1. A square lot has an area of 64x² square units. What is the length of each side with full solution​

Answer: Its c

Step-by-step explanation:

I did it

The function that represents the total cost, in dollars, of a rafting trip at the resort is f(x) = 25x + 45

For given question,

the fixed cost to rent a raft is $45

and the per person cost for each person in the raft is $25.

Here, the variable cost is the per person cost for each person in the raft as it depends on the number of people in the raft.

Let, x be the number people

The cost for 'x' people would be,

25x

So, the function that represents the total cost, of a rafting trip at the resort as a function of the number of people in the raft would be,

f(x) = 25x + 45

Therefore, the function that represents the total cost, in dollars, of a rafting trip at the resort is f(x) = 25x + 45

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Given:

The function g(t) represents the amount of caffeine remaining in your body after drinking the coffee.

\(g(t)=130(.8246)^t\)

where t is time in hours.

To find:

The caffeine remains in your system after day 1.

The caffeine remains in your system after day 2.

Solution:

We know that,

1 day = 24 hours.

2 day = 48 hours.

The given function is

\(g(t)=130(.8246)^t\)

Substitute t=24 in the given function to find the remaining caffeine in the system after day 1.

\(g(24)=130(.8246)^{24}\)

\(g(24)=130(0.00977)\)

\(g(24)=1.2701\)

Therefore, the remains caffeine in your system after day 1 is about 1.2701.

Substitute t=48 in the given function to find the remaining caffeine in the system after day 1.

\(g(48)=130(.8246)^{48}\)

\(g(48)=130(0.000095)\)

\(g(48)=0.01235\)

\(g(48)\approx 0.0124\)

Therefore, the remains caffeine in your system after day 1 is about 0.0124.

Answer: for one day, it’s 0.0124

Step-by-step explanation:1d=24h

g(24)

Answer:

you are correct do not say any other answer

Answer:

The answer is either

y=50000 x 0.8^x

or

y=50000(20%)^x but this just seems wrong

Step-by-step explanation:

The distribution of a continuous uniform is f(x) = 1/10

The average time that he has to wait is E[X] = 5

What is continuous uniform distribution?

The continuous uniform distribution is the probability distribution of random number selection from the continuous interval between a and b.

f(x) = 1/(b-a) is the formula of continuous uniform distribution.

What is average?

an average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean.

A) Given, the time between the successive buses is fixed and that is 10 minutes.

Therefore, the distribution is

The buses arrive always on time every 10' thus the distribution is uniform in [0;10] The density of a continuous uniform is

()=1/−=1/10−0=110

B) Its expectation ( the average time he has to wait) is

()=+/2=0+10/2=5.

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Answer: d) y=4x+17

remember y=mx+b

good luck

The correct answer is "2 * 2 * 2 = 8 treatments." With 3 factors, each having 2 levels, there are a total of 8 treatments. Each treatment represents a unique combination of factor levels. Let's determine:

Understanding the scenario

In experimental design, the number of treatments is determined by the number of levels in each factor and the total number of factors. In this case, we have 3 factors, each with 2 levels. We need to determine the total number of treatments.

Steps to calculate the number of treatments

1. Start by considering each factor separately. Since each factor has 2 levels, there are 2 treatment combinations for each factor.

  - Factor 1: 2 levels

  - Factor 2: 2 levels

  - Factor 3: 2 levels

2. Multiply the number of treatment combinations for each factor to get the total number of treatments.

  - Total number of treatments = Number of treatments in Factor 1 * Number of treatments in Factor 2 * Number of treatments in Factor 3

3. Apply the multiplication rule:

  - Total number of treatments = 2 * 2 * 2 = 8

Therefore, the correct answer is "2 * 2 * 2 = 8 treatments." With 3 factors, each having 2 levels, there are a total of 8 treatments. Each treatment represents a unique combination of factor levels.

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The completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

According to the given question.

We have a polynomial

x^3 + 4x^2 - 9x -36

Since for finding the roots of the above polynomial, first we randomly substitute any value of x and find for which value of x the above polynomial gives 0.

So, for x = 3

The above polymonial gets 0.

So, the one factor of the given polynomial is (x -3).

To find the other factors or completely factored form of the given polynomial we will divide x^3 + 4x^2 - 9x -36 by x - 3, which is called long division.

From the attatched solution or log division we can see that

The factored form of x^3 + 4x^2 - 9x -36 is (x -3)(x^2 + 7x + 12).

Now, the foctorization of x^2 + 7x + 12 is given by

x^2 + 7x + 12

= x^2 + 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

Therefore, the completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

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Answer:

C) (x + 3)(x – 3)(x + 4)

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EDGE2022; Good Luck :D!!!

The horizontal change from triangle ABC to triangle ABC include the following: A. right 5 units.

The vertical change from triangle ABC to triangle ABC include the following: C. down 2 units.

The translation rule in the standard format is: (x, y) → (x + 5, y - 2).

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of triangle ABC horizontally right by 5 units and vertically down 2 units, the coordinate A of triangle ABC include the following:

(x, y)                               →                  (x + 5, y - 2)

A (3, 5)                        →                  (3 + 2, 5 - 2) = A' (5, 3).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we can use either sine or cosine

\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

Hope this helps you

The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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The free cash flow (FCF) for year 1 can be calculated by subtracting the investment in fixed assets and the investment in net working capital from the profit after taxes and adding back the depreciation. In this case, the free cash flow for year 1 is $2 million

Free cash flow (FCF) is a measure of the cash generated by a company after accounting for its expenses and investments in fixed assets and working capital. It represents the amount of cash available to the company for distribution to its shareholders, reinvestment in the business, or debt reduction.

In this case, the given data states that the profit after taxes is $5 million, the depreciation is $2 million, the investment in fixed assets is $4 million, and the investment in net working capital is $1 million.

The free cash flow (FCF) for year 1 can be calculated as follows:

FCF = Profit after taxes + Depreciation - Investment in fixed assets - Investment in net working capital

FCF = $5 million + $2 million - $4 million - $1 million

FCF = $2 million

Therefore, the free cash flow for year 1 is $2 million. This means that after accounting for investments and expenses, the company has $2 million of cash available for other purposes such as expansion, dividends, or debt repayment.

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The area of the triangle def round to the nearest tenth of a square unit is 10.3 square units.

When the two sides and an angle of a  triangle is known, then the area of the triangle can be found out with the following formula.

\(A=ab\sin\left(\dfrac{C}{2}\right)\)

Here, a,b are the adjacent sides and C is the angle made between them.

The image of the triangle DEF is attached below. In this the two adjacent sides are given with the length 5 units ans 8 units long.

The angle made between them has the measure of 31 degrees. Put the values in the above formula as,

\(A=(5)(8)\sin\left(\dfrac{31}{2}\right)\\A=10.3\rm\; unit^2\)

Hence, the area of the triangle def round to the nearest tenth of a square unit is 10.3 square units.

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Answer: A, 10.3

Step-by-step explanation: edge 2022

Answer:

85.71% chance of randomly selecting a student who owns at least one laptop or one desktop

Step-by-step explanation:

Out of a total of 70 students, only 10 own neither a laptop nor a desktop. This means that the probability of selecting a student with at least one of the two is \(\frac{60}{70}\) or \(\frac{6}{7}\).

If we convert this fraction into a percentage and round to the nearest hundredth, it equals:

85.71%

Answer: 7.755 × 10²

Step-by-step explanation:

    To write in scientific notation we write the number as being between 1 and 10 which is then multiplied by a power of 10 so it is still equivalent.

775.5 / 100 = 7.755

[✓] 1 < 7.755 < 10

    Checking our work.

[✓] 7.755 × 10² = 775.5

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The equation that represents Angel's pay in fees based on their number of ATM withdrawals y = 3 + 5x

Information from the question are

Angel's bank allows them 3 free ATM withdrawals each month

then charges a $5 ATM fee

Angel will pay in fees = y

number of ATM withdrawals = x

The Angel's bank  ATM withdrawals can be modeled as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = 3 + 5x

Definition of variables to suit Angel's bank  ATM withdrawals

y = Angel will pay in fees

$5 = charges per withdrawal

x = number of ATM withdrawals

3 = free ATM withdrawals each month

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By solving a linear equation, we can see that the measures of the segments are:

Here we have 3 collinear points, a, b, and c.

We know that the measures are:

ab = 9

ac = x + 19

bc = 2x + 18

If b is between a and c, then we should have that:

ac = ab + bc

Replacing the measures we get:

x + 19 = 9 + (2x + 18)

Now we can solve this linear equation to find the value of x.

x + 19 = 9 + 2x + 18

x + 19 = 27 + 2x

19 - 27 = 2x  -x

-8 = x

Then the measures are:

ab = 9

ac = -8 + 19 = 11

bc = 2*(-8) + 18 = -16 + 18 = 2

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The two independent groups are the King Salmon from Lake Michigan and Lake Superior. The t-test will allow the researchers to analyze the weight data from each lake and determine if there is enough evidence to conclude that the mean weight of King Salmon from Lake Michigan is significantly different from the mean weight of King Salmon from Lake Superior.

To determine whether Lake Michigan King Salmon weigh less than those from Lake Superior, the appropriate statistical test to use would be an independent samples t-test.

The independent samples t-test is used to compare the means of two independent groups to determine if there is a significant difference between them. In this case, the two independent groups are the King Salmon from Lake Michigan and Lake Superior. The t-test will allow the researchers to analyze the weight data from each lake and determine if there is enough evidence to conclude that the mean weight of King Salmon from Lake Michigan is significantly different from the mean weight of King Salmon from Lake Superior.

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Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

The center of the circle is at the point (-5,11) and has the radius of 3 units.

The equation of the circle will be,

lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll\(\lim_{n \to \infty} a_n \\\)

Answer: 9 × 6 = 54

Step-by-step explanation:

In the Product Game, we need to multiply the both number of factor markers.

Chris and Katie were playing The Product Game. Their factor markers were on 9  and 2.

Number = 9 × 2 = 18

Chris decided to move the marker from 2 to 6.

Now, one maker is on 9 and other is on 6. So,

Number = 9 × (2 + 4)

Number = 9 × 6 = 54

Therefore, 9 × 6 = 54 is a numerical expression  to represent his move.​

Answer:

5/28

Step-by-step explanation:

P(oj, then grape) = 2/8 x 5/7 = 10/56 = 5/28

The probability of pulling out a bottle of orange juice and then a bottle of grape juice is 5/28.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

An ice chest contains 2 bottles of orange juice, 5 bottles of grape juice, and 1 bottle of apple juice, all buried in ice.

The probability of pulling out a bottle of orange juice and then a bottle of grape juice is calculated as below:-

Probability = Number of favorable outcomes / Number of sample

P(orange , then grape) = 2/8 x 5/7 = 10/56 = 5/28

Therefore, the probability of pulling out a bottle of orange juice and then a bottle of grape juice is 5/28.

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i) Wealth is not independent of income.

ii) It is unclear whether there is multicollinearity in the model due to the lack of correlation or VIF values.

iii) The a priori sign of X3i is negative, indicating an expected negative relationship between wealth and consumption expenditure. However, without additional information, we cannot determine if the results conform to the expectation.

Let us discuss in a detailed way:

i) To test whether wealth (X3i) is independent of income (X2i), we can examine the coefficient associated with X3i in the regression equation. In this case, the coefficient is -0.0424. To test for independence, we can check if this coefficient is significantly different from zero. Since the coefficient has a value of -0.0424, we can conclude that wealth is not independent of income.

ii) Multicollinearity refers to a high correlation between independent variables in a regression model. To determine if there is multicollinearity, we need to examine the correlation between the independent variables. In this case, we have income (X2i) and wealth (X3i) as independent variables. If there is a high correlation between these two variables, it suggests multicollinearity. We can also check the variance inflation factor (VIF) to quantify the extent of multicollinearity. However, the given information does not provide the correlation or VIF values, so we cannot definitively conclude whether there is multicollinearity in the model.

iii) The a priori sign of X3i can be determined based on the expected relationship between wealth and consumption expenditure. Since the coefficient associated with X3i is -0.0424, we can infer that there is an expected negative relationship between wealth and consumption expenditure.

In other words, as wealth increases, consumption expenditure is expected to decrease. However, without knowing the context or specific expectations, we cannot determine if the results conform to the expectation.

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The measure of <TKZ is 18 degree.

The length of KZ is 17.3082 m.

The  height of the kite K from the ground is 18.3082 m.

We have,

Angle of Elevation = 72

TK = 18.2 m

Using trigonometry

sin 72 = P/ H

sin 72 = P / 18.2

P = 17.3082

Now, cos 72 = B/H

cos 72 = B/ 18.2

B = 5.6238

Now, <TKZ = 180 - 90 - 72 (angle Sum property)

<TKZ = 18 degree

and, length of KZ = 17.3082 m

Not, the height of the kite K from the ground

= 18.3082 m

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Answer: 126 cubic centimeters

Step-by-step explanation:

volume = (pi)(r^2)(1/3)(h)

diameter = 8 so radius = 4

4 squared is 16

multiply height by 3/4

10(3/4) = 30/4 = 15/2

Multiply this value by 1/3

15/2 x 1/3 = 15/6 = 5/2

(pi)(25)(5/2)

16x5/2 = 80/2 = 40

(pi)(40)

note: you can substitute 3.14 with pi or use actual pi depending on whether or not you have access to a calculator. they will both round to 196.

126 cubic centimeters

94.2 cubic centimeters is the approximate volume of water in Anju's cup.

To find the approximate volume of water in Anju's cup, we can calculate the volume of a cone using the formula:

Volume = (1/3) × π × r² × h

Given that the cup has a maximum diameter of 8 cm, the radius (r) would be half of that, which is 4 cm.

The height (h) is 10 cm, but Anju fills the cup to 3/4 of its height, so the filled height would be (3/4) × 10 cm = 7.5 cm.

Substituting these values into the formula:

Volume = (1/3) × π × (4 cm)^2 × (7.5 cm)

Volume = (1/3) × 3.14 × 16 cm^2 × 7.5 cm

Volume = 12.56 cm² × 7.5 cm

Volume = 94.2 cm²

Therefore, the approximate volume of water in Anju's cup is approximately 94.2 cubic centimeters (cm³).

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Answer

1+21

Step-by-step explanation:

Hope this helps :D

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line" is True because simple linear regression is a statistical method used to identify the linear relationship between one independent and one dependent variable, by minimizing the sum of the squared deviations between each value of the dependent variable and the line.

Simple linear regression is a method for estimating the relationship between a dependent variable and an independent variable. The dependent variable is defined as the variable being predicted or estimated. The independent variable is the variable that is predicted or estimated from the dependent variable.

The simple linear regression equation y = a + bx represents a straight line that fits the data, with a being the y-intercept and b being the slope of the line. The goal of simple linear regression is to find the values of a and b that minimize the sum of the squared deviations between each value of y and the line.

The least-squares regression line is the line that best fits the data by minimizing the sum of the squared deviations between each value of y and the line. This is also known as the line of best fit, as it represents the best possible fit to the data.

When creating a simple linear regression equation, the goal is to find the values of a and b that will result in the least-squares regression line. This line represents the line that best fits the data and minimizes the sum of the squared deviations between each value of y and the line.

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The study by the National Institutes of Health suggests that chocolate reduces the probability of getting Alzheimer's Disease if eaten regularly will affect the demand for chocolate.

This finding will increase the demand for chocolate. The determinant of demand being affected is consumer preferences or tastes. The study provides evidence that regular consumption of chocolate can reduce the risk of Alzheimer's Disease, which is likely to influence consumers' preferences and increase their desire to consume chocolate.

Graphically, the demand curve for chocolate will shift to the right, indicating an increase in demand. The original equilibrium quantity and price are marked on the graph with a regular pencil. Using a colored pencil, the new equilibrium quantity and price are marked similarly. The new equilibrium quantity will be higher, and the new equilibrium price will depend on the relative magnitude of the shift in demand compared to any changes in supply.

As the demand for chocolate increases, assuming the supply remains unchanged, there will be a new equilibrium where the quantity demanded matches the quantity supplied at a higher price. This is because the increased demand puts upward pressure on prices as consumers are willing to pay more for chocolate.

The market adjustment process begins with a shortage of chocolate at the original equilibrium price after the effect. The increased demand exceeds the original supply, resulting in a situation where consumers are willing to buy more chocolate than is available.

In response to this shortage, suppliers observe an increase in inventories at the original price. This encourages suppliers to increase their production of chocolate to meet the rising demand. As suppliers increase their production, the available quantity of chocolate in the market gradually increases.

The increased supply from suppliers helps alleviate the shortage, and as the quantity supplied catches up with the quantity demanded, the market moves toward a new equilibrium. The new equilibrium is reached at a higher price and a higher quantity, reflecting the increased demand for chocolate.

These actions by suppliers to increase their production and meet the rising demand affect consumer purchases by making more chocolate available in the market. As the supply increases, consumers are able to purchase more chocolate at the new equilibrium price. The increased availability of chocolate satisfies the higher consumer demand resulting from the study's findings, allowing consumers to benefit from the potential health benefits of regular chocolate consumption.

Overall, the study suggesting that chocolate reduces the probability of getting Alzheimer's Disease if eaten regularly will positively impact the demand for chocolate, leading to a new equilibrium with a higher price and quantity.

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