, 15, 18, 21,

Answer:

[tex]x = 3.6[/tex]

Step-by-step explanation:

To find the area of a rectangle, you multiply its length by its width. The formula is [tex]lw = a[/tex].

We already know the length, 5, and the area, 18, so we can plug it into the equation.

[tex]5\cdot w=18[/tex]

We can simplify this equation by dividing both sides by 5.

[tex]5\cdot w \div5 = 18\div5\\\\w = 3.6[/tex]

Hope this helped!

Answer: x= 13

Step-by-step explanation:

should be 2 3 andd 5

think of the - (- as a plus sign (this is what i was always taught) to add them so it would in turn be (-5) + 12 which equals 7 and choice 3 and 5 also equal this

Answer:

[tex]x {}^{2} - 2x = 48[/tex]

[tex]x { }^{2} - 2x - 48 = 0[/tex]

using quadratic formula,

[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]

[tex]2 + \sqrt{196} \div 2[/tex]

[tex]2 + 14 \div 2[/tex]

[tex]x = 8[/tex]

or

[tex]x = - 6[/tex]

Answer:

4

Step-by-step explanation:

I got it right on Khan

The value of x is 4.

A triangle is a polygon in two dimensional geometry. I has three sides and three angles along with three vertices.

Area of a triangle = [tex]\frac{1}{2}[/tex] × b × h

where b is the base of the triangle and h is the length of height of the triangle.

The given triangle is an obtuse triangle which has an angle equal to greater than 90 degrees. So the height of the triangle is found by drawing a perpendicular line from the base to the opposite vertex.

Here, height = x and base length = 6

Area = 12 units²

[tex]\frac{1}{2}[/tex] × 6 × h = 12

6 × h = 12 × 2

6 × h = 24

h = 24/6

h = 4 units.

Hence the length of the height which is x is 4 units.

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#SPJ2

Answer:

its b and e

Step-by-step explanation:

The statements given in options B and E are   true so options B and E are right options.  

Given some statements we have to determine that which of the following statements are true

The given statements are as follows

A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.

B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.

C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.

D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

We know some facts about each type of geometry

In Euclidean geometry  plane is used to plot the points and line.

In spherical geometry uses the sphere to plot the points and circles

Elliptical geometry is such a geometry where no parallel lines exists.

The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with   and they can be written down in the following points

So from the above observations we can conclude that statements given in options B and E are   true so options B and E are right options.  

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Answer:

65%

Step-by-step explanation:

If 14 are male, then 26 are female.

To find the percent female, divide the number of females by the total.

26/40 = 0.65

So, the percentage of the class that is female is 65%

Answer:

C. 65%

Step-by-step explanation:

We know that of the 40 total students, 14 are male, which means the remaining students are female.

To find how many are female, we subtract 14 from 40:

40 - 14 = 26 females

Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:

(26 / 40) * 100 = 65

The answer is thus C, 65%.

~ an aesthetics lover

Answer:

Step-by-step explanation:

12 eggs in one box

12 boxes = 1 crate

12 x 12 = 144 eggs

144 x 24 crates = 3456 eggs

Answer:

3,456 eggs

Step-by-step explanation:

There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12

12*12=144

144 eggs in one crate.

We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.

144*24=3,456

There are 3,456 eggs in 24 crates.

Answer:

a. 2

b. x^2 + 10x + 26

c. x^2 + 2x + 2

Step-by-step explanation:

For each part, replace x with the value you are given and simplify.

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

a.

f(2) = 2^2 - 2(2) + 2 = 2

b.

f(x + 6) = (x + 6)^2 - 2(x + 6) + 2

= x^2 + 12x + 36 - 2x - 12 + 2

= x^2 + 10x + 26

c.

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

= x^2 + 2x + 2

Answer:

length: 9cm

width: 9cm

Step-by-step explanation:

9×9=81

Answer:

yes

Step-by-step explanation:

Answer:

60/220

Step-by-step explanation:

we use combination,

[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]

[tex]5 \times 4 \times 3 = 60[/tex]

then, all divided by,

[tex] (\frac{12}{3}) = 220 [/tex]

[tex]60 \div 220[/tex]

The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{5}{12}[/tex]

Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is

[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{11}[/tex]

Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{10}[/tex]

Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is

[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]

Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

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Answer:

The 99%  confidence interval is  [tex]97.94 < \mu < 98.26[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  110

     The  sample mean is  [tex]\= x = 98.1 \ F[/tex]

       The standard deviation is  [tex]\sigma = 0.64 \ F[/tex]

Given that the confidence level is  99% the level of significance i mathematically evaluated as

                  [tex]\alpha = 100 - 99[/tex]

                  [tex]\alpha = 1\%[/tex]

                  [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is  

          [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

          [tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]

          [tex]E = 0.1574[/tex]

Generally the  99% confidence interval  is mathematically represented as

               [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

             [tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]

             [tex]97.94 < \mu < 98.26[/tex]

Answer:

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

divide both by two for its simplest form

Answer:4/7

Step-by-step explanation

Divide both the numerator and denominator by 2

The result for the numerator is 8/2=4

that of the denominator is 14/2=7

Therefore the resultant answer is 4/7

Answer:

Explained below.

Step-by-step explanation:

The ANOVA and Regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal is provided.

(A)

The estimated regression equation equation is:

[tex]y=6.1092+0.8931x[/tex]

Here,

y = maintenance expense (dollars per month)

x = usage (hours per week) for a particular brand of computer terminal

(B)

Consider the Regression output.

The hypothesis to test whether monthly maintenance expense is related to usage is:

H₀: The monthly maintenance expense is not related to usage, i.e. β = 0.

Hₐ: The monthly maintenance expense is related to usage, i.e. β ≠ 0.

Compute the test statistic as follows:

[tex]t=\frac{b}{S.E._{b}}=\frac{0.8931}{0.149}=5.99[/tex]

Compute the p-value as follows:

[tex]p-value=2\times P (t_{8}<5.99}=0.00033[/tex]

The null hypothesis will be rejected if the p-value is less than the significance level.

p-value = 0.00033 < α = 0.05

Reject the null hypothesis.

(C)

Monthly maintenance expense​ is related to usage.

(D)

Yes, the estimated regression equation provide a good fit.

Since the regression coefficient is significant it can be concluded that the regression equation estimated is a good fit.

From the regression output given, the solution to the questions given are outlined thus ;

1.)

Regression equation :

Hence, the estimated regression equation is;

2.)

We can calculate the T-statistic value thus ;

Hence, the T-statistic is given as ;

[tex] T-statistic = \frac{0.8931}{0.149} = 5.99[/tex]

Pvalue (2 tailed) = 0.00033

Decison Region :

Since 0.00033 < 0.05 ; we reject the Null hypothesis.

3.)

Hence, we conclude that monthly expense is related to usage.

4.)

Since, the correlation Coefficient, β ≠ 0 ; Yes, the correlation provides a good fit as it is significant.

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Answer:

(a) 1155.84

(b) 48.2%

(c) D

Step-by-step explanation:

The number of total responses is, N = 38,528.

(a)

It is provided that 3% answered with "a lot".

Compute the actual number of responses consisting of "a lot" as follows:

n (a lot) = N × P (a lot)

            = 38528 × 0.03

            = 1155.84

Thus, the actual number of responses consisting of "a lot" is 1155.84.

(b)

The number of responses consisting of "very little or none" is,

n (very little or none) = 18,566

Compute the percentage of responses consisted of "very little or none" as follows:

[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]

                                  [tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]

The percentage is: 0.482 × 100% = 48.2%.

Thus, the percentage of responses consisted of "very little or none" is 48.2%.

(c)

As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.

Thus, making the sample statistic an unbiased estimator of the population parameter.

And proving that the sample is a true representative of the population.

Thus, the correct option is (D).