what 4*4 and how to do it

Answer:

22-5n

Step-by-step explanation:

Answer:

m = 2

Explanation:

A recursive formula for the explicit formula include the following: B. A(n) = A(n - 1) - 6; A(1) = 8.

In Mathematics, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the first term of this arithmetic sequence as follows;

A(n) = 8 + (n − 1)(-6)

A(1) = 8 + (1 − 1)(-6)

A(1) = 8 + (0)(-6)

A(1) = 8

Therefore, the recursive formula based on this explicit formula A(n) = 8 + (n − 1)(-6) is given by;

A(n) = 8 + (n − 1)(-6)

A(n) = A(n − 1) - 6

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The solution for the given problem is (a) P(X ≥ 20,000) = 0.4493, P(X ≤ 30,000) = 0.7769, P(20,000 ≤ X ≤ 30,000) = 0.3276. (b) P(X > 75,000) = 0.0821, P(X > 100,000) = 0.0183.

Solution: a) To find the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000). Now, Mean time until failure is 25,000 hours which is given and is represented by µ. Hence, µ = 25,000 hrs. The parameter used for the Exponential distribution is λ.λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004. Therefore, the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000) =  e -λt = e -0.00004 × 20,000 ≈ 0.4493The probability that a randomly selected fan will last at least 20,000 hours is 0.4493.

To find the probability that a randomly selected fan will last at most 30,000 hours. P(X ≤ 30,000) = 1 - e -λt = 1 - e -0.00004 × 30,000 ≈ 0.7769. The probability that a randomly selected fan will last at most 30,000 hours is 0.7769.

To find the probability that a randomly selected fan will last between 20,000 and 30,000 hours. P(20,000 ≤ X ≤ 30,000) = P(X ≤ 30,000) - P(X ≤ 20,000)P(20,000 ≤ X ≤ 30,000) = (1 - e -λt) - (1 - e -λt)P(20,000 ≤ X ≤ 30,000) = e -0.00004 × 20,000 - e -0.00004 × 30,000 ≈ 0.3276. The probability that a randomly selected fan will last between 20,000 and 30,000 hours is 0.3276.

b) To find the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

z = (X - µ) / σZ = (X - µ) / σ = (X - 25,000) / (25,000)λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004

The formula for z is z = (X - µ) / σ => X = z σ + µ

The standard deviation of the Exponential distribution is σ = 1 / λσ = 1 / 0.00004 = 25,000 hrs

Z = (X - µ) / σ = (X - 25,000) / (25,000)Z > 2z > 2 => (X - 25,000) / (25,000) > 2 => X > 75,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

P(X > 75,000) = e -λt = e -0.00004 × 75,000 ≈ 0.0821

The probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations is 0.0821

To find the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations.

Z > 3z > 3 => (X - 25,000) / (25,000) > 3 => X > 100,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations P(X > 100,000) = e -λt = e -0.00004 × 100,000 ≈ 0.0183

The probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations is 0.0183.

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Answer:

3000

300

3000/300 = 10

Hannah has 10 times greater value of 3 than Greg.

Take 3000 from Hannah and DIVIDE the 300 from Greg. You will get 10 and that is the multiplier or "greater times" amount.

Answer:

  C.  f(x) = 2x⁴ +6x³ +22x² +54x +36

Step-by-step explanation:

You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.

The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.

Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.

The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.

  f(x) = 2x⁴ +6x³ +22x² +54x +36

Answer:

15 hours

Step-by-step explanation:

since 8 reports took him 3 hrs

8+8+8+8+8=60

3+3+3+3+3=15

The magnitude of the j component is 4, and it is positive. It shows that the vector lies in the positive direction of the j-axis. Therefore, this is how we can write the vector in terms of i and j components.

The given vector can be written in terms of ij components as follows: Given vector = -3i + 4j

Now, let's understand how to write a vector in terms of i and j components: In vector form, a vector is represented as -a i + b j, where a and b are the magnitudes of the components of the vector in the i and j direction respectively.

The direction of the vector is indicated by the sign of the magnitudes a and b. If a is negative, it indicates that the vector is in the negative i direction, and if b is negative, it indicates that the vector is in the negative j direction.

Therefore, the vector is -3 i + 4 j. The magnitude of the i component is 3 and it is negative. It shows that the vector lies in the negative direction of the i-axis.

Similarly, the magnitude of the j component is 4, and it is positive. It shows that the vector lies in the positive direction of the j-axis. Therefore, this is how we can write the vector in terms of i and j components.

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Answer:

t ≥ 192

Step-by-step explanation:

To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)

Answer:

Step-by-step explanation:

The IQR is 13.5

min=5

Q1=8

Q2(median)=10

Q3=17

max=19

For a sample of 903 voters from Tampa.

a) The percentage of Tampa, FL voters who self-identify as conservative is equals to 41%.

b) The percent of these Tampa, FL voters who identify themselves as conservatives and are in favor of the citizenship option is equals to 6.31%.

Random or probabilistic sampling is a process in which every person in the population has an equal chance of being included in the sample. The sample is the part of the population that represents the characteristics of the population within a certain margin of error. We have a sample of 903, voters from Tampa, Florida. The table above represents valuable information. From Table we have

a) Number of voters who define themselves as conservative = 372

Total number of registered voters = 903

Percentage of votes who define themselves as conservative = \( \frac{372}{903}\)

= 0.41196013289 = 41%

b)Number of voters who identify themselves as conservatives and are in favor of the citizenship option = 57

The Percent of voters who identify themselves as conservatives and are in favor of the citizenship =\(\frac{57}{903} \)

= 0.0631229235 = 6.31%.

Hence, required value is 6.31%.

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Complete question:

903 randomly sampled registered voters from Tampa, FL were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below.

a) What percent of these Tampa, FL voters identify themselves as conservatives?

b) What percent of these Tampa, FL voters identify themselves as conservatives and are in favor of the citizenship option?

Answer:

139

Step-by-step explanation:

7x2+5^3 = 139

A ratio of 5:7 means out of 12 books, 5 are in one category and 7 are in another. (The “category” isn’t specified in this problem.)

So here we’re STARTING with 36 books; we want to find a ratio that is equal to 5:7 and adds up to 36. Well 36 = 3(12), and so if we multiply each number in the ratio by 3 as well, we might get what we want. Doing that gives us 15:21, which adds up to 36 and is equal to 5:7. Boom, that’s the answer.

P.S. Here’s a question you can think about: why do ratios stay the same when you multiply each number by the same amount? (For example, why is 3:1 the same as 6:2?)

9/2 Sq. units is a Right answer...

Answer:

Step-by-step explanation:

Given ΔABC with vertices:

We observe that

AB is vertical segment with length:

BC is horizontal segment with length:

The area:

The first five terms of the arithmetic sequence with a₁ = 6 and d = 4 are:

a₁ = 6

a₂ = 6 + 4 = 10

a₃ = 10 + 4 = 14

a₄ = 14 + 4 = 18

a₅ = 18 + 4 = 22

The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. As a result, enter the given values for a and d into the formula to determine the nth term.

An arithmetic sequence is created by adding a group of integers together to create a sequence. Because each number is the sum of the two numbers before it, the sequence 2, 4, 6, 8, and 10 is an example of an arithmetic sequence.

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The area of Kimberly's wall hanging will be 32 square units.

Given that:

Points, A(1, 5), B(1, 9), C(7, 9), D(7, 5), E(5, 3), and F(3, 3)

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The polygon is shown in the graph below.

The area of the polygon is given as,

A = Area of rectangle + Area of trapezium

A = 4 x 6 + 1/2 x (6 + 2) x 2

A = 24 + 8

A = 32 square units

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RME is a teaching approach that emphasizes the development of students' mathematical understanding by working from contexts that make sense to them.

RME is a teaching approach that was developed in the Netherlands in the 1970s. It is based on the idea that students learn mathematics best when they are actively engaged in the learning process and when they are working with problems that are meaningful to them.

In RME, students are presented with realistic problems that they need to solve. These problems are typically drawn from everyday life or from other subjects that students are studying. The problems are designed to be challenging, but they are also designed to be accessible to students at their current level of understanding.

To solve the problems, students need to use their mathematical knowledge and skills. They also need to think creatively and to make sense of the information that they are given. As students work on the problems, they develop their mathematical understanding and they learn how to apply their knowledge in new and different contexts.

RME is a student-centered approach to teaching mathematics. It emphasizes the importance of active learning and of providing students with opportunities to construct their own mathematical knowledge.

RME also emphasizes the importance of making connections between mathematics and other subjects.

Some of the key features of RME include:

RME has been shown to be an effective way to teach mathematics. It has been shown to improve students' mathematical understanding and their ability to solve problems. RME has also been shown to be more motivating for students than traditional methods of teaching mathematics.

Sources:

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The second image is larger so the scale needs to be larger than 1.

to find the scale divide the larger k own side by the smaller similar side:

1.5/0.6 = 2.5

The scale factor is 2.5

Answer:

3(a - b)(a + b)

Step-by-step explanation:

Factorize: (2a - b)² - (a - 2b)²​

(2a - b)² - (a - 2b)²​ = [(2a - b) + (a - 2b)] × [(2a - b) - (a - 2b)]

1. Distribute and Simplify:

Distribute the (+) sign on the first bracket and simplify: [(2a - b) + (a - 2b)] → 2a - b + a - 2b → (3a - 3b)

Distribute the (-) sign on the first bracket and simplify: [(2a - b) - (a - 2b)] → 2a - b – a + 2b → (a + b)

We now have:

(3a - 3b)(a + b)

2. Factor out the Greatest Common Factor (3) from 3a - 3b:

(3a - 3b) → 3(a - b)

3. Add "(a + b)" back into your factored expression:

3(a - b)(a + b)

Hope this helps!

Answer:

3[a + b][a - b]

Step-by-step explanation:

Let us recall a useful formula. This formula can factorize any subtraction between perfect squares. The formula is known as a² - b² = (a - b)(a + b).

Let's apply the formula in the given expression as we can see that two perfect squares are being subtracted from each other. Then, we get:

\(\implies (2a - b)^{2} - (a - 2b)^{2}\)

\(\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]\)

Since the expression(s) inside the parentheses ( ) cannot be simplified further, we can open the parentheses ( ). Then, we get:

\(\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]\)

\(\implies [2a - b - a + 2b][2a - b + a - 2b]\)

Now, we can combine like terms and simplify:

\(\implies [2a - b - a + 2b][2a - b + a - 2b]\)

\(\implies [a + b][3a - 3b]\)

Three is common in 3a - 3b. Thus, we can factor 3 out of the expression:

\(\implies [a + b][3a - 3b]\)

\(\implies [a + b] \times [3a - 3b]\)

\(\implies [a + b] \times 3[a - b]\)

\(\implies \boxed{3[a + b][a - b]}\)

Therefore, 3[a + b][a - b] is the factorized expression of (2a - b)² - (a - 2b)²​.

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Answer:

B. 3x+1

Step-by-step explanation:

(3x+3)+(2x+1)+(4x+2)=9x+6

(12x+7)-(9x+6)=3x+1

Answer:

18.84

Step-by-step explanation:

:)

The rotational kinetic energy of the flywheel is  572,819 J.

The flywheel you described has a radius of 1.58 m and a mass of 91.6 kg. It is spinning counterclockwise at 477 rpm. This means it has a certain amount of rotational kinetic energy, which is proportional to both its mass and its speed of rotation. The formula for rotational kinetic energy is 1/2*I*w^2, where I is the moment of inertia (a measure of how spread out the mass is in the object) and w is the angular velocity (the speed of rotation in radians per second).

To find the moment of inertia of the disk, we can use the formula I = 1/2*m*r^2, where m is the mass and r is the radius. Plugging in the values given, we get I = 1/2*91.6 kg*(1.58 m)^2 = 228.6 kg*m^2.

To convert the rotational speed from rpm to radians per second, we need to multiply by 2*pi/60. So, w = 477 rpm * 2*pi/60 = 50.04 rad/s.

Using these values, we can calculate the rotational kinetic energy of the flywheel as 1/2*(228.6 kg*m^2)*(50.04 rad/s)^2 = 572,819 J.

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Given:

Required:

We need to find the point-slope equation of the line that passes through the given points.

Explanation:

Consider the point-slope form of the equation.

Consider the slope formula.

Use the first point (-10,-20) in the point-slope equation.

Final answer:

Conducting a greater number of tosses will provide a better estimate of the true probability based on observed outcomes.

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To obtain an experimental probability closer to the theoretical probability, it is recommended to increase the number of trials or repetitions. In this case, the pair of coins was tossed 20 times, resulting in two heads coming up only 2 times. Since the experimental probability is determined by the ratio of favorable outcomes to the total number of trials, increasing the number of trials will help provide a more accurate estimation.

If you want to achieve a closer approximation to the theoretical probability of 0.25, you can increase the number of tosses. For example, you could try tossing the pair of coins 100 times or even 1000 times. By doing so, you would have a larger sample size, and the experimental probability would likely converge towards the theoretical probability of 0.25.

Remember that experimental probability tends to approach theoretical probability as the number of trials increases. Therefore, conducting a greater number of tosses will provide a better estimate of the true probability based on observed outcomes.

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The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.

The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx

a. Write the formula for P(x < x_0):

Using integration, we can solve this formula as follows:

F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]

= [-4e^(-x_0/3) + 4]/3

b. Find P(x < 2):

To find P(x < 2), we simply substitute x_0 = 2 in the above formula:

F(2) = [-4e^(-2/3) + 4]/3

≈ 0.4866

Therefore, the probability that x is less than 2 is approximately 0.4866.

c. Find P(x > 3):

To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:

P(x > 3) = 1 - P(x < 3) = 1 - F(3)

= 1 - [-4e^(-1) + 4]/3

≈ 0.3528

Therefore, the probability that x is greater than 3 is approximately 0.3528.

d. Find P(x < 5):

To find P(x < 5), we simply substitute x_0 = 5 in the above formula:

F(5) = [-4e^(-5/3) + 4]/3

≈ 0.6321

Therefore, the probability that x is less than 5 is approximately 0.6321.

e. Find P(2 < x < 5):

To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:

P(2 < x < 5) = P(x < 5) - P(x < 2)

= F(5) - F(2)

= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3

≈ 0.1455

Therefore, the probability that x is between 2 and 5 is approximately 0.1455.

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Step-by-step explanation:

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer: 1.  x = 2

2. x = -2

Step-by-step explanation:

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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Answer:

true

true

true

true

true