Let U be the set of all integers from 1 to 20. Let A = {1, 3, 6, 9, 12, 15, 18} and B = {2, 9, 11,
20). Which choice describes the set {4, 5, 7, 8, 10, 13, 14, 16, 17, 19)?

Answer:

14-8

12-9

0-15

2-14

Step-by-step explanation:

Combinations for different rows will be, 14 - 8, 12 - 9, 0 - 15, 2 - 14.

    Given in the question,

Let the number of chess games played = x

And number of Uno games played = y

Therefore, equation for this situation will be,

2x + 4y = 60

For the 1st row given in the table,

If y = 8,

2x + 4(8) = 60

2x = 28

x = 14

For the 2nd row of the table,

If x = 12,

2(12) + 4y = 60

4y = 36

y = 9

For 3rd row of the table,

If y = 15,

2x + 4(15) = 60

x = 0

For 4th row of the table,

If x = 2,

2(2) + 4y = 60

4y = 56

y = 14

    Therefore, combinations for different rows will be, 14 - 8, 12 - 9, 0 - 15, 2 - 14.

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Answer:

Solve 2 1/3 divided by 3 1/2.

Step-by-step explanation:

The number of chicken sandwiches is 10 and the number of hamburgers is 30 if the total number of eatables sold is 40 at the rate that each chicken sandwich sells for $4 and each hamburger sells for $2 and Chris has to make $100.

Let the number of the chicken sandwich be x

the number of hamburgers be y

Total number of eatables sold = 40

x + y = 40 ---- (i)

Money earned after selling one chicken sandwich = $4

Money earned after selling x chicken sandwich = 4x

Money earned after selling one chicken sandwich = $2

Money earned after selling y chicken sandwich = 2y

Total money earned = $100

4x + 2y = 100 -----(ii)

Divide equation (ii) by 2

2x + y = 50 ------ (iii)

Subtract equations (i) and (iii)

2x + y - x - y = 50 - 40

x = 10

Put x in equation (i)

10 + y = 40

y = 40 - 10

y = 30

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The complete question might be:

Chris is selling chicken sandwiches and hamburgers at the fair in his hometown. He has a total of 40 buns so he can sell no more than 40 chicken sandwiches and hamburgers. Each chicken sandwich sells for $4 and each hamburger sells for $2. In order to reach his goal, Chris must make at least $100. So what is the number of chicken sandwiches and hamburgers that he must sell to achieve his goal?

The probability that the next person will pay with a debit card is:

P =  0.63

We want to find he probability that the next customer will pay with a debit card.

That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.

We know that:

15 paid in cash.

50 paid with debit card.

15 paid with credit card.

For a total of 15 + 50 + 15 = 80

Then the probability is:

P = 50/80 = 0.63

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Step-by-step explanation:

Formula:

\(v = \pi \:r {}^{2} \:h\)

radius is 4.5 because 9÷2=4.5

so it would be

\(v = \pi \times \:4.5^{2} \times 7\)

volume = 445.3 units³

Answer:

622

Step-by-step explanation:

The 7 rounds up the .9, adding 1 to the ones place, making it 622

Answer:

620

Step-by-step explanation:

As they said TENS ( and not TENTHS ) place, the 1 ( in ones position) determines the answer hence 620.

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Hence:

IG/GH = FD/DE

x / 19 = 11/6

x = 34.8

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

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Answer:

(5,-4)

Step-by-step explanation:

Hii i don't know how to explain but i hope this helps

The construction of similar triangles are given in attached figure.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Similar shapes are shapes whose lengths are in an equivalent ratio. Triangle ABC and triangle DEF are similar because the side lengths of both triangles are in an equivalent ratio (refer to the attachment).

Step 1: Draw a random triangle ABC

The lengths of two sides and an angle are:

AB=10

BC=6

C=90

Step 2: Draw and measure the length of DE

DE=15

Step3: Calculate the ratio

The corresponding line segment to DE is line segment AB.

So, the ratio (k) is:

k= DE/AB

k= 15/10

k=1.5

Step 4: Multiply the ratio by the other line segment in step 1

In (1), we have:

BC=6

So,

EF=k*BC

EF=1.5*6

EF=9

Step 4: Draw a circle with center F and radius EF  

The center of the circle is point F and the radius of the circle is 9 units

Step 5: Draw a ray from the center (i.e. point F) to DE

Refer to the attached image for

Triangle ABC

Triangle DEF

Circle with center F and radius 9

Ray from F to DE

Therefore, construction of similar triangles are given in attached figure.

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Answer: x= -5

Stexp-by-step explanation:

If you look at the table given, G(x) -20 is alligned with x=-5

Answer:

56.35 meters squared

Step-by-step explanation:

lmk if its inches

Answer:

\(f^{8} + 7\)

Step-by-step explanation:

Answer:

n=45

Step-by-step explanation:

Using n as a variable for the unknown number:

20-5=15

15 is 1/3 of 45.

A group of tourists was rescued on Monday after an elevator malfunction left them stranded in Arizona's Grand Canyon Caverns for nearly 30 hours

How to Determine location?

The most popular method is to locate the place by utilizing coordinates like latitude and longitude or, if a street address is known, by using them. Although less accurate than providing coordinates or an address, absolute location can also be the name of the city, area, or postal code in which a place is located.

So,

According to the question,

A group of tourists was rescued on Monday after an elevator malfunction left them stranded in Arizona's Grand Canyon Caverns for nearly 30 hours

Hence,

A group of tourists was rescued on Monday after an elevator malfunction left them stranded in Arizona's Grand Canyon Caverns for nearly 30 hours

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Answer:

Step-by-step explanation:

The given graph is a parabola and so it a quadratic function.

The y-intercept is the point at which the curve crosses the y-axis.

From inspection of the graph, this is when y = -6.

The x-intercepts are the points at which the curve crosses the x-axis.

From inspection of the graph, the x-intercepts are x = 2 and x = 6.

The vertex is the turning point of the graph, so the minimum point of a parabola that opens upwards, and the maximum point of a parabola that opens downwards.

From inspection of the graph, the vertex is at (4, 2), so the greatest value of y is y = 2, and it occurs when x = 4.

The curve is above the x-axis between the interval x = 2 and x = 6.

Therefore, the function value is equal to zero or positive in this interval.

So the function value in the given interval is y ≥ 0.

Graph is parabola

Y inetercept is the point where the curve crosses y axis

X inetercepts are the points crossing x axis

As it's parabola opening downwards vertex is maximum

So max value of y is 2

y≥0

Answer:

B. 66

Step-by-step explanation:

73+25 = 98

Z = 98-32

Z = 66

The length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

To find the length of IJ in ΔHIJ, we can use trigonometric ratios. In this case, we can use the tangent function since we know the measure of angle I and the length of side HI.

Using the tangent function, we can set up the equation: tan(I) = IJ/HI. Rearranging the equation, we have IJ = HI * tan(I).

In this scenario, I = 26° and HI = 5.7 feet. Substituting these values into the equation, we can calculate the length of IJ.

Calculate the tangent of angle I: tan(26°) ≈ 0.4877.

Multiply the tangent value by the length of HI: 5.7 feet * 0.4877 ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet.

Using the given information, we can apply trigonometry to find the length of side IJ. In a right triangle, the tangent function relates the angle I to the ratio of the lengths of the opposite side (IJ) and the adjacent side (HI).

First, we find the tangent of angle I by using the given measure: tan(26°). This gives us the ratio of IJ to HI.

Next, we substitute the known values: HI = 5.7 feet. By multiplying HI with the tangent of angle I, we get the length of IJ.

In this case, tan(26°) ≈ 0.4877. Multiplying this by HI = 5.7 feet, we find that IJ ≈ 2.7777 feet.

Therefore, the length of IJ in ΔHIJ is approximately 2.8 feet when rounded to the nearest tenth of a foot.

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Step-by-step explanation:

The radius of a circle is half of the diameter. The diamter is a straight line from one end of the circle to the other which must intersect the origin.

in a circle the radius is half the length of its diameter or in other words in a circle the diameter is twice the length of its radius.

have a great day!

a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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1) Point slope form equations are written according to this general formula:

2) Since we've got the slope and one point we can plug them into the formula:

That yields the equation of the line y=4/3x -4 (slope-intercept form). So in Point Slope form, the answer is:

(y-0)=4/3(x-3)

Answer: it is the 4 one which is 3(5-n)=2n+16

At first, there are a total of 17 marbles in the bag.

The probability of pulling out the first red marble = 6/17.

The probability of pulling out the second red marble = (6-1)/(17-1) = 5/16

The probability of pulling out the third red marble = (5-1)/(16-1) = 4/15

Because we need these 3 events to happen consecutively, the probability of it happening = 6/17 x 5/16 x 4/15 = 0.029% (nearest thousandth).

The rate of change of output with respect to unskilled workers when 10 skilled workers and 30 unskilled workers are employed is -32,100 pounds.

A. Let's calculate the weekly number of pounds of fiber that can be produced with 10 skilled workers and 30 unskilled workers.We are given the function z = f(x, y) = 10000 + 4000y + 9x²y - 5x³z = f(10, 30) = 10000 + 4000(30) + 9(10²)(30) - 5(10³) = 10000 + 120000 + 27000 - 5000 = 142000Therefore, the weekly number of pounds of fiber that can be produced with 10 skilled workers and 30 unskilled workers is 142,000 pounds.

B. Let's find an expression (f) for the rate of change of output with respect to the number of skilled workers.We have the function z = f(x, y) = 10000 + 4000y + 9x²y - 5x³, thus by differentiating the function with respect to x, we get;∂z/∂x = 18xy - 15x²Now ∂z/∂x is the rate of change of output with respect to the number of skilled workers.

C. Let's find an expression (fy) for the rate of change of output with respect to the number of unskilled workers.Again we have the function z = f(x, y) = 10000 + 4000y + 9x²y - 5x³, thus by differentiating the function with respect to y, we get;∂z/∂y = 4000 + 9x² - 15x²yNow ∂z/∂y is the rate of change of output with respect to the number of unskilled workers.

D. We need to find the rate of change of output with respect to skilled workers when 10 skilled workers and 30 unskilled workers are employed. ∂z/∂x = 18xy - 15x²Putting the values of x and y, we get;∂z/∂x = 18(10)(30) - 15(10)² = 5400 - 1500 = 3900Therefore, the rate of change of output with respect to skilled workers when 10 skilled workers and 30 unskilled workers are employed is 3900 pounds.

E. We need to find the rate of change of output with respect to unskilled workers when 10 skilled workers and 30 unskilled workers are employed. ∂z/∂y = 4000 + 9x² - 15x²y

Putting the values of x and y, we get;∂z/∂y = 4000 + 9(10²) - 15(10)²(30) = 4000 + 900 - 45000 = -32100

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Answer: There are infinitely many.

For example, 5314410.5 or 93. You are probably looking for (3)^6 tho

The trigonometric function with its right triangle definition is matched as below:

(a) sine

opposite/hypotenuse

(b) cosine

adjacent/hypotenuse

(c) tangent

opposite/adjacent

(d) cosecant

hypotenuse/opposite

(e) secant

hypotenuse/adjacent

(f) cotangent

adjacent/opposite

We Know That,

i) sine =opposite side of the triangle /hypotenuse side of the triangle

ii) cosine=adjacent side of the triangle/hypotenuse side of the triangle

iii) tangent=opposite side of the triangle/adjacent side of the triangle

iv) cosecant=hypotenuse side of the triangle/opposite side of the triangle

v) secant=hypotenuse side of the triangle/adjacent side of the triangle

vi) cotangent=adjacent side of the triangle/opposite side of the triangle.

Therefore, each trigonometric function is matched with its right triangle definition

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Answer:

49% chance

step by step

total number of students is 41, 21 picked chemistry

41-21 =20

20÷41 =0.487

0.487 rounded up to 2 decimal places x 100  =49

=49%

The class width of the given data, when creating 3 classes, is 2.

To determine the class width, we need to find the range of the data and divide it by the number of classes. In this case, the range of the data is the difference between the largest and smallest values. The largest shoe size is 10.5 and the smallest shoe size is 6.5, so the range is 10.5 - 6.5 = 4.

Since we are creating 3 classes, we divide the range (4) by 3 to get the class width. Therefore, the class width is 4/3 = 1.3333.  Since we typically use whole numbers for the class width, we can round it to the nearest whole number. In this case, rounding 1.3333 to the nearest whole number gives us 2.

Therefore, the class width for the given data, when creating 3 classes, is 2.

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Answer:

1. Tan θ = √11/5

2. Cosec θ = 6√11 /11

3. Cos θ = 5/6

Step-by-step explanation:

Let the side opposite to angle θ be y.

The value of y can be obtained by using the pythagoras theory as follow:

b² = 6² – 5²

b² = 36 – 25

b² = 11

Take the square root of both side.

b = √11

1. Determination of Tan θ

Tan θ =?

Opposite = √11

Adjacent = 5

Tan θ = Opposite /Adjacent

Tan θ = √11/5

2. Determination of Cosec θ.

We'll begin by calculating the Sine θ. This is illustrated below:

Sine θ =?

Opposite = √11

Hypothenus = 6

Sine θ = Opposite /Hypothenus

Sine θ = √11/6

Now, we shall determine Cosec θ as follow:

Cosec θ = 1/Sine θ

Sine θ = √11/6

Cosec θ = 1 ÷ √11/6

Cosec θ = 1 × 6/√11

Cosec θ = 6/√11

Rationalise the denominator

Cosec θ = 6/√11 × √11/√11

Cosec θ = 6√11 /11

3. Determination of Cos θ.

Cos θ =?

Adjacent = 5

Hypothenus = 6

Cos θ = Adjacent / Hypothenus

Cos θ = 5/6