A central angle is an angle whose vertex is at center of a circle. Find measure angle ACC

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]

is there a picture included in this problem? if so please comment it so i can answer this problem.

The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

According to the statement

we have given that the property of the hypotenuse of the triangle and we have to complete it.

So, For this purpose, we know that the

A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.

Now we discuss about the properties of the hypotenuse;

And from these properties we have to complete the given property.

So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

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The conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

We know that the conditional probability is given by,

P(B | A) = probability of occurrence of event B, given that event A has

               occurred

           = P(A ∩ B) / P(A)

Here, P(A ∩ B)  means the probability of happening two events A and B at the same time.

We also know that  if  P (B | A ) = P(B)   i.e.,   P(A ∩ B) = P(A) × P(B)  the two events A and B are independent of each other.

For this question, let the dice D1 and D2 are rolled once.  

Let the numbers displayed on the dice be d1 and d2 respectively.  

The dice D1 and D2 are independent.

We need to find the conditional probability that the sum is greater than 6, given that neither die is a two.

Let S represents the sum of the numbers displayed on the dice.

S = d1 + d2

The sum is even, if d1 = d2 is odd OR  if d1 = d2 is even

P(d1 = even) = 3/6

                    =1/2

P(d2=even) = 1/2

P(d1 = odd) = 1/2

P(d2 = odd) = 1/2

So, P(S = even) = [P(d1=even) × P(d2 = even)] + [P(d1= odd) × P(d2=odd)]

                          = [1/2 × 1/2] + [1/2 × 1/2]

                          = 1/2

So, we can say that, the sum is either even or odd which are equally likely and hence its probability is 1/2.

First we find the probability for the sum is greater than 6 i.e., P(S > 6)

The possible combination of d1 and d2 for the sum greater than 6 would be,

{(1,6), (2,5), (2, 6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6) = 21

The number of all possible outcomes = 36

So, P(S > 6) = 21/36

                   = 7/12

Now we find the probability that neither die is a two

⇒ P(neither die is a two) = [P(1) ∪ P(3 ≤ d1 ≤ 6)]  AND  [P(1) ∪ P(3 ≤ d1 ≤ 6)]

⇒ P(neither die is a two) = 5/6 × 5/6

⇒ P(neither die is a two) = 25/36

Now, we find the probability that the sum S > 6 AND  neither die is a two.

The possible combination for  the sum S > 6 AND  neither die is a two would be,

{(1,6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6 AND neither die is a two) = 17

So, P(S > 6 AND neither die is a two) = 17/36

Now we find the conditional probability P(S > 6 | neither die is a two)

⇒ P(S > 6 | neither die is a two) = P(S > 6 AND neither die is a two) ÷

                                                           (neither die is a two)

⇒ P(S > 6 | neither die is a two) = (17/36) / (25/36)

⇒ P(S > 6 | neither die is a two) = 17/25

Therefore, the conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

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Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

At the null hypothesis, it is tested if the mean is of 7 ounces, that is:

[tex]H_0: \mu = 7[/tex]

At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:

[tex]H_1: \mu \neq 7[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given by:

[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]

Hence the value of the test statistic is found as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]

t = 1

Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]

Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

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Answer:

2

Step-by-step explanation:

just because all three numbers are even

Hope this helps

The greatest common factor of 30, 22, and 8 will be 2.

The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.

In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.

For example in 6 and 12 6 is the highest common factor.

The factor of 30 ⇒ 2,3,5

The factor of 22 ⇒ 2,11

The factor of 8 ⇒ 2,4

The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.

Hence "The greatest common factor of 30, 22, and 8 will be 2".

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Answer: 104 degrees farenheit

Step-by-step explanation:    H =  record high temperature. -5 + 109 = H. -5+109 = 109 + (-5) = 109-5 = 104. H = 104.

Answer:

104

Step-by-step explanation:

Let x = record high and y = record low temperature in Charlotte. The difference between the records high and low, x and y, is 109 degrees Fahrenheit, so x - y = 109. Record low is -5, so x - (-5) = 109.

x + 5 = 109

x = 104

Answer:

Find the interval of convergence of the following series

Possible Answers:

(4,6)

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Correct answer:

(4,6)

Explanation:Find the interval of convergence of the following series

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Explanation:

Step-by-step explanation:

Find the interval of convergence of the following series

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Correct answer:

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Explanation:

Find the interval of convergence of the following series

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Correct answer:

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Explanation:Find the interval of convergence of the following series

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Explanation:

Find the interval of convergence of the following series

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Correct answer:

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Explanation:

Find the interval of convergence of the following series

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Correct answer:

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Find the interval of convergence of the following series

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Correct answer:

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Explanation:Find the interval of convergence of the following series

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Correct answer:

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Explanation:Find the interval of convergence of the following series

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Correct answer:

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Explanation:Find the interval of convergence of the following series

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Correct answer:

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Explanation:

Find the interval of convergence of the following series

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Correct answer:

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Explanation:Find the interval of convergence of the following series

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Explanation:

Answer:

The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     [tex]\frac{1}{12}[/tex] turns

9 hours     ⇒     [tex]\frac{1}{12}[/tex]  × 9 = [tex]\frac{9}{12}[/tex]

                                     = [tex]\bf \frac{3}{4}[/tex] turns    (simplified)

∴ The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

The answer is  [tex]\boxed{\frac{3}{4}}[/tex].

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.

For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.

Find the slopes of AB, BC and AC

Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5

Slope of BC = 0-5/7-1
Slope of BC = -5/6

Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11

Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

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Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km.  Point C's distance from A is 5.92 km east and 2.16 km south.

To find the distance from point B to point A, the Cos function should be used.

Point A's distance from B can be found as:

= Cos (143 - 90) x distance from point A

= Cos (53°) x 2.7

= 1.62 km

The distance of C from A eastward is:

= 1.62 + 4.3

= 5.92 km

As C is southward from point A, the function to be used is the Sin function.

The distance southward of c from A is:

= Sin(53°) x 2.7

= 2.16 km

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Answer:

no

Step-by-step explanation:

So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.

x + 1 = 0

x = -1

The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.

Original Equation:

[tex]12x+5x+3x^2-5[/tex]

Plug in -1 as x

[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]

Multiply values

[tex]-12-5+3(1)-5[/tex]

Simplify:

[tex]-17+3-5\\-14-5\\-19[/tex]

Since the value of the polynomial is not 0, this means x+1 is not a factor

You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic

Remainder Theorem:

   If a polynomial P(x) is divided by x-a, the remainder is P(a)

Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states

Factor Theorem:

   The expression "x-a" is a factor of P(x) if and only if P(a) = 0

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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Answer:

see explanation

Step-by-step explanation:

basically Gauss' method simplifies to

Sum = (number of terms) ÷ 2 × (1st term + last term)

43

S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100

44

S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200

45

S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400

46

S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000

Answer:

Sum = (number of terms) = 2 x (1st term + last term) 43

43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100

44 400 400 = 2 × (1+400) = 200 × 401 = 80,200

45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400

46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000

Answer:

[tex]\displaystyle{\sin \theta = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{a^2-b^2}{2ab}}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle{\tan \theta = \dfrac{2ab}{a^2-b^2}}[/tex]

To find other trigonometric ratios, first, we have to know that there are total 6 trigonometric ratios:

[tex]\displaystyle{\sin \theta = \sf \dfrac{opposite}{hypotenuse} = \dfrac{y}{r}}\\\\\displaystyle{\cos \theta = \sf \dfrac{adjacent}{hypotenuse} = \dfrac{x}{r}}\\\\\displaystyle{\tan \theta = \sf \dfrac{opposite}{adjacent} = \dfrac{y}{x}}\\\\\displaystyle{\csc \theta = \sf \dfrac{hypotenuse}{opposite} = \dfrac{r}{y}}\\\\\displaystyle{\sec \theta = \sf \dfrac{hypotenuse}{adjacent} = \dfrac{r}{x}}\\\\\displaystyle{\cot \theta = \sf \dfrac{adjacent}{opposite} = \dfrac{x}{y}}[/tex]

Since we are given tangent relation, we know that [tex]\displaystyle{y = 2ab}[/tex] and [tex]\displaystyle{x = a^2-b^2}[/tex], all we have to do is to find hypotenuse or radius (r) which you can find by applying Pythagoras Theorem.

[tex]\displaystyle{r=\sqrt{x^2+y^2}}[/tex]

Therefore:

[tex]\displaystyle{r=\sqrt{(a^2-b^2)^2+(2ab)^2}}\\\\\displaystyle{r=\sqrt{a^4-2a^2b^2+b^4+4a^2b^2}}\\\\\displaystyle{r=\sqrt{a^4+2a^2b^2+b^4}}\\\\\displaystyle{r=\sqrt{(a^2+b^2)^2}}\\\\\displaystyle{r=a^2+b^2}[/tex]

Now we can find other trigonometric ratios by simply substituting the given information below:

Hence:

[tex]\displaystyle{\sin \theta = \dfrac{y}{r} = \dfrac{2ab}{a^2+b^2}}\\\\\displaystyle{\cos \theta = \dfrac{x}{r} = \dfrac{a^2-b^2}{a^2+b^2}}\\\\\displaystyle{\csc \theta = \dfrac{r}{y} = \dfrac{a^2+b^2}{2ab}}\\\\\displaystyle{\sec \theta = \dfrac{r}{x} = \dfrac{a^2+b^2}{a^2-b^2}}\\\\\displaystyle{\cot \theta = \dfrac{x}{y} = \dfrac{a^2-b^2}{2ab}}[/tex]

will be other trigonometric ratios.

Answer:

2.571428

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean.

To solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

A quadratic equation is solved using the quadratic formula, [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex], when the equation is in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

In the question, we are asked for the first step in solving a² - 5 = -2.

We can see that the provided equation is quadratic in the variable a.

To solve, the equation, we first need to represent the given equation in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

To represent it in the standard form, we add 2 to both sides of the equation, to get a² - 5 + 2 = -2 + 2, or, a² - 3 = 0, which is a standard quadratic equation in the variable a.

Thus, to solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

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[4] Answer: (-4, 1)

[5] Answer: Infinite solutions

        See attached for the graphs.

Step-by-step explanation:

      The solution to a system of equations, when graphing, is the point of intersection. In other words, the point at which the lines intersect each other.

      In the case of problem 5, the equations are equal so they overlap. This means there are infinite solutions.

The first term of the arithmetic progression exists at 10 and the common difference is 2.

let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.

We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula

The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.

9th term = 50

a + 8d = 50 ...............(1)

12th term = 65

a + 11d = 65 ...............(2)

subtract them, (2) - (1), we get

3d = 15

d = 5

If a + 8d = 50 then substitute the value of d = 5, we get

a + 8 [tex]*[/tex] 5 = 50

a + 40 = 50

a = 50 - 40

a = 10.

Therefore, the first term is 10 and the common difference is 2.

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A major advantage of a direct implementation is that people whose roles span modules do not have to switch back and forth between old and new modules.

With this technique, the machine is implemented and tested to make certain it plays well. Then the antique machine is removed and the brand new one is put in its area without any overlap or restricted rollout.

There are three predominant methods used: phased implementation, direct changeover, and parallel going for walks. Phased implementation: A staged technique whereby one part of the overall system that desires change is changed.

Structures implementation is the process of defining how the data device needs to be built (i.e., physical machine design), ensuring that the records gadget is operational and used, and ensuring that the information device meets greatly preferred i.e. nice warranty.

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Step-by-step explanation:

abx^2-aby^2+xya^2-xyb^2

abx^2+xya^2-aby^2-xyb^2

ax(bx+ya)-yb(ay+xb)

ax(bx+ya)-yb(xb+ay)

(ax-yb) (bx+ya)

Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways

We are given the quantity of each type of cupcake as follows;

Number of types of cupcakes = 5

Number of Chocolate Cupcakes = 12

Number of Vanilla Cupcakes = 12

Number of Lemon cupcakes = 12

Number of Strawberry Cupcakes = 12

Number of coffee cupcakes = 12

Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12

Total number of cupcakes = 60

Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)

Thus, number of ways that you can choose 12 cupcakes =

60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways

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The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K). The measure of the missing angle can be found by using the trigonometric function of cosine:

cos m ∠ J = KJ / JL

cos m ∠ J = 12 / 13

m ∠ J = 22.620°

The measure of the angle J within the triangle JKL is approximately 22.620°.

And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:

sin m ∠J = √(1 - cos² m ∠J)

sin m ∠J = √[1 - (12 / 13)²]

sin m ∠J = 5 / 13

The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).

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Answer:

The distance is 36 miles.

Step-by-step explanation:

distance in either direction = d

total time = 5

time going = t

time returning = 5 - t

speed = distance/time

going:

speed = distance/time

18 = d/t

d = 18t       Eq. 1

returning:

speed = distance/time

12 = d/(5 - t)

60 - 12t = d

d =  60 - 12t     Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

d = 18t

d = 60 - 12t

Since d = d, then 18t must equal 60 - 12t

18t = 60 - 12t

30t = 60

t = 2

d = 18t = 18(2) = 36

The distance is 36 miles.

Answer:

x > 6

Step-by-step explanation:

2x - 7 > 5

2x > 5 + 7

2x > 12

x > 6

Answer:

Option 3

Step-by-step explanation:

Since the denominators are the same, you can just subtract the numerators.

Answer:

105.

Step-by-step explanation:

x/120 = 56/64   where x is the length of missing segment

64x = 120*56

x =  (120*56)/64

  =  105.

Answer: -49152

Step-by-step explanation: the pattern here is that each term is subtracting 3 times its absolute value. Going from -3 to -12 there is a difference of 9 which is 3 times to absolute value of -3. So, the sequence will continue like this : -192, - 768, -3072, - 12288, -49152.