Please help me with this

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]

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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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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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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The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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In the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

In the given diagram, we have ACDE as a quadrilateral, and we know that CD is congruent to CE. To identify two congruent angles, let's examine the properties of the quadrilateral.

Since ACDE is not specified to be a particular type of quadrilateral (such as a parallelogram or rectangle), we cannot directly infer congruent angles from its properties.

However, we can make use of some general properties of quadrilaterals to identify two congruent angles. One property is that the sum of the interior angles of a quadrilateral is always 360 degrees.

Let's consider angle C as one of the angles in ACDE. Since CD is congruent to CE, we can denote angle CDE as angle C' to represent the congruent angles.

Now, using the property that the sum of the interior angles of a quadrilateral is 360 degrees, we can express the relationship between the angles of ACDE as:

∠ACD + ∠CDE + ∠DEA + ∠EAC = 360 degrees

Since CD is congruent to CE, angles CDA and CEA are also congruent (opposite angles in a quadrilateral). So, we can rewrite the equation as:

∠ACD + ∠CDA + ∠C'EA + ∠EAC = 360 degrees

Since we want to identify two congruent angles, let's focus on angles CDA and C'EA. These two angles are formed by the intersection of the congruent sides CD and CE with different adjacent sides.

Therefore, we can conclude that angles CDA and C'EA are congruent in ACDE.

In summary, in the quadrilateral ACDE, we can identify two congruent angles: angle CDA and angle C'EA.

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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.

Answer:

Step-by-step explanation:

4 then add 5 + 1 which would = 4

Answer: 1 2/4 ft or 1.5 ft

Step-by-step explanation:

- f°g: Domain is x ≤ 0 or x ≥ 4

- g°f: Domain is x > 0

- f°f: Domain is x > 0

- g°g: Domain is all real numbers

To find the compositions f°g, g°f, f°f, and g°g, we need to substitute the functions into each other and simplify the expressions. Let's calculate them one by one:

1. f°g:

To calculate f°g, we substitute g(x) into f(x):

f(g(x)) = f(x^2 - 4x)

Substituting f(x) = 1/[tex]\sqrt{x}[/tex], we have:

f(g(x)) = 1/[tex]\sqrt{(x^2 - 4x)}[/tex]

The domain of f(g(x)) is determined by the domain of g(x). Since g(x) involves a square root, we need to ensure that the expression inside the square root is non-negative [tex](x^2[/tex] - 4x ≥ 0). Solving this inequality, we find the domain of g(x) to be x ≤ 0 or x ≥ 4.

Therefore, the domain of f°g is x ≤ 0 or x ≥ 4.

2. g°f:

To calculate g°f, we substitute f(x) into g(x):

g(f(x)) = (1/[tex]\sqrt{x)^2}[/tex] - 4(1/[tex]\sqrt{x}[/tex])

Simplifying the expression, we have:

g(f(x)) = 1/x - 4/[tex]\sqrt{x}[/tex]

The domain of g(f(x)) is determined by the domain of f(x). Since f(x) involves a square root, we need to ensure that the argument of the square root is positive (x > 0). Additionally, we need to exclude any values of x for which 1/x is undefined (x = 0).

Therefore, the domain of g°f is x > 0.

3. f°f:

To calculate f°f, we substitute f(x) into f(x):

f(f(x)) = 1/[tex]\sqrt{(1/\sqrt{x} )}[/tex]

Simplifying the expression, we have:

f(f(x)) = [tex]\sqrt{x}[/tex]

The domain of f(f(x)) is determined by the domain of f(x). Since f(x) involves a square root, we need to ensure that the argument of the square root is non-negative (1/[tex]\sqrt{x}[/tex] ≥ 0). Solving this inequality, we find the domain of f(x) to be x > 0.

Therefore, the domain of f°f is x > 0.

4. g°g:

To calculate g°g, we substitute g(x) into g(x):

g(g(x)) =[tex](x^2 - 4x)^2 - 4(x^2 - 4x)[/tex]

Simplifying the expression, we have:

g(g(x)) = [tex]x^4 - 8x^3 + 16x^2 - 4x^2 + 16x[/tex]

Combining like terms, we get:

g(g(x)) = [tex]x^4 - 8x^3 + 12x^2 + 16x[/tex]

The domain of g(g(x)) is the same as the domain of g(x), which is all real numbers.

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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.

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:

Second answer choice:  

Mean before the change = 84.  Mean after the change = 86

Median before the change =  81.  Median after the change = 85

Step-by-step explanation:

Defining the mean:

Mean before the change:

Thus, we can find the mean before the change by dividing the sum of 75, 78, 81, 90, and 96 by 5:

Mean = (75 + 78 + 81 + 90 + 96) / 5

Mean = (420) / 5

Mean = 84

Thus, the mean before the change is 84.

Mean after the change:

Now we can find the mean after the change by dividing the sum of 78, 81, 85, 90, and 96 by 5:

Mean = (78 + 81 + 85 + 90 + 96) / 5

Mean = (430) /5

Mean = 86

Thus, the mean after the change is 86.

Defining the median:

Median before the change:

Thus, the median before the change is 81.

Median after the change:

Thus, the median after the change is 85.

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

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

The interest accumulated in the account after the first and second year indicates;

The amount Miguel originally put into the bank is about $728

An interest is a reward or cost of borrowing or lending money.

Let P represent the amount Miguel deposited in the bank, and let r represent the interest rate in percentage, therefore, we get;

The amount in the account after the first year is; P + r·p = P·(1 + r)

P·(1 + r) = $757.12...(1)

The amount in the account after the second year can be obtained using the following formula;

Principal at the start of the second year = P·(1 + r)

Therefore; Amount = P·(1 + r)  + P·(1 + r) × r = P·(1 + r) × (1 + r) = P·(1 + r)²

P·(1 + r)² = $787.40...(2)

Equation (1) indicates that we get; (1 + r) = 757.12/P

Therefore; P·(1 + r)² = P·(757.12/P)² = 787.40

757.12²/P = 787.40

P = 757.12²/787.40 ≈ 728

The amount Miguel deposited in the bank is about $728

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The total volume of the wedding tent is 14560 ft³.

To find the total volume of the wedding tent, we need to calculate the volume of both the rectangular prism and the rectangular pyramid, and then add them together.

The volume of a rectangular prism is given by the formula:

Volume_prism = length * width * height

In this case, the dimensions of the prism are 32 ft by 35 ft by 9 ft, so the volume of the prism is:

Volume_prism = 32 ft * 35 ft * 9 ft = 10080 ft³

The volume of a rectangular pyramid is given by the formula:

Volume_pyramid = (length * width * height) / 3

The dimensions of the top of the pyramid are the same as the base of the prism, so the length and width of the pyramid are both 32 ft. The height of the pyramid is 4 ft. Using these values, we can calculate the volume of the pyramid:

Volume_pyramid = (32 ft * 35 ft * 4 ft) / 3 = 4480 ft³

To find the total volume of the tent, we add the volume of the prism and the volume of the pyramid:

Total_volume = Volume_prism + Volume_pyramid

Total_volume = 10080 ft³ + 4480 ft³ = 14560 ft³

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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:

We get approximately 86.96%. T herefore, the teenager should charge his sister an annual simple interest rate of approximately 86.96%.

Step-by-step explanation:

Answer:

To calculate the interest rate that the teenager should charge his sister, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal (the amount borrowed), r is the interest rate, and t is the time period.

We know that the teenager wants to earn $25 in interest ($75 - $50). We also know that the principal is $50 and the time period is 15 weeks. Plugging these values into the formula, we get:

25 = 50 * r * (15/52)

Solving for r, we get:

r = 13.04%

Therefore, the teenager should charge his sister a simple interest rate of 13.04%. Rounded to the nearest hundredth, this is 13.05%.

hope it helps you

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.

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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Answer:

3^(-4) = 1/3^4 = 1/81

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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Looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

The distribution closest to the mean is determined by comparing the mean of the dataset, to the given mean.

The mean of the various distributions is determined as;

Distibution 1; mean = (9 x 5) = 45/9 = 5

Distibution 2; mean = (2x3  + 3 +  4x2  +  8 + 9 + 11) /9 = 5

Distibution 3; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

Distibution 4; mean = (2x3  +  4x2  +  5 + 7 + 9 + 10) /9 = 5

The mean of the remaining distributions, from 5 to 8 is also 5, as already given in the statement.

If we look at all the distributions, we would see that, all the data of distribution 1 lie on 5, making it the most closest the mean of the distribution.

Thus, looking at the distribution sets 1-8 the one that seems to be closest to the mean is distribution 1 because all the data of distribution 1 lie on 5.

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Answer:

slope =2

y-intercept=(0,5)

Step-by-step explanation:

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 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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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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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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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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