Which angle are adjacent
to each other ?

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = \(\frac{n!}{(n-x)!x!} p^xq^{(n-x)}\)

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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Answer:

m= -7

Step-by-step explanation:

The values of p and q are 3 and 2.

Given:

The equation of the graph is y = pq^x where p and q are positive constants.

From the graph:

curve linear course points are:

(0,3) and (1,6)

substitute points in y = pq^x

3 = pq^0

3 = p*1

p = 3

y = pq^x

6 = pq^1

6 = p*q

6 = 3*q

divide by 3 on both sides

6/3 = 1

q = 2

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Answer:

3. Acute and scalene

5. Acute isosceles

Explanation:

Those are the two answers that had mistakes

Answer:

140x+36

Step-by-step explanation:

hope this helps :)

Answer:

4^3 x 5^2

Step-by-step explanation:

Answer:

27 is 30% of what number?

D. 90

Step-by-step explanation:

You're welcome.

In this case, since the eigenvalue λ2 = 4 is positive, the solution decays exponentially towards the origin along the line defined by the eigenvector [1; 1].

To solve the system dx/dt = [6, -2; 20, -6]x with x(0) = [-2; 2], we can find the eigenvalues and eigenvectors of the coefficient matrix [6, -2; 20, -6]. Let's denote the coefficient matrix as A.

The characteristic equation of A is given by det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix. So we have:

|6 - λ, -2|

|20, -6 - λ| = 0

Expanding the determinant, we get:

(6 - λ)(-6 - λ) - (-2)(20) = 0

(λ - 2)(λ - 4) = 0

Solving for λ, we find two eigenvalues: λ1 = 2 and λ2 = 4.

To find the corresponding eigenvectors, we substitute each eigenvalue back into the equation (A - λI)v = 0 and solve for v. Let's find the eigenvectors for each eigenvalue.

For λ1 = 2:

(A - 2I)v1 = 0

|4, -2|v1 = 0

|20, -8|v1 = 0

Simplifying, we get the equation 4v1 - 2v2 = 0, which gives us v1 = v2.

For λ2 = 4:

(A - 4I)v2 = 0

|2, -2|v2 = 0

|20, -10|v2 = 0

Simplifying, we get the equation 2v1 - 2v2 = 0, which gives us v1 = v2.

So, the eigenvectors for both eigenvalues are v = [1; 1].

Now we can express the general solution of the system as:

x(t) = c1 * e^(λ1 * t) * v1 + c2 * e^(λ2 * t) * v2

Substituting the values, we have:

x(t) = c1 * e^(2t) * [1; 1] + c2 * e^(4t) * [1; 1]

Since x(0) = [-2; 2], we can solve for the constants c1 and c2. Plugging t = 0 into the equation, we get:

[-2; 2] = c1 * e^0 * [1; 1] + c2 * e^0 * [1; 1]

[-2; 2] = c1 * [1; 1] + c2 * [1; 1]

[-2; 2] = [c1 + c2; c1 + c2]

From the first component of the vector equation, we have -2 = c1 + c2.

From the second component of the vector equation, we have 2 = c1 + c2.

Solving these equations, we find c1 = 0 and c2 = -2.

Therefore, the particular solution to the system dx/dt = [6, -2; 20, -6]x with x(0) = [-2; 2] is:

x(t) = -2 * e^(4t) * [1; 1]

The trajectory of the solution represents a line in the direction of the eigenvector [1; 1], with exponential growth/decay based on the eigenvalues.

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Answer:

4

Step-by-step explanation:

The degree is equal to the highest power of the polynomial.

Answer:

3x + 4

or

3x + (4)

Step-by-step explanation:

You can shape that problem into many more but these are just 2 examples.

hope this helped DON'T forget to mark this as the brainliest answer and give it a 5 star and a heart for support and for people asking this same question in the future. have a nice day!!

The point guard has to decide whether to shoot a three-point attempt or pass the ball to another player for a two-point shot. The point guard has a 30% success rate for three-point shots, while the teammate has a 48% success rate for two-point shots.

To determine the best option, we can compare the expected values for each decision. Here's a step-by-step explanation:

1. Calculate the expected value of the point guard's three-point attempt:
  - Success rate: 30% (0.3)
  - Point value: 3
  - Expected value: 0.3 (3 )= 0.9

2. Calculate the expected value of the teammate's two-point shot:
  - Success rate: 48% (0.48)
  - Point value: 2
  - Expected value: 0.48 (2) = 0.96

3. Compare the expected values:
  - Three-point attempt: 0.9
  - Two-point shot: 0.96

Since the expected value of the teammate's two-point shot (0.96) is higher than the point guard's three-point attempt (0.9), it would be a better decision for the point guard to pass the ball to the teammate for a two-point shot.

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we have a single logarithm which can be expressed as ln (x+²/x+2)ⁿ/(X-2).

To write the expression as a single logarithm, express the powers as factors and simplify. We can write the expression as a single logarithm using the following steps:

Recall the following properties of logarithms:

. loga(xy) = loga(x) + loga(y)

2. loga(x/y) = loga(x) - loga(y)

3. loga(xn) = nloga(x)

4. loga(1) = 0loga(x) + loga(y) - loga(z)= loga(xy) - loga(z)= loga(x/y)

Firstly, we will use property (1) and (2) to obtain a single logarithm.

logX(X-2) + logX(x²+²) - logX(x²-4)logX[(X-2)(x²+²)/(x²-4)]

Next, we will simplify the expression using the following identities:

(x²+²) = (x+²)(x-²)(x²-4) = (x+2)(x-2)

logX[(X-2)(x²+²)/(x²-4)]logX[(X-2)(x+²)(x-²)/(x+2)(x-2)]

Cancel out the common factors:

logX[(X-2)(x+²)]/ (x+2)

Finally, we can rewrite the expression using property (3):

nlogX(X-2) + logX(x+²) - logX(x+2)n

logX(X-2) + logX(x+²/x+2)

Taking the reciprocal on both sides: 1/(nlogX(X-2) + logX(x+²/x+2))

= 1/[logX(X-2)n(x+²/x+2)]

Rewriting in terms of logarithm using property (4):

logX[X-2)ⁿ√((x+²)/(x+2))

= logX (x+²/x+2)ⁿ/(X-2)

Therefore, we have a single logarithm which can be expressed as ln (x+²/x+2)ⁿ/(X-2).

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Answer:

0.15

Step-by-step explanation:

15% = 0.15

__________________________________

Solution,

15%

=15/100

=0.15

So, 0.15 decimal is equivalent to 15%

Hope this helps

Good luck on your assignment

_______________________________

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

Hunter's investment will be $11290 in ten years.

According to the question,

We have the following information:

Hunter plans to invest $1,000.00 into an investment account every year. If he earns an average of 2.9%.

We know that following formula is used to find the compound amount:

P\((1+r/100)^{t}\) where t is the time in years

In this case, time is 1 year.

1000(1+2.9/100)

1000*112.9/100

$1129

Now, his investment in ten years can be easily found by following the given steps:

10*1129

$11290

(Note that when $1000 is invested into the same account every year then the answer will be different because principal amount for each year will be 1000 more than the compound amount of last year.)

Hence, Hunter's investment will be $11290 in ten years.

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Answer:

Step-by-step explanation:

Due to the '+1', the graoph of x^2 is shifted 1 unit to the left.  The '+9' results in the entire graph being shifted downward 9 units.

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 \(\div\) 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 \(\times\) 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 \(\div\) 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 \(\div\) 23 = 7

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Answer:

The area is 45 inches

Step-by-step explanation:

L×W=A

Answer:

   x = 8

Step-by-step explanation:

The halves of a bisected segment are congruent, so we have ...

  YZ = YX

  3x -5 = 2x +3

  x = 8 . . . . . . . . add 5-2x

__

Additional comment

The right triangles are congruent, so ...

  WZ = WX

  2y +7 = 5y -8

  15 = 3y

  5 = y

Answer:

b

Step-by-step explanation:

trust me

Answer:

A

Step-by-step explanation:

Answer:

y=50x

Step-by-step explanation:

The dots rise up by 50 and go right by one. rise/run=slope

There is no y-intercept because the line intersects at the origin, (0,0)

So, the answer is y=50x.

Answer: 60 cm three squared

You can observe in the picture attached that the box is a rectangular prism.

The volume of a rectangular prism can be found with this formula:

Where "l" is the length, "w" is the width and "h" is the height.

You know that the lenght of each side of those cubes is 1 centimeter. Therefore, you can multiply the number of cubes on each side of the box by 1 centimeter in order to find the lenght, the width and the height of the box:

Now you can substitute the lenght, the width and the height of the box into the formula shown at the beginning of the explanation:

Finally, evaluating, you get that the volume of the box is:

223 units

Step-by-step explanation:

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Answer:

6.43 × 10^-4 or 0.000643

Step-by-step explanation:

0.00067 - 2.3 × 10^-5 = 6.7 × 10^-4 - 2.5 × 10^5

6.7 × 10^-4 = 67 × 10^-5

67 × 10^-5 - 2.3 × 10^-5 = 64.3 × 10^-5 = 6.43 × 10^-4

Answer: you're right, it is D.

Step-by-step explanation:

No (for recording the genders of 150 people in a statistics class), Yes (for asking 1000 adults about their favorite color).

Recording the genders of 150 people in a statistics class does not result in a binomial distribution. A binomial distribution requires a fixed number of independent trials, each with the same probability of success. In this case, the number of people in the statistics class is fixed, but the probability of being male or female may vary. Additionally, the genders of the individuals in the class may not be independent, as there could be correlations or biases present.

On the other hand, asking 1000 adults about their favorite color can result in a binomial distribution if we assume that each adult's response is independent and has the same probability of choosing a specific favorite color.

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The means to study and analyze economic phenomena, formulate economic models, make predictions, and derive policy recommendations.

1. Importance of studying mathematics in economics:

a. Modeling and Analysis: Mathematics provides the tools and techniques for constructing models that represent economic phenomena.

These models help economists analyze and understand complex economic systems, predict outcomes, and make informed decisions.

b. Quantitative Analysis: Economics involves analyzing numerical data and making quantitative assessments. Mathematics equips economists with the necessary skills to handle and manipulate data, perform statistical analysis, and draw meaningful conclusions from empirical evidence.

c. Logical Reasoning and Problem Solving: Mathematics trains students to think critically, logically, and abstractly. These skills are essential in economics, where students need to formulate and solve economic problems, derive solutions, and interpret results.

2. Mathematical tools used in economics:

a. Calculus: Calculus plays a crucial role in economics by providing techniques for analyzing and optimizing economic functions and models. Concepts such as derivatives and integrals are used to study economic relationships, marginal analysis, and optimization problems.

b. Linear Algebra: Linear algebra is employed in various economic applications, such as solving systems of linear equations, representing and manipulating matrices, and analyzing input-output models.

c. Statistics and Probability: Statistics is used to analyze economic data, estimate parameters, test hypotheses, and make inferences. Probability theory is essential in modeling uncertainty and risk in economic decision-making.

d. Optimization Theory: Optimization theory, including linear programming and nonlinear optimization, is used to find optimal solutions in various economic problems, such as resource allocation, production planning, and utility maximization.

e. Game Theory: Game theory is a mathematical framework used to analyze strategic interactions and decision-making among multiple agents. It is widely applied in fields such as industrial organization, microeconomics, and international trade.

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Answer:

See the attached histogram.

Step-by-step explanation:

Using the Cramer's Rule, the solution of the given system of equation is (-17/11, 48/11)

The given system of equations are

10x+4y=2

-6x+2y=18

Solving the equations by using Cramer's rule.

We know that, the solution of a system of linear equations in two unknowns

a(1)x+b(1)y = c(1)

a(2)x+b(2)y = c(2)

is given by ∆x=∆1, and ∆y=∆2.

where,

\(\Delta=\text{det}\left [ \begin{matrix} a(1)&b(1) \\ a(2) & b(2)\end{matrix} \right ], \Delta(1)=\text{det}\left [ \begin{matrix} c(1)&b(1) \\ c(2) & b(2)\end{matrix} \right ]\text{ and }\Delta(2)=\text{det}\left [ \begin{matrix} a(1)&c(1) \\ a(2) & c(2)\end{matrix} \right ]\)

Since the given equations are;

10x+4y=2

-6x+2y=18

Now,

\(\Delta=\text{det}\left [ \begin{matrix} 10&4 \\ -6 & 2\end{matrix} \right ]\)

∆ = [(10×2)-(-6×4)]

∆ = 20+24

∆ = 44

\(\Delta(1)=\text{det}\left [ \begin{matrix} 2&4 \\ 18 & 2\end{matrix} \right ]\)

∆(1) = [(2×2)-(18×4)]

∆(1) = 4-72

∆(1) = -68

\(\Delta(2)=\text{det}\left [ \begin{matrix} 10&2 \\ -6 & 18\end{matrix} \right ]\)

∆(2) = [(10×18)-(-6×2)]

∆(2) = 180+12

∆(2) = 192

By Cramer's Rule,

∆x = ∆(1)

44 × x = -68

x = -68/44

x = -17/11

Now,

∆y = ∆(2)

44 × y = 192

y = 192/44

y = 48/11

Hence, the solution of the given system of equation is (-17/11, 48/11).

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The right question is:

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.

10x+4y=2

-6x+2y=18