(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.

(b) Write the equation using function notation where .

Answer: 0.51

Step-by-step explanation:

To find the value of P(F|B), we need to use the formula:

P(F|B) = P(F and B) / P(B)

where P(F and B) is the probability that a student prefers brand B and their strongest stroke is freestyle, and P(B) is the probability that a student prefers brand B.

From the given table, we can see that:

P(F and B) = 26/95

P(B) = 51/95

Therefore, we can calculate

:P(F|B) = (26/95) / (51/95) = 26/51 ≈ 0.51

So, the correct value of P(F|B) is approximately 0.51, which can be interpreted as the probability that a student's strongest stroke is freestyle given that they prefer brand B.

Answer:

y=6x-8

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.

Point-slope form: y - y1 = m(x - x1)

Substitute the values of m, x1, and y1:

y - (-2) = 6(x - 1)

Simplify the right side:

y + 2 = 6x - 6

Subtract 2 from both sides:

y = 6x - 8

This is the equation of the line in slope-intercept form.

The solution to the equation 5 – 6x = 8x + 17 is x = -6.

Using the general solution for linear equations, we can rewrite the given equation as x = (a - d)/(c + b). This means that the solution for x is equal to the fraction (a - d) divided by (c + b).

Now let's use this general solution to solve the equation 5 – 6x = 8x + 17. First, we need to identify the values of a, b, c, and d in the equation. From the given equation, we can see that a = 5, b = -6, c = 8, and d = 17.

Next, we can substitute these values into the general solution and simplify:

x = (a - d)/(c + b)

x = (5 - 17)/(8 - 6)

x = -12/2

x = -6

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Answer:-6/7

Step-by-step explanation: got it right on ed

The probability of rolling a sum of 7 or less on two dice is 11/36. This can be expressed as a decimal number rounded to four decimal places as 0.3056.

We need to look at the possibilities when rolling two dice. Each die has six sides, which means the total number of outcomes when rolling two dice is 36. There are 11 combinations of two dice that produce a sum of 7 or less: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2). So, 11/36 can be simplified to 1/4, or 0.3056.

To understand this in a more visual way, you can draw a table and use colored dots to indicate the possible combinations. This will show you that out of 36 total possibilities, 11 of them produce a sum of 7 or less.

In summary, the probability of rolling a sum of 7 or less on two dice is 11/36, which can be expressed as a decimal number rounded to four decimal places as 0.3056.

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Based on the given information, the scout should choose Player A if they are looking for consistency.

What are range and standard deviation?

Range is the difference between the highest and lowest scores in the set.

Standard deviation measures how spread out the scores are from the mean.

To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.

The smaller the range, the more consistent the player's scores are.

A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.

Using the data provided, we can calculate the range and standard deviation for both players:

Player A:

Range = 21 - 0 = 21

Standard deviation = 5.70

Player B:

Range = 48 - 3 = 45

Standard deviation = 10.89

From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.

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[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2.7 \end{cases}\implies SA=4\pi (2.7)^2\implies SA\approx 91.61~cm^2[/tex]

The solution to the system of equations is x = 5 and y = -3.

We can use the elimination method by multiplying the second equation by 2 and adding it to the first equation to eliminate y:

= -4y + 11x - 67 + 2(2y + 5x - 19) = 0

-4y + 11x - 67 + 4y + 10x - 38 = 0

21x - 105 = 0

Dividing both sides by 21, we get:

x - 5 = 0

So x = 5.

Now we can substitute x = 5 into either of the original equations:

2y + 5x - 19 = 0

2y + 5(5) - 19 = 0

y = -3

Thus, the solution to the system of equations is:

x = 5, and y = -3.

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The coordinates of point Q in the parallelogram is (2b + 2a,2c)

The coordinates are given as:

P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)

The parallelogram form of the object indicates that the distances PQ and RS are equal.

The distance RS is calculated as:

RS = ( 2a - 0, 0)

This gives

RS = (2a, 0)

Coordinate Q is calculated as:

Q = P + RS

This gives

Q = (2b,2c) + (2a,0)

Evaluate the sum

Q = (2b + 2a,2c)

Hence, the coordinates of point Q is (2b + 2a,2c)

Midpoint of SQ=(b+ a ,c)

Midpoint of PR=(a+ b, c)

hence, SQ and PR bisect each other.

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The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)

Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.

Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.

However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.

Hence option (c) is correct.

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Answer:

domain is [-11 , -3]

Step-by-step explanation:

domain is x

range is y

x values are from -11 to -3

The sοlutiοn tο the system οf equatiοns is x = 17/5, which is apprοximately equal tο 3.4. Nοne οf the given answer chοices match this value exactly, sο there is nο sοlutiοn amοng the given chοices.

A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal plane.

We can sοlve the system οf equatiοns by substituting the secοnd equatiοn intο the first equatiοn and then sοlving fοr x:

3x + 2y = 7 (equatiοn 1)

y = x - 5 (equatiοn 2)

Substituting equatiοn 2 intο equatiοn 1, we get:

3x + 2(x - 5) = 7

Simplifying the equatiοn, we get:

5x - 10 = 7

Adding 10 tο bοth sides, we get:

5x = 17

Dividing bοth sides by 5, we get:

x = 17/5

Therefοre, the sοlutiοn tο the system οf equatiοns is x = 17/5, which is apprοximately equal tο 3.4. Nοne οf the given answer chοices match this value exactly, sο there is nο sοlutiοn amοng the given chοices.

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0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

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a) There are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b) The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, and the absolute maximum value of g is 90

a. To check if there is a value of x for -3 ≤ x ≤ 2 such that g(x) = 0, we can plug in each value in the interval and see if any of them make g(x) equal to 0:

g(-3) = -3² + 5(-3) + 6 = 0

g(-2) = -2² + 5(-2) + 6 = 0

g(-1) = -1² + 5(-1) + 6 = 0

g(0) = 0² + 5(0) + 6 = 6

g(1) = 1² + 5(1) + 6 = 12

g(2) = 2² + 5(2) + 6 = 20

So, we can see that there are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can first find the critical points of g by taking its derivative:

g'(x) = -2x + 5

Setting g'(x) = 0, we get:

-2x + 5 = 0

-2x = -5

x = 5/2

So, the only critical point of g is x = 5/2.

We can now check the values of g at the endpoints of the interval and the critical point:

g(-7) = -7² + 5(-7) + 6 = 20

g(9) = 9² + 5(9) + 6 = 90

g(5/2) = (5/2)² + 5(5/2) + 6 = 43.25

Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, which occurs at x = -7, and the absolute maximum value of g is 90, which occurs at x = 9.

We can justify this by noting that g is a quadratic function with a negative leading coefficient, which means that it opens downward and has a maximum value at its vertex (which occurs at x = 5/2). Since the vertex is within the given interval, and the function is decreasing on the left and increasing on the right of the vertex, the maximum and minimum values of g must occur at the endpoints of the interval.

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The value of angle CI is equal to 40 for the triangle.

What is geometry?

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that I is the incenter of the triangle AI = 3x+7, BI = 5x-11, and CI = 52-2x.

The value of BI will be calculated as,

AI = BI

3x + 7 = 5x - 11

2x = 18

x = 6

Now for the value of angle CI:

CI = 52 - 2x

CI = 52 - 2 x 6

CI = 52 - 12

CI = 40

Therefore, the value of angle CI is equal to 40 for the triangle.

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Answer:

Area of the figure=126.5cm²

Step-by-step explanation:

As we can see based on the shape of the figure, we can divide it into a;

→ Triangle

→ Rectangle

Formulas that we need are;

⇒ Area of triangle =1/2×base×height

⇒ Area of rectangle =length × width

Let's solve the area of the triangle first;

Then the area of the rectangle;

Finally, we add the triangle and rectangle together-

Area of Triangle + Area of Rectangle = 38.5cm²+88cm²

Area of the figure=126.5cm²

RevyBreeze

The area beyond the z-score in the tail for a z-score of .63 is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63.

To understand this concept, it is important to first have a basic understanding of the z-score and the normal distribution. A z-score is the number of standard deviations away from the mean of a normal distribution. It is also referred to as a standard score. It is a measure of how far a sample is from the mean. For a given sample, the higher the z-score, the farther away it is from the mean.

When looking at the normal distribution, the area of the tail is the area beyond the z-score. This means that the area of the tail is the area of the distribution that is beyond the z-score of the given sample. In other words, it is the area of the distribution that is farther away from the mean than the z-score. For example, for a z-score of .63, the area of the tail is the area of the distribution that is farther away from the mean that .63 standard deviations.

When finding the area beyond the z-score, it is important to understand that it is divided into two parts, the area in the left tail and the area in the right tail. The area in the left tail is the area beyond the z-score in the direction of the negative standard deviations. This means that it is the area of the distribution that is farther away from the mean than the negative z-score. The area in the right tail is the area beyond the z-score in the direction of the positive standard deviations. This means that it is the area of the distribution that is farther away from the mean than the positive z-score.

For the given z-score of .63, the area beyond the z-score in the tail is 0.2643. This means that there is a 26.43% chance that a sample is at least as extreme as the z-score of .63. This area is divided into the areas in the left tail of -.2643 and the area in the right tail of 0.2357.

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The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]

To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula

CI = X ± Zα/2 (σ/√n)

where

X = sample mean = 35.8

Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.

σ = sample standard deviation = 2.5

n = sample size = 40

Substituting these values into the formula, we get

CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].

Therefore, the correct option is (a) [34.7296, 36.8704]

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There is not enough evidence to suggest that the difference between the two population means is statistically significant at the 5% significance level.

To test the hypothesis that the difference between two population means is zero, the researcher can use a two-sample t-test. The test statistic is calculated as the difference between the sample means divided by the standard error of the difference.

In this case, the sample means are 106.4 and 99.2, and the standard error of the difference is 6.1. Therefore, the test statistic is (106.4 - 99.2) / 6.1 = 1.18.

To decide whether to reject the null hypothesis that the difference between the two population means is zero, the researcher needs to compare the test statistic to the critical value. The critical value needed to reject the null hypothesis at a 5% significance level with 2 degrees of freedom (n1 + n2 - 2 = 2) is 2.09.

Since the test statistic of 1.18 is less than the critical value of 2.09, the researcher fails to reject the null hypothesis.

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The mean absolute deviation (MAD) of the given set of data is 3.875.

To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:

Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8

Mean = 8

Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:

|12 - 8| = 4

|10 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|8 - 8| = 0

|4 - 8| = 4

|2 - 8| = 6

|12 - 8| = 4

Then, we find the mean of the absolute deviations:

Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8

Mean absolute deviation = 26 / 8

Mean absolute deviation = 3.875

Therefore, the mean absolute deviation of the given set of data is 3.875.

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Complete Question:

what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.

The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.

In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.

The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.

Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565

The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.

Therefore, the expected value of a ticket is:$5565 / 833 = $6.68

Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.

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The college instructor is most concerned with equity standards.

Equity standards are when an instructor adjusts grades to ensure fairness to all students regardless of their individual performances.

This means that if a class as a whole does not do as well as last year, the instructor will alter the distribution of grades so that the overall grades reflect the effort put in by the class.

For example, if the class average is a C, the instructor may raise some grades to a B or even A in order to ensure that the grades are fair to all students in the class.

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Answer:

1/12

Step-by-step explanation:

Out of the total number of candies, 1/2 of the pink candies are round.

To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:

pink candies = 5/6

round candies among the pink ones = 1/5

Therefore, the fraction of candies that are pink and round is:

(5/6) x (1/2) x 1/5 = 1/12

So, 1/12 of the candies are pink and round.

The mass of dog having weight as 19 kg has its mass in grams as 1.9 x 10⁴ grams, option C.

In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.

Measuring units to determine the size, weight, or quantity of any object. Seven fundamental measurement units are utilized in daily life and across the globe.

A dog has a mass of 19 kg

The mass of the dog in grams is:

1 kilogram = 1000 grams

19.5 kg × (10³ g/1 kg) = 1.95 × 10⁴ g.

Thus, the mass of the dog in grams is 1.95 × 10⁴ g.

1000 grammes make to 1 kilogram (kg) (g).

1 kg = 1000 g

The mass m in kilogram (kg) multiplied by 1000 gives the mass m in grams (g)

m(g) = m(kg) × 1000.

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The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.

Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.

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Complete Question is attached below:

Answer: 75 [tex]m^{2}[/tex]

Step-by-step explanation:

5*5 + 5*10 = 25 + 50 = 75

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Changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.

What is function?

A relationship or expression involving one or more variables

The function g(x) = 6x^2 is a quadratic parent function, which means it is the simplest form of a quadratic function.

When we change the value of "a" in the general form of a quadratic function:

f(x) = ax^2 + bx + c

we change the shape of the graph of the function. Specifically, changing the value of "a" stretches or compresses the graph vertically, and changes the direction of the opening of the parabola.

If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The larger the absolute value of "a", the more stretched or compressed the parabola becomes.

In the case of g(x) = 6x^2, "a" is positive and equal to 6, which means the graph is stretched vertically by a factor of 6 compared to the parent function. The parabola opens upwards and is narrower than the parent function.

If we were to change the value of "a" to a different positive value, for example "a" = 3, the graph would still open upwards but would be less stretched than g(x) = 6x^2. On the other hand, if we were to make "a" negative, for example "a" = -6, the graph would open downwards, and be a reflection of the graph of g(x) = 6x^2 about the x-axis.

In summary, changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.

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Answer:

7/4

Step-by-step explanation:

if you divide 7/4, you will get 1.75 which is greater than 1.43.

Answer:

Hi, your answer is 7/4

Step-by-step explanation:

Hope this helps :D