Help please with this maths I need to check it it’s right

The standard deviation of the boys' marks is 0.33.

Standard deviation is a measure of the amount of variation or dispersion of a set of values from the mean. It is calculated as the square root of the variance. It is the most commonly used measure of spread. It is used to measure the degree of variation from the mean of the data set. It is a measure of the variability of the data. It is usually expressed as a positive number.

The standard deviation of the boys' marks can be calculated by subtracting the mean of the girls' marks from the mean of all 12 marks, and then dividing by the number of boys.

To calculate the mean of the girls' marks, add the three marks together (92 + 80 +71) and divide by 3 (243/3 = 81).

To calculate the mean of all 12 marks, add all 12 marks together (92 + 80 + 71 + …) and divide by 12 (1044/12 = 84).

Therefore the mean of the boys' marks is 84 - 81 = 3.

Now we can calculate the standard deviation of the boys' marks by dividing this value by the number of boys (3/9 = 0.33).

Therefore, the standard deviation of the boys' marks is 0.33.

Standard deviation is a measure of the spread of data around the mean. In this case, the boys' marks had a lower standard deviation than the overall marks, indicating that the boys' marks were more consistent than the girls' marks. This could be due to the fact that there were fewer boys taking the exam, so the boys had a smaller spread of scores than the girls.

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Answer:

1. The new coordinates after the rotation would be D' (-2, -2) E' (-5, 1) and F' (1, 4).

2. The new coordinates after reflection across the x-axis would be K' (2, 9), L' (3,-8) and J' (1,-6).

3. The new coordinates after the rotation by 180 degrees around the origin would be N' (-12, 3), P' (-1, -2) and Q' (-9, 0).

The point C and point D are approximately 23.4 meters apart.

Trigonometric functions are a set of mathematical functions that relate the angles of a right-angled triangle to the ratios of the lengths of its sides.

We can use trigonometry function to solve for the distance between points C and D. Let x be the distance CD, then we have:

tan(48°) = h / (x + 24m)

where h is the height of the flagpole.

We can solve for x by rearranging the equation:

x = (h / tan(48°)) - 24m

Substituting the given values, we get:

x = (42m / tan(48°)) - 24m

x ≈ 23.4m

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Answer:

I think is 30km/h

if it's wrong I'm sorry

The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.

Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.

In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.

Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.

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The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.

Degrees of freedom refer to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of experimental or analytical flexibility to accommodate new data or observations.

In this case there are 8 degrees of freedom. To find the t value, we need to refer to the t table. A t-table is a plot of t-values ​​for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 is 0.95. The t-table is organized so that rows represent the degrees of freedom and columns represent the area under the curve. For example, if you have 8 degrees of freedom and the area under the curve is 0.95, find the t-value in the row with 8 degrees of freedom and the column with area under the curve of 0.95. In this case, the t-value in the t-table is 1.86.

Therefore, the value of t is such that the area under the curve between 1 and 11 is 0.95, assuming 8 degrees of freedom is 1.86.

The area between -t and t = 0.95

P(t₈ > t) = P(t₈ - t)

= 0.025

As t - distⁿ is symmetrical and are under the curve is 1 and degree of freedom is 8.

Hence, from t - table; the t - value = 2.306

i.e. P(t₈ > 2.306) = 0.025

or P(-2.306 < t₈ < 2.306) = 0.95

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The complete question is as follows:

Answer:

a) 2*(x+4)

b) 1/4*x + 1/3*x

Answer:

a) 2(x+4)

b) 7x/12

Step-by-step explanation:

a) Sum of x and 4 is (x+4). Since the number is doubled,

2 * (x+4) = 2(x+4)

b) One fourth of a number x is x/4 and one third of the number is x/3.

Adding these two:

x/4 + x/3

The LCM of 4 and 3 is 12 and so,

(4x + 3x)/12

= 7x/12

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The cashier gave Mary an amount of  $49.64 in change.

Mary's mom gave her $100.00 to go shopping.

She spent $22.65 on a shirt and $33.31 on a skirt. She had a coupon for 10% off. Mary's total expenditure can be calculated by adding the cost of the skirt and the shirt:

Shirt + Skirt = $22.65 + $33.31 = $55.96

The cost of the items with the discount is the Total cost after discount

= $55.96 − 10% of $55.96 = $55.96 − $5.596 = $50.36

Since Mary was given $100.00 by her mother, she has to subtract the total amount she spent from the total she was given.

This will give us her total change:

$100.00 − $50.36 = $49.64

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Ben's Gross Profit for the last quarter is $3,425. This is calculated by subtracting the Cost of Goods ($575) and Total Expenses ($5,000) from the Income ($9,000).

Gross profit is the difference between a business’s total sales revenue and its cost of goods sold (COGS). It is calculated by subtracting the cost of goods sold from total revenue. Gross profit is also referred to as gross margin and is expressed as a percentage of total sales. This figure is important to businesses because it shows the profitability of the company’s products after accounting for the cost of the materials used to manufacture those products. Additionally, gross profit is a key indicator of the company’s overall financial health and ability to remain profitable.

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105 divided by 15 is represented as 15 groupings of 7. We will obtain a full number quotient in each instance with no residual.

117 divided by 13 is equal to 9 with a residual of 0; 136 divided by 17 is equal to 8 with a remnant of 0; and 231 divided by 11 is equal to 21 with a remainder of 0;

We may use a model of equal groups to get the quotient for each division issue. Drawing 15 groups of 7 to represent 105 divided by 15 and 13 groups of 9 to represent 117 split by 13 and 17 groups of 8 to represent 136 divided by 17 is possible. We will obtain a full number quotient in each instance with no residual.

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(a)

i. The mean of all 855 salaries of 2012 professional baseball players to 3 decimal places is 3.319 million dollars.

ii. The standard deviation of all 855 salaries of 2012 professional baseball players to 3 decimal places is 4.104 million dollars.

iii. The values in parts (a) and (b) above are:

Parameter: the mean and standard deviation of the population.

Numerical summaries of the population.

iv. The distribution of salaries for professional baseball players in 2012 is right-skewed with a single peak and several outliers at the high end.

(b)

i. The mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 3.319 million dollars.

ii. The standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 1.298 million dollars.

iii. The shape of the sampling distribution of the sample mean when n = 10 is approximately normal.

(c) The value of the sample mean (in millions of dollars) from the first random sample of size n = 10 is 2.167 million dollars.

(d) The value of the sample mean (in millions of dollars) from the second random sample of size n = 10 is 2.384 million dollars.

(e) The value of the sample mean (in millions of dollars) from the third random sample of size n = 10 is 3.913 million dollars.

(f)

i. The mean of the three sample means is 2.821 million dollars.

ii. The standard deviation (i.e., standard error) of the three sample means is 0.911 million dollars.

(g)

i. We would expect to see a value of 3.319 million dollars for the mean of the sample means (in millions of dollars) of size n = 10.

ii. We would expect to see a value of 1.298 million dollars for the standard error of the sample means (in millions of dollars) of size n = 10.

The mean and standard error are obtained from the applet and are reported to 3 decimal places. The shape of the sampling distribution of the sample mean when n=10 is approximately normal due to the Central Limit Theorem.

The applet provides the histogram of the 10 observations selected for the sample, as well as the mean and standard deviation of the observations in the sample. The student is required to click "Generate 1 Sample" three times and report the sample means from each of the three random samples of size n=10.

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Answer:

y = -2x + 17.

Step-by-step explanation:

To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.

First, we need to rearrange the equation of the given line 4x + 2y = 10 into slope-intercept form y = mx + b:

4x + 2y = 10

2y = -4x + 10

y = -2x + 5

So, the slope of the given line is -2.

Since the line we're looking for is parallel to the given line, it will have the same slope of -2. We also have a point (7,3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the point.

Plugging in the values, we get:

y - 3 = -2(x - 7)

Simplifying:

y - 3 = -2x + 14

y = -2x + 17

So, the equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10 is y = -2x + 17.

PR = 16 units

Similar triangles are two triangles that have the same shape but not necessarily the same size. This means that their corresponding angles are equal, and their corresponding sides are proportional in length.

Here, ΔPRQ similar with ΔPST

So, we can say that their corresponding sides are in proportion (i.e., have the same ratio).

[tex]\frac{PR}{PS} = \frac{RQ}{ST}[/tex]

[tex]\frac{(x+7) + (x-1) }{(x+7)} = \frac{8}{6}[/tex]

Simplification,

12x + 36 = 8x + 56

x = 5

So, the value of PR = (x+7) + (x-1)

PR = (5+7) + (5-1) = 16

Therefor, PR = 16 units

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The triabgles ae similar. Their corresponding sides are in proportion.

PR = 16 units

Triangles that are similar to one another in shape but not necessary in size are called similar triangles. Their respective sides are proportional in length, and their corresponding angles are equal. Three edges, three angles, and three vertices make up a triangle. The sum of a triangle's three internal angles is 180 degrees. The triangle's third side is longer than the sum of its two longest sides.

Here, ΔPRQ similar with ΔPST

Thus, their respective sides are proportional, as we can see. (i.e., have the same ratio).

[tex]\frac{PR}{PS} =\frac{RQ}{ST} \\\\\frac{(x+7)+(x-1)}{(x+7)} =\frac{8}{6}[/tex]

Simplification,

12x + 36 = 8x + 56

x = 5

So, the value of PR = (x+7) + (x-1)

PR = (5+7) + (5-1)

    = 16

Therefor, PR = 16 units

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The overall transformation of the point (1,2) is (-6,3).

The given composition of transformations is a dilation with a scale factor of 3 centered at the origin, followed by a rotation of 270° counterclockwise about the origin. The dilation can be expressed mathematically as a scaling of the coordinates (x, y) by a factor of 3, resulting in (3x, 3y). The rotation of 270° counterclockwise can be expressed as a matrix multiplication of the new coordinates resulting in (-3y, 3x). Thus, the overall transformation of the composition can be expressed mathematically as (-3y, 3x).

To illustrate this with an example, let us consider a point (1,2). After the dilation, the coordinates become (3,6). After the rotation, the coordinates become (-6,3).

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The minimum number of quarters that she could have is: 14

Let x represent the number of dimes = 4

Let y represent the number of quarters

She has no more than 21 coins

Thus:

x + y ≤ 21

Plugging in relevant values gives:

4 + y ≤ 21

y ≤ 21 - 4

y ≤ 17

0.10x + 0.25y ≥ 3.75

0.10(4) + 0.25y ≥ 3.75

0.40 + 0.25y ≥ 3.75

0.25y ≥ 3.75 - .40

0.25y ≥ 3.35

y ≥ 3.35/.25

y ≥ 13.4

Therefore, the minimum number of quarters she can have would be 14 because the "y" value must be a whole number and the next whole number above 13.4 is 14.

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The values of the first four terms of the sequence with the definition a(n) = 3n² - n are 2, 10, 24 and 239

A sequence can be arithmetic or geometric of neither

The definition of the function is given as

a(n) = 3n² - n

The above definitions imply that we simply add -n to the three multiplied by 3 and n to get the current term

Using the above as a guide,

So, we have the following representation

a1 = 3 * 1² - 1

a1 = 2

Next. we have

a₂ = 3 * 2² - 2

a₂ = 10

Also, we have

a₃ = 3 * 3² - 3

a₃ = 24

Lastly, we have

a₄ = 3 * 3² - 4

Evaluate the equation

a₄ = 239

Hence, the value of a₄ is 239

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The value of D is 49.1º to the nearest degree using the law of sines.

To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle D:

sin(D)/d = sin(F)/f

sin(D) = (d/f) × sin(F)

sin(D) = (76/20) × sin(17º)

sin(D) = 0.7588

Taking the inverse sine of both sides, we get:

D = [tex]sin^{-1}[/tex] × (0.7588)

D = 49.1º (rounded to the nearest tenth of a degree)

The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.

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There is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6

The given radical expression are:

g(x) = √(x-5) + 6

f(x) = √(x-5) + 6

The graph of both function is plotted, which have the exact same value on graph.

Thus, there is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6

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The critical value of p in a test to determine if a filling system under-fills less than 10% of all boxes, with a significance level of 0.10 and a random sample of size 200, is -1.28.

Assuming that the filling system under-fills with probability p, the null hypothesis is:

H0: p >= 0.10

Ha: p < 0.10 (one-tailed test)

To find the critical value of p, we need to use the inverse cumulative distribution function (ICDF) of the standard normal distribution.

At a significance level of 0.10, the critical value is the value z such that P(Z <= z) = 0.10, where Z is a standard normal random variable. We can find this value using a standard normal table or calculator, or by using the function norm.inv(0.10) in Microsoft Excel, which gives the result -1.28 (rounded to two decimal places).

Since the sample size is large (n = 200), we can use the normal approximation to the binomial distribution to test the null hypothesis. The test statistic is:

z = (x/n - p0) /  √(p0*(1-p0)/n)

where x is the number of boxes that under-fill, n is the sample size, and p0 is the null hypothesis value of the proportion. We want to reject the null hypothesis if the test statistic is less than the critical value of -1.28.

Since we do not have any information about the sample proportion, we can use the null hypothesis value of p0 = 0.10. Then the critical value of the test statistic is:

z_critical = -1.28

Substituting the values into the test statistic formula, we get:

z = (x/200 - 0.10) / √(0.10*(1-0.10)/200)

Simplifying, we get:

z = (x - 20) / 4.24

To reject the null hypothesis at the 0.10 significance level, we need the test statistic z to be less than -1.28. Therefore, we can write the rejection region as:

z < -1.28

Substituting this inequality into the test statistic formula, we get:

(x - 20) / 4.24 < -1.28

Solving for x, we get:

x < 14.5

Therefore, if the number of boxes that under-fill is less than or equal to 14 (out of 200), we reject the null hypothesis at the 0.10 significance level and conclude that there is sufficient evidence to suggest that the filling system under-fills less than 10% of all boxes.

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Answer:

Step-by-step explanation:

The answer is 50.3  An easy way to find the answer is by using this link. https://www.calculator.net/right-triangle-calculator.html

Just plug the 29 and 44 in.

Answer:

-6=x

Step-by-step explanation:

substitute 21 into j(x) in other equation

21=-2x+9

-9 -9

12=-2x

-6=x

Sοlving the equatiοns, we can find that, Nicο, Raj and Sandra are cοrrect.

Each term in a linear equatiοn has an expοnent οf 1, and when this algebraic equatiοn is graphed, it always prοduces a straight line. It is called a "linear equatiοn" fοr this reasοn.

Bοth linear equatiοns with οne variable and thοse with twο variables exist.

In the questiοn,

2/5(5+x) = 8

Methοd 1

Sοlve fοr x.

We have,

2/5(5+x) = 8

Multiply by 5/2 bοth sides:

5+x = 20

⇒ x = 15

Similarly, Methοd 4 and Methοd 5 are cοrrect.

Hence, Nicο, Raj and Sandra are cοrrect in sοlving the equatiοn.

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Answer:

After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor of

1

8

each hour after it's consumed.

Step-by-step explanation:

The exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink is y= 160(1/8)⁽ˣ⁾. After 6 hours, the amount of caffeine left in John's body will be y=160(1/8)⁽⁶⁾ ≈ 1.96 milligrams (rounded to the nearest milligram).

The exponential equation y=a(b)² can be used to model the amount of caffeine left in John's body x hours after consuming an energy drink. In this equation, a represents the initial amount of caffeine in the body (160 milligrams), and b represents the factor by which the amount of caffeine decreases each hour (1/8). To find the amount of caffeine left in John's body after 6 hours, we can simply substitute x=6 into the equation and solve for y. The result is y=160(1/8)⁽²*⁶⁾ ≈ 6 milligrams. This means that after 6 hours, John will have approximately 6 milligrams of caffeine left in his body if he doesn't consume any more caffeine.

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Complete question:

After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor 1/8 of each hour after it's consumed.

Write an exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink.

Use whole numbers, decimals, or simplified fractions for the values of a and b,

To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't consume any more caffeine?

The probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

To find the probability that a person surveyed went to the concert given they are a fan club member, we need to use conditional probability. We can use the following notation:

P(concert | fan club)

This means the probability of going to the concert given that the person is a fan club member.

Let's assume that Jennifer surveyed 100 classmates, and 40 of them are in the Panic Squadron Fan Club and also went to the concert. Also, let's assume that 60 of Jennifer's classmates are in the Panic Squadron Fan Club.

Then, we can use the formula for conditional probability:

P(concert | fan club) = P(concert and fan club) / P(fan club)

Plugging in the values we know, we get:

P(concert | fan club) = 40/60 = 2/3 or approximately 0.667

Therefore, the probability that a person surveyed went to the concert given they are a fan club member is 2/3 or approximately 0.667.

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Hence, in response to the provided question, we can say that As a result,  equation the item's selling price after both markdowns is 166.40$.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

Then, we may determine the item's price after the initial 20% discount.

20% of 520$ equals (20/100) * 520$ = 104$, hence the item's new price is 520$ - 104$ = 416$.

After another six months of not selling, the item gets reduced by 60%.

60% of 416$ equals (60/100) * 416$ = 249.60$, therefore the item's ultimate sale price after both markdowns is 416$ - 249.60$ = 166.40$.

As a result, the item's selling price after both markdowns is 166.40$.

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Using equations, we can find that the item's selling price after both markdowns is 166.40$.

In an algebraic equation, the equals symbol (=), which represents equality, can be used to connect two quotes. In algebra, an explanation is a declarative statement that establishes the similarity of two formulas. For example, the integers 3x + 5 and 14 are divided by the same letter.

A linear equation can be used to identify the relationship between the texts written on the various sides of a letter. Applications and products can typically be used interchangeably. In this instance, 2x – 4 = 2.

After applying the initial 20% discount, we may determine the item's price as:

20% of 520$ equals (20/100) × 520$ = 104$

Hence the item's new price is 520$ - 104$ = 416$.

After another six months of not selling, the item gets reduced by 60%.

60% of 416$ equals (60/100) × 416$ = 249.60$

Therefore, the item's ultimate sale price after both markdowns is

416$ - 249.60$ = 166.40$.

As a result, the item's selling price after both markdowns is 166.40$.

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The tower is 2,200 feet tall.

To find the height of the tower, we can use the Pythagorean theorem for a right triangle. The given information can be represented as:

Hypotenuse (cable) = 2,230 feet

Base (distance from the starting point to the point under the tower) = 370 feet

Height (height of the tower)

Write the Pythagorean theorem formula:

[tex]a^2 + b^2 = c^2,[/tex]

where a and b are the two shorter sides (base and

height) and c is the hypotenuse.

Plug in the given values: [tex]height^2 + 370^2 = 2,230^2[/tex]

Square the given numbers: [tex]height^2 + 136,900 = 4,972,900[/tex]

Subtract the base squared from both sides: [tex]height^2 = 4,972,900 - 136,900[/tex]

Calculate the difference: [tex]height^2 = 4,836,000[/tex]

Find the square root of the difference: height = √4,836,000

Calculate the height: height = 2,200 feet

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Answer:

Length: 14m

Breadth: 10m

Area: 140m^2

Step-by-step explanation:

Let length = l and breadth = b,

l = 4 + b

Perimeter = 2(l+b)

= 2(4 + b + b)

= 2(4 + 2b)

= 8 + 4b

Perimeter = 48

Hence,

4b + 8 = 48

4b = 40

b = 10m

l = 4 + b = 14m

A = lb = 10 * 14 = 140m^2

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Answer:

96

Step-by-step explanation:

The pοssible first steps tο simplify the equatiοn are:

Multiply bοth sides οf the equatiοn by -2.

Distribute Negative οne-half οver (x + 4).

Multiply bοth sides οf the equatiοn by -2, tο get rid οf the fractiοn:

-2 * Negative οne-half (x + 4) = -2 * 6

This simplifies tο: (x + 4) = -12

Distribute Negative οne-half οver (x + 4):

Negative οne-half (x + 4) = Negative οne-half * x + Negative οne-half * 4

This simplifies tο: (-1/2)x - 2 = 6

Therefοre, the pοssible first steps tο simplify the equatiοn are:

Multiply bοth sides οf the equatiοn by -2.

Distribute Negative οne-half οver (x + 4).

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The experimental probability of someone having 6 letters in their name based on this experiment  is [tex]\frac{1}{6}[/tex].

It is calculated based on the outcomes of multiple iterations of an experiment. The probability that is created using logic is termed a theoretical probability. A probability is a number that falls between (and includes) 0 and 1.

[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]

Given, Total number of the Student = 8

Persons having 6 (Six)letters in their name = 1

Other 7 (Seven) persons says different number of letters.

So, Experimental probability of someone having 6 letters in their name is determined,

[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]

[tex]= \frac{1}{6}[/tex]

Hence, we can say that the experimental probability of someone having  letters in their name based on this experiment  is [tex]\frac{1}{6}[/tex].

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This quadrilateral is a trapezoid because it has one pair of parallel sides. The sides Q1U and AD are parallel, while the other two sides (U1 and DA) are not.

A trapezoid is a four-sided shape with two parallel sides, called the bases, and two non-parallel sides, called the legs. The opposing angles of the trapezoid are equal in measure, and the two adjacent angles are supplementary. A trapezoid can also be defined as a quadrilateral with exactly one pair of parallel sides. Trapezoids are often used in mathematics to define and calculate area, perimeter and other geometric properties. They can also be used to construct shapes and patterns in architecture, engineering and design.

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Answer:

I'm pretty sure it's a rectangle

Step-by-step explanation:

the reason why is because there are 2 pairs that are equal to each other but each seem to be perpendicular in slope form.