A is the center of the circle, and the length of CD is 15 centimeters.
1. Select a segment that is a radius.

The probability of rolling a 5 on at least one of the four standard six-sided dice is 671/1296.


The probability of rolling a 5 on a single standard six-sided die is 1/6. To find the probability of rolling a 5 on at least one of the four dice, we can use the concept of complementary probability.

The complementary probability is the probability of the event not occurring. In this case, it would be the probability of not rolling a 5 on any of the four dice.

The probability of not rolling a 5 on a single die is 5/6, since there are five other possible outcomes (1, 2, 3, 4, and 6).

To find the probability of not rolling a 5 on all four dice, we multiply the probabilities together: (5/6) * (5/6) * (5/6) * (5/6) = 625/1296.

Since the complementary probability is the probability of the event not occurring, the probability of rolling a 5 on at least one of the four dice is 1 - 625/1296 = 671/1296.

Therefore, the probability of rolling a 5 on at least one of the four six-sided dice is 671/1296.

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The sum of (6a + 6) + (3.22x - 2) + (2a + 4) is 8a + 3.22x + 8

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒ (6a + 6) + (3.22x - 2) + (2a + 4)

⇒ 6a + 6 + 3.22x - 2 + 2a + 4

⇒ 6a + 2a + 3.22x + 6 -2 +4

⇒ 8a + 3.22x + 8

hence, The sum of (6a + 6) + (3.22x - 2) + (2a + 4) = 8a + 3.22x + 8

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Answer:

D

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = \(\frac{opposite}{adjacent}\) = \(\frac{7}{4}\) , then

θ = \(tan^{-1}\) (\(\frac{7}{4}\) ) ≈ 60° ( to the nearest degree )

Answer:

9,11

Step-by-step explanation:

let the numbers be x, x+2 (since consecutive odd integers have a difference of 2)

therefore;

x(x+2)= 99

x²+2x=99

I usually solve the sum like this,

we need to find the nearest square number ( number smaller than the number on the R.H.S)

here, it is 81, whose square root is 9. therefore the solution is 9

verification:

(9)²+2*9=99

81+18=99

99=99

hence, 9 is the solution. therefore the positive odd consecutive integers are  

x=9

x+2=9+2= 11

verification:

9*11=99

99=99

L.H.S=R.H.S

-> 3rd answer is correct

Answer:

Area = 9 cm²

Step-by-step explanation:

The shape given is a kite.

Area of a kite = ½(D1*D2)

Where,

D1 = 6 cm

D2 = 3 cm

Therefore:

Area = ½(6*3)

Area = ½(18)

Area = 9 cm²

the slope of the given point is m=2/17

Given info:There is a favourite sport and number of people watching and participating in the colony is given.

Draw the double bar graph for the data ?

Explanation:

See the attachment

Number of people watching cricket = 1240

Number of people participating cricket =620

Number of people watching Basket ball =470

Number of people participating Baskets ball=320

Number of people watching Swimming =510

Number of people participating Swimming= 320

Number of people watching Hockey=430

Number of people participating Hockey =250

Number of people watching Athletics =250

Number of people participating Athletics =105

Scale:-

On X - axis taking favourite sport

On Y-axis taking Number of people in the colony

First bar represents Watching

Second bar represents Participating

On Y-axis 1 cm = 100 units

(i)

⇛The number of people who are watching and participating in their favourite sport.

(ii)

⇛Cricket is the most popular of all other sports .

⇛It has the most watching people and the more participants

(iii)

⇛Watching is more preferred than Participating according to the given data of the colony.

Bar graph:-

⟨Hope this helps.⟩

Answer:

0+4=4

So new temperature was 4 degrees Celsius

Step-by-step explanation:

To make a geometric shape with 100 points, there are many options depending on the desired shape.

There are many possible geometric shapes you can make with 100 points, depending on the specific constraints and requirements you have. Few examples are,

Circle: One way to create a circle with 100 points is to evenly distribute the points around the circumference of a circle with a given radius.

Square: Another option is to create a square with 100 points. To do this, you can divide the sides of the square into 25 segments, and then place 4 points at each segment endpoint.

Regular polygon: You can create a regular polygon with 100 sides by following a similar method to the circle.

Spiral: You can create a spiral shape with 100 points by placing the points along a logarithmic spiral.

Fractal: Finally, you can create a fractal shape with 100 points by applying a recursive algorithm to divide and subdivide segments of an initial shape.

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a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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Answer:

i can't rly read number 22 srry

b x+1>0=x>-1

c x+1<0=x<-1

Hope This Helps!!!

The given p, α, and i using the exponentiation by squaring algorithm.

To prove that 2 is a primitive root of 11, to show that every integer a with 1 ≤ a ≤ 10 can be expressed as a ≡ 2²i (mod 11) for a unique i with 0 ≤ i ≤ 9.

verify this by checking the powers of 2 modulo 11:

2² ≡ 1 (mod 11)

2²≡ 2 (mod 11)

2² ≡ 4 (mod 11)

2³ ≡ 8 (mod 11)

2² ≡ 5 (mod 11)

2³ ≡ 10 (mod 11)

2³ ≡ 9 (mod 11)

2³ ≡ 7 (mod 11)

2² ≡ 3 (mod 11)

2³ ≡ 6 (mod 11)

The remainders obtained from the powers of 2 cover all the integers from 1 to 10 modulo 11. Additionally, each remainder is unique, express any integer between 1 and 10 as a power of 2 modulo 11.

To find log₂(9), to determine the exponent i such that 9 (mod 11). From the list of powers of 2 above, that 2³= 9 (mod 11). Therefore, log₂(9) = 6.

A given p, α, and i, where α is a primitive root of p and i is the discrete logarithm or index use the algorithm of exponentiation by squaring.

The algorithm for computing a given p, α, and i is as follows:

Set result = 1.

Initialize a binary representation of i, e.g., i = b[m]b[m-1]...b[1]b[0].

For j from m to 0:

a. Square the current result: result = result × result (mod p).

b. If bj = 1, multiply the current result by α: result = result × α (mod p).

Return the final result.

This algorithm takes advantage of the binary representation of i to compute a efficiently. By squaring the current result and multiplying by α only when necessary, compute a in logarithmic time complexity with respect to i.

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Answer: 32

Step-by-step explanation:

Answer:

m= -29

Step-by-step explanation:

This is a bit of a complex equation, but let's work through it.

2/3 (m-1/2) +3= m/3-7

First, we need to distribute the 2/3.

(2/3)(m)+(2/3)(−1/2)+3=m/3+−7

Now we simplify that.

2/3m+−1/3+3=1/3m+−7

We can now combine like terms.

2/3m+8/3=1/3m+−7

The goal is to isolate the variable, so we should subtract 1/3m from both sides.

1/3m+8/3=−7

Lets keep going! We can subtract 8/3 from both sides.

1/3m=-29/3

Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!

m=-29

We did it! m=-29

Answer:

(x^2−2xy+y^2)−z^2

⇒[x(x−y)−y(x−y)]−z^2

⇒(x−y)(x−y)−z^2

⇒(x−y)^2−z^2

⇒[(x−y)+z][(x−y)−z]

⇒(x−y+z)(x−y−z)

det(A) = -5 and det(B) = 9, the determinants of various matrix expressions are as follows: det(AB) = -45, det(3A) = -125, det(A^T) = -5, det(B^-1) = 1/9, and det(B^4) = 6561.

The determinant of a matrix represents a scalar value that provides information about the matrix's properties. Here are the explanations for each determinant calculation:

det(AB): The determinant of the product of two matrices is equal to the product of their determinants. Hence, det(AB) = det(A) * det(B) = (-5) * (9) = -45.

det(3A): The determinant of a scalar multiple of a matrix is equal to the determinant of the original matrix raised to the power of the scalar. Therefore, det(3A) = (3^3) * det(A) = 27 * (-5) = -125.

det(A^T): The determinant of a matrix remains the same when taking its transpose. Hence, det(A^T) = det(A) = -5.

det(B^-1): The determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix. Thus, det(B^-1) = 1/det(B) = 1/9.

det(B^4): The determinant of a matrix raised to a power is equal to the determinant of the original matrix raised to the same power. Therefore, det(B^4) = (det(B))^4 = (9)^4 = 6561.

These determinants can be useful in understanding the properties and transformations of matrices in various mathematical and scientific applications.

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Answer:

9 : 13

Step-by-step explanation:

Here is the complete question :

there are 13 apples in a basket 4 of these apples are green the rest of them are red​

What what is the ratio of red apples to all the apples in the basket

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

ratio of red apples to all the apples in the basket​ = Number of red apples : total number of apples

Number of red apples = total number of apples - number of green apples

13 - 4 = 9

9 : 13

Answer:

  m = 1, b = 0

Step-by-step explanation:

You want to know the values of m and b and where to find them on a graph of y = x.

The variables m and b are used for the slope and y-intercept, respectively, when the slope-intercept equation for a line is written generically as ...

  y = mx + b . . . . . . . . equation for line with slope m and y-intercept b

The equation for the line y = x can be written in the slope-intercept form by recognizing the identity elements involved:

  y = x

  y = 1x + 0 . . . . . . . . identity elements shown

Comparing this to ...

  y = mx + b

we see that m = 1 and b = 0.

The attachment shows where these are found on the graph.

__

Additional comment

You may recall that 1 is the multiplicative identity element. Anything multiplied by 1 is itself.

Zero is the additive identity element. Anything added to zero is itself.

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4,-1) and (-3,-1)

The distance between them is

\(d = \sqrt{ ({ - 4 + 3})^{2} + ({ - 1 + 1})^{2} } \\ = \sqrt{ ({ - 1})^{2} } \\ = \sqrt{1} \)

We have the final answer as

1 unit

Hope this helps you

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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Answer:

Hi! The answer to your question is B) He can walk 12 miles in 1 minute.

To find Unit rate divide the biggest number by the smallest; Example: \(120/10\)

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

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- Brooklynn Deka

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Answer:

what grade are you in so i can help

Step-by-step explanation:

Answer:

4.36 to 4.46

good luck buddy

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

Answer:

40

Step-by-step explanation:

4*5=20

5*8=40

I hope you got it....

Answer:

There needs to be 174 Students in the 8th grade class.

Step-by-step explanation:

173(1/3) is 58

58+17=75

Answer:

Quadrant III

Step-by-step explanation:

sin and cos are both less than zero thus negative

the x and y axis are both negative in QIII

sorry if the explaination is wrong but I know the answer is right bc I took the test

Hello! Mikosan here to help doll!

The Answer is: Quadrant 3

I hope this helps doll!

Have a great day love~