14 Find the distance between the two points. Imagine a right triangle connecting the two points. (-3,2) www (2,-2) Hint: Find the base of the triangle by calculating the distance between the x-values of each point. Jay |2 - (-3) = [?]​

We represent it as -5. Thus, the common difference/ratio of the given sequence in the simplest form is -5.

To determine if a sequence is arithmetic or geometric, we have to find the differences (common differences) between the terms in the sequence.

The differences between the terms are calculated to determine if they are consistent for the arithmetic sequence or if they have a common ratio for the geometric sequence.

Therefore, the sequence below is arithmetic:19, 14, 9, ...To determine the common difference, we subtract each term from the previous term.19 – 14 = 5; 14 – 9 = 5Therefore, the common difference is 5. Hence, this is an arithmetic sequence with a common difference of 5.

Also, we can say that 14 - 19 = -5, 9 - 14 = -5, and so on. This is a common difference of 5 in the opposite direction. We can say that the difference is -5.

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Answer:

0

Step-by-step explanation:

Certainly! Let's solve the equation step by step:

1. Write down the equation:

3x + 5 = 3x - 5

2. Attempt to isolate x by subtracting 3x from both sides:

3x - 3x + 5 = 3x - 3x - 5

3. Simplify the equation:

5 = -5

At this point, we see that the equation 5 = -5 is not true. This means there is no solution for x in the given equation, as the two sides of the equation cannot be equal.

Answer:

2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 then add 5 + 1 which would = 4

Answer:

The list price would be $420.

To solve the proportion 5/2.5 = X/2, we can cross-multiply:

5 * 2 = 2.5 * X

10 = 2.5X

Divide both sides by 2.5:

10/2.5 = X

4 = X

Therefore, X is equal to 4.

The function that represents exponential growth is f(x) = 3x. Exponential growth is a type of growth in which the growth rate of a quantity increases over time, resulting in a continuously accelerating rate of growth.

In this function, the base of the exponent is 3, which means that the growth rate is tripling with each increase of x.

This is a characteristic of exponential growth.
Exponential growth can be seen in many real-world situations, such as population growth, compound interest, and the spread of diseases.

In each of these cases, the growth rate increases over time, leading to exponential growth.

The function f(x) = 3x is an example of exponential growth because it represents a situation in which the growth rate is increasing over time.
In summary, the function that represents exponential growth is f(x) = 3x.

Exponential growth is a type of growth in which the growth rate increases over time, leading to a continuously accelerating rate of growth.

This type of growth can be seen in many real-world situations and is characterized by a base exponent that is greater than one.

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a) The total number of days to finish by the builders is: 112 days

b) The speed per 1 hour is: 19 km/hr

An algebraic expression is the idea of ​​representing numbers in letters or alphabets without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values. These characters are called variables here. Algebraic expressions can use a combination of variables and constants. Any value that comes before the variable and is multiplied is a factor.

a) The builders complete 3/8 of a project in 42 days.

If the total number of days to finish is x, then we can say by proportion that:

(3/8)x = 42

x = (42 * 8)/3

x = 112 days

b) The rate of speed is 38 km per 2 hours.

Thus speed per hour = 38/2 = 19 km/hr

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The  12 feet of carpet is needed.

To round 11.5 feet to the nearest foot, we look at the decimal part, which is 0.5. According to the Rounding Rules, if the number being looked at is 5 or above, we round up by giving it a shove! Since 0.5 is exactly 5, we round up to the next whole number, which is 12 feet.

So, after rounding 11.5 feet to the nearest foot, we get 12 feet.

To determine how much carpet is needed, we use the rounded measurement, which is 12 feet.

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The set A U U is:

A U U = {a, b, c, d, e, f, g, h}

A set is a collection or grouping of distinct objects, which are called elements or members of the set. These objects can be anything: numbers, letters, shapes, or even other sets.

We have:

A= {c, d, g, h}

U= {a, b, c, d, e, f, g, h}

A U U is the set of all elements (letters) that appear in both A and U. Thus, we can say:

A U U = {a, b, c, d, e, f, g, h}

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The value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

To determine the values that should be excluded in the equation x/(x - 3) + 1/3 = 1, we need to find the values of x that would make the equation undefined or result in a division by zero.

In this case, the expression x - 3 appears in the denominator, so we need to find the values of x that would make x - 3 equal to zero.

x - 3 = 0

x = 3

Therefore, the value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

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Step-by-step explanation:

Weighted Average = (A * 1 + B * 1 + C * 2) / (1 + 1 + 2)

Since the weights are 1, 1, and 2 respectively, we can simplify the equation further:

Weighted Average = (A + B + 2C) / 4

Therefore, the average of the points A, B, and C with weights 1, 1, and 2 respectively is (A + B + 2C) / 4.

The average of the points A, B, and C with respective weights of 1, 1, and 2 can be calculated using the weighted average formula: (1*a + 1*b + 2*c) / (1+1+2). The values of points A, B, and C are represented as a, b, and c.

The question asks for the average of points A, B, and C, which are weighted 1, 1, and 2 respectively. To calculate a weighted average, we multiply each value by its respective weight and then sum these products. We then divide this sum by the sum of the weights. So, let's assume the values of points A, B, and C be a, b, and c respectively. Using the formula for weighted average we get Average = (1*a + 1*b + 2*c) / (1+1+2)This formula will give us the average of the points A, B, and C with the specified weights.

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Answer:

1400

Step-by-step explanation:

To preface, we should think about how percentages are taken from original numbers, and we may apply the operations oppositely.

First, let's set up an equation.

Let 3.5% equal to 49, where 3.5% is multiplied by x and x = the unknown factor.

3.5x = 49

Divide both sides by 3.5 to get x by itself.

3.5x/3.5 = 49/3.5

= x = 14.

Multiply the number by 100 and you will get your answer of 1400.

Check:

3.5% to decimal is... 3.5/100 = 0.035.

Multiply the quotient by the answer 1400 and you will obtain the given number of a percentage.

0.035 x 1400 = 49.

Answer:

x<2

Step-by-step explanation:

Solve for X

5x<10

1. Get X by itself by dividing both sides by 5

x<2

2. Graph the dotted asymptote on (0,2) and shade everything to the left since x<2

If Store C sells 145,670 products then Store B sells 9,711 products. Option A is the correct answer.

To determine the number of products Store B sells, we need to calculate it based on the information given in relation to Store C.

Given that Store C sells 145,670 products, and Store A sells one-third as many as Store C, we can find the number of products Store A sells:

Store A = (1/3) * Store C = (1/3) * 145,670 = 48,557

Now that we know Store A sells 48,557 products, and it sells five times as many products as Store B, we can calculate the number of products Store B sells:

Store B = (1/5) * Store A = (1/5) * 48,557 = 9,711

Therefore, Store B sells 9,711 products. Option A is the correct answer.

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The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

The null hypothesis (H₀): The company's heaters have a mean lifespan of 5 years or more.

The alternative hypothesis (H₁): The company's heaters have a mean lifespan of less than 5 years.

In hypothesis testing, the null hypothesis represents the claim or assumption that is being tested. In this case, the null hypothesis assumes that the mean lifespan of the company's heaters is equal to or greater than 5 years. The alternative hypothesis, on the other hand, challenges this claim and suggests that the mean lifespan is less than 5 years.

To determine which hypothesis is supported by the evidence, statistical analysis would need to be conducted using appropriate data and methods. The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

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Step-by-step explanation:

2). 5/2

3). 7/9

4). 12/5

5).5/6

Answer:

126000

Step-by-step explanation:

if from 2010 to 2012 there was an increase of 23000 that means every two years 23000 people are added then add 23000 to 80000 for four years and you will get 126000.In other words if you get 23000 divide it by two to get the amount for one year then multiply it by 8

Answer:

The slope of a line parallel to the equation y = (6/5)x - 2 is 6/5.

Step-by-step explanation:

In general, when two lines are parallel, they have the same slope. Therefore, any line that is parallel to the given equation will have a slope of 6/5.

Evaluating when [tex]\( n = 1 \)[/tex], the value of S is: S = 1

Evaluate:

[tex]\[ S = 108(2)^{n-1} \][/tex]

When n = 1.

Remember: For a geometric series, the sum can be calculated using the formula:

[tex]\[ S = 108(2)^{n-1} \][/tex]

In this case, we have r = 2, since each term is multiplied by 2 to get the next term.

Substituting the values into the formula, we get:

[tex]\[ S = \frac{{(1 - 2^n)}}{{1 - 2}} \][/tex]

Simplifying further:

[tex]\[ S = \frac{{1 - 2^n}}{{-1}} \][/tex]

Since the denominator is -1, multiplying the numerator and denominator by -1, we get:

[tex]\[ S = 2^n - 1 \][/tex]

Therefore, when [tex]\( n = 1 \)[/tex], the value of S is:

S = [tex]2^1[/tex]- 1 = 2 - 1 = 1

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The value of the American put futures option using a one-time step tree is $0.

To value the American put futures option using a one-time step tree, we can follow these steps:

Step 1: Calculate the risk-neutral probability of an up move (p) and a down move (1-p) based on the volatility and time step. Given that the volatility is 25% and the time to maturity is 1 year, we can calculate the time step as √(1 year) = 1.

Since this is a one-time step tree, there are two possible outcomes: an up move or a down move. We need to find the risk-neutral probabilities of these moves.

To calculate p, we use the formula:

p =[tex](e^(r * t) - d) / (u - d)[/tex]

Where:

r is the interest rate per annum (6% = 0.06),

t is the time step (1),

u is the up move factor (1 + volatility) = (1 + 0.25) = 1.25,

d is the down move factor (1 - volatility) = (1 - 0.25) = 0.75.

Substituting the values, we get:

p =[tex](e^([/tex]0.06 * 1) - 0.75) / (1.25 - 0.75)

p = (1.06183 - 0.75) / 0.5

p = 0.31183 / 0.5

p = 0.62366

Step 2: Calculate the option values at each possible outcome. Since this is a put option, the payoff at each node is the difference between the strike price and the future price at that node.

At the up move node:

Option value (up) = max(strike price - future price (up), 0)

                = max(0.55 - 0.60, 0)

                = max(-0.05, 0)

                = 0

At the down move node:

Option value (down) = max(strike price - future price (down), 0)

                  = max(0.55 - 0.55, 0)

                  = max(0, 0)

                  = 0

Step 3: Calculate the expected option value at the current node by taking the risk-neutral weighted average of the option values at the next nodes.

Expected option value = p * option value (up) + (1 - p) * option value (down)

                    = 0.62366 * 0 + (1 - 0.62366) * 0

                    = 0

Therefore, the value of the American put futures option using a one-time step tree is $0.

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The value of c in the triangle is (b) 5 units

From the question, we have the following parameters that can be used in our computation:

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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It will take 14 days for 46 workers to build similar house.

When building a house, the number of days required to build is inversely proportional to the number of workers.

Therefore,

d α 1 / w

d = k / w

k = dw

where

Therefore,

k = 161 × 4

k = 644

Let's find the number of days to build similar house with 46 workers.

Therefore,

d = 644 / 46

d = 14 days

Therefore, it will take 14 days.

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The correct matches for the polynomial are:

x - 3 (matches) f(x) = x³ − 3x² − 13x + 15

x - 2 (matches) f(x) = x⁴ + 3x³ − 8x² + 5x − 25

x - 1 (matches) f(x) = x³ − 2x² − x + 2

x + 3 (matches) f(x) = -x³ + 13x − 12

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, and multiplication. The variables in a polynomial are raised to non-negative integer exponents.

f(x) = x³ − 3x² − 13x + 15:

Factor: x - 3

f(x) = x⁴ + 3x³ − 8x² + 5x − 25:

Factor: x - 2

f(x) = x³ − 2x²− x + 2:

Factor: x - 1

f(x) = -x³ + 13x − 12:

Factor: x + 3

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Outliers can be useful in detecting whether a sample is representative of the population or not, but they should be treated with caution as they may skew the results.

a) The shape of each dot plot can be described as follows: The dot plot of river otters is symmetrical. The dot plot of sea otters is skewed to the right.

b) The dot plot of river otters has a larger center compared to sea otters. This means that the average weight of river otters is larger than that of sea otters. Therefore, in terms of otters, river otters are heavier on average compared to sea otters.

c) There are no outliers in the dot plot of river otters. However, there is one outlier in the dot plot of sea otters. The outlier represents the weight of a sea otter that is much larger or smaller than the rest of the sea otters in the sample. This may be due to various reasons such as measurement error, or simply because the otter is much larger or smaller than the rest of the sea otters.

d) The dot plot of sea otters has a larger spread compared to the dot plot of river otters. This means that the weights of sea otters vary more widely compared to the weights of river otters.

e) Outliers can affect the spread of the dot plot by increasing it or decreasing it. In this case, since there is only one outlier in the dot plot of sea otters, it does not have a significant effect on the spread of the dot plot. However, if there were more outliers, they would increase the spread of the dot plot.

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Answer:

(A) -76

(B) 4/81

(C) -1/16

(D) 3

Step-by-step explanation:

It is given that u and v are functions of x and are differentiable at x=0 and that u(0) = -8, u'(0) = -4, v(0) = 9, and v'(0) = 5. We are asked to find the following derivatives at x=0.

(A) - [tex]\dfrac{d}{dx}[uv][/tex]

(B) - [tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big][/tex]

(C) - [tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big][/tex]

(D) - [tex]\dfrac{d}{dx} [-5v-7u][/tex]

[tex]\hrulefill[/tex]

Part (A) - Using the product rule.

[tex]\dfrac{d}{dx}[uv]=uv'+vu'[/tex]

Substituting in our values:

[tex](-8)(5)+(9)(-4)\\\\\\\therefore \boxed{=-76}[/tex]

Part (B) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big]=\dfrac{vu'-uv'}{v^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(9)(-4)-(-8)(5)}{(9)^2}\\\\\\\therefore \boxed{=\frac{4}{81} }[/tex]

Part (C) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big]=\dfrac{uv'-vu'}{u^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(-8)(5)-(9)(-4)}{(-8)^2}\\\\\\\therefore \boxed{=\frac{-1}{16} }[/tex]

Part (D) - Deriving the function.

[tex]\dfrac{d}{dx} [-5v-7u]=-5v'-7u'[/tex]

Substituting in our values:

[tex]-5(5)-7(-4)\\\\\\\therefore \boxed{=3}[/tex]

Thus, all parts have been solved.

Therefore, the missing angle = (1080° - 947°) = 133°

Step-by-step explanation:

Given: Octagon

7 Interior Angles: 122°, 143°, 152°, 107°, 128°, 130° & 165°

Find: The measure of the missing angle:

Plan: Determine total sum of an octagons interior angles and subtract the total of the given angles

Sum of the Interior Angles of an Octagon:S = (n-2) 180°

S = (8 - 2)180° = 6 x 180° = 1080°

Sum of 7 Given Angles: S7IA = 947°

Answer:

30

Step-by-step explanation:

ahora:

edad de Kevin = k

edad de Gabriela = g

k = 2g

hace 12 años:

edad de kevin = k - 12

edad de gabriela = g - 12

k - 12 = 6(g - 12)

k = 2g

k - 12 = 6(g - 12)

2g - 12 = 6(g - 12)

2g - 12 = 6g - 72

4g = 60

g = 15

k = 2g = 2 × 15 = 30

Answer:

Step-by-step explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

v(t) = (initial amount)×(decay factor)^(t/(decay time))

v(t) = 600,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

 v(4) = 600,000×(0.90^(4/3)) = 521364.2677 gallons

[tex]\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &600000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=hours\dotfill &4\\ c=period\dotfill &3 \end{cases} \\\\\\ A=600000(1 - 0.10)^{\frac{4}{3}}\implies A=600000(0.9)^{\frac{4}{3}}\implies A\approx 521364[/tex]

The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.

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