help fast please and good night also happy Valentine's day​

Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.

The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

Part A:

The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:

P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²

Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.

P(X = 3) = 10 × 0.68³ × 0.32²

P(X = 3) = 0.267

Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.

Part B:

The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.

Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.

Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.

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Answer:

If just combining like terms: 3x^2 + 12

If solving for x: 2i, -2i

Step-by-step explanation: Combine like terms, so 3x^2 + 12 = 0; move the 12 to the other side by subtracting (3x^2 = -12), then divide both sides by 3, which gives x^2 = -4. Then get the square root of both sides to cancel out the power on the x. Since -4 is negative, use imaginary numbers, which makes x = 2i and x = -2i

Answer:

-13

Step-by-step explanation:

-4-3(3)

-4-9 = -13

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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1. Observe problem

2. Plug in values

|-54|+30=

54+30=

84

Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:

Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10

To find the variance, we first find the deviation of each score from the mean:

5 - 10 = -5

12 - 10 = 2

8 - 10 = -2

14 - 10 = 4

11 - 10 = 1

We square each deviation and sum them up:

(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26

Then, we divide by the number of scores to find the variance:

Variance = 26 / 5 = 5.2

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √5.2 = 2.28

2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:

C(5,2) = 5! / (2! * (5 - 2)!) = 10

Therefore, there are 10 simple random samples of size 2 that can be constructed.

3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:

Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6

The standard error of the sampling distribution is the square root of the variance:

Standard error = √2.6 = 1.61

4.The variance of the sampling distribution is 2.6, as we found in part

5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.

Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:

Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5

Step-by-step explanation:

The solutions to the equation x² + 6x + 1 = 0 are x = -3 + 2√(2) or x = -3 - 2√(2)

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0 where a, b, and c are constants, and x is the variable. The solutions can be found using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) or by factoring the quadratic expression into two linear factors.

To solve the quadratic equation x² + 6x + 1 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. Substituting the values from our equation, we get:

x = (-6 ± √(6²- 4(1)(1))) / (2(1))

Simplifying inside the square root, we get:

x = (-6 ± √(32)) / 2

We can simplify the square root further by factoring out a 4:

x = (-6 ± 4√(2)) / 2

Simplifying the fraction, we get:

x = -3 ± 2√(2)

Therefore, the solutions to the equation x² + 6x + 1 = 0 are:

x = -3 + 2√(2) or x = -3 - 2√(2)

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From the above explanation, the value of y gotten from the function when x = -3 does not match with the value given

Answer:

7*100=700(times)

70/700=0.1 =1/10 millimeters long

The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵

Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y

Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²

Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³

Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴

Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)

Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

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Replace z with the number inside the parenthesis:

f(z) = 3z-8

a. 3(-4) - 8 = -12-8 = -20

b. 3(1/2)-8 = 1 1/2 - 8 = -6 1/2

c. 3(z-7) - 8 = 3z-21-8 = 3z-29

The coordinates of the point in the graph is (3, 2)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following

Represent the point with x

So, we have

X = (3, 2)

Hence, the coordinates of the point in the graph is (3, 2)

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Answer: C

Step-by-step explanation:

The cat is not hungry, or doesn't like the can of tuna food, which is why they refused to eat it when it was given to them.

Try to give the cat the food again and see their reaction, if that fails, try to give the cat other foods and note the reaction to determine if the cat just doesn't like the tuna in a can or just wasn't hungry at the moment.

Answer:

0.6429

Step-by-step explanation:

Let, s = play a sport

c = participate in a club

P(s) = 0.14

P(s n c) = 0.09

probability that a student participates in

a club given that they also play a sport = P(c | s)

P(c | s) = P(c n s) / P(s)

P(c | s) = 0.09 / 0.14

P(c | s) = 0.64285

= 0.6429

Answer:

I believe it would be division.

Step-by-step explanation:

Sorry if its wrong, i havent done a question like this in a long time, please forgive me!

Answer:

is it not the plus sign? (+)

Step-by-step explanation:

Answer:

The ratio for the first print job is 150/30 = 5 pages per second.

The ratio for the second print job is 130/20 = 6.5 pages per second.

Since the ratios are different, the data do not represent a proportional relationship. In a proportional relationship, the ratio between two variables remains constant.

Step-by-step explanation:

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.

Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).

The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.

2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.

The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.

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Question :

Which mixed numbers have 12 as the LCD (lowest common denominator)?

2 11/12

3 1/7

5 3/4

6 4/5

8 38/47

Answer:

73

Step-by-step explanation:

x/5+7=16

times 5 both sides

x + 7 = 80

  -7        -7

 x=73

A skewness value of -1.25 indicates that the distribution is right-skewed, which is consistent with the given information. The mean is less than the median and the mode, which is usually the case for a right-skewed distribution.

This distribution is likely skewed to the right. Skewness is a measure of asymmetry of a distribution, and a right-skewed distribution has a mean that is less than the median, which is less than the mode. In this case, the mean is 23, the median is 28, and the mode is 28.

To calculate skewness of a distribution, we use the following formula:

Skewness = (3 * (mean - median)) / Standard Deviation

To calculate the standard deviation, we can use the following formula:

Standard Deviation = √[∑(X - Mean)2 / N]

Where X is the value of each observation and N is the number of observations.

Using the given information, we can calculate the skewness as follows:

Skewness = (3 * (23 - 28)) / Standard Deviation

Skewness = -1.25

A skewness value of -1.25 indicates that the distribution is right-skewed, which is consistent with the given information. The mean is less than the median and the mode, which is usually the case for a right-skewed distribution.

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Answer:

no

Step-by-step explanation:

No, because none of the factors of 29 equal to -1

sorry I don't know Ab = cd and bc = ad

Using SAS postulate triangles formed by ABC = abd

Opposite sides are equal and each angle is 90 degrees so by definition it is a rectangle.Ab = cd and bc = ad

Using SAS postulate triangles formed by ABC = abd

Opposite sides are equal and each angle is 90 degrees so by definition it is a rectangle.

Answer:

I think the answer is .

Step-by-step explanation:

C= 12

Hope this helps

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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The exact values of sin(x/2), cos(x/2), and tan(x/2) are:

Sin (x/2) = √ [ 2 - √2)/4 ]

cos (x/2) = √[ (2 + √2)/4 ]

Tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

The tangent of an angle can be expressed in terms of the sine and cosine of the same angle using the identity: tan(x) = sin(x) / cos(x)

Here we have

tan x = 1

If tan(x) = 1, we can determine the values of sin(x) and cos(x) using the identity:

=> tan² (x) + 1 = sec² (x)

Substituting tan(x) = 1, we get:

1 + 1 = sec²(x)

2 = sec²(x)

sec(x) = √2

As we know sec(x) = 1/cos(x), so:

=> cos(x) = 1/sec(x) = 1/√2 = √2/2

Similarly, sin(x) = tan(x) × cos(x) = 1 × √2/2 = √2/2

Use the half-angle identities to find sin(x/2), cos(x/2), and tan(x/2):

=> sin(x/2) = ±√[(1 - cos(x))/2 ]

= ± √[(1 - √2/2)/2]

= ± √ [ 2 - √2)/4 ]

Since tan(x) = 1 is positive, we know that x is in the first quadrant, which means x/2 is also in the first quadrant.

Therefore, sin(x/2) is positive, so:

sin(x/2) = √ [ 2 - √2)/4 ]

cos(x/2) = ±√[ (1 + cos(x))/2]

= ±√ [ (1 + √2 /2)/2]  

= ± √[ (2 + √2)/4 ]

Since x/2 is in the first quadrant, cos(x/2) is also positive, so:

cos(x/2) = √[ (2 + √2)/4 ]

Finally, we can find tan(x/2) using the identity:

tan(x/2) = sin(x/2) / cos(x/2)

tan(x/2) = √[ (2 + √2)/4 ]/ √[ (2 + √2)/4 ]

tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

Therefore,

The exact values of sin(x/2), cos(x/2), and tan(x/2) are:

Sin (x/2) = √ [ 2 - √2)/4 ]

cos (x/2) = √[ (2 + √2)/4 ]

Tan (x/2) = √[ (2 + √2)]/ √[ (2 + √2)]

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