Find the radius of the circle if the center is at (1, 2) and the point (-5, 6) lies on the circle.

On a coordinate plane, a circle has center point (1, 2). A point on the circle is at (negative 5, 6).

Answer:

The answer is B since the chance is expontential since it gets bigger over time and each one is farther apart

The best-fitting regression model for the scatterplot is Exponential, the correct option is B.

When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve(exponential) on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.

We are given;

The graph representation

Now,

By visual inspection of the scatterplot, we can see that the points do not follow a clear pattern that suggests an exponential or quadratic relationship. However, there appears to be a linear relationship between the variables.

Therefore, the answer will be exponential.

Learn more about exponential regression here:

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Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

[tex]\lambda = \frac{29742}{365} = 81.485[/tex]

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]

0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

how many layers of bricks are used ?

also, I assume, the thickness of bricks means actually their height when laid.

but still, I cannot answer that, as nothing indicates if there is only one layer of bricks or 2 or 3 or 4 or ...

Answer:

1. Tyler

2. 8.33

3. 8.5

4. Tyler

Step-by-step explanation:

this is just playing with the numbers. no complex math concepts.

Tyler's graph shows she reached 1 mile after 8 1/3 minutes (8 minutes and 20 seconds). that is 25/3 minutes.

according to Elena's equation she reached 1 mile (x=1) after 8.5 minutes. that is 8 1/2 minutes or 8 minutes and 30 seconds.

so, we see that Elena took more time (10 seconds longer) to run 1 mile, so Tyler was faster.

to generally compare the 2 we can write also Tyler's graph as function (like for Elena) :

8 1/3 = 8.333333....

y = 8.33x

but that is just FYI (not asked for here).

since Tyler was faster (and her graph also showed a straight line of time and distance up to 10 minutes and beyond, so, she did not slow down after the first mile), she also ran further after 10 minutes. that is the definition of "being faster" - to go further in the same amount of time.

Tyler needed 8.33 minutes per mile.

Elena needed 8.5 minutes per mile.

and so, Tyler was faster.

points 1 and 4 are directly coupled. they both express the same thing.

Answer:

3

Step-by-step explanation:

x 1，2，3，4

y-3，-5，-7，-9

[tex]y = - 3 - (x - 1) \times 2[/tex]

The linear function is given by y = 7x - 4

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

From the table, using the points (1, 3) and (4, 24):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]

The linear function is given by y = 7x - 4.

Find out more on linear function at: https://brainly.com/question/4025726

Answer:

(2,3) (4,2) (5,2) (1,4) (0,2)

Step-by-step explanation:

because all these points have something common to each other. Now pay attention in your class and stop cheating!!

Answer:

Step-by-step explanation:

eq. of circle is (x-2)²+(y-3)²=10²

now substitute the values of x and y

which satisfies the above eq.that point lies on the circle.

Answer:

The participants can be assigned in 224 different ways.

Step-by-step explanation:

Given that you are designing an experiment using human subjects, and the study will include 30 participants, of which 16 will be placed in the experimental group and the remaining 14 will be placed in the control group, to determine in how many ways can you assign participants to the two groups the following calculation must be performed:

16 x 14 = X

224 = X

Therefore, the participants can be assigned in 224 different ways.

Answer:

79.5, 110.5, 141.5, 172.5, 203.5, 234.5

Step-by-step explanation:

Given

The attached distribution

Required

The lower class limits

To do this, we simply subtract 0.5 from the lower interval

From the attached distribution, the lower intervals are:

80.0, 111.0, 142.0, 173,0 .......

So, the lower class limits are:

[tex]80.0-0.5 = 79.5[/tex]

[tex]111.0-0.5 = 110.5[/tex]

[tex]142.0-0.5 = 141.5[/tex]

[tex]173.0-0.5 = 172.5[/tex]

[tex]204.0-0.5 = 203.5[/tex]

[tex]235.0-0.5 = 234.5[/tex]

Answer:

y = -x.

Step-by-step explanation:

The slope of the line (m) = -1.  ( because of the -x in y = -x - 5)

y - y1 = m (x - x1)    where (x1, y1) is a point on the line, so we get;

y - 2 = -1(x - (-2))

y - 2 = -x + -1 * +2

y - 2 = -x - 2

y = -x.

Answer:

No mode

Step-by-step explanation:

Mode = number that appears the most

No number appears more than 1 time

Hence there is no mode

Answer:Should be no mode tell me if i'I'm wrong

Step-by-step explanation:

Answer:

main age = total age/total people

if Main age is = 27

[tex]27 = \frac{ \times }{5} [/tex]

and x = 135

Total age is = 135

then main age is 35

[tex][35 = \frac{y}{6} [/tex]

and y = 210

first main age - second main age = age of the person participating

210 - 135 = 75

HAVE A NİCE DAY

Step-by-step explanation:

GREETINGS FROM TURKEY

Answer:

The center of the circle is found at h,k

These values represent the important values for graphing and analyzing a circle.

Center: 0,0

And also,

Algebra Graph x^2+y^2=25 x2 + y2 = 25 x 2 + y 2 = 25 This is the form of a circle.

And also,

Simple and best practice solution for X2+y2=25 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework. If it's not what You are looking for type in the equation solver your own equation and let us solve it.

And also,

Match the values in this circle to those of the standard form. The variable r r represents the radius of the circle, h h represents the x-offset from the origin, and k k represents the y-offset from origin. The center of the circle is found at (h,k) ( h, k).

And also,

Ox (0) 6°x= 1) 6x ** + y = 25 SOLUTION (a) Since f(x) = 25 - x2 0, we can interpret this integral as the area under the curve y = 25 - x2 from 0 to 5 . But since y2 = 25 - x2 , we get x2 + y2 = 25, which shows that the graph of fis a quarter-circle with radius 5 in the top figuer

And also,

(3x2y2)3 Final result : 32x2y2 Reformatting the input : Changes made to your input should not affect the solution: (1): "y2" was replaced by "y^2".

And thats all!

Solution graph is image 2.

We first graph [tex]x^2+y^2=25[/tex]. This is a circle with center = (0,0) and radius = [tex]\sqrt{25} =5[/tex].

For [tex]x^2+y^2<25[/tex], we'll shade inside the circle.

[tex]y^2=6x[/tex] is a parabola.

we make a table for it.

x   -1   0   1

y   -6  0   6

For [tex]y^2<6x[/tex] we'll shade inside the parabola.

So the graph will be image 1.

So the solution region is image 2.

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9514 1404 393

Answer:

  517 minutes

Step-by-step explanation:

There are 60 minutes in an hour, so 8×60 = 480 minutes in 8 hours.

In 8 hours 37 minutes, there are ...

  480 min + 37 min = 517 minutes

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

∴

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Answer:

See Below.

Step-by-step explanation:

We can write a two-column proof.

Statements:                                                Reasons:

[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex]                                                   Given

[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex]                                                   Vertical Angles are Congruent

[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex]                                          Linear Pair

[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex]                                          Substitution

[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex]                                          Substitution

[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex]                  Definition of Supplementary Angles

Answer:

[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]

Step 2: Find

B is the answer.

The triangles doesnt creates a SSS,SAS,SAA, scenario.

This triangle isn't ASA because the triangles share the same side but it have different angles that include the side.

Answer:

Costco

Step-by-step explanation:

We find the cost per egg for each of the three stores.

Costco:

$9.35/(60 eggs) = $0.15583/egg

Safeway:

$4.79/(12 eggs) = $0.39917/egg

Trader Joe's:

$6.18/(18 eggs) = $0.34333/egg

The best deal is Costco.

Answer:

Costco

Step-by-step explanation:

[tex]\frac{60}{9.35}: \frac{1}{y}[/tex]

60 × y = 1 × 9.35

60y = 9.35

60y ÷ 60 = 9.35 ÷ 60

[tex]y=\frac{187}{1200}[/tex]

[tex]\frac{12}{4.79}: \frac{1}{y}[/tex]

12 × y = 1 × 4.79

12y = 4.79

12y ÷ 12 = 4.79 ÷ 12

[tex]y=\frac{479}{1200}[/tex]

[tex]\frac{18}{6.18}: \frac{1}{y}[/tex]

18 × y = 1 × 6.18

18y = 6.18

18y ÷ 18 = 6.18 ÷ 18

[tex]y=\frac{103}{300}=\frac{412}{1200}[/tex]

Answer:i think its 20

Step-by-step explanation: 20 x 2 is 40 plus 5 is 45

Answer:

✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20

Step-by-step explanation: Algebra.com

Answer:

a) 0.4658 = 46.58% probability that the chosen ball is blue

b) 0.322 = 32.2% probability that it came from the first urn

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. What is the probability that the chosen ball is blue?

6/20 = 0.3 of 0.5(first urn)

12/19 = 0.6316 out of 0.5(second urn).

So

[tex]P(A) = 0.3*0.5 + 0.6316*0.5 = 0.4658[/tex]

0.4658 = 46.58% probability that the chosen ball is blue.

b. If the chosen ball is blue, what is the probability that it came from the first urn?

Event A: Blue Ball

Event B: From first urn

From item a., [tex]P(A) = 0.4658[/tex]

Probability of blue ball from first urn:

0.3 of 0.5. So

[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.4658} = 0.322[/tex]

0.322 = 32.2% probability that it came from the first urn

Answer:

4 + 5i

Step-by-step explanation:

To calculate this you have to combine the like terms until they cannot be combined any further:

7 + 10i + 4 - 10i - (7 - 5i)

11 + 0i - 7 - 5i

7 & 4 are liked terms so add them together + subtract 10i and 10i

4 + 5i  <--- Final answer

Hope this helps!

Answer:

4 + 5i

Step-by-step explanation:

(7 + 10i) + (4 - 10i) - (7 - 5i)

7 + 10i + 4 - 10i - (7 - 5i)

11 - 7 + 5i

4 + 51

Answer:

C. 468 mm²

Step-by-step explanation:

Surface area of the composite solid = 2(LW + LH + WH)

Length (L) = 12 mm

Width (W) = 6 mm

Height (H) = 2 + 7 = 9 mm

Plug in the values into the formula

Surface area = 2(12*6 + 12*9 + 6*9)

Surface area = 2(72 + 108 + 54)

Surface area = 2(234)

= 468 mm²

Answer:

B

Step-by-step explanation:

B is the correct equation

Answer:

[tex]x = - \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]x = \frac{ - b}{2a} = \frac{1}{ - 2} [/tex]

Answer:

58°

Step-by-step explanation:

Given that,

The measure of two interior angles are 68° and 54º.

We need to find the measurement of the third interior angle.

We know that, the sum of angles of a triangle is equal to 180°. Let the angle is x. So,

x+68+54 = 180

x+122 = 180

x = 180-122

x = 58°

So, the measure of the third interior angle is equal to 58°.

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex],  cos A = [tex]\frac{\sqrt{13} }{3}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]2\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex],  cos A = [tex]\frac{\sqrt{13} }{2}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = [tex]\sqrt{1872}[/tex]

⇒ AB = [tex]12\sqrt{13}[/tex] ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]             -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]

sin A = [tex]\frac{2}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex]             -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]

cos A = [tex]\frac{3}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = [tex]\frac{opposite}{adjacent}[/tex]             -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = [tex]\frac{24}{36}[/tex]

tan A = [tex]\frac{2}{3}[/tex]

Answer:

[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

Hope it helps you! ＼(^ᴥ^)／