What is the probability of drawing the Ace of Diamonds from a deck of cards, putting it back in the deck, shuffling the deck, and then drawing the Ace of Clubs?

Solution

The remainder is obtained when we plug in x=5 into the polynomial function

The final answer is 114

Answer:

196.1

Step-by-step explanation:

Area of a circle is \(\pi r^{2}\) so in order to find the radius you divide the diameter by 2 to get 7.9

Then you do \(7.9^{2}\) x \(\pi\) to get around 196.1

The area of each polygon in this problem is given as follows:

a) 252 square units.

b) 65 square units.

For item a, we have a rectangle of dimensions 12 and 21, hence the area is the multiplication of the dimensions, as follows:

A = 12 x 21 = 252 square units.

For item b, we have a triangle with base 13 and height 10, hence the area is half the multiplication of the base by the height, as follows:

A = 0.5 x 13 x 10 = 65 square units.

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The solution for 20 degrees in the first quadrant is:

20 degrees = 20π/180 = 0.349 radians.

Starting with the given equation:

7cos(20) + 3 = sin(20) + 4

Rearranging:

7cos(20) - sin(20) = 1

Using the trig identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b):

cos(20-70) = cos(-50) = cos(50)

Using the fact that cosine is an even function:

cos(50) = cos(-50)

So we can write:

cos(50) = 1/7

Therefore, the solution for 20 degrees in the first quadrant is:

20 degrees = 20π/180 = 0.349 radians.

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The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Answer:

Each side is 35.78 mm

Step-by-step explanation:

A square would have 4 equal sides.  Since area of a square is x^2, where x is one side, we can write:

x^2 = 1280

x = 35.78 mm

Each side is 35.78 mm

Answer:

Step-by-step explanation:

The total wattage for the four light bulbs is 4 bulbs * 60 watts/bulb = 240 watts. Since 1 kilowatt is equal to 1000 watts, this is equivalent to 240/1000 = 0.24 kilowatts. If these light bulbs are used for 5 hours per day, the energy used per day is 0.24 kilowatts * 5 hours/day = 1.2 kilowatt-hours/day. Over the course of a month with 30 days, the total energy used by these light bulbs is 1.2 kilowatt-hours/day * 30 days/month = 36 kilowatt-hours/month.

If electricity costs $0.11 per kilowatt-hour, the cost of using these light bulbs for one month would be $0.11/kilowatt-hour * 36 kilowatt-hours/month = $3.96/month.

From the graph and the given information, the value of the given function, fg(-3), is 9

From the question, we are to determine the value of the function, fg(-3).

First , we will determine the value of g(-3)

From the given information,

g(x) = 1/(2 + x)

Substitute x = -3 in the function to determine the value of g(-3)

g(-3) = 1/(2 + (-3))

g(-3) = 1/(2 - 3)

g(-3) = 1/-1

g(-3) = -1

Now,

fg(-3) = f(g(-3))

Thus,

fg(-3) = f(-1)

Now, we will determine the value of f(-1) from the given graph.

From the graph, we can read that the value of f(-1) is 9

Hence,

The value of fg(-3) is 9

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The equation of the first graph is

y > 2x - 4

The equation of the first graph is

y ≥ -x + 4

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculating using the points on the graph (0, -4) and  (2, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (-4 - 0) / (0 - 2)

m = (-4) / (-2)

m = 2

c = y intercept, from the graph

c = -4

The equation of the line is y = 2x - 4

shading above the line is greater than and dotted lines means it does not have equal to

hence y > 2x - 4

for the second graph

the slope, m calculating using the points on the graph (0, 4) and  (4, 0)

m = (y₀ - y₁) / (x₀ - x₁)

m = (4 - 0) / (0 - 4)

m = (4) / (-4)

m = -1

c = y intercept, from the graph

c = 4

The equation of the line is y = -x + 4

shading above the line is greater than and solid lines means there is equal to in the inequality

hence y ≥ -x + 4

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The value of angle ∠ABD=144° and ∠DBC=36°.

An endless figure without width is a straight line. It consists of an infinite number of points connected at both ends. It doesn't have any curves at all. It can be straight, angled, or vertical. We use a sleeping straight line or a standing straight line when explaining geometry to preschoolers.

\(ABC\) is a straight line,

Hence,

∠ABD+∠DBC=180°

(4x+8)+(x+2)=180°

5x+10=180°

5x=170°

x=34°

Hence,

∠ABD=4*34+8

∠ABD=144°

∠DBC=36°

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Answer:

can we be friends

Step-by-step explanation:

sddds

Answer:

ribbon ata yan

Step-by-step explanation:

ssa

Answer:

I think x  2  +3x−5

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.

Since m is greater than or equal to 6, we know that:

2m+3 > m+8 > m-3

Answer:

-15,14

Step-by-step explanation:

Answer:

Last choice:

  3/10 · 2/9

Step-by-step explanation:

The total number of marbles and the number of red marbles is not provided but only one answer fits the problem solution

3/10 x 2/9 which is the last choice

It can be deduced that there are 10 marbles totally and 3 of them are red

The probability of a red marble on first draw = 3/10

After the first draw given a red marble was drawn, there are 2 red marbles and total of  marbles so the probability of a second red marble = 2/9

The combined probability is 3/10 x 2/9

Answer:

8 pounds of almonds

4 pounds of macadamia

Step-by-step explanation:

Let x be the pounds of almond

then 12 - x is the pounds of macadamia

5.25x + 9(12 - x) = 12(6.50)

distribute

5.25x + (108 - 9x) = 78

Combine like terms

-3.75x + 108 = 78

subtract 108 from both sides

-3.75x = 30

Divide both sides by -3.75

x = 8    pounds of almond

12 - x = 4    pounds of macadamia

Answer: I would personally say 1/3

Answer:

Cost of each roast beef sandwich = $7

Cost of each ham sandwich = $8

Step-by-step explanation:

x = cost of each roast beef sandwich

y = cost of each ham sandwich

2x + 5y = 54 (1)

5x + 3y = 59 (2)

Multiply (1) by 5 and (2) by 2

10x + 25y = 270

10x + 6y = 118

Subtract to eliminate x

25y - 6y = 270 - 118

19y = 152

Divide both sides by 19

y = 152 / 19

= 8

y = $8

Substitute y = 8 into (1)

2x + 5y = 54 (1)

2x + 5(8) = 54

2x + 40 = 54

2x = 54 - 40

2x = 14

x = 14 / 2

x = $7

Cost of each roast beef sandwich = $7

Cost of each ham sandwich = $8

Answer:

1/9a

Step-by-step explanation:

i used math.way lm.ao hope it helps

Answer: x= (2/3,0) y=(0,2)

X=(4,0) y=(0,8)

X=(-3,0) y=(0,-3)

Step-by-step explanation:

Hello there!

If we divide 9894 by 34, we will get the following answer:

291

Hope this helps!

\(GraceRosalia\)

Brainliest if it's correct! :)

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Answer:

740

Step-by-step explanation:

The n th term of an arithmetic series is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then

a₁ + 2d = 7 → (1)

a₁ + 6d = 23 → (2)

Subtract (1) from (2) term by term

4d = 16 ( divide both sides by 4 )

d = 4

Substitute d = 4 into (1)

a₁ + 2(4) = 7

a₁ + 8 = 7 ( subtract 8 from both sides )

a₁ = - 1

The sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ] , thus

\(S_{20}\) = \(\frac{20}{2}\) [ (2 × - 1) + (19 × 4) ]

     = 10(- 2 + 76) = 10 × 74 = 740

Answer:

17 feet

Step-by-step explanation:

We have to use the pythagorean theorem, this is actually a bit more complicated than it seems at a first glance.

If Tony is 8 feet to Lexi's right, then we can form a triangle as such

I can't paste it (sorry)

but we can use the formula a^2+b^2=c^2, so 15^2=225, and 8^2=64, and 225+64=289, and \(\sqrt289=17\)

so they're 17 feet apart!

Each child will receive 27 acres of land when they turn 18, based on the given conditions.

To find out how many acres (x) each child will receive when they turn 18, we can set up an equation based on the given information.

Total land owned by the family: 239 acres

Land the parents wish to keep: 50 acres

Remaining land to be divided among the 7 children: 239 - 50 = 189 acres

We can represent the number of acres each child will receive as x. Since the remaining land is to be divided equally among the 7 children, the equation becomes:

x = (Remaining land) / (Number of children)

x = 189 / 7

Simplifying the equation, we find:

x = 27

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Answer:

(a)

• C(x)=88000+5500x

• R(x)=7500x

(b)55 times

Explanation:

Let the number of performances = x

• The cost of producing the musical = $88,000

• The cost per performance = $5900

(a)Thus, the total cost for x performances:

The revenue per performance is $7500, therefore, the equation for revenue is:

(b)To break even, the cost must be equal to revenue.

Next, solve for x.

The musical must be performed 55 times to break even.

The single stage leaching process involves the contact of a slurry of flaked soya beans with pure hexane. The slurry consists of 100 kg of inert solids suspended in 25 kg of a 10 wt% solution of oil in hexane. The goal is to estimate the amounts and composition of the underflow and overflow leaving the stage.

To graphically represent the single stage leaching process, we can use a diagram. The diagram should show the input of the slurry and the pure hexane, as well as the output of the underflow and overflow.

Now, let's estimate the amounts and composition of the underflow and overflow leaving the stage.

First, we need to calculate the amount of hexane in the slurry. Since the slurry consists of 100 kg of inert solids and 25 kg of a 10 wt% solution of oil in hexane, the amount of hexane in the slurry is 25 kg x 0.10 = 2.5 kg.

Next, we need to calculate the amount of hexane in the pure hexane input. The pure hexane input is 100 kg, so the amount of hexane in the input is 100 kg.

Now, let's calculate the total amount of hexane in the system. The total amount of hexane is the sum of the hexane in the slurry and the hexane in the input, which is 2.5 kg + 100 kg = 102.5 kg.

To estimate the amount of underflow, we need to use the given information that the underflow contains 2 kg of solution for every 3 kg of insoluble solids. Since the slurry consists of 100 kg of inert solids, the amount of solution in the underflow is 2 kg x (100 kg / 3 kg) = 66.67 kg.

To estimate the amount of overflow, we can subtract the amount of underflow from the total amount of hexane. So, the amount of overflow is 102.5 kg - 66.67 kg = 35.83 kg.

Now, let's calculate the composition of the underflow and overflow in terms of oil and hexane. Since the slurry is a 10 wt% solution of oil in hexane, the amount of oil in the slurry is 25 kg x 0.10 = 2.5 kg. The amount of oil in the underflow can be calculated using the ratio of solution to insoluble solids. So, the amount of oil in the underflow is 2.5 kg x (66.67 kg / 100 kg) = 1.67 kg.

To calculate the amount of hexane in the underflow, we subtract the amount of oil from the total amount of hexane in the underflow. So, the amount of hexane in the underflow is 66.67 kg - 1.67 kg = 65 kg.

Similarly, we can calculate the composition of the overflow. The amount of oil in the overflow is 2.5 kg - 1.67 kg = 0.83 kg. The amount of hexane in the overflow is 35.83 kg - 0.83 kg = 35 kg.

In summary, the estimated amounts and composition of the underflow leaving the stage are 66.67 kg with 1.67 kg of oil and 65 kg of hexane. The estimated amounts and composition of the overflow leaving the stage are 35.83 kg with 0.83 kg of oil and 35 kg of hexane.

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Answer:

27

Step-by-step explanation: