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ABCD is a trapezium with AB ║DC what is the area of the trapezium?

The number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.

To find the number of different simple random samples of size 4 that can be obtained from a population whose size is 48, we can use the combination formula. The combination formula is written as:

C(n, k) = n! / (k!(n-k)!)

where n is the population size (48), k is the sample size (4), and ! denotes a factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).

So, in this case:

C(48, 4) = 48! / (4!(48-4)!)

C(48, 4) = 48! / (4!44!)

C(48, 4) = (48 × 47 × 46 × 45) / (4 × 3 × 2 × 1)

C(48, 4) = 194580

Therefore, the number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.

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The probability of obtaining 126 or more individuals with the characteristic, P(p ≥ 0.63) is 0.5.

The binomial distribution is used to approximate the probability.

The mean of the binomial distribution is np is 200 * 0.63

mean = 126

The standard deviation is √(np(1-p)) = √(200 * 0.63 * 0.37)

standard deviation = 5.18.

Standardize the random variable p as follows:

z = (x - μ) / σ

z = (126 - 126) / 5.18 = 0

Using a calculator to find the probability of z being greater than or equal to 0, the given probability is 0.5.

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The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.

Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.

The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:

TR = PQ - ST = 60 - 24 = 36 inches

The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:

UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches

So, the dimensions of section B are 36 inches by 48 inches.

Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.

The area of rectangle B is the product of its length and breadth, which is:

Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches

The area of rectangle WVTX is the product of its length and breadth, which is:

Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches

The area of rectangle PQRS is the product of its length and breadth, which is:

Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches

Therefore, the area of the piece of sheet metal after both sections are cut and removed is:

Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX

= 8640 - (1728 + 576)

= 8640 - 2304

= 6336 square inches

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H0: p1 = p2 (the proportions are equal)

Ha: p2 > p1 (the proportion in Population 2 exceeds that in Population 1)

Hypothesis testing involves making a statement about a population parameter (such as a mean or a proportion) based on a sample of data. The statement is made in the form of two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).

The null hypothesis is the default assumption that there is no significant difference between the two populations being compared. In this case, the null hypothesis would be that the proportion found in Population 2 is not significantly different from the proportion found in Population 1.

The alternative hypothesis is the statement we are trying to support with our evidence. In this case, the alternative hypothesis would be that the proportion found in Population 2 exceeds the proportion found in Population 1.

So, in step 1 of hypothesis testing, we would state the null and alternative hypotheses as follows:

H0: p1 = p2 (the proportions are equal)

Ha: p2 > p1 (the proportion in Population 2 exceeds that in Population 1)

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i. To find the component form of the vector AB, we subtract the coordinates of A from the coordinates of B:
AB = <52 - 12, 33 - 41> = <40, -8>
To find the magnitude of the vector AB, we use the formula:
|AB| = sqrt((40)^2 + (-8)^2) = sqrt(1600 + 64) = sqrt(1664) ≈ 40.79

ii. Similarly, we find the component form of AB:
AB = <12 - 8, 3 - 14> = <4, -11>
And the magnitude of AB:
|AB| = sqrt((4)^2 + (-11)^2) = sqrt(157) ≈ 12.53

iii. To find the component form of AB in 3D space, we subtract the coordinates of A from the coordinates of B:
AB = <8 - 9, 5 - (-2), 11 - 5> = <-1, 7, 6>
To find the magnitude of AB, we use the formula:
|AB| = sqrt((-1)^2 + (7)^2 + (6)^2) = sqrt(86) ≈ 9.27

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(a) The values of u is 140 g and o is 13.42 g. (b) The value of K in (300 - K. 300 + K) grams is 27.15 g. C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. The values of LI is 272.85 g and L2 is 327.15 g.

(a) The mean weight of blueberries is:

300 g - 160 g = 140 g

The standard deviation of the weight is:

Var(X + Y) = Var(X) + Var(Y)

Adding the variances:

15^2 = 10^2 + o^2

Solving for o:

o = sqrt(15^2 - 10^2) = 13.42 g

Therefore, the values of u and o are u = 140 g and o = 13.42 g.

(b) Since the distribution is normal, we can use the standard normal distribution to find K.

The middle 96.6% of a standard normal distribution corresponds to the interval (-1.81, 1.81) (using a table or calculator). Therefore,

K = 1.81 * 15 = 27.15 g

Therefore, the weights of the middle 96.6% of fruit cups are between 300 - 27.15 = 272.85 g and 300 + 27.15 = 327.15 g.

(c) Using the standard normal distribution to find the corresponding interval on the standard normal scale:

(-1.81, 1.81)

We can then scale this interval to the distribution of the weight of fruit cups by dividing by the standard deviation and multiplying by 15 g:

L1 = 300 + (-1.81) * 15 = 272.85 g

L2 = 300 + 1.81 * 15 = 327.15 g

Therefore, the weights of the middle 96.6% of fruit cups are between 272.85 g and 327.15 g.

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The use of regression modeling in retail analytics can help businesses make data-driven decisions that ultimately lead to increased profits and growth.

Based on the information given, it seems that the large sports supplier is interested in predicting the annual revenue of a particular store based on various factors, such as population, promotion expenditure, and distance from the city center. This is a common approach in retail analytics, where regression models are often used to predict sales or revenue based on different variables.

By constructing a regression model, the sports supplier can gain valuable insights into which factors are most strongly associated with revenue, and how they can optimize their operations to increase sales. For example, they may find that stores located closer to the city center tend to have higher revenue, or that increased promotion expenditure leads to a greater increase in revenue in smaller towns.

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The area of the rectangle is 13, 950 square unit.

We have,

length = 150

width= 93

So, Area of rectangle

=  length x width

= 150 x 93

= 13950 square unit.

Thus, the required Area is 13, 950 square unit.

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The value of the identity sin N = 3/5

To determine the value of the identity, we need to know the different trigonometric identities. These identities are;

From the information given, we have that;

The angle of the triangle is N

The opposite side of angle N is 3

The hypotenuse side of angle N is 5

Using the sine identity, we have;

sin N = 3/5

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The table that shows a linear function include the following: B. table B.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we have:

Slope = (0 - 2)/(-3 + 5) = (2 - 0)/(-3 + 1) = -1

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The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.

Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:

p = 0.716

Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Substituting in the values of n and p, we get:

σ = sqrt(9 * 0.716 * (1 - 0.716))

σ = 1.168

Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

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Answer:

In/out

-18, -19

-17, -18

-15, -16

-7, -8

0, -1

14, 13

Step-by-step explanation:

the rule states "subtract 1" so if you look at the In, -15 for example goes to -16 for the out which proves that -15-1 is -16. so for all the In's you subtract each number by 1. to FIND a In from the out you just add 1. So just follow the rules and look at the rules carefully!

f(x,y) = x + y; if both x & y are even f(x,y) = x - y; if both & y are odd f(x, y) = 2x – y2, if any one of them is odd & other is = even. Then the result of f(2,3) - f(2,4) is -11, which corresponds to option c).

Determining f(2,3)

Since x = 2 (even) and y = 3 (odd)

Then, the function definition for this case is f(x,y) = 2x - y²

f(2,3) = 2(2) - 3² = 4 - 9 = -5

Determining f(2,4)

Since x = 2 (even) and y = 4 (even)

Then, the function definition for this case is f(x,y) = x + y.

f(2,4) = 2 + 4 = 6

Now, Calculating f(2,3) - f(2,4)

f(2,3) - f(2,4) = -5 - 6 = -11

Therefore, the answer is option c) -11.

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Tom increased his investment by 16.67% percent when he sold the merchandise at the flea market.

Given that Tom bought $72 worth of merchandise at a yard sale

Tom sold it for $84 at a flea market.

We have to find the percent did he increase his investment

Tom's initial investment was $72, and he sold the merchandise for $84. The difference between these amounts is:

$84 - $72 = $12

To express this difference as a percentage of his initial investment, we can use the formula:

percent increase = (difference / initial investment) x 100%

Substituting the values we have:

percent increase = ($12 / $72) x 100%

= 0.1667 x 100%

= 16.67%

Hence,  Tom increased his investment by approximately 16.67% when he sold the merchandise at the flea market.

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The zeroes of the function as required to be determined in the task content are; 0, 2, -4, 4.

It follows from the task content that the zeroes of the given function; f(x) = -5x (x - 2) (x² - 16) is to be determined.

To determine the zeroes; we have;

-5x = 0; x = 0

x - 2 = 0; x = 2

x² - 16 = 0; x² = 16; x = ± 4.

Ultimately, the zeroes of the function are; 0, 2, -4, 4.

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The null hypothesis states that the average age of community college students is equal to 24.6 years. The alternative hypothesis states that the average age of community college students is not equal to 24.6 years.

In other words, the null hypothesis assumes that the given average age is accurate, and the alternative hypothesis suggests that the given average age is either higher or lower than 24.6 years. These hypotheses can be tested through statistical analysis to determine if there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. This analysis can provide insights into the characteristics of the community college student population and inform decisions related to education policy and programs.

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The area of the circle is approximately 55.39 square inches.

The circumference of the circle is approximately 26.38 inches.

The area of a circle = πr²

The circumference of the circle = 2πr

Where, r is the radius of the circle, which is half of the diameter of the circle.

Therefore, we have:

radius (r) = 8.4/2 = 4.2 inches

π = 3.14

Thus:

The area of the circle = πr² = 3.14 * 4.2²

Area ≈ 55.39 square inches [nearest hundredth]

The circumference of the circle = 2πr = 2 * 3.14 * 4.2

Circumference ≈ 26.38 inches.

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The value of x is equal to 17.

In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the triangle BHY is equal to the measure of angle x (∠NYB);

m∠BHY + m∠HBY = m∠NYB

(2x + 7)° + (8x - 18)° = (4x + 91)°

10x - 11 = 4x + 91

10x - 4x = 91 + 11

6x = 102

x = 102/6

x = 17.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

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

Volume of cylinder formula:

We are given values:

Substitute and calculate the volume:

Answer:

Step-by-step explanation:

The number in your question is expressed in scientific notation, which is typically used to express numbers that are either too large or too small.  The number in scientific notation is expressed as a power of 10.  A positive exponent means the # is large whereas if the exponent is negative, then the # is small.

3.652 x 10-4 --> negative exponent, therefore, # is small.

All you need to do is to convert this number to standard notation by moving the decimal 4 places to the left.

3.652 x 10-4 = 0.0003652

The percent markup is 20%

The selling price of the Nu is 900

The cost price of the Nu is 750

The percent markup can be calculated as follows

= 900-750/750 × 100

= 150/750 × 100

= 0.2 × 100

= 20%

Hence the percent markup is 20%

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Answer: 36 quarts

Step-by-step explanation:

pretty much just do 9 * 4 qts

hope this helped!!

Answer: Parker has 36 Quarts of water.

We are given the following:

We are asked to find:

This question strictly revolves the around the conversion of units. In other words, in order to answer this question, we must know how many quarts are in a gallon.

Fortunately, we know that 4 quarts = 1 gallon.

Since Parker possesses 9 gallons of water, we would do [tex]4*9=36[/tex]. Arriving us at our answer of 36 quarts of water.

Parker has 36 quarts of water.

Answer:

Step-by-step explanation:

To find the optimal ticket price that will maximize revenue, we need to determine the price point where the increase in revenue from selling each ticket at a higher price is greater than the decrease in revenue from selling fewer tickets due to the higher price.

Let's start by calculating the current revenue generated at the current ticket price of $6.00:

Current revenue = 1800 x $6.00 = $10,800

Now, we need to determine the effect of increasing ticket prices by $0.50 on the number of tickets sold:

For each $0.50 increase in ticket price, 100 fewer people will attend. So, for a $0.50 increase, the new ticket price will be $6.50, and the number of attendees will be:

1800 - 100 = 1700

For a $1.00 increase, the new ticket price will be $7.00, and the number of attendees will be:

1700 - 100 = 1600

And so on.

We can create a table to calculate the revenue at different price points:

Ticket Price Number of Tickets Sold Revenue

$6.00                 1800                                $10,800

$6.50                 1700                                $11,050

$7.00                 1600                          $11,200

$7.50                 1500                                $11,250

$8.00                  1400                          $11,200

$8.50                  1300                          $11,050

$9.00                  1200                          $10,800

As we can see from the table, the optimal ticket price that will maximize revenue is $7.50, where the revenue is $11,250. Beyond this point, the decrease in attendance outweighs the increase in ticket price, resulting in a decrease in revenue.

Therefore, the owner should increase the ticket price to $7.50 to maximize revenue.

For made a fruit punch, Kim used the 3 batches of this fruit punch recipe. From unit conversion, the total quantity in litres used to fruit punch is equals to the 2.570 L.

We have Kim made 3 batches of this fruit punch recipe. It includes the combination of following,

quantity of strawberry juice = 70 mL

quantity of apple juice = 2 L

quantity of pineapple juice = 500 mL

We have to determine the number of liters of fruit punch he made. Using the unit conversion,

one liters = 1000 mililiters

=> 1 mL = 0.001 L ( conversion factor)

so, quantity of strawberry juice = 70 mL = 70× 0.001 L = 0.070 mL

quantity of pineapple juice = 500 mL = 500× 0.001 L = 0.500 L

So, total quantity of fruit punch made by Kim in liters = strawberry juice + pineapple juice + apple juice

= 0.070 L + 0.500 L + 2 L

= 2.570 L

Hence, the required value is 2.570 liters.

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Answer:

Volume formal= L × W × W

Volume formal= 6 × 8 × 9

Answer= 6×8×9= 432

For a bounded martingale Xₙ and stopping time T (not necessarily bounded), E[XT] = E[X] is proved by considering the stopping times Tₙ= min(T, n) and using the Optional Stopping Theorem.

To prove that E[XT] = E[X], we can utilize the Optional Stopping Theorem.

First, we know that since Xₙ is a bounded martingale, it satisfies the conditions for the Optional Stopping Theorem stating that for any stopping time T, [tex]E[X_{T}] = E[X_{0}][/tex], where [tex]X_{0}[/tex] is the initial value of Xₙ.

Now, taking into consideration stopping times Tn = min(T, n). As Tn is a bounded stopping time, we utilize the Optional Stopping Theorem to get:

[tex]E[X_{Tn}] = E[X_{0}][/tex]

We can rewrite this as:
[tex]E[X_{Tn}] - E[X_{0}] = 0[/tex]

Now, if we take the limit as n→∞.As Xn is a bounded martingale, it follows that E[|Xn|] < infinity for all n. Thus, utilizing Dominated Convergence Theorem, we get:

[tex]lim_{n} E[X_{Tn}] = E[lim_{n} X_{Tn}] = E[XT][/tex]

Similarly, [tex]lim_{n} E[X_{0}] = E[X].[/tex]

Therefore, taking the limit as n→∞ in our previous equation, we get:

E[XT] - E[X] = 0

Or, equivalently:

E[XT] = E[X]

So, E[XT] = E[X] by considering the stopping times Tn= min(T, n)].

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The range for the scores is 1.0 (from 9.9 to 8.9). The range is the difference between the highest and lowest numbers in a set of numbers. In this case, the highest score is 9.9 and the lowest score is 8.9, so the range is 1.0.

In mathematics, the range of a function can refer to one of two similar terms:

the common area of ​​the function

The image of the function

Given two groups X and Y, the binary relation f between X and Y is a (exact) function (X to Y), if there is a y in Y for every x in X, so f is associated with y. The sets X and Y are called the area of ​​f and the common domain, respectively.

The range is a measure of dispersion in a set of numbers. To find the range, you need to subtract the lowest score from the highest score. In this case, the scores for the Olympic gymnast are: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8.

First, identify the highest and lowest scores:
Highest score: 9.9
Lowest score: 8.9

Next, subtract the lowest score from the highest score:
Range = 9.9 - 8.9

The range for the scores is 1.0 (9.9 to 8.9).

Your answer: 1.0 (9.9 to 8.9)

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Step-by-step explanation:

Area of a triangle = 1/2 base leg  * height

                area =  1/2 * 9 * 6 = 27 cm^2

Answer: 27 cm²

Step-by-step explanation:

     To find the area of the base of this right triangular prism we can use the area formula for a triangle. Make sure you are using the correct base (b) and height (H) in the formula that apply to the base triangle.

Given:

   A = [tex]\frac{bH}{2}[/tex]

Substitute known values:

   A = [tex]\frac{(9\;cm)(6\;cm)}{2}[/tex]

Multiply:

   A = [tex]\frac{54\;cm^2}{2}[/tex]

Divide:

   A = 27 cm²

The number 7.1 x 10⁴ in standard form is: 71,000

In standard form, a number is expressed as a coefficient multiplied by a power of 10, where a coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 represents the number of places the decimal point must be moved to obtain the number's value.

In this case, the coefficient is 7.1, which is greater than or equal to 1 and less than 10. The power of 10 is 4, which means that the decimal point must be moved 4 places to the right to obtain the value of the number. Therefore, we get 71,000.

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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