Find the estimated standard error for the sample mean for the following samples: (a) n= 9 with SS =1152

The solutions to the equation are x = a and x = a/2.

We can simplify the left-hand side of the equation using the common denominator of x^3:

(x-a)x/x^3 + (x-a)(-1)/(3a^2 x^3) + (x-a)(-2)/(3a x^3) + (x-a)(1)/(x^3)

= [(x-a)x^2 - (x-a)/(3a^2) - 2(x-a)/(3a) + (x-a)x]/x^3

= [(x^3 - a^3)/x^2 - (1/(3a^2))(x-a) - (2/(3a))(x-a)]/x

= [(x^2 + ax + a^2)(x-a)/(x^2 a^2) - (x-a)/(3a^2) - (2/3)(x-a)/a]/x

= (x^2 + ax + a^2)/(x^2 a^2) - 1/(3a^2) - 2/(3a)/x

= (3x^2 + 3ax + 3a^2 - x^2 a - ax^2 - a^3)/(3a^2 x^2)/x

= (2x^2 + 3ax + 3a^2 - ax^2 - a^3)/(3a^2 x^2)/x

= (x^2 + 3ax + 3a^2 - a^3)/(3a^2 x^2)/x

Now, we can see that the expression on the right-hand side is:

(x-a)/(x^3)

Multiplying both sides by x^3, we get:

(x-a)x = (x^2 + 3ax + 3a^2 - a^3)/3a^2

Multiplying both sides by 3a^2, we get:

(x-a)3a^2x = x^2 + 3ax + 3a^2 - a^3

Expanding (x-a)(3a^2)x, we get:

3a^2x^2 - 3a^3x = x^2 + 3ax + 3a^2 - a^3

Moving all terms to one side, we get:

2x^2 - 3ax + 2a^2 = 0

This is a quadratic equation, and we can solve for x using the quadratic formula:

x = [3a ± sqrt((9a^2 - 8a^2)/4)]/4

x = [3a ± a]/4

x = a or x = 2a/4 = a/2

Therefore, the solutions to the equation are x = a and x = a/2.

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Answer:

Step-by-step explanation:

a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:

15 nCr 5 * 5 * 4 = 3,003,600

b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:

(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000

c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:

9 * 10^5 = 9,000,000

Answer:

------------------------------

Supplementary angles add up to 180°:

Substitute and solve for x:

Find the measure of ∠B:

To add 2/5 and 3/6, we need to find a common denominator for the two fractions. The smallest number that both 5 and 6 divide into evenly is 30. So, we can convert the two fractions to have a denominator of 30:

2/5 = 12/30 3/6 = 15/30

Now, we can add the two fractions by simply adding their numerators (since they have the same denominator):

12/30 + 15/30 = 27/30

We can simplify the fraction by reducing it to the lowest terms. Both the numerator and denominator have 3 as a factor, so we can divide them both by 3:

27/30 = (3 x 9) / (3 x 10) = 9/10

Therefore, the sum 2/5 + 3/6 is equal to 9/10.

Answer:

a = 8

Step-by-step explanation:

4 x 2 = 8

8 x 2 = 16

Helping in the name of Jesus.

Answer: First one (top left)

Step-by-step explanation:

Answer:

One in the top left corner

Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

To express the difference in mean weights as a multiple of the MAD for both dog breeds, we can use the formula:

(difference in means) / (mean absolute deviation)

Let's plug in the values given in the problem:

(difference in means) = 13 - 11.5 = 1.5

(mean absolute deviation) = 2 + 1.8 / 2 = 1.9 (taking the average of the two MADs)

Now we can calculate:

(difference in means) / (mean absolute deviation) = 1.5 / 1.9 ≈ 0.7895

Therefore, the difference in mean weights between the two breeds is approximately 0.7895 times the average MAD for both breeds.

Each product of the fractions are

Part1. =17.33

Part2.= 0.73

Part3.=45.93

Multiplication is a mathematical operation that involves combining two or more numbers to obtain a product or result. Multiplication is a fundamental arithmetic operation that is used in a wide range of mathematical applications, from simple calculations such as calculating the area of a rectangle, to more complex problems in algebra, geometry, and calculus.

⅔×26

Multiplying 2 and 26, we get

52/3

Now, dividing it with3, we get

17.33

⅞×5/6

Multiplying 7 and 5 and 8 and 6, we get

35/48

Now, dividing 35 and 48, we get

.73

5 ⅕× 8 ×⅚

Solving the improper fractions;

26/5×53/6

Multiplying 26 and 53 and 5  and 6, we get

1378/30

Now, dividing 35 and 48, we get

45.93.

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The equation of the line is 3y-5x=3 and the graph is attached.

Geometrically speaking, a line is a one-dimensional figure because it has length but no width. A group of points can be extended endlessly in opposing directions to form a line. Two points in a two-dimensional plane determine it. There are, however, additional ways to formulate the equation of a line in a two-dimensional coordinate system. The three most popular methods are the point-slope form, slope-intercept form, and general or standard form of the equation of a line. As its name suggests, the point-slope form combines a line point and a straight-line slope. The equations of infinite lines with a particular slope can be expressed, however when we specify that the line passes through a particular point, we get a singularity.

the equation of a line is

y-y'=m(x-x')

[tex]y+4=\frac{5}{3}(x+3)\\\\3y+12=5x+15\\3y-5x=3[/tex]

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Answer: (D) 12 to 4

Step-by-step explanation:

        First, we will find the number of people waiting in line for each activity.

➜ Bumper cars is 12

➜ Slingshot is 4

        Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.

➜ 12 to 4

Answer:

Step-by-step explanation:

For the 90°/right angle part, we can subtract 35° from 90° to get the degree of that area.

90° - 35° = 55°

We can check off the "55°" box

----------------------------------------------

Now, for the other half of the straight angle including the right angle, we can subtract 90° from 180°.

Getting 90°

We can check off the "90°" box

-------------------------------------------------

To find the degree of the "(7x + 5°)" -- assuming that that angle is vertical to the "other" -- we can make an equation of

⇒ 7x + 5° = 90° + 55°

Solve:

Add together 90 and 55 which is 145°

New equation:

7x + 5° = 145°

Subtract 5° from both sides, getting the equation

7x = 140°

Isolate x by dividing both sides by 7

x = 20°

Substitute what we have for x into the equation "7x + 5°"

7(20°) + 5

= 145°

We can check off the "145°" box

------------------------------------------

All the boxes checked off:

Hopefully this helps! -- mark me brainliest if you want ofc

As 80 percentage of 25 classmates is equal to 20. Krysti should have ordered 20 small t-shirts for her 25 classmates

Error is when a mistake is made while solving a mathematical problem.

Krysti's error in finding the number of small t-shirts is that she forgot to multiply the percentage by the total number of classmates.

If Krysti wanted to find the number of small t-shirts she should have ordered, she should have multiplied

80% * 25.

=0.8 * 25

= 20.

To explain it in another way, Krysti could have also 100/25 and then 80 divided by the answer that is 4. This would also give the same result of 20.

Krysti's error was that she did not correctly use percentages to find the number of small t-shirts she should have ordered.

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Answer: Let's call the scale factor between the two containers "k". Then, we know that the ratio of their surface areas is equal to the square of the scale factor:

(surface area of B) / (surface area of A) = k^2

We also know that the ratio of their volumes is equal to the cube of the scale factor:

(volume of B) / (volume of A) = k^3

We can rearrange the first equation to solve for k:

k^2 = (surface area of B) / (surface area of A) = 10478 mm^2 / 1550 mm^2 = 6.75

Taking the square root of both sides, we get:

k = sqrt(6.75) = 2.6 (rounded to one decimal place)

Now we can use the second equation to find the volume of container A:

(volume of B) - (volume of A) = 62160 mm^3

(k^3)(volume of A) - (volume of A) = 62160 mm^3

Simplifying and solving for the volume of A, we get:

volume of A = 62160 mm^3 / (k^3 - 1) = 62160 mm^3 / (2.6^3 - 1) ≈ 4477 mm^3

Therefore, the volume of container A is approximately 4477 mm^3.

Step-by-step explanation:

When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32     y = 9 .Hence, x=3 and y=9.

A log is a mathematical function used to calculate how many times the base, or initial value, must be increased by itself to produce the target value. In other terms, a logarithm is an exponent's negative action.

The base-10 logarithm is the most widely used type of logarithm, though there are other types as well. Some many mathematical and scientific tasks include the usage of logarithms, such as estimating the pH of a solution, gauging the volume of sound, and estimating population growth rates.

given

As we are aware that log x of y = 2, x2 = y.

We also understand that xy = 27.

When we change y in the second equation to x2, we obtain:

[tex]xx^{2} =7^{2} \\x^{3} = 27\\[/tex]

x = 3

When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32     y = 9 .Hence, x=3 and y=9.

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Answer:

x = 20

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

x × [tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

x = 20

The assertion is accurate. This mean option that is selected should be true

The formula c = √(a 2 + b 2), where a and b are the lengths of the semi-major and semi-minor axes, respectively, yields the foci of a hyperbola.

. A hyperbola is a particular kind of conic section that resembles two slightly mirrored parabolic curves. It is described as the collection of all points in a plane where the difference between the locations of two fixed points (referred to as foci) is always constant.

Each of the two branches of a hyperbola resembles a parabola. In relation to the hyperbola's centre, the branches are symmetric. The semi-major axis is the distance between the centre and each vertex, whereas the semi-minor axis is the distance between the centre and each terminal of the transverse axis.

When a² = 25 and b² = 9,

the hyperbola (x-1)2/25 - (y+3)2/9=1 can be calculated.

In light of this, c = √(25 + 9) = √ (34).

The hyperbola's center is located at (1, -3).

The foci are at (1 + √(34), -3) and (1 - √(34), -3), respectively.

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Answer:

4/64

Step-by-step explanation:

The spinner is independent (the total won't be effected)

we know there is 2 whites with 8 coloured option.

we want the probability of getting two whites.

2/8 x 2/8 = 4/64

there is 3 ways to work out probability, fraction, decimal and percentage (i'd personally say fraction is the most easiest)

Answer:

x=1/3

          ≈ 0.333333333

x=4

Step-by-step explanation:

The total surface area must be calculated by adding the areas of all five faces, the four triangular faces, and the square base.

The term "square pyramid" refers to a three-dimensional geometric form with a square base and four triangular faces or sides that meet at a single point (known as a vertex). Because it has five faces, it is referred to as a pentahedron.

Given :

Let s represent the square base's side length and h represent the slant height of each triangle face. The area of a single triangle is then determined by:

A = (1/2) * s * h

The areas of all five face the four triangular faces and the square base must be added up in order to determine the overall surface area of the pyramid.

The overall surface area is: since the square base has a simple area of s2.

When we replace A with the expression, we obtain:

We require further details regarding the pyramid in order to determine the values of s and h.

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The function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

To find the local maximum and minimum of a function over a given interval, we need to find the critical points of the function within that interval and then apply the second derivative test to classify those critical points as local maximum or minimum.

To find the critical points, we first take the derivative of the given function:

f'(x) = 6x² - 6x - 12 = 6(x² - x - 2)

x = -1 or x = 2

Both of these critical points fall outside the given interval [2, 3]. Therefore, there are no critical points of the function within the interval [2, 3], and so there are no local maximum or minimum values of the function over this interval.

In other words, the function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].

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To translate a shape, all of its vertices must be moved in the same direction and by the same amount. The responses to the five sections of the question are as follows:

Coordinates are used to identify the position of an object on a two-dimensional grid or in three-dimensional space. They are usually written as pairs of numbers, separated by a comma.

1. We must deduct 2 from all of the y-coordinates of the vertices of the parallelogram ABCD in order to translate it two units down. Let's assume that the vertices' initial coordinates are A(a,b), B(c,d), C(e,f), and D. (g,h). The vertices will then have the new coordinates A'(a,b-2), B'(c,d-2), C'(e,f-2), and D' (g,h-2). To obtain the translated parallelogram, plot these new vertex points.

2. To move the rhombus EFGH 2 units to the left and 4 units down, we must deduct 2 from all of its vertices' x-coordinates and 4 from all of its y-coordinates. Let's assume that the vertices' initial coordinates are E(a,b), F(c,d), G(e,f), and H. (g,h). The vertices will then have the new coordinates E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H' (g-2,h-4). To obtain the translated rhombus, plot these additional vertices.

3. If we want to translate a square with coordinates L(-5,5), M(-5,5), N(5,5), and O(5,5) 3 units to the right and 2 units up, we must add 3 to all of its x-coordinates and subtract 2 from all of its y-coordinates. The vertices' new coordinates are L'(-2,-7), M'(-2,3), N'(8,3), and O' (8,-7). To obtain the translated square, plot these new vertex points.

4. The new coordinates of triangle XYZ after translating 4 units down will be X' (2,-3), Y' (4,1) and Z' (5,-2). This is happening because when a triangle is translated 4 units down, the y-coordinate of each vertex is decreased by 4 units, while the x-coordinate remains the same.

5. I (4,-2) P (-4,-2) G (5,2) Q (6,-4) R (-2,2)

S (6,4) J (1,-1) U (-5,0) H (3,-1) K (-6,-5)

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The correct statements are:

Explanation:

The function f(x) represents the total amount of money that Mailani has saved after x years. The first term 500 represents the initial amount she saved in the box under her bed, and the second term (1+0.04)^x represents the amount she deposited into the savings account, which earns an interest rate of 4% compounded annually. The third term +200 represents the additional amount she deposited every year into the savings account.

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Full question:

Mailani saves some money in a box under her bed. She deposits an additional amount into a savings account where it earns interest compounded annually. . This situation can be modeled by the function  

[tex]f(x)= 500(1+0.04)^x+200[/tex]

Which statements are true? Select all that apply.

Answer: 363+368=731

Step-by-step explanation:

The function has the maximum revenue of $348,480 with the increasing rate of $33.

The highest and smallest values of a function, respectively, can either be found inside a specific range or distributed throughout the entire domain. They are also sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, accordingly.

Given data:

The overall revenue is thus:

y = (36 - 0.50x)(9600 + 160x)

Differentiate with respect to x.

y ' = (-0.50)(9600 + 160x) + 160(36 - 0.50x)

y' = -4800 - 80x + 5760 - 80x

y' = 960 - 160x

To find x, put y' = 0

960 - 160x = 0

x = 960/160 = 6 (critical point)

Function is decreasing in interval - [6, +∞)

Increasing Function in interval - (-∞, 6]

Thus, the function has the maximum value at x = 6.

maximum revenue f(6):

f(6) = (36 - 0.50x)(9600 + 160x)

f(6) = (36 - 0.50(6))(9600 + 160(6))

f(6) = $348,480

Rate : 36 - 0.50(6) = $33

The function has the maximum revenue of $348,480 with the increasing rate of $33.

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The missing amounts for Work in Process - Blending Department are: 25,700 units, and $70,944 for direct materials.

Cost of Production Report

Bavarian Chocolate Company processes chocolate into candy bars.

The process begins by placing direct materials (raw chocolate, milk, and sugar) into the Blending Department.

All materials are placed into production at the beginning of the blending process.

After blending, the milk chocolate is then transferred to the Molding Department, where the milk chocolate is formed into candy bars.

The following is a partial work in process account of the Blending Department at October 31:

ACCOUNT Work in Process—Blending Department ACCOUNT NO.

Date Item Debit Credit Balance

Debit Balance

Credit

October 1 Bal., 2,300 units, 3/5 completed 46,368

31 Direct materials, 26,000 units 429,000 475,368

31 Direct labor 100,560 575,928

31 Factory overhead 48,480 624,408

31 Goods transferred, 25,700 units.

1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Blending Department. If an amount is zero enter "0". If required, round your cost per equivalent unit answers to the nearest cent.

Bavarian Chocolate Company

Cost of Production Report—Blending Department

For the Month Ended March 31

Bavarian Chocolate Company

Cost of Production Report—Blending Department

For the Month Ended October 31

Equivalent Units Schedule

Direct Materials Conversion Costs

Units to be accounted for:

Work in process, October 1 (3/5 completed) 2,300 2,300

Units started in October 26,000 26,000

Total units to be accounted for 28,300 28,300

Units accounted for:

Goods transferred to the Molding Department (25,700 units × 100%) 25,700 25,700

Work in process, October 31 (1/5 completed):

Total units accounted for:

Costs to be accounted for:

Direct materials cost $429,000

Direct labor cost $100,560

Factory overhead cost $48,480

Total costs to be accounted for $578,040

Costs accounted for:

Direct materials cost (26,000 units × $15 per unit) $390,000

Direct labor cost (2,300 units × $44 per unit) 101,200

Factory overhead cost (2,300 units × $21.12 per unit) 48,576

Total costs accounted for $539,776

Cost per Equivalent Unit:

Direct materials cost ($429,000 ÷ 28,300 units) $15.16

Direct labor cost ($100,560 ÷ 2,300 units) $43.74

Factory overhead cost ($48,480 ÷ 2,300 units) $21.12

Total cost per equivalent unit $80.02

Work in Process—Blending Department

Direct Materials Conversion Costs Total

Balance, October 1 $27,820 $18,548 $46,368

Current costs $352,380 $222,548 $574,928

Total cost $380,200 $241,096 $621,296

Less: Goods transferred to the Molding Department (25,700 units × $80.02 per unit) (2) $2,048 $2,048

Balance, October 31 (2) $378,152 (2) $239,048 (2) $617,200

(1) Equivalent units of direct materials and conversion costs have been calculated based on the weighted-average method.

(2) The missing amounts for Work in Process—Blending Department are:

Units, October 31: 2,600 units (28,300 total units – 25,700 transferred units).

Direct Materials, October 31: $352,380 (current costs) - $390,000 (costs accounted for) = -$37,620 (overallocated)

Conversion Costs, October 31: $222,548 (current costs) - $241,096 (costs accounted for) = -$18,548 (overallocated).

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The probability that the next person will purchase more than one costume as a percent to the nearest whole number is 3%

.Out of the total 80 + 32 + 3 = 115 visitors, 80 did not purchase any costumes and 32 purchased exactly one costume. This means that the remaining 3 visitors purchased more than one costume.

Therefore, the probability that the next person will purchase more than one costume is 3/115, which is approximately 0.0261.

To express this as a percentage to the nearest whole number, we need to multiply by 100 and round to the nearest integer. Thus, the answer is:

0.0261 × 100 ≈ 3%

Therefore, the probability that the next person will purchase more than one costume is approximately 3%.

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The quadratic function's equation, when given the numbers in the table, can be found to be f(x) = x^2 - 5x + 6.

We are given a table of values and need to find the quadratic function in standard form: f(x) = ax^2 + bx + c. Let's use the points (-6, 72), (-4, 42), and (-3, 30).

For point (-6, 72):

72 = a(-6)^2 + b(-6) + c

For point (-4, 42):

42 = a(-4)^2 + b(-4) + c

For point (-3, 30):

30 = a(-3)^2 + b(-3) + c

Let's use the elimination method.

1 - 3) 42 = 27a - 3b

2 - 3) 12 = 7a - b

b = 7a - 12

Substitute this expression for b into the first equation:

42 = 27a - 3(7a - 12)

42 = 27a - 21a + 36

6 = 6a

a = 1

Now that we know a = 1, let's find b:

b = 7(1) - 12

b = -5

Finally, let's find c by substituting a and b into any of the original equations. We'll use the first one:

72 = 36(1) - 6(-5) + c

72 = 36 + 30 + c

6 = c

So, the quadratic function in standard form is:

f(x) = x^2 - 5x + 6

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Answer:

Step-by-step explanation:

[tex]\frac{275}{8}=34,375[/tex]

Answer:

It will take Jaime 36 days to run 96 miles.

Step-by-step explanation:

The formula for rate is:

[tex]\boxed{\sf Rate=\dfrac{Distance}{Time}}[/tex]

Therefore, Jaime's run rate is:

[tex]\implies \sf Rate=\dfrac{8\;miles}{3\;days}=\dfrac{8}{3} \;miles\;per\;day[/tex]

Rearrange the rate formula to isolate time:

[tex]\implies \sf Time=\dfrac{Distance}{Rate}[/tex]

To find how long it will take for Jaime to run 96 miles, substitute the distance and rate into the formula and solve for time:

[tex]\implies \sf Time=\dfrac{96\;miles}{\frac{8 \;miles}{3\;days}}[/tex]

[tex]\implies \sf Time=96\;miles \times \dfrac{3\;days}{8\;miles}[/tex]

[tex]\implies \sf Time= \dfrac{288}{8}\;days[/tex]

[tex]\implies \sf Time= 36\;days[/tex]

Therefore, it will take Jaime 36 days to run 96 miles.