Find the side of a square whose diagonal measures 15v2 cm

Therefore , the solution of the given problem of function comes out to be  f(g(4)) = 66.

The midterm examination will have questions on each subject, mathematics, variable design, and both real and imagined locations. a list of the relationships between different elements that collaborate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Each postbox also has a distinct address, which may be an enclave.

Here,

a) We must multiply f(x) and g(x) in order to obtain f(x)  g(x):

=>  f(x) · g(x) = (-2x+ 4)

The formula is

=> (-6x - 7) = 12x² + 14x - 24x - 28 = 12x² - 10x - 28.

As a result,

=>  12x² - 10x - 28 is what f(x)  g(x) equals.

b) We must first determine g(4) in order to obtain f(g(4)):

=> g(4) = -6(4) - 7

=>    -31

We can now change g(4) to f(x) as follows:

=> f(g(4)) = f(-31)

=>   -2(-31) + 4

=>  62 + 4

Consequently, f(g(4)) = 66.

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Number of ways that  can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices is 49,825

One member holds all three offices: There are 25 options for choosing the member who will hold all three offices.

Two members hold two offices each: There are 25 options for choosing the first member, and 24 options for choosing the second member (since one member cannot hold all three offices). Then, for the first member, there are 3 options for which offices they will hold, and for the second member, there are 2 options for which offices they will hold. Here we have to use the permutation. So the total number of ways is

25 × 24 × 3 × 2 = 36,000

Three members hold one office each: There are 25 options for choosing the first member, 24 options for choosing the second member, and 23 options for choosing the third member. So the total number of ways is

25 × 24 × 23 = 13,800

Therefore, the total number of ways to choose the officers is

25 + 36,000 + 13,800 = 49,825

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In this particular question, the following statements can be used to complete each sentence with either "increases" or "decreases":

- Phytic acid decreases the absorption of zinc from grains.

Oxalic acid decreases the absorption of calcium from spinach.

- Refinement of grains decreases the mineral content of grain products.-

Vitamin C increases the absorption of iron from foods.-

Vitamin D increases the absorption of calcium from foods.

Explanation:

Bioavailability refers to the proportion of a nutrient that is absorbed from food and made available for use in the body. Factors that alter bioavailability of minerals from foods include phytic acid, oxalic acid, refinement of grains, and vitamins C and D. Phytic acid, for instance, decreases the absorption of zinc from grains while oxalic acid decreases the absorption of calcium from spinach.

           Refinement of grains, on the other hand, decreases the mineral content of grain products. Conversely, vitamin C increases the absorption of iron from foods while vitamin D increases the absorption of calcium from foods.

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The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.

An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.

Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.

Angle ABC = Angle ABD + Angle ACD

replacing the specified values:

110° = Angle ABD + 75°

Simplifying:

Angle ABD = 110° - 75°

Angle ABD = 35°

Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:

AC / CD = AB / BD

replacing the specified values:

AC / 10 = 16 / 8

Simplifying:

AC = 20

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Complete Question:

Find the angle ∠ABD jn the given figure

Answer:

1/1296 or 0.0007716049382716

Step-by-step explanation:

asking how probable it is for the rolls to be rolled in that sequence

so first off in the first roll its a 1/6th chance

then second roll should be 1/6th chance too, right?

but you have to consider the first roll too

how likely is it for the first roll AND the second roll to be in that sequence?

1/6 x 1/6

aka

6 x 6

36

for the first two rolls there are a 1/36 chance for that sequence to happen

so for four its

1/6 x 1/6 x 1/6 x 1/6

6 x 6 x 6 x 6

1296

1/1296 probability OR 0.0007716049382716 (decimals)

hope this helps x

For the following data, the slope of the linear relationship is option D.

A line's direction and steepness are measured by the line's slope. by solving the slope of the line we can determine whether the lines are perpendicular, parallel, or none at all.

from the given data the first two coordinate points are:

(2,5) and (1,2)

The representation of the slope is given by the variable m.

The slope formula is :

m = (y2 - y1) / (x2 - x1)

by substituting the values in the equation

m = (2 .0- 5.0) / (1.0 - 2.0)

m = -3 / -1

m = 3

Therefore, the slope of the linear relationship is m = 3.

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a) mv = Mv.

b) The columns of M are dependent where [v1, v2, ..., vn]T is a vector combination

If a matrix M is multiplied by a vector v, the result will be a linear combination of the columns of the matrix. That is, if M is an m×n matrix and v is a vector with n entries, then the product Mv is a linear combination of the columns of M with coefficients from v. Thus, mv = Mv.

If the columns of M are linearly dependent, it implies that they are multiples of each other, i.e., one column is equal to a scalar multiple of another column, which can be written as an equation of the form, ci = aj where c and a are scalar multiples of jth and ith columns of M, respectively.

Hence, when we compute Mv, the linear combination of the columns of M will depend on the scalar multiples c and a.

For instance, let us assume that column j and i of M are linearly dependent. We have;

ci = aj or

M(:,j) = a*M(:,i)

where M(:,j) and M(:,i) represent jth and ith columns of M, respectively. Then, we can express M as;

M = [M(:,1), ..., M(:,j-1), M(:,i), M(:,j+1), ..., M(:,n)] = [M(:,1), ..., M(:,j-1), a*M(:,i), M(:,j+1), ..., M(:,n)]

Thus, we can rewrite the product Mv as;

Mv = [M(:,1), ..., M(:,j-1), a*M(:,i), M(:,j+1), ..., M(:,n)][v1, v2, ..., vn]T

where [v1, v2, ..., vn]T is a vector combination of the columns of M.

Therefore, if a linear combination of the columns of M results in the zero vector, it implies that the columns of M are dependent.

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Rounding to the nearest whole number, we would expect approximately 251 Dutch men out of a random sample of 1000 to be taller than 190 cm.

To determine how many Dutch men we would expect to be taller than a certain height out of a random sample of 1000, we can use the normal distribution and the properties of the standard normal distribution. We are given that the average height of Dutch men is 183 cm with a standard deviation of 10.5 cm.

To find the probability of a Dutch man being taller than a certain height, we need to convert that height to a standard score or z-score using the formula:

z = (x - μ) / σ

where x is the height we are interested in, μ is the population mean height of Dutch men, and σ is the population standard deviation of Dutch men.

Once we have calculated the z-score, we can use a standard normal distribution table or calculator to find the probability of a Dutch man being taller than that height.

For example, if we want to find the number of Dutch men we would expect to be taller than 190 cm, we can calculate the z-score as:

z = (190 - 183) / 10.5 = 0.67

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being greater than 0.67 is approximately 0.2514.

To find the number of Dutch men we would expect to be taller than 190 cm out of a sample of 1000, we can multiply the probability by the sample size:

1000 * 0.2514 = 251.4

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Complete question is:

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a men of 183 cm and standard deviation of 10.5cm. out of a random sample of 1000 dutch men, how many would we expect to be taller than cm (rounded to the nearest whole number)?

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to create an equation, and to find the measures of each angle.}[/tex]

[tex]\textsf{Angle 1 and Angle 2 form a Linear Pair.}[/tex]

[tex]\large\underline{\textsf{What is a Linear Pair?}}[/tex]

[tex]\textsf{A Linear Pair is 2 Adjacent angles that form a 180 Degree angle.}[/tex]

[tex]\textsf{This means that Angle 1 and Angle 2 add up to 180}^{\circ}.[/tex]

[tex]\large\underline{\textsf{Creating an Equation:}}[/tex]

[tex]\textsf{We are given 2 expressions for Angles 1 and 2. Add them together to equal 180}^{\circ}.[/tex]

[tex]\large\boxed{\mathtt{5x+x-18=180^{\circ}}}[/tex]

[tex]\large\underline{\textsf{Solving the Equation:}}[/tex]

[tex]\textsf{Solve x by isolating the variable. Let's first add 18 to both sides of the equation.}[/tex]

[tex]\mathtt{5x+x=198^{\circ}}[/tex]

[tex]\textsf{Because 5x and x are like terms, we can combine them.}[/tex]

[tex]\mathtt{6x=198}[/tex]

[tex]\textsf{Now, divide each side of the equation by 6 to find x.}[/tex]

[tex]\mathtt{\frac{6x}{6}=\frac{198}{6} }[/tex]

[tex]\large\boxed{\mathtt{x=33^{\circ}}}[/tex]

[tex]\large\underline{\textsf{Finding the Measures:}}[/tex]

[tex]\textsf{Because we know the value x, we can substitute the known value of x into the expressions given.}[/tex]

[tex]\boxed{\mathtt{\angle 1 =5(33)=165^{\circ}}}[/tex]

[tex]\boxed{\mathtt{\angle 2=33-18=15^{\circ}}}[/tex]

The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.

The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.

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The annual temperature range for Los Angeles, CA is 28.6°F.

The annual temperature range for Los Angeles, CA can be found by subtracting the minimum monthly mean temperature from the maximum monthly mean temperature.

According to data from the National Oceanic and Atmospheric Administration (NOAA), the average maximum monthly temperature for Los Angeles is 77.8°F, while the average minimum monthly temperature is 49.2°F.

Add the greatest number to the lowest number in the collection. The resultant value is the range of the collection of temperature readings.

Therefore, the annual temperature range for Los Angeles, CA can be calculated as follows:

Maximum Monthly Temperature - Minimum Monthly Temperature

Temperature Range = 77.8°F - 49.2°F

Temperature Range = 28.6°F

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Answer:

1) x= 2

Step-by-step explanation:

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

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Answer:

The median and mean are two different measures of central tendency that provide different information about a data set. The median is the middle value in a data set, where half of the values are above and half are below. The mean, on the other hand, is the sum of all values divided by the total number of values.

In this case, the median number of reviews is much lower than the mean number of reviews, indicating that there are likely a few very high review counts that are skewing the data towards the higher end. This is because the mean is more affected by extreme values, while the median is not. It is possible that there are a few apps with an extremely large number of reviews, which are driving up the mean.

The mean number of reviews would be significantly higher than the median.

The difference between the median and mean number of reviews can be explained by the fact that some apps have very large numbers of reviews, whereas others have very few. The median is the middle value of the dataset, and does not take into account the outliers, which can have a large effect on the mean. For example, if there is one app with 1 million reviews, the mean number of reviews would be significantly higher than the median.

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The expression to represent how much Mason's mom spent for "g" games online is 12g + 7

An expression is a combination of numbers, variables, and operators that represent a mathematical phrase or statement. Expressions can be used to represent mathematical operations and relationships, and they can be simplified or evaluated using mathematical rules and techniques.

Let's say that Mason's mom bought "g" games online.

Each game costs $12, and there is an additional $7 shipping fee per order.

Therefore, the total amount spent on g games can be represented by the expression:

12g + 7

Here, 12g represents the cost of the games, and 7 represents the shipping fee.

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The given question is incomplete, the complete question is:

Mason's mom bought g games online. The games cost $12 each plus a $7 shipping fee. Write an expression to represent how much Mason's mom spent for the games

The number of nickels Bill has is 10.

Therefore, Bill has 10 nickels and 30 dimes.

The given question is as follows.

Bill has a collection of 40 nickels and dimes.

Together, they add up to $3.50.

Bill have of each coin :

To solve the given problem, let's consider the following steps.

Step 1: Let x be the number of nickels and y be the number of dimes.

Based on the given data, we can form the following two equations:

x + y = 40 ... (1) (because Bill has 40 nickels and dimes)

0.05x + 0.10y = 3.50 ... (2) (because the sum of 40 nickels and dimes is $3.50)

Step 2: Solve the equations (1) and (2) by elimination method by multiplying equation (1) with 0.05 and subtracting it from equation (2).

0.05x + 0.05y = 2 ... (3)0.05x + 0.10y = 3.50 ... (4)

Subtracting equation (3) from equation (4),

we get0.05y = 1.50

Dividing both sides by 0.05, we get

y = 30

Therefore, the number of dimes Bill has is 30.

Step 3: Now, substitute the value of y in equation (1), we get

x + 30 = 40

Subtracting 30 from both sides, we get x = 10.

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The area of the shaded region of the circle is 63.24 ft²

We know that the area of a circle of radius R is given by the formula:

Area = pi*R²

Where pi = 3.14

If we have only a section of a circle defined by an angle θ, the area of that section will be:

area = (θ/360°)*3.14*R²

Here we know that the radius is 5 feet, and that AOB (the non-shaded part) is 70°, then we will have:

θ = 360° - 70° = 290°

Then the area of the shaded region is:

area = (290°/360°)*3.14*(5 ft)² = 63.24 ft²

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The surface area of the playhouse is 564 square feet.

Frank is building a playhouse for his daughter.

The playhouse is a composite figure with a floor and no windows.

The playhouse is a rectangular prism and a triangular prism.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh,

where l is the length,

w is the width,

and h is the height.

Therefore, the surface area of the rectangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the rectangular prism = 2lw + 2lh + 2wh

For the rectangular prism, l = 10 feet, w = 8 feet, and h = 6 feet.

Substituting the values in the formula.

Surface area of the rectangular prism

= 2lw + 2lh + 2wh

= 2 (10 feet × 8 feet) + 2 (10 feet × 6 feet) + 2 (8 feet × 6 feet)

= 160 feet2 + 120 feet2 + 96 feet2= 376 feet2

The surface area of the rectangular prism of the playhouse is 376 square feet.

The formula for the surface area of a triangular prism is 2lw + lh + ph,

where l is the length, w is the width, h is the height, and p is the slant height.

Therefore, the surface area of the triangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the triangular prism = 2lw + lh + ph

For the triangular prism, l = 8 feet, w = 5 feet, h = 6 feet, and p = 10 feet.

Substituting the values in the formula.

Surface area of the triangular prism = 2lw + lh + ph= 2 (8 feet × 5 feet) + (8 feet × 6 feet) + (10 feet × 6 feet)= 80 feet2 + 48 feet2 + 60 feet2= 188 feet2

The surface area of the triangular prism of the playhouse is 188 square feet.

The total surface area of the playhouse can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism.

Surface area of the playhouse = surface area of rectangular prism + surface area of triangular prism.

= 376 square feet + 188 square feet

= 564 square feet.

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Micah received 1/2 of Savi's share and Juan got the balance.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

total amount = $280=x

savi= 4*juan= 11

micah= 1/2 savi= 1/2*280/100= 1.4

juan got balance= 267.6

Hence, Micah received 1/2 of Savi's share and Juan got the balance.

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Approximately 7.30% of the bearings produced will not be acceptable.

We know that the mean value of the diameters of the ball bearings produced after the change in setting is 0.499 inches and the standard deviation is 0.002 inches. We need to find the percentage of bearings produced that will not be acceptable, i.e., the diameter of the bearing will be outside the range of (0.500 - 0.004) inches to (0.500 + 0.004) inches.

Let X be the diameter of a ball bearing produced after the change in setting. Then, X is normally distributed with mean µ = 0.499 inches and standard deviation σ = 0.002 inches.

We need to find P(X < 0.496 or X > 0.504), which is the probability that the diameter of a ball bearing will be outside the acceptable range.

Using the standard normal distribution, we can find the z-scores corresponding to the lower and upper limits of the acceptable range:

z1 = (0.496 - 0.499) / 0.002 = -1.5

z2 = (0.504 - 0.499) / 0.002 = 2.5

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(Z < -1.5) = 0.0668

P(Z > 2.5) = 0.0062

Therefore, the probability that a ball bearing produced after the change in setting will not be acceptable is:

P(X < 0.496 or X > 0.504) = P(Z < -1.5 or Z > 2.5) = P(Z < -1.5) + P(Z > 2.5) = 0.0668 + 0.0062 = 0.0730

So, the percentage of the bearings produced that will not be acceptable is:

0.0730 x 100% = 7.30%

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Answer:

(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))

Step-by-step explanation:

In standard position, the initial side of an angle lies on the positive x-axis, and the terminal side rotates counterclockwise from the initial side.

Since the angle measures 2π/5 radians, we need to find the point on the unit circle that is π/5 radians past the positive x-axis.

Let (x, y) be the coordinates of the point on the unit circle where the terminal side intersects. We can use the following trigonometric identities to find the values of x and y:

cos(2π/5) = x

sin(2π/5) = y

These values can be determined using either a calculator or the unit circle. Alternatively, we can use the fact that the angle 2π/5 is a special angle and can be expressed exactly in terms of square roots:

cos(2π/5) = (1/4)(-1 + √5)

sin(2π/5) = (1/4)(2√5 + 2)

Therefore, the exact coordinates of the point where the terminal side intersects the unit circle are

(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))

The water surface in the conical tank is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.

To solve for this, we can use related rates. Since the tank is being filled with water at a constant rate of 2 ft³/min , we know that the rate of change of the volume of water in the tank is constant. We can use the formula for the volume of a cone to relate the volume of water in the tank to the height of the water in the tank:

V = (1/3) * pi * r² * h

Taking the derivative of both sides with respect to time gives:

dV/dt = (1/3) * pi * r² * dh/dt

We know that dV/dt = 2 ft³/min, r = 2 ft, and h = 5 ft. Solving for dh/dt:

dh/dt = (3 / pi * r²) * dV/dt

dh/dt = (3 / 4 * pi) * 2

dh/dt = 0.16 ft/min

Therefore, the water surface is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.

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There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.

To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.

Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.

Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.

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Answer:

Ashok's salary increases by 4%, which means his new salary will be:

New salary = Old salary + (4% of old salary)

New salary = 2500 + (4/100) * 2500

New salary = 2500 + 100

New salary = 2600

In addition to the increase, Ashok also gets an extra ₹75 per week, so his new salary will be:

New salary = Old salary + Increase + Extra amount

New salary = 2500 + 100 + 75

New salary = ₹ 2675 per week

Therefore, Ashok's new salary next week will be ₹ 2,675 per week.

Mitchelle will receive R7200 and Angela will receive R10800.

How to find the value of one part by dividing the total amount won by the total number of parts?

To determine how much Mitchelle and Angela will each receive in the ratio of 2:3, we need to first find the total number of parts in the ratio, which is 2 + 3 = 5.

Value of one part = R18000 ÷ 5 = R3600

Therefore, one part of the ratio 2:3 is equal to R3600.

How to find out how much Mitchelle and Angela will each receive?

we can multiply their respective parts by the value of one part:

• Mitchelle's share = 2 parts × R3600 per part = R7200

• Angela's share = 3 parts × R3600 per part = R10800

Therefore, Mitchelle will receive R7200 and Angela will receive R10800.

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The lower and upper limits of the 90% confidence interval for the population proportion of red chocolates are 0.182 and 0.238, respectively.

To calculate the confidence interval, we can use the formula:

CI = p ± zα/2 * √(p(1 - p) / n)

where p is the sample proportion (in this case, 110/550 = 0.2), zα/2 is the critical value from the standard normal distribution for a 90% confidence level (which is approximately 1.645), and n is the sample size (which is 550).

Substituting these values into the formula, we get:

CI = 0.2 ± 1.645 * √(0.2(1 - 0.2) / 550)

Simplifying the formula, we get:

CI = 0.2 ± 0.028

Therefore, the lower limit of the confidence interval is 0.2 - 0.028 = 0.172, rounded to the thousandth place as 0.182, and the upper limit is 0.2 + 0.028 = 0.228, rounded to the thousandth place as 0.238.

Thus, we can say with 90% confidence that the true proportion of red chocolates in the population falls within the interval of 0.182 to 0.238.

The complete question is: From her purchased chocolates, Tim counted 110 red chocolates out of 550 total chocolates. Using a 90% confidence interval for the population proportion, what are the lower and upper limits of the interval? Answer choices are rounded to the thousandth place.

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Answer: 3 5/8 pizzas were there at the start of the party.

Step-by-step explanation:

At the party let number of pizzas were = x Aisha and her friends ate 2 1/2 pizzas after which 1 1/8 pizzas were left.

Therefore the equation formed will be

x- 2 1/2= 1 1/8

x-(5/2)= 9/8

x= 9/8 + 5/2

x= 29/8= 3 5/8

Therefore 3 5/8 pizzas were there at the start of the party.

The fact that the sample averages are not all the same can be an illustration of the concept of the central limit theorem, while the fact that the sample averages systematically overestimate the true population average can be an illustration of the concept of bias.

The given statement is incomplete, we need additional information in order to provide a solution. It is important to provide the complete statement so that we can help you in the best way possible.

However, based on the given options, we can provide a general explanation of the concepts mentioned, which are the concepts of the central limit theorem and bias.

The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. In other words, as the sample size increases, the means of the samples drawn from a population tend to be normally distributed. The central limit theorem has important implications for statistics and hypothesis testing.

Bias, on the other hand, refers to a systematic error in data collection or analysis. Bias can be caused by a variety of factors, such as the selection of participants or the measurement instruments used. A biased sample or analysis can lead to inaccurate conclusions about a population.

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