How many different types of triangles are there?
 Draw and name the 4 different triangles.
 Write the properties of each triangle.
 Draw a circle and name the different parts of the circle.
 Find the relationship between radius and diameter.

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The probability that exactly 1 train will pass Mary's house is 0.00889.

According to the given question.

On average, 18 trains pass by Mary's house daily i.e. in 24 hours.

As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".

Therefore,

The probability that exactly one train will pass Mary's house in a 3 hour period

= \(\frac{^{18C_{1} } }{^{24} C_{3} }\)

\(= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }\)

\(= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }\)

\(=\frac{18}{8\times23\times\ 11}\)

= 18/2024

= 0.00889

Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.

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An x-bar and R-chart were constructed using the given data. The x-bar chart displays the sample averages, while the R-chart shows the sample ranges. By analyzing these charts, we can determine if the process is in control.

To construct the x-bar and R-charts, we use the sample averages and sample ranges provided in the table. The x-bar chart helps us monitor the central tendency of the process, while the R-chart monitors the variability or dispersion within the samples.

Plotting the x-bar chart:

   Calculate the overall mean (x-double bar) by averaging all the sample averages.

   Calculate the average range (R-bar) by averaging all the sample ranges.

   Calculate the control limits for the x-bar chart using the formulas: Upper control limit (UCL) = x-double bar + A2 * R-bar, Lower control limit (LCL) = x-double bar - A2 * R-bar, where A2 is a constant factor depending on the sample size.

   Plot the sample averages on the x-bar chart along with the control limits.

Plotting the R-chart:

   Calculate the control limits for the R-chart using the formulas: UCL = D4 * R-bar, LCL = D3 * R-bar, where D3 and D4 are constant factors depending on the sample size.

   Plot the sample ranges on the R-chart along with the control limits.

By examining the x-bar and R-charts, we can assess whether the process is in control. If the data points fall within the control limits, with no specific patterns or trends, the process is considered in control. If any data points fall outside the control limits or show non-random patterns, it suggests the process is out of control and further investigation is required.

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THIS QUESTION IS INCOMPLETE HERE IS THE GENERAL SOLUTION.

Answer:

The number is 13

Step-by-step explanation:

To write the equation, we know that more than comes after

7 times a number

7n

more more than means add

7n+5

is means equals

7n+5 = 96

Subtract 5 from each side

7n+5-5 = 96-5

7n = 91

Divide each side by 7

7n/7 = 91/7

n =13

Answer:

A 2

B 1

C 4

D 3

Step-by-step explanation:

( ) means not including (also used for infinity)

[ ] means including

The answer choices are in interval form, showing all the possible answer choices between two numbers and if the answer choice includes or excludes a number using the () []

Explanation for A:

x < 7.8 means x won't include 7.8 since the symbol is "less than" and not "less than or equal to".

x can be anything, it just has to be less than 7.8, so the answer is:

2 (-infinity, 7.8)

Explanation for B:

x <= 7.8 means x will include 7.8 since the symbol means "less than or equal to".

x can be anything, it just has to be less than or equal to 7.8, so the answer is:

1 (-infinity, 7.8]

Explanation for C:

x >= 7.8 means x will include 7.8 since the symbol means "greater than or equal to".

x can be anything, it just has to be greater than or equal to 7.8, so the answer is:

4 [7.8, infinity)

Explanation for D:

x > 7.8 means x won't include 7.8 since the symbol means "greater than" and not "greater than or equal to".

x can be anything, it just has to be greater than 7.8, so the answer is:

3 (7.8, infinity)

Hope it helps (●'◡'●)

Answer:

A:2 B:1 C:4 D:3

Step-by-step explanation:

Answer:

29%

Step-by-step explanation:

Amount of girls in his class: 13/24

13/24 x 13/24 = 169/576 or 0.2934...

Basically, 29%

9514 1404 393

Answer:

  A)  {( –2, 5), (–3, 3), (6, 4), (–7, –1)}

Step-by-step explanation:

The ordered pairs of an inverse relation are the reverse of the ordered pairs of the original relation.

You will be looking for ordered pairs that have first values the same as the original relation's second values: {-2, -3, 6, -7}. That list is found in choice A.

According to the z table, there is a 0.3814 percent chance that such a standard normal random variable would fall between 0.3 and 3.2.

What is the probability?

The possibility of an event occurring is stated as a number between 0 and 1, where 0 indicates that the event cannot occur and 1 indicates that the event is guaranteed to occur. The probability of an event A is defined mathematically as the number of positive outcomes divided by the total number of alternative outcomes.

We must determine the likelihood that a standard normal random variable would occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The probability therefore should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value

P(0.3<z<3.2)=0.9993−0.6179

P(0.3<z<3.2)=0.3814

Therefore, there is a 0.3814 percent chance that a standard normal random variable would fall between 0.3 and 3.2.

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Two supplementary angles equal 180 degrees.

Let the first angle = x

The second angle is 30 degrees more so this would be x + 30

Now add the two angles together to equal 180:

X + x+ 30 = 100

Combine like terms:

2x + 30 = 180

Subtract 30 from both sides:

2x = 150

Divide both sides by 2:

X = 75

One angle = x = 75

The other angle is x + 30 = 75 + 30 = 105

The smaller angle is 75 degrees.

To construct a confidence interval for the proportion of defectives, we should use the plus four method.

Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes. 

The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.

To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.

This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.

The equation for the certainty interim utilizing the also four strategies is:

p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)

where:

p is the test extent (number of defectives/test estimate)

zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2

n is the test estimate (counting the included four nonexistent perceptions)

Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

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Answer:

D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft

The initial value problem is y' = 1/x(x^2 + y), and the initial condition is y(4) = 2. The step size for Euler's method is h = 0.2. The table provides the approximate values of y at x = 4.2, 4.4, 4.6, and 4.8 using Euler's method.

To apply Euler's method, we start with the initial condition y(4) = 2. We increment x by the step size h = 0.2, and at each step, we approximate the value of y using the differential equation y' = 1/x(x^2 + y) and the previous value of y.

Using the given step size and initial condition, we can calculate the approximate values of y at each point:

For x = 4.2:

Using Euler's method: y(4.2) ≈ y(4) + h * f(4, y(4))

where f(x, y) = 1/x(x^2 + y)

Substituting the values: y(4.2) ≈ 2 + 0.2 * (1/4(4^2 + 2)) ≈ 2.019

For x = 4.4, 4.6, and 4.8, we repeat the same process and update the value of y at each step.

The table for the approximate values using Euler's method is as follows:

n x Euler's Method

1 4.2 2.019

2 4.4 ...

3 4.6 ...

4 4.8 ...

The values for x = 4.4, 4.6, and 4.8 can be calculated using the same procedure as for x = 4.2, substituting the appropriate values and updating the y-values at each step.

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Answer:

512x+1 over 2^x ........................

Step-by-step explanation:

:)

Answer:

(x - 3)(x - 2)(x + 2)

Step-by-step explanation:

Given

x³ - 3x² - 4x + 12 ( factor the first/second and third/fourth terms )

= x²(x - 3) - 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(x² - 4) ← x² - 4 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4

= x² - 2²

= (x - 2)(x + 2)

Thus

x³ - 3x² - 4x + 12 = (x - 3)(x - 2)(x + 2) ← in factored form

Answer:

(x - 2)(x - 3)(x + 2).

Step-by-step explanation:

The Factor Theorem states that if x - a is a factor of f(x) the f(a) = 0.

f(x) = x^3 - 3x^2 - 4x + 12​

We try the factors of 12:

f(2) =  2^3 - 3*4 - 8 +12

= 8 - 12 - 8 + 12  = 0

- so (x - 2) is a factor of f(x)

Dividing:

        x^2  -  x -  6            <-----------Quotient

       -----------------------------

x - 2 )x^3 - 3x^2 - 4x + 12​

        x^3 - 2x^2

                  -x^2 - 4x

                  -x^2 + 2x

                          -6x + 12

                          -6x + 12

So we factor x^2 - x - 6:

= (x - 3)(x + 2)

To analyze the variables Birth Rate and Death Rate at the same time the scatter plot would be appropriate to use.

A scatter chart, also called as a scatter plot, is a graph that displays the correlation between two variables. They are a very effective type of chart because they enable viewers to see relationships or trends that would be nearly impossible to see in any other form right away.

Modern scatter charts are based on René Descartes' 17th-century cartesian coordinates system, albeit their exact origins are unknown. The majority of scatter plots used in science journals and publications may be found there.

One of the most adaptable and practical inventions in the history of statistical graphs is the scatter chart. This can seem like a bold statement, but scatter charts help make sense of muddled data. They are a tool for discovery as well as visualisation, which is a much bigger role for them.

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Step-by-step explanation:

The fraction she will complete is   1/2  /  3/5   = 1/2 * 5/3 =  5/6 completed

The correct options are:

1: the amount of space occupied by a three-dimensional figure as measured in cubic units (as inches, quarts, or centimeters): cubic capacity. 2: the amount of a substance occupying a particular volume.

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.

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Your question was incomplete. The complete questions is:

A box covers an area of 6 1/2 in² when resting on its base. The volume of the box is 45 1/2 in³.

Which of the following can you find from the given information? Select all that apply.

A. The height of the box

B. The width of the base of the box

C. The length of the base of the box

D. The surface area of the base of the box

Answer:

X=4

Step-by-step explanation:

3x-2y=8

x+y=6

multiply second equation by 2 so you can eliminate y

2(x+y)=2(6)

2x+2y=12

now add two equations together

first equation:                          3x-2y=8

modified second equation     2x+2y=12

added together eliminates y. 5x+0=20

                                                   X=4

Answer:

.

Step-by-step explanation:

a) The probability model for rolling two 4-sided dice can be represented as a table or matrix with 16 equally likely outcomes, each with a probability of 1/16.

b) The probability the sum of the numbers is 5 based on the probability model is 25%

a) The probability model for rolling two 4-sided dice can be represented using a table or a matrix, where the rows and columns represent the possible outcomes of the first and second die, respectively. Since each die has four equally likely outcomes, there are 4 x 4 = 16 possible outcomes in total. We can list these outcomes as ordered pairs (blue, yellow), where blue and yellow represent the numbers on the bottom of the blue and yellow dice, respectively

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

Each outcome has a probability of 1/16, since each die has four equally likely outcomes.

b) To find the probability that the sum of the numbers is 5, we need to count the number of outcomes where the sum is 5 and divide by the total number of outcomes. There are four outcomes where the sum is 5: (1,4), (2,3), (3,2), and (4,1). Therefore, the probability is

4/16 = 1/4 = 0.25 = 25%

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Answer:

(5,1)

or

x=5, y=1

Step-by-step explanation:

Blue Graph has the point: (-2,2) and Red Graph has the point: (-2,0). Therefore, when you remove 2 units of y for blue graph you represent the red graph.

Answer Letter A

Answer:(6,-22)

Step-by-step explanation:

The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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Answer:

8,640 square inches

Step-by-step explanation:

Answer:

70.9%

Step-by-step explanation:

"56 out of 79" can be written as (56/79).  This is equal to a decimal value of 0.708861, or a percentage of 70.8861%.  Round to 1 decimal point to give 70.9%.

Answer:

• (a) x-10

• (b) (1-10x)/x

Explanation:

Part A

Given the function:

First, swap x and y:

Next, make y the subject of the equation:

Therefore:

Part B

Given the function:

First, swap x and y:

Next, make y the subject of the equation:

Therefore:

The values of the variables are computed below

Find x

This is calculated as

16x + 1 + 35 = 180 ---- sum of adjacent angles in a parallelogram

Evaluate

16x = 144

Divide

x = 9

Find x and y

This is calculated as

3x + 4 = 16

y - 60 = 56

Evaluate

3x = 12 and y = 60 + 56

So, we have

x = 4  and y = 106

Find x

This is calculated as

43x - 1 = 85 ----  opposite angles in a parallelogram

Evaluate

43x = 86

Divide

x = 2

Find m and n

This is calculated as

2n - 1 = 9

m + 8 = 3m

Evaluate

n = 5 and m = 4

Find CBE

This is calculated as

21x - 5 + 4x + 1 + 34 = 180 --- sum of angles in a triangle

Evaluate

25x = 150

So, we have

x = 7

From the figure, we have

CBE = 34 + 4x + 1

CBE = 34 + 4 * 7 + 1

CBE = 63

Find JKL

This is calculated as

10x + 14 + 50 + 36 = 180 --- sum of angles in a triangle

Evaluate

10x = 80

So, we have

x = 8

From the figure, we have

JKL = 10x + 14

JKL = 10 * 8 + 14

JKL = 94

Find x

This is calculated as

2(2x - 13) = 14

So, we have

2x - 13 = 7

This gives

2x = 20

So, we have

x = 10

Find V

This is calculated as

7x  - 2 + 8x + 2 = 180 ---- sum of adjacent angles in a parallelogram

So, we have

15x = 180

This gives

x = 12

So, we have

V = 8x + 2

V = 8 * 12 + 2

V = 98

Find x and y

This is calculated as

y + 10 = 2y - 40

y = 50

Next, we have

4x + y + 10 = 180

4x + 50 + 10 = 180

Evaluate

4x = 120

So, we have

x = 30

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The given statement is true

One benefit of statistical sampling compared to non-statistical sampling is that statistical sampling provides mathematically-sound methods to control for sampling risk. Statistical sampling techniques allow for the application of probability theory to estimate and control sampling errors and uncertainties.

By using statistical methods, one can determine the appropriate sample size, select samples randomly or systematically, and apply inferential statistics to make reliable inferences about the population being sampled. Non-statistical sampling, on the other hand, does not provide the same level of rigor in terms of controlling for sampling risk and may not yield reliable and representative results.

Therefore, given statement is true.

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Answer:  b)  x = 6 and total line is 52

                c)  x = 5.5 and total line is 20

Step-by-step explanation:

b) (x+20) = (5x-4)

   4x = 24

     x = 6

     Line (x+20) = 26

     Line (5x-4) = 26

Total line = 52

  c)  (4x-12) = (-2x+21)

          6x = 33

           x = 5.5

      Line (4x+12) = 10.0

      Line (-2x+21) = 10.0

Total line = 20

Answer:

40

Step-by-step explanation:

We can see that at 1 minute there is 40 beats, at 2 minutes there is 80 beats, at 3 minutes there is 120 beats, at 4 minutes there is 160 beats and at 5 minutes there is 200 beats. If we divide each of the beats by its corresponding minute we will get 40

40 beats at 1 minute → 40 ÷ 1 = 40

80 beats at 2 minutes → 80 ÷ 2 = 40

120 beats at 3 minutes → 120 ÷ 3 = 40

160 beats at 4 minutes → 160 ÷ 4 = 40

200 beats at 5 minutes → 200 ÷ 5 = 40

9514 1404 393

Answer:

  1

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

  8 = 2×2×2 = 2³

  4 = 2×2 = 2²

so the problem can be rewritten as ...

  \(\dfrac{8^4}{4^6}=\dfrac{(2^3)^4}{(2^2)^6}=\dfrac{2^{3\cdot4}}{2^{2\cdot6}}=\dfrac{2^{12}}{2^{12}}=\boxed{1}\)

__

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

______

Alternate solution

You could use 8^2 = 64 and 4^3 = 64. Then this is (8^2)^2/(4^3)^2 = 64^2/64^2, where the common base is 64, not 2.