a point P is 13cm from the centre of the circle. the lenght of the tangent drawn from P to the circle is 12cm find the radius of the circle
​

The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

To find the total area of the solid figure, we need to determine the areas of each face and then add them together.

The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.

First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:

Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches

Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches

Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.

Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:

Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.

Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:

Total area = Area of rectangular prism + Area of triangular pyramid

Total area = 90 square inches + 27sqrt(3) / 4 square inches.

Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

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Step-by-step explanation:

so, we had

4+3+2+2+6 = 17 experiments

I assume the spinner has 5 equality sized fields with different colors.

so, normally we would assume that in average each color has the same probability : 1/5 (desired results over totally possible results).

the experiments with the actual spinner give us now observational data and probabilities.

after all, a spinner (as a die, or a roulette wheel, or ...) can have slightly different probabilities for the individual outcomes based on design and manufacturing.

so, based on these results we see the actual probabilities like this

red 4/17

blue 3/17

green 2/17

yellow 2/17

purple 6/17

so, the observed probability shows us a probability of blue in the next spin to be 3/17.

please note, that after that next (18th) spin all the observed probabilities have to be updated depending on the actual result.

so, if the result of spin 18 is indeed blue, the probabilities for spin 19 would change to

red 4/18

blue 4/18

green 2/18

yellow 2/18

purple 6/18

What is a Matrix?

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

A)

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)

B)

\(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

C)

A x B = C

\(\left[\begin{array}{cccc}$3.15& $3.79& $2.99&$3.49 \\$2.99& $2.89& $2.79 &$3.29\\ $3.74 &$2.98& $2.89& $2.99\end{array}\right]_{3 x 4}\)  X    \(\left[\begin{array}{c}5*5\\4*5\\5*1\\4*5\end{array}\right]_{4x1}\)

=

\(\left[\begin{array}{c}183.46\\159.66\\179.51\end{array}\right]_{3x1}\)

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Answer:

y=-3x+2

Step-by-step explanation:

y=mx+b

8=-2(-3)+b

8=6+b

b=2

y=-3x+2

Answer:

adult $8.00

child $5.50

Step-by-step explanation:

Let the price of 1 adult ticket = x.

Let the price of 1 child ticket = y.

2x + 4y = 38

3x + 3y = 40.5

Multiply the first equation by 3. Multiply the second equation by -2. Then add them.

         6x + 12y = 114

(+)      -6x - 6y = -81

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

                  6y = 33

y = 33/6

y = 5.5

2x + 4y = 38

2x + 4(5.5) = 38

2x + 22 = 38

2x = 16

x = 8

Answer:

adult $8.00

child $5.50

Answer:

An adult ticket is $8.00 and a child's ticket is $5.50.

Step-by-step explanation:

We form a system of 2 equations and solve them.

Let a be the price of adult ticket and c the price of a child's.

2a + 4c = 38         (A)

3a + 3c = 40.5      (B)

Multiply equation A by 3 and equation B by -2:

6a + 12c = 114

-6a - 6c = -81        Adding these 2 equations:

0 + 6c = 33

c = 33/6 = 5.5.

Now we substitute for c in equation A:

2a + 4(5.5) = 38

2a = 38 - 22

2a = 16

a = 6.

Let's now check these results by substitution in equation B:

3a + 3c = 40.5

3(8) + 3(5.5) = 24.0 + 16.5 = 40.5

- so it checks out.

Answer:

400 ounces

Step-by-step explanation:

x pound(s) = (16*x) ounces

25 pounds=(16*25) ounces

25 pounds= 400 ounces

400 ounces of quarters were stolen.

Given,

The robber stole only 25 pounds of quarters out of the coin machine. Quarters are weighed in ounces.

If there are 16 ounces in 1 pound.

We need to find out how many ounces of quarters were stolen.

16 ounces = 1 pound

Find how many pounds of quarters were stolen.

= 25 pounds of quarters.

Convert 25 pounds of quarters into ounces of quarters.

1 pound = 16 ounces

Multiplying 25 on both sides.

25 x 1 pound = 25 x 16 ounces.

25 pounds = 400 ounces.

This means 25 pounds of quarters is 400 ounces of quarters.

Thus 400 ounces of quarters were stolen.

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\(\\ \rm\bull\rightarrowtail y=(1x^2)+3(x)\)

\(\\ \rm\bull\rightarrowtail y=1(-6)^2+3(-6)\)

\(\\ \rm\bull\rightarrowtail y=1(36)+(-18)\)

Note the rule

\(\\ \rm\bull\rightarrowtail y=36-18\)

\(\\ \rm\bull\rightarrowtail y=18\)

Answer:

36     -18

18

Step-by-step explanation:

This is slightly confusing, since the question says "find the y coordinate if x = -4" yet underneath if appears they want x = -6 !

If x = -6

Substitute -6 into the equation in place of x

⇒ y = 1 × (-6)² + 3(-6)

Apply the rule (-a)² = a²  and  a(-b) = -ab:

⇒ y = 1 × (6)² + -3×6

⇒ y = 1 × 36 + -18

Using order of operations, carry out the multiplication first:

⇒ y = 36 + -18

Then the addition (subtraction)

⇒ y = 36 - 18

⇒ y = 18

Probability = (3.4 - 1.6) / (5.2 - 1.6)= 0.556Thus, P(X < 3.4) = 0.556.

Given that X has a continuous uniform distribution over the interval (1.6, 5.2] we need to find the following:(a) Determine the mean of X.

(b) Determine the variance of X.

(c) What is P(X< 3.4)?

(a) Determine the mean of X.

The mean of X can be calculated as follows:

Mean of X = (a+b) / 2Here, a = 1.6, b = 5.2

Therefore, Mean of X = (1.6 + 5.2) / 2 = 3.4

Thus, the mean of X is 3.4.(b) Determine the variance of X.

The variance of X can be calculated as follows:

Variance of X = (b - a)² / 12

Here, a = 1.6, b = 5.2

Therefore, Variance of X = (5.2 - 1.6)² / 12= 0.64

Thus, the variance of X is 0.64.

(c) What is P(X < 3.4)?

Since X has a continuous uniform distribution, the probability can be calculated as follows:

Probability = (X - a) / (b - a)Here, a = 1.6, b = 5.2, X = 3.4

Therefore, Probability = (3.4 - 1.6) / (5.2 - 1.6)= 0.556Thus, P(X < 3.4) = 0.556.

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Answer:

Do know sorry I can help but maby

The completed table for the amount of water in the tank at the given time given a constant flow rate of 1.6 is given below :

From the table given :

0.8 gallons of water flowed into the tank in 0.5 minutes ;

Since the flow rate is constant ; we can relate the amount of water, w, flowing into the tank at time, t as thus ;

w α t

w = kt ; where, k = constant of proportionality ;

We can obtain the value of k when w = 0.8 and t = 0.5

Therefore,

0.8 = 0.5k

Divide both sides by 0.5

(0.8÷0.5) = k

k = 1.6

Hence the flow rate of water into the tank is 1.6 ; the equation can be then be written thus ;

w = 1.6t

Let's find ;

w, when t = 1

w = 1.6(1)

w = 1.6

w, when t = 3

w = 1.6(3)

w = 4.8

4.8t, when w = 40

40 = 1.6t

Divide both sides by 1.6

(40 ÷ 1.6) = t

t = 25

Therefore, the constant of proportionality, k is 1.6

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By the De Moivre's formula, the complex numbers i⁷¹, i⁴⁷, i¹⁹ are equivalent to - i.

In this question we have eight cases of powers of complex numbers, of which we must determine what cases are equivalent to the complex number - i. This can be checked by means of De Moivre's formula:

zⁿ = rⁿ · (cos nx + i sin nx)

Where:

Please notice that nx must be in radians.

If we know that r = 1, cos nx = 0, sin nx = - 1 and x = π / 2, then we find that:

The complex numbers i⁷¹, i⁴⁷, i¹⁹ are equivalent to - i.

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Answer:

b)280° and c) 270°

A reflex angle is an angle which is more than 180° but less than 360°

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Step-by-step explanation:

180 is reflex angle.

hope it's helpful

Answer:

120 is the right answer . mark as brainliest

Answer:

90 degrees in clockwise direction on a graph? Rotation of point through 90° about the origin in clockwise direction when point M (h, k) is rotated about the origin O through 90° in clockwise direction. The new position of point M (h, k) will become M' (k, -h).

Step-by-step explanation:

(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcenter

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Answer:

7 inches

Step-by-step explanation:

Volume 1 - 300 pages 2 inches

back cover 1/4 inch

Volume 2 - front cover 1/4 inch

300 pages 2 inches

back cover 1/4 inch

Volume 3 - front cover 1/4 inch

300 pages 2 inches

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

d. Dummy coding. Categorical variables need to be converted into numerical variables to be used in regression analysis. Dummy coding involves creating binary variables for each category of the categorical variable.

For example, if the categorical variable is "color" with categories "red," "green," and "blue," dummy coding would involve creating three binary variables: "red" (0 or 1), "green" (0 or 1), and "blue" (0 or 1). These binary variables can then be used in the regression analysis. In conclusion, to use categorical variables in regression analysis, dummy coding is necessary.


In order to use categorical variables in a regression analysis, they must be converted into numerical values. This process is called dummy coding (also known as one-hot encoding). Dummy coding involves creating new binary variables (0 or 1) for each category of the categorical variable. This allows the regression model to incorporate the categorical data while maintaining its numerical nature.

To use categorical variables in a regression analysis, you must apply dummy coding to convert them into numerical values.

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1. The average time it takes a customer from when they arrive at the truck until they receive their taco is 141.67 seconds.

2. The average utilization of the truck 141.67 seconds.

3. On average, there is 1 person waiting in line.

4. In order to achieve a delay probability of under 10%, a minimum of 1 server is required.

1 The arrival rate is 1 customer every 2 minutes, which is equivalent to 0.5 customers per minute. The service rate is 1 customer per 50 seconds, which is equivalent to 1.2 customers per minute (since there are 60 seconds in a minute).

2 Average Number of Customers = (0.5 / 1.2) + 1 = 1.4167.

Average Waiting Time = 1.4167 * (50 + 50)

= 141.67 seconds.

3 The average utilization of the truck is given by the formula: Utilization = Arrival Rate / Service Rate.

Utilization = 0.5 / 1.2

= 0.4167 (or 41.67%).

The average number of people waiting in line can be calculated using the formula: Average Number of Customers - Average Utilization.

Average Number of Customers - Average Utilization = 1.4167 - 0.4167

= 1.

4 Given that the desired delay probability is 10% (or 0.1), we can rearrange the formula to solve for the utilization:

Utilization = Delay Probability / (1 + Delay Probability).

=

Utilization = 0.1 / (1 + 0.1) = 0.0909 (or 9.09%).

The utilization we calculated represents the maximum utilization to achieve a delay probability of 10%. In conclusion, to achieve a delay probability of under 10%, a minimum of 1 server is required.

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ANSWER:

5 positive integers

STEP-BY-STEP EXPLANATION:

We have the following inequality:

Solving for x:

Being only positive numbers, it would then remain:

Being only integers, it would then remain:

Which means that 5 positive integers satisfy the inequality (10, 11, 12, 13, 14)

Answer:

Set 2

Step-by-step explanation:

First find the median of each set (the median being the number in the middle):

(1) { 4,7,10,13,16} = 10

(2) {8,9,10,18,19} = 10

(3) {8,9,10,11,12} = 10

(4) {1,2,10,11, 12} = 10

Then find the mean of each set (the mean being average of all the numbers, to find the average add up all the numbers and divide by the amount of numbers):

(1) { 4,7,10,13,16} = 10

(2) {8,9,10,18,19} = 12.8

(3) {8,9,10,11,12} = 10

(4) {1,2,10,11, 12} = 7.2

the answer being 12.8 since 12.8 is greater than 10

(4) {1,2,10,11, 12}

Answer:

Solution given:

1:

{ 4,7,10,13,16}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={ 4+7+10+13+16}/{5}=10

(2)

{8,9,10,18,19}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={8+9+10+18+19}/{5}=12.8

3) {8,9,10,11,12}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={8+9+10+11+12}/{5}=10

(4) {1,2,10,11, 12}

n=5

median={n+1)/2th term=6/2=3th term=10

mean=sum/n={1+2+10+11+13}/{5}=7.4

In above

1: mean=median

2:mean>median

3:mean=median

4:mean<median

so median is greater than mean is in 4th one.

(4) {1,2,10,11, 12}

A quadratic function is a polynomial of the form f(x) = a·x² + b·x + c, where a, and b are coefficients and c, a constant, are numbers, a is a non zero number

The correct options are;

4. c. -3·x² + 2·x + 9 = 0

5. d. -9 and 7

6. b. 4·x² - 25 = 0

7. c. Real irrational and not equal

8. c. m² + 4·m + 13 = 0

9. a. y = x² - 4·x - 21

10. c. Parabola

The reasons why the above options are selected are given as follows:

4. The given equation, x·(2 - 3·x) + 9 = 0, can be rewritten as follows;

x·(2 - 3·x) + 9 = 2·x - 3·x² + 9 = -3·x² + 2·x + 9 = 0

Therefore, correct option is c. -3·x² + 2·x + 9 = 0

5. The given quadratic equation, x² + 2·x - 63 = 0, can be factorized as follows;

Given that he coefficient f x² is 1, and  9 × (-7) = -63, and 9 - 7 = 2, we have;

x² + 2·x - 63 = (x + 9)·(x - 7) = 0

The roots of the equation are -9, and 7

The correct option is option d. -9 and 7

6. The equation that can be easily solved by extracting the square root is the equation that is separable into squares of the constant and square of the required variable

4·x² = 25

\(x = \sqrt{\dfrac{25}{4} } = \dfrac{5}{2}\)

The correct option is b. 4·x² - 25 = 0

7. A quadratic equation that has a discriminant of 20, gives values of x in the forms;

\(x = \dfrac{-b \pm \sqrt{20} }{2\cdot a}\)

Given that √20 = 2·√5, is an irrational number, we have that the results are real irrational and not equal

The correct option is option c. Real irrational and not equal

8. The given equation is (m + 2)² + 9 = 0

(m + 2)² + 9 = m² + 4·m + 4 + 9 = m² + 4·m + 13 = 0

The correct option is c. m² + 4·m + 13 = 0

9. A quadratic function is a function given in the form f(x) = a·x² + b·x + c

Where, f(x) = y, the correct option is option a.

a. y = x² - 4·x - 21

10. The shape of a quadratic function is the shape of a parabola

The correct option is option c.

c. Parabola

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Answer:

Try 2

Step-by-step explanation:

Mean means add all the numbers and divide by how many there are so:

1+2+3+4=10

Then divide how many there are which is 5

so lastly 10÷5=2

Answer:

Hello! answer: 7

Step-by-step explanation:

80 + 80 = 160 360 - 160 = 200 200 ÷ 2 = 100 and 14 × 7 = 98 and 98 + 2 = 100 therefore x = 7 HOPE THAT HELPS!

Answer:

\(A) ~7\)

Step-by-step explanation:

\(80+14x+2=180\)

\(14x+82=180\)

\(14x=98\)

\(x=7\)

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

hope it helps..

have a great day!!

Nintendo switch dock = 15.60%

Nintendo Joy-Con = 17.53%

Nintendo Joy-Con Wrist Straps = 3.15%

Nintendo Joy-Con Grip = 7.01%

High Speed 4k HDMI Cable 6 Feet = 1.51%

Nintendo Switch AC Adapter = 2.60%

Nintendo Switch Console = 52.59%

To determine the number of WINS by which one occurrence of the maximum value can be reduced without changing the value at the 55th percentile.

We need to find the maximum value in the dataset and evaluate its impact on the percentile.

Let's assume the maximum value for WINS is X. To maintain the value at the 55th percentile (23.5), we need to find the threshold value below which the dataset will not be affected by reducing the maximum value.

We can start by arranging the data in ascending order and finding the value at the 55th percentile. Since we have 44 seasons, the 55th percentile would be approximately at the (55/100) * 44 = 24.2nd value.

Now, we compare the value at the 24th position and the value at the 25th position in the dataset. If both of these values are below 23.5, reducing the maximum value by any amount will not change the value at the 55th percentile.

For example, if the value at the 24th position is 23 and the value at the 25th position is 24, reducing the maximum value by any amount will still keep the 55th percentile at 23.5.

However, if either the value at the 24th position or the value at the 25th position (or both) is 23.5 or higher, reducing the maximum value will impact the 55th percentile.

Therefore, to accurately determine the number of WINS by which one occurrence of the maximum value can be reduced without changing the value at the 55th percentile, we need to know the specific values at the 24th and 25th positions in the dataset.

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