A survey is given to students about the servings of friuts and vegetables that each student typically eats in a day. The students in the survey represent a popultion of 200

α = 0.1

Answer: (a) Suppose X ∼ Bin(n, p). The likelihood function isL(p) = [n!/x!(n − x)!] px (n−p)−x.Then, we get the likelihood ratio asLR = [L(p1)] / [L(p0)]=[p1^x * (1−p1)^(n−x)] / [p0^x * (1−p0)^(n−x)]Let X be a binomial random variable. We can write the likelihood function as L(p) = [nCx px(1−p)n−x] . (b) Most powerful test: To derive the most powerful test, we need to find the likelihood ratio as LR = (p1/p0)x(1−p1/1−p0)n−x. Accept H0 if LR < c and reject H0 if LR ≥ c for some constant c.LRc= (0.8/0.5)^15*(0.2/0.5)^5 / (0.8/0.5)^15*(0.2/0.5)^5= (8/5)^15 = 34.99We reject H0 if the LR ≥ 34.99. Accept H0 if the LR < 34.99. (c) Reject H0 if the LR ≥ 34.99.LR = (0.8/0.5)15*(0.2/0.5)5 = 20.96Since 20.96 < 34.99, we accept H0. Therefore, at α = 0.1, we do not reject H0.

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Answer:

I really want to help you!

Factored completely:

2x2(−x−2)(x−7)

Step-by-step explanation:

Yes, the political party can conclude that the Hispanic proportion of the population has changed since 2010

Now, let's look at the given information. In 2010, the percentage of Hispanic or Latino people in Oregon was 11.7%. This means that out of every 100 people in Oregon, approximately 12 were Hispanic or Latino.

The political party conducted a survey of 853 adults in Oregon and found that 113 of them were Hispanic or Latino. To determine if the percentage of Hispanic or Latino people in Oregon has changed since 2010, we need to compare the survey results to the 2010 percentage.

To do this, we can calculate the percentage of Hispanic or Latino people in the survey by dividing the number of Hispanic or Latino people in the survey (113) by the total number of people surveyed (853), and then multiplying by 100. This gives us a percentage of approximately 13.2%.

Using this formula, we can estimate the margin of error for this survey to be approximately +/- 2.8%.

This means that the true percentage of Hispanic or Latino people in Oregon could be as low as 10.4% or as high as 15.6%, based on the survey results.

Since the margin of error includes the 2010 percentage of 11.7%, we cannot conclude that the Hispanic proportion of the population has definitively changed based on this survey alone.

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The popcorn container can hold 432 cubic inches of popcorn.First, we need to find the volume of the popcorn container. The formula for the volume of a square pyramid is:

Volume = (1/3) * base area * height

To find the base area, we need to first find the area of one of the square sides. Since each side measures 6 inches, the area of one square side is:

Area = side length^2 = 6^2 = 36 square inches

Since the popcorn container is a square pyramid, it has four identical square sides, so the total base area is:

Base area = 4 * 36 square inches = 144 square inches

Now we can plug in the values for the base area and height into the formula for volume:

Volume = (1/3) * 144 square inches * 9 inches

Volume = 432 cubic inches

So the popcorn container can hold 432 cubic inches of popcorn.

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The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.

To find the area of the rectangle, we need to multiply its length by its width.

First, we need to convert the mixed numbers to improper fractions:

Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm

Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm

Now, we can multiply the two fractions to get the area of the rectangle:

Area = length × width

= (31/6 cm) × (16/7 cm)

= (31 × 16) / (6 × 7) cm²

= 496/42 cm²

= 248/21 cm²

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:

248/21 cm² = (8 × 31)/ (8 × 3) cm²

= 31/3 cm²

= 10 1/3 cm²

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Answer:

x=1

Step-by-step explanation:

3x-2=7-6x

3x-2 +2=7-6x +2

3x+6x=9-6x +6x

9x=9

x=1

Answer:

x = 1

Step-by-step explanation:

3x -2 = 7 -6x

9x - 2 = 7

9x = 9

x = 1

Let's check

3(1) -2 = 7 - 6(1)

3 - 2 = 7 - 6

1 = 1

So, x = 1 is the correct answer.

Answer: Let's work through the problem step by step:

"Treble it": If we call the unknown number "x", then "trebling" it means multiplying it by 3, so we have 3x.

"Take 6 from my answer": We subtract 6 from 3x, giving us 3x - 6.

"If the result is 18": We set 3x - 6 equal to 18 and solve for x.

So, we have:

3x - 6 = 18

Adding 6 to both sides:

3x = 24

Dividing both sides by 3:

x = 8

Therefore, the answer is 8.

Step-by-step explanation:

The ordered pair that represents the location of vertex A after the dilation is (8, 20).

Vertex is a point in geometry that describes the location of a object in a two-dimensional or three-dimensional space. In two-dimensional space, it is a point where two lines, curves, or surfaces intersect. In three-dimensional space, it is the point where three planes intersect. In a graph, it is the point where two lines intersect.

Vertex A of the original kite is located at (6, 15).
The center of dilation is at (1, 1). To dilate the kite by a scale factor of 4/3, each point (x,y) of the kite must be multiplied by the scale factor, 4/3. In this case, vertex A will transform to (8, 20) after the dilation.
Therefore, the ordered pair that represents the location of vertex A after the dilation is (8, 20).

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The coordinate of points of the image are:

A' = (-1, 1), B' = (1, 1) and C' = (1, -1)

To dilate the preimage about the origin using a scale factor of 1/3, we can use the following formula:

image coordinate = scale factor * preimage coordinate

Substituting the values, we get:

A' = 1/3 * (-3, 3)

A' = (-1, 1)

B' = 1/3 * (3, 3)

B' = (1, 1)

C' = 1/3 * (3, -3)

C'  = (1, -1)

Thus, the coordinate of points of the image are A' = (-1, 1), B' = (1, 1) and C'  = (1, -1)

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Answer:

16.8π cm or 52.78 cm

Step-by-step explanation:

We are given the radius of one planet and the diameter of the other.

So, we have perimeter (circumference) of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle.

For the first planet with a radius of 16.8 cm, we can calculate its circumference as:

C1 = 2π(16.8) = 33.6π cm

For the second planet with a diameter of 16.8 cm, we can calculate its radius as half of the diameter:

r2 = d/2 = 16.8/2 = 8.4 cm

And then, we can calculate its circumference as:

C2 = 2π(8.4) = 16.8π cm

The difference between the perimeters of the two planets is:

C1 - C2 = (33.6π - 16.8π) cm

C1 - C2 = 16.8π cm

Therefore, the difference between the perimeters of the two planets is approximately 52.78cm, rounded to two decimal places.

The length οf the thermοmeter is 16 1/4 inches.

Any instrument that measures temperature οr a thermal diffusivity is called a thermοmeter (the degree οf hοtness οr cοldness οf an οbject). Twο crucial cοmpοnents make up a thermοmeter:

(1) a temperature sensοr that changes in respοnse tο changes in temperature (fοr example, the mercury-in-glass thermοmeter's bulb οr an infrared thermοmeter's pyrοmetric sensοr);

(2) a way tο translate this change intο a specific number (e.g. the visible scale that is marked οn a mercury-in-glass thermοmeter οr the digital readοut οn an infrared mοdel). In technοlοgy, business, meteοrοlοgy, medicine, and scientific research, thermοmeters are frequently used tο track prοcesses.

Tο find the length οf the thermοmeter, we need tο add the distance abοve the water tο the distance belοw the water.

Distance abοve water: 3/4 inch

Distance belοw water: 31/2 inches

The tοtal length οf the thermοmeter:

3/4 + 31/2 = 6/8 + 124/8 = 130/8 = 16 1/4 inches

Therefοre, the length οf the thermοmeter is 16 1/4 inches.

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The result of 3 divided by the difference of 4 and 2 is 1.5.

Formula:

3 / (4 - x)

Let's take the number x to be equal to 2.

Therefore, the calculation is 3 divided by the difference of 4 and 2, which is 3 / (4 - 2) or 3 / 2.

The answer is 1.5.

To explain further, when we divide the number 3 by the difference of 4 and 2, we are essentially dividing the number 3 by the result of subtracting 2 from 4. The result of subtracting 2 from 4 is 2. When we divide 3 by 2, the answer is 1.5.

Therefore, 3 divided by the difference of 4 and a number is equal to 1.5 when the number is equal to 2.

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Complete question:

What is 3 divided by the difference of 4 and a number?

Answer:

"The sales for the spring play (Increased) by (30) tickets"

Step-by-step explanation:

The opening night sales were 200, to 230 by closing night so it increased by 30.

Answer:

1,723,176

Step-by-step explanation:

By plugging this into a calculator, you will receive 1,723,176.

Answer: 234 x 7364 = 1,723,176

Answer:∠A = 9

Step-by-step explanation:In a Parallelogram opposite angles are always equal thus,  14x - 4 = 15x - 13.

Start by isolating the variable on one side of the equation. You can do this by subtracting 14x from both sides:

14x - 4 - 14x = 15x - 13 - 14x

Simplifying the left side gives:

-4 = x - 13

Now, isolate x by adding 13 to both sides:

-4 + 13 = x - 13 + 13

Simplifying the left side gives:

9 = x

Therefore, the solution to the equation 14x - 4 = 15x - 13 is x = 9

The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.

The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).

The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.

Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.

Answer:

I think you could just add a zero onto the end of the two digit decimal, assuming it's not a decimal that continuously repeats, but is just like 2.25 or something like that. So to add 3.184 to 2.25, you would ads a 0 to the 2.25, making it 2.250.

Step-by-step explanation:

4x+3+43=180

46+4x=180

4x=180-46

4x/4=134/4

X=33,5

The area of triangle will be 1/2*area of rectangle.

what exactly is a triangle?

A triangle is a geometric shape that consists of three line segments or sides, and three angles. Triangles are among the simplest and most fundamental shapes in geometry, and they are used in many fields of mathematics, science, engineering, and art.

The sum of the three interior angles of a triangle is always 180 degrees. The length of each side of the triangle is related to the size of the angles opposite to it, and to the length of the other sides, through various trigonometric functions.

Now,

The area of given triangle can be found by making a whole rectangle by making equal and parallel lines base and perpendicular.

let 1 box represent 1 unit if length

then area of rectangle=L*B

=5*4

=20 unit²

then, area of triangle=1/2*area of rectangle

=20/2

=10 unit²

hence,

           The area of triangle will be 1/2*area of rectangle.

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The area of the rectangular prism from the net is 209.8 square meters

From the question, we have the following parameters that can be used in our computation:

The net of a rectangular prism

Start by calculating the areas of each labelled rectangle by multiplying tthe dimensions

So, we have

A = 2 * 11.5 * 4 = 92

Two B's

B = 2 * 3.8 * 4 = 30.4

Two C's

C = 2 *  3.8 * 11.5 = 87.4

Add the individual areas to get the net area

Area = 92 + 30.4 + 87.4

Evaluate the sum

Area = 209.8

Hence, the total area is 209.8 square meters

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In linear equation, 103000  is the minimum acceptable settlement on a case on which the attorney spent 110 hours.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let x be the amount settlement.

  amount he earn from client = 175 * 110

                                         = 19250

     amount he earn from settlement = x * 25/100  = x/4

        according to given condition

                         19250 + x/4 ≥ 45000

                     x/4 ≥ 45000 - 19250

                    x/4 ≥ 25750

                    x ≥ 25750 * 4

                     x ≥ 103000

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Answer:

i) here a=8 d=3 nth term= 8+(n-1)3

ii)50th term= 8+49×3=155

Step-by-step explanation:

i hope you find it helpful

Step-by-step explanation:

hope you understood the answer

To round to the nearest tenth, we can say that a cell phone's battery life is typically 2 hours after two years.

Generally speaking, the battery life of a cell phone will depend on the type of phone and usage habits. Most cell phones will last about 18-24 months before needing to be replaced.

The battery life of a cell phone is determined by a variety of factors, including battery capacity, phone usage habits, and battery age. We can, however, make certain assumptions and calculate how long it would take for a common mobile phone battery to decline to 2 hours of battery life.

Considering that a typical lithium-ion battery, which is often used in mobile phones, has a capacity of approximately 3,000 mAh when new and that its capacity drops by roughly 20% after 2-3 years of usage, we may estimate that the battery capacity would be around 2,400 mAh after 2-3 years.

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Answer:

25(5x - 2y)

Step-by-step explanation:

25 is the common factor for the equation. so the answer will be 25( 5x - 2y )

The expression√{y²-81} can be simplifies to trigonometry as  9|tanx|.

If an algebraic expression has no like terms and no parenthesis, it is said to be in its simplest form. Use the Distributive Property to add or subtract the coefficients to combine like terms with variables. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

We start by substituting 9 sec x for y:

√{y²-81} = √{(9 sec x)²-81}

= √{81(sec²x) - 81}

= √{81(sec²x-1)}

= 9√{sec²x-1}

Using the trigonometric identity sec²x - 1 = tan²x, we can simplify further:

9√{sec²x-1} = 9√{tan²x}

= 9|tanx|

Therefore, the simplified expression is 9|tanx|.

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The volume of this cylinder is equal to 7,771.5 cubic millimeter

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Since the radius of the base is 15 mm and the height of this cylinder is 11 mm, the volume of the cylinder in cubic millimeter can be calculated as follows;

Volume of a cylinder, V = 3.14 × 15² × 11

Volume of a cylinder, V = 3.14 × 2,475

Volume of a cylinder, V = 7,771.5 cubic millimeters.

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the area of the figure will be 15cm²

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

the area will be = area of square+area of rhombus

area of square = 3² = 9 cm²

area of rhombus = 2cm * 3cm =6cm²

The total area will be 15cm²

Hence the area of the figure will be 15cm²

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Answer:

watch sean delete this LOL IMAGINE HAVING TO DO THAT BC YOU SUK

the area of the figure will be 15cm²

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognized by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

We are given that rajiv wishes to make a cube without lid with cardboard.

the area will be = area of square+area of rhombus

area of square = 3² = 9 cm²

area of rhombus = 2cm * 3cm =6cm²

The total area will be 15cm²

Hence the area of the figure will be 15cm²

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Step-by-step explanation:

The length of the corresponding side of the larger polygon is 5/4.

What is polygon?

A polygon is a two-dimensional shape that is formed by connecting a sequence of straight lines (called sides or edges) end-to-end to form a closed loop. The term "poly" means "many," and "gon" means "angle," so a polygon literally means "many angles."

Polygons can have any number of sides, from three (a triangle) to infinity. The most common polygons are the quadrilateral (four sides), pentagon (five sides), hexagon (six sides), heptagon (seven sides), octagon (eight sides), nonagon (nine sides), and decagon (ten sides).

Let's assume that the smaller polygon has n sides and the larger polygon has m sides. Since the polygons are similar, their corresponding sides are proportional. Therefore, we can set up the following proportion:

n/m = 4/x

where x is the length of the corresponding side of the larger polygon.

We also know that the perimeter of the smaller polygon is 20, so each of its sides has length 20/n. Similarly, the perimeter of the larger polygon is 28, so each of its sides has length 28/m.

Since the polygons are similar, their corresponding sides are proportional, so we can set up another proportion:

(20/n) / (28/m) = 4/x

Simplifying this expression, we get:

20m = 28nx

Dividing both sides by 4, we get:

5m = 7nx

Substituting n/m = 4/x, we get:

5m = 28x

Solving for x, we get:

x = (5m)/28

Now, we need to find the value of m. The perimeter of the smaller polygon is 20, so the sum of its sides is 20. Since each side has length 20/n, we can write:

20 = (20/n)*n

Simplifying, we get:

n = 4

The perimeter of the larger polygon is 28, so the sum of its sides is 28. Since each side has length 28/m, we can write:

28 = (28/m)*m

Simplifying, we get:

m = 7

Now, we can substitute the value of m into the expression for x that we derived earlier:

x = (5m)/28 = (5*7)/28 = 5/4

Therefore, the length of the corresponding side of the larger polygon is 5/4.

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The sheet would be approximately 93.13 cm wide if flattened out.

The length of an arc is determined by the degree measure of the central angle that subtends the arc. For example, if a circle has a radius of 5 units and an arc has a central angle of 90 degrees, the length of the arc can be found using the formula:

arc length = (central angle / 360) x 2πr

where r is the radius of the circle. In this case, the length of the arc would be:

arc length = (90/360) x 2π(5) = 1.25π units

The length of each arc can be found using the formula:

length = (angle / 360) x 2πr

where angle is the central angle of the arc in degrees, r is the radius of the arc, and π is pi (approximately equal to 3.14).

In this case, the radius is 10 cm and the central angle is 120 degrees, so the length of each arc is:

length = (120/360) x 2π(10) = (1/3) x 20π = (20/3)π cm

There are 14 such arcs in one sheet, so the total length of the sheet when flattened out is:

total length = 14 x (20/3)π = (280/3)π cm

This is approximately equal to 93.13 cm if we use the approximation π ≈ 3.14.

Therefore, the sheet would be approximately 93.13 cm wide if flattened out.

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The function graph for each of the cases with the description of the graph is plotted.

a. The ratio of the height of such a baseball thrown across outfield to home plate to the distance from centerfield.

This, will a parabolic graph as shown.

b. The volume of people who visit the mall per hour during regular business hours on such a particular day.

Thus, this graph will be step wise function as the value of people visiting the mall varies with the time.

c. A cup of coffee's temperature x minutes after it has been poured.

This, will be decreasing graph as the temperature of the coffee will keep on decreasing.

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