What is the width of heng’s area model??

La forma factorizada de la ecuación cuadrática 2 · a² - 2 es equivalente 2 · (a + 1) · (a - 1).

En esta pregunta tenemos una ecuación cuadrática de la forma a² - b², cuya forma factorizada es la siguiente:

a² - b² = (a + b) · (a - b)

Si sabemos que a = √2 · a y b = 2, entonces la forma factorizada de binomio es:

2 · a² - 2 = (√2 · a + √2) · (√2 · a - √2)

Esta expresión puede simplificarse mediante propiedades asociativa y distributiva:

(√2 · a + √2) · (√2 · a - √2)

2 · (a + 1) · (a - 1)

La ecuación cuadrática es equivalente 2 · (a + 1) · (a - 1).

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Given:

The faces on a number cube are labeled 1,2,2,3,4, and 5.

The number cube is rolled 114 times.

To find:

How many times would you expect the number 2 to appear?

Solution:

We have,

Total outcomes = 1,2,2,3,4, and 5.

Number of total outcomes = 6

Favorable outcomes = 2 and 2

Number of favorable outcomes = 2

The probability of getting 2 is:

\(P(2)=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}\)

\(P(2)=\dfrac{2}{6}\)

\(P(2)=\dfrac{1}{3}\)

Now, the expected number of times when 2 to appear is:

\(E(x)=114\times P(2)\)

\(E(x)=114\times \dfrac{1}{3}\)

\(E(x)=38\)

Therefore, the expected number of times is 38.

Answer:

20

Step-by-step explanation:

The probability that 5 hearts are chosen when 7 cards are drawn from a well-shuffled deck of 52 playing cards is option (d) 0.00000962.

Step 1: Determine the total number of ways to choose 7 cards from a deck of 52 playing cards, which can be calculated using the combination formula: C(52, 7) = 52! / (7! * (52 - 7)!), where "!" denotes the factorial.

Step 2: Determine the number of ways to choose 5 hearts from the deck. There are 13 hearts in a standard deck, so we can calculate the number of ways to choose 5 hearts from 13: C(13, 5) = 13! / (5! * (13 - 5)!).

Step 3: Calculate the probability by dividing the number of favorable outcomes (choosing 5 hearts) by the total number of possible outcomes (choosing 7 cards from the deck): P(5 hearts) = C(13, 5) / C(52, 7).

Step 4: Evaluate the probability numerically using a calculator or math software, and the result is approximately 0.00000962.

Therefore, the correct answer is option (d) 0.00000962.

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To find the largest number of passengers in the tram, we need to calculate the maximum number of passengers who can go without a ticket.

Given that 12% of passengers go without a ticket, we can set up the following equation:

12% of x = 60

To solve for x, we can divide both sides of the equation by 0.12:

x = 60 / 0.12

x = 500

Therefore, the largest number of passengers in the tram, if it is not greater than 60, would be 500.

To find the largest number of passengers in the tram, we use the percentage given and set it equal to the number of passengers. By solving for x, we determine that the largest number of passengers in the tram is 500.

The largest number of passengers in the tram, if it is not greater than 60, is 500.

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The true statements are:

1) The relationship is proportional

2) y = -3x is equation of the line.

3) The slope is negative.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

A graph of the line is given.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

And line passes through the points (4, -12) and (6, -18).

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = -3

The slope is negative.

Then the equation of the line is,

y + 12 = -3(x -4)

y + 12 = -3x + 12

y = -3x

This equation shows the proportional relationship.

Therefore, all the required values are given above.

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The correct explanation is (4). The spinner is likely fair, since in the output the player wins once or twice in the majority of the simulations.

The spinner is considered fair if the probability of winning each spin is 0.1, which means that the player should win about 1 out of every 10 spins. The output of the simulation shows that in the majority of the simulations, the player won once or twice, which is consistent with the expected probability of winning.

The fact that Miles lost all 10 times when he spun the spinner is just a matter of chance. It is possible to lose 10 times in a row even if the spinner is fair. In fact, the probability of losing 10 times in a row is about 0.1%, which is not very likely, but it is still possible.

Therefore, there is no evidence to suggest that the spinner is unfair. It is more likely that Miles simply lost due to chance.

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Based on the information given in the question, the completion time of runner B is lower than that of Runner A ; Hence, runner B completed the race faster.

Given the running time of two runners :

The runner with the lesser running time will complete the marathon faster as this means he has a higher speed.

Comparing the running times of both runners :

Therefore, Runner B completed the race faster than runner A.

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Answer: C

Step-by-step explanation:

Answer:

the answer is 8 pallent

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

she refuses to pay because the owners of the place shes living is supposed to fix damage and they have not done so she refuses to pay the rent.

Answer: Line 1: (2, 3) , (4, 12)

m = (12 - 3)/(4 - 2) = 9/2  This is the slope of the line

y = (9/2)x + b

3 = (9/2)(2) + b

3 = 9 + b

b = -6

y = (9/2)x  - 6

Line 2: (5, 10) , (14,8)

m = (8 - 10)/(14 - 5) = -2/9

this slope is the opposite sign, and inverse of the first equation's slope.  Therefore, the line is perpendicular.

y = mx + b

8 = (-2/9)(14) + b

8 = -28/9 + b

11.11 = b

y = (-2/9)x + 11.11

Step-by-step explanation: Hope this helps :)

Answer:

3n <  12.9

Step-by-step explanation:

Answer:

It's the last answer

Step-by-step explanation:

Answer:

10)

11x-1+20x-3=151 (the exterior angle of an triangle is equal to the sum of two opposite interior angles)

31x-4=151

31x=151+4

31x=155

x=155/31

x=5°

11)

14x-13=4x+13+6x+2

14x-4x-6x=13+13+2

4x=28

x=28÷4

x=7°

Answer:

an = 60 x 1/5^n-1

Step-by-step explanation:

correct me if i am wrong, but I just learned about this stuff so hopefully this helps. The explicit rule/formula is an = a1 x r^n-1. In this formula, a1 is the first term (60), and r is the common ratio (1/5). Now all that is left to do is to write the equation which would be 60 x 1/5^n-1.

Answer:70

Step-by-step explanation: notice the pattern is adding by 8 after the first term

P(3 to 7) = P(3) + P(4) + P(5) + P(6) + P(7).To solve the given probabilities, we can use the binomial probability formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

Where:

- P(x) is the probability of exactly x successes

- C(n, x) is the number of combinations of n items taken x at a time

- p is the probability of success for each trial

- n is the number of trials

Given that 8% (0.08) of all Americans live in poverty, and we are selecting 36 Americans randomly, we can calculate the following probabilities:

a) Probability that exactly 1 of them live in poverty:

P(1) = C(36, 1) * (0.08)^1 * (1 - 0.08)^(36 - 1)

b) Probability that at most 2 of them live in poverty:

P(at most 2) = P(0) + P(1) + P(2)

             = C(36, 0) * (0.08)^0 * (1 - 0.08)^(36 - 0) + C(36, 1) * (0.08)^1 * (1 - 0.08)^(36 - 1) + C(36, 2) * (0.08)^2 * (1 - 0.08)^(36 - 2)

c) Probability that at least 1 of them live in poverty:

P(at least 1) = 1 - P(0)

d) Probability that between 3 and 7 (including 3 and 7) of them live in poverty:

P(3 to 7) = P(3) + P(4) + P(5) + P(6) + P(7)

Using the formula and the provided values, we can calculate these probabilities.

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Answer:

your answer is 48

Step-by-step explanation:

mark me as brainliest

Answer:

the answer should be square units

The equation of the quadratic polynomial f(x) with a horizontal tangent at x=2 and a y-intercept of 1 is f(x) = (x-2)^2 + 1. The function f(x) is decreasing on the open interval (-∞, 2).

To find a quadratic polynomial with a horizontal tangent at x=2 and a y-intercept of 1, we can use the general form f(x) = ax² + bx + c. We know that the derivative f'(x) is (x-2)(x+1). Taking the derivative of the general form and equating it to f'(x), we get 2ax + b = (x-2)(x+1).

From the equation, we can solve for a and b:

2a = 1, which gives a = 1/2.

b = -2 - a = -2 - 1/2 = -5/2.

Therefore, the quadratic polynomial is f(x) = (x-2)² + 1.

a) To determine where f(x) is decreasing, we can look at the sign of f'(x). Since f'(x) = (x-2)(x+1), it changes sign at x = -1 and x = 2. Thus, f(x) is decreasing on the open interval (-∞, 2).

b) At x = 2, f(x) has a critical point, and since f(x) is decreasing to the left of x = 2 and increasing to the right, it is a local minimum.

c) Since f(x) is continuously increasing to the right of x = 2, it does not have a local maximum.

d) f(x) does not have a point of inflection since the second derivative f''(x) = 2 is a constant.

To find a cubic polynomial with horizontal tangents at x = -1 and x = 5 and a y-intercept of 8, we can use the general form f(x) = ax³ + bx² + cx + d. We know that the derivative f'(x) should be zero at x = -1 and x = 5.

Setting f'(-1) = 0 and f'(5) = 0, we get:

-3a - 2b + c = 0

75a + 10b + c = 0

To satisfy these equations, we can choose a = -1/5, b = 3/5, and c = -3/5.

Therefore, the cubic polynomial is f(x) = (-1/5)x³ + (3/5)x² - (3/5)x + d. Substituting the y-intercept (0, 8) into the equation, we find d = 8.

Hence, the cubic polynomial is f(x) = (-1/5)x³ + (3/5)x² - (3/5)x + 8.

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According to Siegler, the pattern of learning math concepts involves a gradual development and refinement of strategies. Siegler's theory, known as the overlapping waves model, suggests that learners use multiple strategies simultaneously and gradually shift towards more efficient ones over time. This process allows for a better understanding and application of math concepts, ultimately leading to improved problem-solving skills.

According to Siegler, the pattern of learning math concepts involves a gradual progression from using counting strategies to more efficient and accurate strategies. Children initially rely on counting strategies to solve math problems, such as counting fingers or objects. As they progress, they begin to use more advanced strategies, such as decomposition or mental math, which allow them to solve problems more quickly and accurately. Siegler also emphasizes the importance of practice and repetition in developing math skills and the role of feedback and instruction in promoting learning. Overall, Siegler's theory suggests that children's math skills develop through a combination of innate abilities and environmental factors, including exposure to math concepts and opportunities for practice and instruction in time.

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Answer:

340

Step-by-step explanation:

Multiply both sides by 20.

Answer:

f=340

Step-by-step explanation:

17 times 20 equals 340

Hope I helped!! :)

Sorry if it's wrong! :(

Pls mark brainlist!!

Answer:

length=12; breadth=8

Step-by-step explanation:

l=w+4

w(w+4)=96

w²+4w-96=0

(w+12)(w-8)=0

width=8

length=w+4=12

Answer:

length=12; breadth=8

Step-by-step explanation:

Hope this helped have an amazing day!

The residual for this observation is 31.05.

As per given data in question ,

Starting price of a used game with one wheel = 0.99

Total observed price = 37.04

We have to calculate the residual, we need to first calculate the predicted value using the linear regression equation, then subtract the predicted value from the observed value.

Linear regression equation: `

y = mx + b`

Here, `y` is the dependent variable, which is the total price of the sale. `x` is the independent variable, which is the starting price of the used game. `m` is the slope of the regression line, which can be calculated as:

`m = (y2 - y1) / (x2 - x1)

`Where `(x1, y1)` and `(x2, y2)` are any two points on the line.

Let's use the following two points:

`(0.99, 5.99)` and `(40.00, 44.00)`.

Therefore, `m = (44.00 - 5.99) / (40.00 - 0.99) = 0.9303`

Now, to find `b`, we need to substitute the slope and one of the points in the equation `y = mx + b`.

Let's use the point `(0.99, 5.99)`.

Therefore, `5.99 = 0.9303(0.99) + b`,

which gives `b = 5.10`.

Thus, the linear regression equation is `y = 0.9303x + 5.10`.

Now, to calculate the predicted value, we need to substitute the starting price in the equation.

Here, the starting price is 0.99. Therefore, `y = 0.9303(0.99) + 5.10 = 5.99`.

Hence, the predicted value is $5.99.

To calculate the residual, we need to subtract the predicted value from the observed value.

Therefore,

`residual = observed value - predicted value = 37.04 - 5.99 = 31.05`.

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Answer: x=10

Step-by-step explanation:

Let x = the number

Solve:

x + (-6) = 4

Subtract -6 on both sides ( or as add 6 on both sides)

x + (-6) - (-6) = 4 - (-6)

Answer: x=10

Step-by-step explanation:

Let x = the number

Solve:

p + (-6) = 4

p + (-6) - (-6) = 4 - (-6)

Answer:

what is this it looks so hard I don't have the answer

Answer:

(f + g)(x) = 4x + 1

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x + 2

(f + g)(x) = f(x ) + g(x)

            = 3x - 1 + x + 2

            = 4x + 1    

Answer: one hundred + fourteen point six hundred + seventy four

Step-by-step explanation:

Answer:

One hundred and fourteen point six seven four

The money invested in stock X is $8,800.

Given,

Total investment in stock portfolio=$10000

Expected return from stock X=13%=0.13

Expected return from stock Y=8%=0.08

Expected return from portfolio=12.4%=0.124

The portfolio return is calculated by taking the weighted average of individual stock returns.

Let x represent the portfolio weightage of stock X.

1-x is the portfolio weightage of stock Y.

money invested in stock X be

0.124=0.13x+0.08(1-x)

0.124=0.13x+0.08-0.08x

0.124-0.08=0.05x

0.044=0.05x

x=0.88

money invested in stock X=0.88*10000=$8800

Thus, the money invested in stock X is $8,800.

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