Jessica and her friend measured the lengths of the fish they caught one day. Make a line plot of their data

Answer:

Answer:

See attached image and explanation below

Step-by-step explanation:

For the first table:
The cumulative frequency for each class interval is obtained by adding that class frequency to the sum of all frequencies less than that class interval

So the table will look as in the first image attached

The second table talks about cumulative relative frequency and it uses the same technique as above but we are dealing with relative rather than absolute frequencies

The second image shows the correct values

Your relative frequency table (the third image you posted) is correct

Answer:

Step-by-step explanation:

Let's call the distance from Planet A to one of the possible positions of Planet B "x". We can use trigonometry to relate the angle between the star and Planet B (19°), the distance from the star to Planet A (65 million miles), and the distances from Planet A to Planet B (x).

In a right triangle with angle 19°, the opposite side is x and the adjacent side is 65 - 45 = 20 million miles. Therefore, we can use the tangent function to relate these sides:

tan(19°) = x / 20

Solving for x, we get:

x = 20 tan(19°) ≈ 6.7 million miles

So one possible distance from Planet A to Planet B is approximately 6.7 million miles.

However, there is another possible position for Planet B, which is on the other side of Planet A as shown in the figure. In this case, the distance from Planet A to Planet B is:

y = 65 + 45 + 20 = 130 million miles

Therefore, the two possible distances from Planet A to Planet B are approximately 6.7 million miles and 130 million miles (rounded to the nearest tenth).

The sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the centre of dilatation. The dilation transformation is determined by the scale factor and the centre of dilation.

The image stretches when the scaling factor exceeds 1.

When the scale factor is between 0 and 1, the image gets smaller.

The resulting image and the original image are identical if the scale factor is 1.

The coordinates of the triangle ABC are:

A(0, -1)

B (0, 1)

C (0, 1.8)

First the triangle is rotated by 90 degrees thus following the transformation rule:

(x, y) → (y, -x)

The new coordinates are:

A(0, -1) → A (1, 0)

B (0, 1) → B (-1, 0)

C (0, 1.8) → C (1.8, 0)

Then, the rotated figure is dilated using a scale factor of:

SF = 6/2 = 3

Hence, the sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

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So, in response to the above question, we can state that  The differential equation has a second solution, which is this.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical.

When we differentiate y2(x) with regard to x, we obtain:

[tex]y2'(x) = v'(x)y1(x) plus v(x)y1' (x)\\v"(x)y1(x) + 2v'(x)y1'(x) + v(x)y1" = y2"(x) (x)\\y2'(x) - y2(x) = 6y2"(x)\\[v"(x)y1(x), 2v'(x)y1'(x), and v(x)y1'(x)] [v(x)y1'(x) + v'(x)y1(x)] - v(x)y1(x) = 0\\3 + 2ex/3)v'(x) + 6v"(x) = 0\\[/tex]

A first-order linear differential equation in v' is shown below (x).

[tex]e(x/2 + (2/9)e(x/3)) = u(x)\\3 + 2ex/3 + 6u(x)v"(x)\\u(x)v'(x) = 0\\6u(x)v'(x) = C1[/tex]

where C1 is an integration constant. Calculating v'(x), we obtain:

[tex]v'(x) = C1/(6u(x))[/tex]

the expression [tex]v(x) = C1e(-x/2 - (2/9)e(-x/3)) dx/6[/tex]

[tex]y2(x) = y1(x)e(-P(x) dx)e(-P(x) dx)y1(x)e(-2) dx[/tex]

where P(x) = (3 + 2ex/3)/6 is the differential equation's coefficient for y'(x). When we replace y1(x) = ex/3 and P(x), we obtain:

y2(x) = (ex/3)

∫e^(-∫(3+2ex/3)/6 dx)

[tex](e^{(-2x/3)/9)} ex/3 e(x/2 - (2/9)e(x/3)) dx y2(x) =[/tex]

[tex]y2(x) = C1y1(x) (x)[/tex]

[tex]"e" (-x/2 - (2/9)e" (-x/3)") dx/6[/tex]

where C1 is an integration constant. The differential equation has a second solution, which is this.

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Answer:

Estimate of 938,617 - 254 is  938, 300

Step-by-step explanation:

To round to the nearest hundred we look at the digit in the hundreds place and examine the digit to the right of it. If the digit to the right of the 100's place is 5 or greater round the hundreds digit up, else leave it as is. Make all the digits to the right of the 100's digit zeros

938,617 rounded to the nearest 100 is 938,600
The 6 in the hundreds place stays the same, because the digit to the right in the tens place is 1 which is less than 5

254 rounded to 100's place = 300
The digit in the 100's place is 2; the digit to the right of it is 5 so round 2 to 3 and make all digits to its right as 0

Estimate of 938,617 - 254 = 938,600 - 300 = 938, 300

Actual value of 938,617 - 254 = 938,363 so we are off by only a small margin

(a) The vertex of ∠1 is B.

(b) The sides of ∠ABC are BA and BC.

(c) Two other names for ∠2 are ∠CBD and  ∠DBC

In geometry, the vertex of an angle is the common endpoint of the two rays that form the angle. The rays that form the angle are called the sides of the angle.

In the figure, the point B is the vertex of the angle ∠ABC (angle ∠ABC is equal to ∠1). The sides of the angle are BA and BC.

Thus, the vertex of ∠1 is B.

The sides of ∠ABC are BA and BC.

Two other names for ∠2 are ∠CBD and  ∠DBC

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Answer:

the perimeter of the rectangle is 26 meters.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:

width = area / length = 36 / 9 = 4 meters

Now we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

Substituting the given values, we get:

perimeter = 2(9 + 4) = 2(13) = 26 meters

Therefore, the perimeter of the rectangle is 26 meters.

The value for the expression 1/3x² for x = 6 is 1/108. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," are said to allow every real number to be stated, according to mathematicians. Divide, multiply, add, and subtract are the four mathematical operations that result in quotient, product, sum, and difference, respectively.

We are given an expression as  1/3x².

We need to find its value for x = 6.

Substituting this in the expression, we get

⇒1/3(6)²

⇒1/3(36)

⇒1/108

Hence, the value for the expression 1/3x² for x = 6 is 1/108.

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The solution of the given compound inequality in the interval notation is (∅).

What is compound inequality?

Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols. Typically, we use the not equal symbol to indicate that two values are not equal.  But to compare the values, whether it is less than or greater than, different inequalities are used.

Given a compound inequality,

 1/4 x - 3  ≥ 1 and -3(x - 2) ≥ 2

To solve this we take the first inequality.

1/4 x - 3  ≥ 1

1/4 x ≥ 4

x ≥ 16

Now solve the second inequality.

-3(x - 2) ≥ 2

-3x +6 ≥ 2

-3x ≥ -4

x ≤ 4/3 (The inequality sign reverses because we are dividing by a negative number, -3)

Now from both solved inequalities, we can see that x should be greater than 16 as well as it should be less than 4/3.

There exists no such number.

Therefore the solution of the given compound inequality in the interval notation is (∅).

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When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.

Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.

The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.

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Answer:

Step-by-step explanation:

If a ball plus a bat costs 1.10 dollars and the price of the bat is 1 dollar more than the ball, what is the cost of the bat?

If we represent the price of the ball as "p", then the price of the bat will be "p + 1", since the problem tells us that the price of the bat is 1 dollar more than the price of the ball.

We also know that the sum of the price of the ball and the bat is 1.10 dollars. We can write this as an equation:

p + (p + 1) = 1.10

Simplifying and solving for p, we get:

2p + 1 = 1.10

2p = 0.10

p = 0.05

Therefore, the price of the ball is 0.05 dollars. To calculate the price of the bat, we can add 1 dollar to the price of the ball:

p + 1 = 0.05 + 1 = 1.05

So, the price of the bat is 1.05 dollars.

Answer:

15 degrees for the first one

90 degrees for the second one

Step-by-step explanation:

Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

What is the least common multiple (LCM)?

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them

To solve this problem, we need to find the least common multiple (LCM) of the numbers 2, 3, and 5. The LCM is the smallest number that is a multiple of all three numbers.

Prime factorizing the numbers, we have:

2 = 2

3 = 3

5 = 5

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers, and multiply them together. Therefore, the LCM of 2, 3, and 5 is:

LCM = [tex]2^1 * 3^1 * 5^1 = 30[/tex]

Hence, Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.

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The area under the curve of the standard normal​ distribution is 98.61% of the area between equals negative 2. 2 and zequals2. 2

The area under the curve of a standard normal distribution between z = -2.2 and z = 2.2 is given by the integral of the normal distribution function from -2.2 to 2.2. This can be calculated using a table of standard normal probabilities or using a calculator with a normal distribution function.

The result is approximately 0.9861. To convert this to a percentage, simply multiply by 100: 0.9861 * 100 = 98.61%. Therefore, about 98.61% of the area is between z = -2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the z-distribution or the unit normal distribution. It is often used in statistical tests, such as the z-test, t-test, and chi-square test. It is also used to determine confidence intervals, to calculate probabilities, and to measure the probability of a given event.

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The appropriate hypotheses for the researcher are: Null hypothesis: p <= 0.5 and Alternative hypothesis: p > 0.5.

In statistics, a hypothesis is an assumption or proposition about a population parameter, based on sample data. A hypothesis is a statement that is tested to determine whether it is true or false. It is an important component of statistical inference, which involves drawing conclusions about a population based on a sample of data. There are two types of hypotheses in statistics: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that is tested against the alternative hypothesis. It is usually a statement of "no effect" or "no difference" between two groups or conditions. The alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected. It is usually a statement of an effect or difference between two groups or conditions.

Here,

The null hypothesis states that the proportion of households in the city that gave a charitable donation in the past year is less than or equal to 50 percent. The alternative hypothesis states that the proportion of households that gave a charitable donation is greater than 50 percent. The researcher will test these hypotheses using the sample data to determine whether there is convincing statistical evidence to support the alternative hypothesis.

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In many contexts, we can estimate distances between objects or locations, but we may not always be able to measure them precisely. There are several reasons why we might only be able to estimate distances rather than measure them exactly:

Limitations of measuring instruments: The precision of a measuring instrument can limit our ability to measure distances accurately. For example, a ruler may only have markings up to a certain level of precision, so we may need to estimate distances between the markings.

The variability of the distance: In some cases, the distance we are measuring may be constantly changing, making it difficult to measure with precision. For example, if we are trying to measure the distance between two moving objects, the distance between them will constantly change, and we may need to estimate the distance at a particular moment in time.

Environmental factors: The environment can also make it difficult to measure distances precisely. For example, atmospheric conditions such as haze or fog can obscure objects and make it difficult to judge their distance accurately.

Human perception and judgment: Finally, our own perception and judgment can also limit our ability to measure distances accurately. For example, when estimating the distance to an object, our perception of the size of the object can affect our judgment of its distance.

In many cases, despite these limitations, estimates of distances can still be useful and informative. For example, in navigation, we may not need to know the exact distance between two points, but only an estimate that is accurate enough to help us navigate from one point to the other

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Verified Answer ✅

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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The required turtle's speed is 12/5 miles per hour, as of the given condition.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
To find the turtle's speed in miles per hour, we need to convert the fraction of miles traveled in a fraction of an hour to miles per hour.

First, we can simplify the fraction 3/5 by dividing the numerator and denominator by 1/4,

speed = distance/time

Substitute the value in the above expression,
Speed = 3/5 / [1/4]
Speed = 12/5

Therefore, the turtle's speed is 12/5 miles per hour.

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A claw arcade machine contains stuffed animals and mystery boxes.

A claw arcade machine is a popular type of game machine found in many arcades and amusement parks. It typically consists of a glass cabinet that contains a variety of stuffed animals and other prizes, such as mystery boxes, that can be won by using a mechanical claw.

The player inserts a designated amount of money and then uses the joystick to position the claw over the desired prize. Once the player is satisfied with the claw's position, they press a button to make the claw descend and attempt to grab the prize. If the claw is successful in grabbing the prize, it will lift it up and drop it into the prize chute, where the player can then collect it.

The prizes in a claw machine can vary from small plush toys to larger stuffed animals, and even mystery boxes that contain unknown items or a chance to win a bigger prize. The claw's strength and grip are adjustable, which can make winning a prize more difficult or easier depending on the machine's settings.

Claw machines are a popular form of entertainment for all ages, and the thrill of successfully grabbing a coveted prize can be a source of excitement and satisfaction for players.

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Answer:

Step-by-step explanation:

18.) 19 - 3x = 14 + 2x

To solve for x, we can simplify the equation by moving all the x terms to one side and all the constant terms to the other side:

19 - 3x = 14 + 2x

19 - 14 = 2x + 3x

5 = 5x

x = 1

To check our solution, we can substitute x = 1 back into the original equation and see if it holds true:

19 - 3(1) = 14 + 2(1)

19 - 3 = 14 + 2

16 = 16

Since both sides of the equation are equal when x = 1, we have verified that x = 1 is the correct solution.

19.) 2(7 + 5y) - 3y = -35

We can start by simplifying the left-hand side of the equation by using the distributive property:

2(7 + 5y) - 3y = 14 + 10y - 3y = 14 + 7y

Now, we can solve for y by moving the constant term to the other side:

14 + 7y = -35

7y = -49

y = -7

To check our solution, we can substitute y = -7 back into the original equation and see if it holds true:

2(7 + 5(-7)) - 3(-7) = -35

2(7 - 35) + 21 = -35

-56 + 21 = -35

-35 = -35

Since both sides of the equation are equal when y = -7, we have verified that y = -7 is the correct solution

20.) 14 + 4(x - 5) = 6 - 2x

We can start by simplifying the left-hand side of the equation by using the distributive property:

14 + 4(x - 5) = 14 + 4x - 20 = 4x - 6

Now, we can solve for x by moving the constant term to the other side:

4x - 6 = 6 - 2x

6x = 12

x = 2

To check our solution, we can substitute x = 2 back into the original equation and see if it holds true:

14 + 4(2 - 5) = 6 - 2(2)

14 - 12 = 6 - 4

2 = 2

Since both sides of the equation are equal when x = 2, we have verified that x = 2 is the correct solution.

Step-by-step explanation:

The difference between 1 and 7/8  is  0.125

The difference between 1 and 1(1/5) is 0.2

The number closer in value to 1 is the one with a lesser difference therefore, the correct answer is 7/8

Step-by-step explanation:

[tex]1 - \frac{7}{8} = 0.125[/tex]

while:

[tex] 1 \times \frac{1}{5} - 1 = 0.2[/tex]

then: 0.125<0.2

Answer:

7 + (8 × t) = p, 15 + (6 × t) = p

Step-by-step explanation:

The equation you can use for charging a $7 entrance fee and then $8 for each ride ticket can look like this:

(let t = ride ticket & p = price)

The equation you can use for charging a $15 entrance fee and then $6 for each ride ticket can look like this:

Therefore, the equations you can use are listed above.

There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Answer:

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

From the above equation given in the question , we get that g(x)  have a value of 3x.

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

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Answer:

Below

Step-by-step explanation:

Due to vertical angles:

5x+21 =9x -55     shows x = 19°

then WOZ = 9x-55 = 116 degrees

WOZ and WOY  are supplemenrary (add to a 180 ° straight line)

116 + WOY = 180      so WOY = 64°

The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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The mean of the sampling distribution is 200, and the standard deviation of the sampling distribution is 4.

The sampling distribution is a theoretical distribution that represents the behavior of sample means from all possible samples of a given size that can be drawn from a population.

However, the standard deviation of the sampling distribution is not the same as the standard deviation of the population.

Mathematically, we can represent the mean of the sampling distribution as follows:

μ(x) = μ = 200

Where μ(x) represents the mean of the sampling distribution and μ represents the mean of the population.

We can also calculate the standard error of the mean using the following formula:

σ(x) = σ / √(n)

Where σ(x) represents the standard deviation of the sampling distribution, σ represents the standard deviation of the population, and sqrt(n) represents the square root of the sample size.

Plugging in the values given in the problem, we get:

σ(x) = 20 / √(25) = 4

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The way to solve a 3 column table depends on the information in the table but there are general steps to follow shown below.

First, identify the headings for each column. Then, determine the type of data being presented in each column because the data may be numerical (such as measurements or quantities), categorical (such as types or classifications), or a combination of both.

Analyze the data in each column and use mathematical operations or formulas to calculate or analyze the data, if necessary. Finally, draw conclusions or make inferences based on the data in the table.

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Answer:

Step-by-step explanation:

We can start by combining the two fractions by finding a common denominator:

sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)

= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))

= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2

= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))

= (2 + 2cos(a)) / (sin(a) + cos(a))^2

= 2(1+cos(a)) / (sin(a) + cos(a))^2

= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)

= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2

This expression cannot be simplified further without additional information or context.

Answer:

Step-by-step explanation: you need to rewrite the formula but with the numbers that are given to you so then you multiply and divide by 2 and BOOM you got your answer