Let X count the number of suits in a 5-card hand dealt from a standard 52-card deck. 4 a) Complete the following table: value of X 1 2 3 0.00198 b) Compute the expected number of suits in a 5-card hand. probability

Answer:

4/7

Step-by-step explanation:

6-2/2+5=4/7=.57142857142 but usually you can just keep it as a fraction

Answer:

h = 28.5 ft

Step-by-step explanation:

the 2 situations are similar, that is the triangles formed in both cases are similar.

then the ratios of corresponding sides are in proportion

let h be the height of the house , then

\(\frac{4.7}{h}\) = \(\frac{9.4}{57}\) ( cross- multiply )

9.4h = 4.7 × 57 = 267.9 ( divide both sides by 9.4 )

h = 28.5 ft

Answer:

Since the shape is an corresponding angle, you would work out the question like this:

(3x + 22) = (x + 30)

X = 4

Therefore X is equal to 4. No rounding is needed.

I'm NOT a math teacher, please double check my answer!

Cheers! :)

To number the pages from 1 to 150, we need to use the digits 0 to 9.

For the numbers from 1 to 9, we need 1 digit each, for a total of 9 digits.

For the numbers from 10 to 99, we need 2 digits each, for a total of 180 digits.

For the numbers from 100 to 150, we need 3 digits each, for a total of 153 digits.

Therefore, the printer will have to use a total of 9 + 180 + 153 = 342 pieces of type.

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Answer:

8 girsl can sing

8 girls cannot sing

Total number of girls = 16

Step-by-step explanation:

The ratio of girls who csan sing to girls who cant sing is 1:1

Which means the number of girls who can sing and cannot sing are equal .

IF the number of girls who can sing is 8 then the number of girls who cant sing is also 8.

8:8

Dividing both sides by 8 gives

1:1

The total number of girls would be (8+8= )16.

\(\underline{\underline{\large\bf{Solution:-}}}\\\)

\(\leadsto\)Let us assume entry fee for child be x

\(\leadsto\)Let us assume entry fee for adult be y

\(\\\)

\(\longrightarrow\)Since Entry fees for 2 children and 1 adult is $90 an equation for entry fees will be formed as -

\(\begin{gathered}\\\implies\quad \sf 2\times x + 1 \times y = 90 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 2 x + y = 90 \\\end{gathered} \_\_\_\_\_(1) \)

\(\longrightarrow\)Similarly, Entry fees for 3 children and 2 adult is $155 , so an equation for entry fees will be formed as -

\(\begin{gathered}\\\implies\quad \sf 3\times x + 2\times y = 155 \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 3x + 2y = 155 \\\end{gathered} \_\_\_\_\_(2) \)

Multiplying eq (1) by 2 it will be -

\(\begin{gathered}\\\implies\quad \sf 4x + 2y = 180\\\end{gathered}\_\_\_\_\_(3) \)

Subtracting eq(2) from eq(3) -

\(\begin{gathered}\\\implies\quad \sf 4x+2y - (3x+2y) = 180-155\\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 4x + 2y - 3x - 2y = 35\\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 4x - 3x +2y- 2y = 35\\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \bf x = 35\\\end{gathered} \)

Thus , entry fee for a child at the amusement park = $ 35

Answer:

use microsoft maths solver

Answer:

102

Step-by-step explanation:

On quadrilateral ABCD it shows BC = 20 and CD = 30

20+30 = 50

on quadrilateral A'B'C'D'

it says B'A' = 22

and D'A' = 32

22+32 = 52

52+50 = 102

Answer:

55units

Step-by-step explanation:

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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We can see that the problem is bounded, and the feasible region is not empty.

The linear programming problem given:

Max: 2X1 + 3X2

Subject to:

X1 + X2 >= 4

6X1 + 9X2 <= 54

X1, X2 >= 0

To determine the nature of the problem, we need to analyze the constraints and the objective function.

The constraints:

X1 + X2 >= 4

6X1 + 9X2 <= 54

X1, X2 >= 0

The objective function:

Max: 2X1 + 3X2

From the given constraints and objective function, we can see that the problem is bounded, and the feasible region is not empty. Therefore, the problem has at least one feasible solution.

Hence, the correct answer is:a. Has an optimal solution

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We can see that the problem is bounded, and the feasible region is not empty.

The linear programming problem given:

Max: 2X1 + 3X2

Subject to:

X1 + X2 >= 4

6X1 + 9X2 <= 54

X1, X2 >= 0

To determine the nature of the problem, we need to analyze the constraints and the objective function.

The constraints:

X1 + X2 >= 4

6X1 + 9X2 <= 54

X1, X2 >= 0

The objective function:

Max: 2X1 + 3X2

From the given constraints and objective function, we can see that the problem is bounded, and the feasible region is not empty. Therefore, the problem has at least one feasible solution.

Hence, the correct option is : (a). Has an optimal solution

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The radius of circle B is 8/9 units.

In the question, we are asked to find the radius of the circle with a center at B, given that the radius of a circle with a center at A is 1 unit, and circles with a center at B and C are congruent.

The radius of the circle with a center at D is twice that of A, making the radius of the circle with a center at D to be 2.

We assume the radius of circle B to be r units.

Now, we have AD = 1, AB = 1 + r, DE = x (assumed), AE = 1 + x, BE = r, and BD = 2 - r.

Thus, in triangle BDE, using the Pythagoras Theorem, we can write:

BD² = DE² + BE²,

or, (2 - r)² = x² + r²,

or, 4 + r² - 4r = x² + r²,

or, x² = 4 - 4r ... (i),

or, x² = 4(1 - r),

or, x = 2√(1 - r) ... (ii).

In triangle ABE, using the Pythagoras Theorem, we can write that:

AB² = AE² + BE²,

or, (1 + r)² = (1 + x)² + r²,

or, 1 + r² + 2r = 1 + x² + 2x + r²,

or, 2r = x² + 2x.

Substituting the values of x² and x from (i) and (ii), we get:

2r = (4 - 4r) + 2(2√(1 - r)),

or, r = 2 - 2r + 2√(1 - r),

or, 3r - 2 = 2√(1 - r),

or, 9r² + 4 - 12r = 4 - 4r,

or, 9r² - 8r = 0,

or, r(9r - 8) = 0.

Thus, either, r = 0, which is not possible,

or, 9r - 8 = 0, or, r = 8/9.

Thus, the radius of circle B is 8/9 units.

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The provided question is incomplete. For the complete question, refer to the attachment.

Answer:

9:15

girls : boys

Step-by-step explanation:

Answer:

9:15

Or 3:5 when reduced

Step-by-step explanation:

Answer:

y=55x

given y=385

x=gallons of gas = 385/55 = 7 gallons

inverse function

y=55x

change x to y and y to x

x=55y

y=x/55

inverse function is x/55

Step-by-step explanation:

Answer:

y = -53x

Step-by-step explanation:

since 0,0 is a point, there is no b, and -5/3 times 3 is -5

Answer:

.003   .03%

Step-by-step explanation:

The number of cubic yards of each component needed are 3.99 cubic yards of cement, 7.97 cubic yards of sand  and 15.94 cubic yards of gravel

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another

Since a total of 18.6 cu yd of concrete is required and the total amount of these components must be 1½ times the volume of concrete needed. We can say:

total amount of these components = 1½ × 18.6 cu yd = 27.9 cu yd

Also, since the ratio of cement to sand to gravel for this application is 1:2:4. We have:

Total share = 1 + 2 + 4 = 7

cement = 1/7  × 27.9 =  3.99 cubic yards

sand  = 2/7  × 27.9 =  7.97 cubic yards

gravel = 4/7  × 27.9 =  15.94 cubic yards

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Answer:

Step-by-step explanation:

The line goes aross horizontially (left to right), it hits the crosses the y axis at 0,2.

X would be any number, y would be only 2.

To find the local maximum, local minimum, and saddle points of the function f(x, y) = 3 sin(x) sin(y), we need to compute its partial derivatives with respect to x and y, and then find the critical points by setting the derivatives equal to zero.

First, let's find the partial derivatives:

∂f/∂x = 3 cos(x) sin(y)

∂f/∂y = 3 sin(x) cos(y)

Next, we set these derivatives equal to zero and solve for x and y:

For ∂f/∂x = 3 cos(x) sin(y) = 0:

cos(x) = 0   or   sin(y) = 0

If cos(x) = 0, then x = π/2 + nπ, where n is an integer.

If sin(y) = 0, then y = mπ, where m is an integer.

For ∂f/∂y = 3 sin(x) cos(y) = 0:

sin(x) = 0   or   cos(y) = 0

If sin(x) = 0, then x = nπ, where n is an integer.

If cos(y) = 0, then y = π/2 + mπ, where m is an integer.

Now, we can evaluate f(x, y) at the critical points (x, y) we found:

1) (x, y) = (nπ, mπ)

  f(x, y) = 3 sin(nπ) sin(mπ) = 0

  These are saddle points since the value of f is zero at these points.

2) (x, y) = (π/2 + nπ, mπ)

  f(x, y) = 3 sin(π/2 + nπ) sin(mπ) = 3\((-1)^n\) sin(mπ) = 0

  These are also saddle points since the value of f is zero at these points.

Therefore, the function f(x, y) = 3 sin(x) sin(y) has saddle points at all the critical points (x, y) = (nπ, mπ) and (x, y) = (π/2 + nπ, mπ), where n and m are integers. There are no local maximum or local minimum points for this function.

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Under some circumstances, notably when the sample size is high enough and the population from which the samples are drawn has a normal distribution, the distribution of sample means will be roughly normal. The Central Limit Theorem refers to this.

Regardless of the population distribution's form and provided that the population has a finite standard deviation, the Central Limit Theorem states that as sample size grows, the distribution of sample means tends to resemble a normal distribution.

Additionally, even if the population distribution is not perfectly normal, if the sample size is high enough (often thought to be 30 or more), the combined effects of the Centrbal Limit Theorem and the Law cause the sample means to generally follow a normal distribution.

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Answer:

There are many possible arrays that could be used to model a rectangular quilt with 24 paper squares. Here are a few examples:

A 3x8 array could be created by gluing the paper squares into a rectangle that is 3 squares wide and 8 squares long. This could be represented by the equation 3x8 = 24.

A 4x6 array could be created by gluing the paper squares into a rectangle that is 4 squares wide and 6 squares long. This could be represented by the equation 4x6 = 24.

A 6x4 array could be created by gluing the paper squares into a rectangle that is 6 squares wide and 4 squares long. This could be represented by the equation 6x4 = 24.

A 8x3 array could be created by gluing the paper squares into a rectangle that is 8 squares wide and 3 squares long. This could be represented by the equation 8x3 = 24.

These are just a few examples, but there are many other possible arrays that could be created with 24 paper squares. Some other examples might include a 2x12 array, a 6x4 array, or even a 1x24 array. The key is to find combinations of width and length that will multiply together to equal 24.

Step-by-step explanation:

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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Answer:

B. 0

Step-by-step explanation:

The < sign means whatever is on the right side of the symbol should be greater than whatever is on the left side.

To solve this we need to understand that 0 is greater than -10. Then we need to make sure that 0 is greater than -5 and it is greater than -5.

Therefore the answer is 0

Hope this helps! If you have any more questions or need further clarification on anything please comment down below or message me! Good luck!

Answer:

the most logical answer is

n^2-1

20th term is then 399

Step-by-step explanation:

The rule behind the sequence could be anything, but it is very likely that we're supposed to notice that the terms are all squares minus 1

0 = 1*1 - 1

3 = 2*2 - 1

8 = 3*3 - 1

15 = 4*4 - 1

24 = 5*5 - 1

So we expect that the explicit formula is n^2-1 and the 20th term is 399

Answer:

5/24 ft²

Step-by-step explanation:

A = bh

A = 5/8 * 1/3

A = 5/24 ft²

The probability that any given car will have a brake failure if it is make a is 0.0065%

The complete question is added as an attachment

From the table in the question, we have:

P(Brake failure|car a) = 0.0065%

The above represents the required conditional probability

Hence, the probability that any given car will have a brake failure if it is make a is 0.0065%

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Answer: The probability that any given car will have a brake failure if it is making A, is 0.0065%.

Step-by-step explanation:

I got it right on Edmentum!

Answer:

m=25

Step-by-step explanation:

A. m=25

B.15