Josh lit a 14-inch candle. She noticed that it was getting an inch shorter every 30 minutes. Let x be the number of hours and y be the total height of the candle

System of Equations

Given the system of equations:

2x + y = -6

y = 1/4x + 3

It's required to solve it by graphing.

The graph of a line can be drawn by only knowing two points of it.

To graph the first equation, solve for y:

y = -2x - 6

Now give x two values. For example, x = -5 and x = -1.

For x = -5:

y = -2(-5) - 6

y = 10 - 6 = 4

Point (-5, 4)

For x = -1:

y = -2(-1) - 6

y = 2 - 6 = -4

Point (-1, -4)

With these points, we can graph the first equation. The graph will be shown below in red.

Now graph the second equation:

y = 1/4x + 3

For x = -8

y = 1/4(-8) + 3

y = -2 + 3 = 1

Point (-8, 1)

For x = 0:

y = 1/4(0) + 3

y = 0 + 3 3

y = 3

Point (0,3)

The second line is drawn in blue below.

Since the joint probability distribution is not equal to the product of the marginal probability distributions for all combinations of X and Y, we can conclude that the random variables X and Y are not independent. Therefore, the answer is that these random variables are not independent.

To determine whether two random variables X and Y are independent, we need to check if the joint probability distribution of X and Y is equal to the product of their marginal probability distributions.

Given the probability space (S, M, P) and the random variables X and Y defined as:

X(a) = X(b) = X(c) = 1

X(d) = X(e) = X(f) = 0

Y(a) = Y(d) = 2

Y(b) = Y(c) = Y(e) = Y(f) = 3

We can calculate the joint probability distribution as follows:

P(X = 1, Y = 2) = P({a, d}) = f(a) + f(d) =  +  =

P(X = 1, Y = 3) = P({b, c, e, f}) = f(b) + f(c) + f(e) + f(f) =  +  +  +  =

P(X = 0, Y = 2) = P({}) = f() =  =

P(X = 0, Y = 3) = P({}) = f() =  =

Next, we calculate the marginal probability distributions:

P(X = 1) = P({a, b, c, d, e, f}) = f(a) + f(b) + f(c) + f(d) + f(e) + f(f) =  +  +  +  +  +  =

P(X = 0) = P({}) = f() =  =

P(Y = 2) = P({a, d}) = f(a) + f(d) =  +  =

P(Y = 3) = P({b, c, e, f}) = f(b) + f(c) + f(e) + f(f) =  +  +  +  =

Now, let's check if the joint probability distribution is equal to the product of the marginal probability distributions:

P(X = 1, Y = 2) = P(X = 1) * P(Y = 2)

P(X = 1, Y = 3) = P(X = 1) * P(Y = 3)

P(X = 0, Y = 2) = P(X = 0) * P(Y = 2)

P(X = 0, Y = 3) = P(X = 0) * P(Y = 3)

Since the joint probability distribution is not equal to the product of the marginal probability distributions for all combinations of X and Y, we can conclude that the random variables X and Y are not independent.

Therefore, the answer is that these random variables are not independent.

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Answer:

33/2

Step-by-step explanation:

6 * 11/4 = 66/4 = 33/2

Answer:

84

Step-by-step explanation:

\(A\)trapezoid= \(\frac{h(b_{1} + b_{2})}{2}\)

Substitute the values into the equation: \(A=\frac{12(9 + 5)}{2}\)

\(A=\frac{12(9 + 5)}{2}\) (add 9 and 5)

↓

\(A=\frac{12(14)}{2}\) (multiply 14 by 12)

↓

\(A=\frac{168}{2}\)(divide 168 by 2)

↓

\(A=84\) (your answer)

Hope this helps! Have a good day! :)

The upper limit of the control chart such that it will include roughly 97 percent of the sample means when the process is in control is 1.008.

For a process with a normal distribution, the mean of the sample means is equal to the population mean and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size. In this case, the mean of the output is 1.0 liter and the standard deviation is 0.01 liter, so the standard deviation of the sample means is 0.01 / √25 = 0.002.

To construct a control chart for the sample means, we need to determine the upper and lower control limits such that the process is in control when the sample means fall within these limits. Assuming the process is in control, we want to find the upper limit such that roughly 97% of the sample means fall below this limit.

Using the standard normal distribution, the Z-score corresponding to the 97th percentile is approximately 1.88.

Therefore, the upper control limit is 1.0 + 1.88(0.002) = 1.008. Any sample mean above this limit should be investigated for potential process issues.

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Answer:

2, 6

Step-by-step explanation:

x always go first

Mike's monthly payments are approximately $19,407.43. At the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.

To solve the given problem, we can use the formula for calculating the monthly mortgage payments:

P = (r * A) / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate
A = Loan amount
n = Total number of payments

First, let's calculate the monthly interest rate. The nominal interest rate is given as 1.8%, which means the monthly interest rate is 1.8% divided by 12 (number of months in a year):

r = 1.8% / 12 = 0.015

Next, let's calculate the total number of payments. The mortgage has a 30-year amortization period, which means there will be 30 years * 12 months = 360 monthly payments.

n = 360

Now, let's calculate Mike's monthly payments using the formula:

P = (0.015 * (1.3m - 300k)) / (1 - (1 + 0.015)^(-360))

Substituting the values:

P = (0.015 * (1,300,000 - 300,000)) / (1 - (1 + 0.015)^(-360))

Simplifying the expression:

P = (0.015 * 1,000,000) / (1 - (1 + 0.015)^(-360))

P = 15,000 / (1 - (1 + 0.015)^(-360))

Calculating further:

P = 15,000 / (1 - (1.015)^(-360))

P ≈ 15,000 / (1 - 0.22744)

P ≈ 15,000 / 0.77256

P ≈ 19,407.43

Therefore, Mike's monthly payments are approximately $19,407.43.

To calculate the balance at time 60, we can use the formula for calculating the remaining loan balance after t payments:

Bt = P * ((1 - (1 + r)^(-(n-t)))) / r

Where:
Bt = Balance at time t
P = Monthly payment
r = Monthly interest rate
n = Total number of payments
t = Number of payments made

Substituting the values:

B60 = 19,407.43 * ((1 - (1 + 0.015)^(-(360-60)))) / 0.015

B60 = 19,407.43 * ((1 - (1.015)^(-300))) / 0.015

B60 ≈ 19,407.43 * ((1 - 0.19025)) / 0.015

B60 ≈ 19,407.43 * 0.80975 / 0.015

B60 ≈ 19,407.43 * 53.9833

B60 ≈ 1,048,446.96

Therefore, at the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.

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The number of missed shots after 6 is weeks of practice is 0.

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

The graph shows the number of weeks of practice (x).

the number of shots missed in a free-throw drill (y).

The equation of the trend line that best fits the data is y = -x + 6.

Since, after 6 weeks of practice, the number of missed shots be

y= -6+6

y=0y=0

Thus, the number of missed shots after 6 weeks of practice is 0.

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Answer:

The first one is right

Step-by-step explanation:

The square root of 42 is 6.5 so you just use the square root of 42 and 2 because the perfect trinomial is x squared minus 4x+4=38+4. which is (x-2) so that is where the 2 comes from.

The roots of the equation x² - 4x - 38 = 0 are 2 ± √(42).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement x squared minus 4 x minus 9 = 29 wich can be numerically expressed as,

x² - 4x - 9 = 29.

x² - 4x - 38 = 0.

Applying Sridhar acharya's formula,

x = [4 ± √(16 + 152)]/2.

x =  [4 ± √(168)]/2.

x =  [4 ± √(2×2×2×3×7)]/2.

x =  [4 ± 2√(42)]/2.

x =  [2 ± √(42)].

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The Binary Search Tree is as follows:

                                                   E

                                            /            \

                                         S                T

                                        /                    \

                                      I                       W

                                   /                            \

                                A                               M

                              /                                    \

                             C                                     G

                              \

                                D

The set of letters is {I, D, S, A, E, T, C, G, M, W} and len (I, D, S, A, a) = 5

Binary Search Tree:The binary search tree based on the alphabetical ordering of the letters is:

post-order sequence is: C, D, A, G, M, I, W, T, S, E.

To draw the binary search tree for the given post-order sequence, follow the steps below:

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To find positive integers $a$, $b$, and $2009$ such that $a + b = a \cdot b = 2009$, we observe that $2009$ is a prime number. Since the product of two positive integers is equal to their sum only when they are both equal to $2$, it follows that $a = b = 2$. Thus, the solution is $a = b = 2$.

The problem asks for positive integers $a$, $b$, and $2009$ such that $a + b = a \cdot b = 2009$. First, we note that $2009$ is a prime number. Since the product of two positive integers is equal to their sum only when they are both equal to $2$, we conclude that $a = b = 2$. This can be understood by considering the prime factorization of $2009$, which is $7^2 \cdot 41$. Since $7$ and $41$ are both prime factors, they cannot be expressed as the sum of two positive integers. Therefore, the only solution is $a = b = 2$.

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Step-by-step explanation:

The formula for the lateral area of a right cone is :

LA = rs

Where

r is the radius of the base and s is the slant height of the cone

Equivalent expression,

\(r=\dfrac{LA}{s}\)

or

\(s=\dfrac{LA}{r}\)

Hence, this is the required solution.

In this exercise we have to use the formula for volume of the cone and we find that:

\(s=\frac{LA}{r}\)

The formula for the lateral area of a right cone is :

LA = rs

Where:

Equivalent expression is:

\(s=\frac{LA}{r}\)

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Answer:

16 weeks

Step-by-step explanation:

Answer:16 weeks

Step-by-step explanation:

Answer:

CD = 16

Step-by-step explanation:

We can see that both AC and AB are radii. This means that they are equal, so AC = AB = 17. From segment addition postulate we can say AB = AE + BE

We are given BE, and we found the length of AB, so we can substitute and solve for AE:

AB = AE + BE

17 = AE + 2

AE = 15

Since we are given that AB is perpendicular to CD, ∠AEC would be a right angle, making ΔAEC a right triangle.

Now, we can use the pythagorean theorem to find the length of CE.

a^2 + b^2 = c^2

We are given the hypotenuse, c or AC in this case, and one leg, b, or AE in this case. We can plug in the values we are given:

CE^2 + AE^2 = AC^2

CE^2 + 15^2 = 17^2

CE^2 + 225 = 289

CE^2 = 64

CE = 8

Now, if a chord is perpendicular to a radius(AB in this case) we can say that it is split in half by the radius. This is basically saying that CE = DE = 8.

Again, using segment addition postulate, we can say:

CE + DE = CD

CD = 8 + 8

CD = 16

Answer:

540 is the answer

Step-by-step explanation:

Move the decimal point 2 places to the right.

I hope my answer was helpful!:)

Step-by-step explanation:

1 meter = 100 centimeter = 1000 millimeter

therefore, 1 cm = 10 mm

4.6 m = 4.6 × 1000 = 4600 mm

88 cm = 880 mm

and so, they cut off

880 mm + 1630 mm = 2510 mm

that means

4600 - 2510 = 2090 mm = 2.09 m

are left.

To calculate the receivable days, divide the trade receivables (RM63,000) by the average daily sales (RM1,400) to get approximately 45 days.



To calculate the receivable days, we need to determine the average daily sales and then divide the trade receivables by that figure.

First, we calculate the average daily sales by dividing the total sales by the number of days in the year:

Average daily sales = Total sales / Number of days

Since the year ended on 30th June 2019, there are 365 days in total.

Average daily sales = RM511,000 / 365 = RM1,400

Next, we divide the trade receivables by the average daily sales to find the receivable days:

Receivable days = Trade receivables / Average daily sales

Receivable days = RM63,000 / RM1,400 ≈ 45 days

Therefore, Alice's receivable days on 30th June 2019 is approximately 45 days.

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The journal entry obtained from the lump sum and fair value of the assets can be presented as follows;

Land........................520,000

Building..................650,000

Equipment.............130,000

Cash........................1,300,000

A journal entry consists of a record of the financial transactions within the general journal of a system of accounting.

The lump sum for which the Arlington Company purchased the land, building and equipment = $1,3000,000

The purchase price are allocated to the assets according to their relative fair values as follows;

The total fair value for the land, building and equipment = $600,000 + $750,000 + $150,000 = $1,500,000

The percentage of the total fair value represented by each asset are;

Percentage of the total fair value represented by Land = $600,000/$1,500,000 = 40%

The amount allocated to land is therefore;

$1,300,000 × 0.4 = $520,000

Percentage of the fair value represented by building = $750,000/$1,500,000 = 1/2

The amount allocated to building = $1,300,000 × 1/2 = $650,000

Percentage of the fair value allocated to equipment = $150,000/$1,500,000 = 0.1

The amount allocated to equipment = $1,300,000 × 0.1 = $130,000

The journal entry to record the purchase, will therefore be as follows;

Land .................520,000

Building............650,000

Equipment.......130,000

Cash..................1,300,000

Part of the question, obtained from a similar question on the internet includes; to prepare the journal entry for the record of the purchase

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Answer:

what are you asking?

Step-by-step explanation:

Answer:

\(a=-13\)

Step-by-step explanation:

We can use substitution to find the value of \(a\):

\(qt+a=-1\)

\(3(4)+a=-1\)

\(12+a=-1\)

\(a=-13\)

Hope this helps :)

Answer:

80

Step-by-step explanation:

The base which is eight times the height which is 10 would equal the area ( 80)

Hope this helps and have a great day/night!!

Answer:

5, 6 are the solutions

step-by-step explanation:

Here, the cost of attending the festival is constant, the bottles of hot sauce keeps changing until less amount of money reached.

Inequality:

5h + 16 = 50

5h = 50 - 16

5h = 34

h = 34/5

h = 6.8

So, he can buy max or less than 6 bottles of hot sauce.

Answer:

A = -17

Step-by-step explanation:

F(5) = -4(5) + 3

F(5) = -20 + 3

F(5) = -17

Answer:

D. 23

Step-by-step explanation:

f(-5) = -4(-5) + 3

= 20 + 3

= 23

therefore f(-5) is 23

Answer:

7

Step-by-step explanation:

87 - 80 = 7

Brass is an alloy of copper and zinc with a density of approximately 8.5 g/cm³. In addition, brass is a malleable and ductile metal that can be bent, stretched, and compressed without breaking. The sphere's volume can be reduced using a minimum pressure of 12,750 Pa.
First, let us comprehend the formula used in this case: Percentage decrease in volume = (change in volume/original volume) x 100. Now, we will obtain the change in volume.
Change in volume = (percentage decrease in volume/100) x Original volume
Here, percentage decrease in volume = 0.00003 %

Original volume can be derived from the formula of the volume of a sphere, which is:
V = 4/3πr³
As a result, the following is the equation for the original volume:
V = 4/3 π (d/2)³ = πd³/6
Where d is the diameter of the brass sphere.
Now we can find the change in volume:
Change in volume = (0.00003/100) x πd³/6
The change in volume is calculated to be 0.00000157πd³.
According to the formula of pressure, pressure = force/area, we can find the force necessary to decrease the volume by the required percentage using the Young’s modulus of brass, which is approximately 91 GPa (gigapascals) or 91 × 10⁹ Pa (pascals).
So, we can write:
Force = Young's modulus x (Change in volume/Original volume) x (Original diameter)²/4
Thus, the force needed to decrease the volume of the sphere is as follows:
F = 91 × 10⁹ x (0.00000157πd³) / (πd³/6) x (d/2)²
F = 3.53 × 10⁷ d² N
Finally, we can find the minimum pressure required to reduce the volume by dividing the force by the surface area of the sphere.
Minimum pressure = F/ Surface area of the sphere
= F/(4πr²)
= 3.53 × 10⁷ d²/ (4π (d/2)²)
= 12,750 Pa approximately
Therefore, the sphere's volume can be reduced using a minimum pressure of 12,750 Pa.

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Answer:huh,

Step-by-step explanation:I don’t understand you’re saying

The correct answer is: 2. y = 26

To solve for the dependent variable (y), we need to use the given information that the individual wants to have two hot dogs for each guest and 6 extra hot dogs for potential friends.

If the independent variable is 10, then the total number of guests would be 10.

So, the equation to find the number of hot dogs needed (y) would be:

y = (2 hot dogs per guest) x 10 guests + 6 extra hot dogs

y = 20 + 6

y = 26

.
An individual is hosting a cookout for the kickball team and wants to have two hot dogs for each guest (x), and 6 extra hot dogs in case some teammates bring friends. The independent variable (x) is 10. To solve for the dependent variable (y), we use the equation:

y = 2x + 6

Now, substitute the value of x:

y = 2(10) + 6

y = 20 + 6

y = 26

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Answer: 2

Step-by-step explanation:

Answer:

It's D) compressed horizontally