for a normal population, a sample of n = 9 scores has a standard error of 10. for the same population, a sample of n = 25 scores would have a standard error of

To find the standard form of the equation of an ellipse, we need to know the center, the lengths of the major and minor axes, and the orientation of the ellipse.

Given that the center is (1, 8) and the vertices are (1, 0) and (1, 16), we can see that the major axis is vertical and has a length of 16 (since the distance between the vertices is the length of the major axis). Therefore, the length of the minor axis is 2c = 8 (where c is the distance from the center to one of the foci).

To find c, we can use the relationship a^2 = b^2 + c^2, where a is half the length of the major axis (8 in this case) and b is half the length of the minor axis (4 in this case).

a^2 = b^2 + c^2
8^2 = 4^2 + c^2
c^2 = 48
c = sqrt(48) = 4sqrt(3)

Now we have all the information we need to write the standard form of the equation of the ellipse. Since the major axis is vertical, we have the equation:

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

where (h, k) is the center of the ellipse, a is half the length of the major axis (8 in this case), and b is half the length of the minor axis (4 in this case).

Plugging in the values, we get:

(x - 1)^2 / (4^2) + (y - 8)^2 / (8^2) = 1

Simplifying, we get:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1

Therefore, the standard form of the equation of the ellipse is:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1.
Given the center (h, k) = (1, 8), vertices (1, 0) and (1, 16), and the relation a = 2c, we can determine the standard form of the ellipse equation.

From the vertices, we can see that the ellipse is vertically oriented. The distance between the center and a vertex is the major radius "a." Therefore, a = 8 (half of the distance between the vertices).

Since a = 2c, we can solve for c:
c = a / 2 = 8 / 2 = 4.

Now, we can find the minor radius "b" using the relationship a² = b² + c²:
64 = b² + 16
b² = 48

Finally, the standard form of the ellipse equation is:

((x - h)² / b²) + ((y - k)² / a²) = 1

Substitute the values of h, k, a, and b:

((x - 1)² / 48) + ((y - 8)² / 64) = 1

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Answer:

both statements are correct

Step-by-step explanation:

Answer:

Both statements are correct

Step-by-step explanation:

Khan Academy

With the survey, the following statements are true;

1. 11th graders and 12th graders equally likely to prefer soccer

2. A 12th grade student is less likely to prefer soccer to a 11th grade student and

3 A 11th grade student is more likely to prefer basketball than a 12th grade student.

4. The data suggests there is an association between what grade the student are in and their preference of soccer or basketball

A statement is true if what it asserts is the case, and it is false if what it asserts is not the case. For instance, the statement “The trains are always late” is only true if what it describes is the case, i.e., if it is actually the case that the trains are always late.

The true statement of a data are the positive facts that can be derived from the data. For example, with the survey of 84 students, 48, 11th graders and 36, 12th graders. The following facts can be obtained:

A. 11th graders and 12th graders equally likely to prefer soccer

B. . A 12th grade student is less likely to prefer soccer to a 11th grade student and

C. A 11th grade student is more likely to prefer basketball than a 12th grade student.

d . The data suggests there is an association between what grade the student are in and their preference of soccer or basketball.

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Carina have 300 cows and 400 goats originally.

for cows:

\(\frac{240}{(100-20)} =300\)

for goats:

\(\frac{240}{3} *5=400\)

Therefore, Carina have 300 cows and 400 goats originally.

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Answer:

i think \(g(12)=\frac{5.12}{6}=10\) because if t = 12, t will not satisfy the first and last equation (in the first equation, t<6 and in the last equation t> 12)

so t = 12 only satisfy the second equaton with 6≤t≤12

Step-by-step explanation:

Answer:

$15,246.97

Step-by-step explanation:

12,300 / 18900/12300 =1.53658537 = 53.658% from 1-6 years total

we want 1 year percentage and know its 7.4% as 53.658/6 = 8.943% a year - 1.5 being 1/4 = 7.4%

= 12300 x 1.074219^6

12300 x 1.074219^6 = 189000

We try again including all decimals

12300 x 1.074219^3 =15246.9719 = 15246.97 rounded to nearest 100th decimal.

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

The length of the hypotenuse is $x=\sqrt{2}$ units. ($x=\√2$)

Explanation:

If one of the angles of a right triangle is 45 degrees, then the other acute angle is also 45 degrees. Let's label the other leg of the triangle as $y$ units.

Using the Pythagorean Theorem, we have:

$1^2 + y^2 = x^2$

Simplifying:

$1 + y^2 = x^2$

We can also use the fact that the ratio of the sides of a 45-45-90 triangle is $1:1:\sqrt{2}$ to write:

$\frac{x}{1}=\sqrt{2}$

Simplifying:

$x=\sqrt{2}$

Now, substituting this value of $x$ into our equation $1 + y^2 = x^2$, we have:

$1 + y^2 = (\sqrt{2})^2$

Simplifying:

$1 + y^2 = 2$

$y^2 = 1$

$y = 1$ (since we're looking for a positive length)

Therefore, the length of the hypotenuse is $x=\sqrt{2}$ units.

Hope this helps you, if not I'm sorry. If you need more help, ask me! :]

Answer:

The answer is in the 4th quadrant

Step-by-step explanation:

I really hope this helped!!! have a great day. :)

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Dhara's lifetime earning be when he retire at the age of 65 is$1,901,250

What is lifetime earning?

Total earnings during a period of 50 years, from age 20 to age 69, are referred to as lifetime earnings. The highest level of education a person has achieved is called educational achievement.

Given that Dhara starts his work at 26 old age.

He retires at the age of 65.

The number of years that he works is 65 - 26 = 39 years

Bi-weekly wage means after 2 weeks, he get $1,875. 00.

There is 52 weeks in a year.

In a year, he got (52/2) = 26 salary.

Therefore lifetime earning is ( $1,875. 00 × 26 × 39) = $1,901,250.

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Step-by-step explanation:

there are so many numbers that can be divided into 980 like 2,3,4,5 etc....

Answer:

8 crayons

Step-by-step explanation:

1/4= 25%

25% of 32 =8

in other words-32/4=8

Answer:

8

Step-by-step explanation:

Sherry has 8 crayons because 8 is 1/4 of 32. A way to figure this out is to divide 32 by 4 which will give you the answer 8.

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

-√36

Step-by-step explanation:

The first (approx. 3.567) is obviously irrational, as it continues forever; the decimal values do not end.

The next (√18) is approx. 4.243 and is irrational.

The next (π/3) is irrational because it involves an irrational number, π.

The last (-√36) is -6 and is therefore rational.

The slope (m) of the given line, 4x + 2y + 3 = 0, is -2.To find the slope of a straight line, we need to rewrite the given equation in slope-intercept form, which is in the form y = mx + b, where m represents the slope.

Let's rearrange the given equation, 4x + 2y + 3 = 0, to solve for y:

2y = -4x - 3

Dividing both sides by 2:

y = (-4/2)x - 3/2

Simplifying further:

y = -2x - 3/2

Comparing this equation with the slope-intercept form y = mx + b, we can see that the coefficient of x (-2) represents the slope of the line.

Therefore, the slope (m) of the given line, 4x + 2y + 3 = 0, is -2.

In summary, the answer is m = -2. The negative sign indicates that the line has a downward slope, and the absolute value of 2 represents the steepness of the line.

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Thus, the probability that the focus group will have two males and two females is 0.3.

To determine the total number of possible ways to select four members from a department of 10. This is known as the sample space and is calculated using the combination formula, which is:
n C r = n! / r! (n - r)!

where n is the total number of individuals (in this case, 10) and r is the number of individuals being selected (in this case, 4).

So, the sample space for selecting four members from a department of 10 is:
10 C 4 = 10! / 4! (10 - 4)! = 210

Next, we need to determine the number of ways to select two males and two females from a department with 7 males and 3 females.

This is calculated using the multiplication principle, which states that the total number of ways to perform a sequence of events is equal to the product of the number of ways to perform each individual event.

So, the number of ways to select two males and two females from a department with 7 males and 3 females is:
(7 C 2) x (3 C 2) = 21 x 3 = 63

Finally, we can calculate the probability of selecting a focus group with two males and two females by dividing the number of ways to select two males and two females by the total number of possible ways to select four members:
63 / 210 = 0.3

Therefore, the probability that the focus group will have two males and two females is 0.3. The answer is d.

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The weighted average cost per unit under the perpetual inventory system is $55.76.

To calculate the weighted average cost flow method under the perpetual inventory system, follow these steps:

1. Calculate the total cost of inventory on hand at the beginning of the year: 10,000 units * $75.00 = $750,000.

2. Calculate the cost of goods sold for each sale:
- For the first sale on March 18, the cost of goods sold is 8,000 units * $75.00 = $600,000.
- For the second sale on August 9, the cost of goods sold is 15,000 units * $77.50 = $1,162,500.

3. Calculate the total cost of purchases during the year:
- The purchase on May 2 is 18,000 units * $77.50 = $1,395,000.
- The purchase on October 20 is 7,000 units * $80.25 = $561,750.
- The total cost of purchases is $1,395,000 + $561,750 = $1,956,750.

4. Calculate the total number of units available for sale during the year: 10,000 units + 18,000 units + 7,000 units = 35,000 units.

5. Calculate the weighted average cost per unit: $1,956,750 ÷ 35,000 units = $55.76 per unit.

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Answer:

25%

6.5%

35%

Step-by-step explanation:

Given the invoice :

Bill for a pair of Jean

Jeans ______39.99

Discount ___ - 10.00

Subtotal ____ 29.99

Sales tax ____ 1.95

Total _______ 31.94

A) % of discount to the nearest %

Discount amount = % discount * price

10 = x% * 39.99

10/39.99 = x%

0.2500625 = x%

x = 0.2500625 * 100%

% discount = 25%

% of sales tax:

Sales tax amount = % tax * Subtotal

1.95 = x% * 29.99

1.95/29.99 = x%

0.06502 = x%

x = 0.06502 * 100%

x = 6.5%

Markup before discount = 60%

Markup after discount = (60 - 25)% = 35%

Answer:

$588

Step-by-step explanation:

$294 = 6 Guests

$588 = 12 Guests

The manufacturer must add 13,000 gallons of washer fluid that is 13.5% antifreeze to the existing 500 gallons of washer fluid that is 11% antifreeze to obtain a total volume of washer fluid with a 13% antifreeze concentration.

Let's denote the number of gallons of washer fluid that needs to be added as 'x'.

The amount of antifreeze in the 500 gallons of washer fluid is given by 11% of 500 gallons, which is 0.11 * 500 = 55 gallons.

The amount of antifreeze in the 'x' gallons of washer fluid is given by 13.5% of 'x' gallons, which is 0.135 * x.

To yield washer fluid that is 13% antifreeze, the total amount of antifreeze in the mixture should be 13% of the total volume (500 + x gallons).

Setting up the equation:

55 + 0.135 * x = 0.13 * (500 + x)

Simplifying and solving for 'x':

55 + 0.135 * x = 0.13 * 500 + 0.13 * x

0.135 * x - 0.13 * x = 0.13 * 500 - 55

0.005 * x = 65

x = 65 / 0.005

x = 13,000

Therefore, the manufacturer must add 13,000 gallons of washer fluid that is 13.5% antifreeze to the 500 gallons of washer fluid that is 11% antifreeze to yield washer fluid that is 13% antifreeze.

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Just evaluate the line in the values of the point and check if the equation is true or not.

So let's say line l has an equaiton known:

y = a*x +b

To check if a point is on the line, just replace the values of the point on the line equation, if the equation is true, then that point belongs to the line, if don't, then the point does not belong to the line.

That is the only way to check that.

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Answer:

Step-by-step explanation:

Since one side of the square is 16 cm, the diameter of the circle is also 16 cm. Which means that the radius is 8. the area of a circle is pi times radius square. so it is pi times 8 squared, which is 64pi

The change in elevation after 19 seconds is -42.75 meters.

Elevation simply means the height above the sea level.

From the information given, it should be noted that there's a constant of proportionality. This was given as -2.25 for every seconds.

Therefore, the change in elevation will be:

= -2.25 × Time used

= -2.25 × 19

= -42.75 meter.

The complete question is written below

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An elevator descends at a constant speed. What is the

change in elevation after 19 seconds?

Time

(Sec.)

1

6

10

12

Elevator Descent

Change in Elevation

(Meters)

-2.25

- 13.5

-22.5

- 27

Answer:

The answer is E, 38.

Step-by-step explanation:

6×1/3 can be written as 19/3.

Use the reciprocal of 1/6, which is 6, and multiply 19/3 and 6.

6 and 3 can be simplified with 2.

So: 19 × 2, which is 38.

Step-by-step explanation:

please it my steps to work on paper whorksheet

Answer:

c

Step-by-step explanation:

edge 2020

Answer:

C. the phase shift

Step-by-step explanation:

edge 2020

From the given information in question, we can sat that, The  regular polyhedron have 30 edges.

A polygon that is based on the solid in the three dimensions is known as  a polyhedron. It has flat faces, straight edges and corners. A polyhedron is something like a cube, prism, or pyramid. Cones, spheres, and cylinders do not have polygonal sides, hence they are not polyhedra. Polyhedron is also the name of the polyhedron's plural form. They are classified as prisms, pyramids, and regular polyhedra. Polyhedra include, for instance, cubes (regular polyhedrons), square prisms, triangular prisms, square pyramids, and square pyramids. Consider the diagram below displaying different sorts of polyhedra.

chris discovered that the centers of the faces of a regular icosahedron are also the vertices of another regular polyhedron and he  regular polyhedron have 30 edges.

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The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

2pi/3 radians

Step-by-step explanation:

In the following way we can get the answer:

The measure of m∠POQ is (2/3)π radians.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

we have,

Triangle POQ is an isosceles triangle.

PO = OQ

Sin P = 3/6

Sin P = 1/2

Sin P = Sin 30°

P = 30

m∠P = m∠Q = 30°

m∠P + m∠Q + m∠O = 180

30 + 30 + m∠Q = 180

m∠Q = 180 - 60

m∠Q = 120°

180° = π

120° = π x (120/180)

120° = (2/3)π radian.

Thus,

The measure of m∠POQ is (2/3)π radians.

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To find the area of the part of the surface z = x^2 + y^2 that lies under the plane z = 16, we need to determine the region of intersection between the two surfaces.

First, we set the equation of the surface z = x^2 + y^2 equal to the equation of the plane z = 16:

x^2 + y^2 = 16

This equation represents a circle with radius 4 centered at the origin in the xy-plane. To find the area of the region under the plane, we need to integrate the function representing the surface over this region. Using polar coordinates, we can rewrite the equation of the circle as r = 4. In polar coordinates, the equation for the surface becomes z = r^2.

To find the area, we integrate the function r^2 over the region enclosed by the circle with radius 4: A = ∫∫(r^2) dr dθ The limits of integration for r are 0 to 4, and for θ are 0 to 2π. Evaluating this double integral will give us the desired area.

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