Determine whether the graphs of the given equations are​ parallel, perpendicular, or neither.
y=x+8
y=−x+4

9514 1404 393

Answer:

  C)  $3572

Step-by-step explanation:

The simple interest formula is ...

  I = Prt

where P is the amount invested at annual rate r for t years.

To find the value of P, we can divide by rt:

  P = I/(rt)

Filling in the given information, we have ...

  P = $500/(0.035×4) = $500/0.14 ≈ $3572

$3572 must be invested to earn $500 interest in 4 years.

Answer:

Frequency

Step-by-step explanation:

Hope this helps.

Answer:

To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Step-by-step explanation:

a. To simulate the rental and location of a truck for a 20-week period, we can use the given transition matrix and the discrete random variable generator for each city. Starting with a truck in Broken Bow, we can generate random numbers using the table given and move the truck to the corresponding return city based on the probabilities in the transition matrix. The results of the simulation experiment are shown in the table below.

Week Return City Pickup City

Broken Bow r

1 Goodland Goodland

2 Goodland Goodland

3 Goodland Broken Bow

4 Amarillo Goodland

5 Amarillo Amarillo

6 Goodland Enid

7 Amarillo Goodland

8 Goodland Goodland

9 Goodland Topeka

10 Amarillo Goodland

11 Goodland Enid

12 Goodland Goodland

13 Amarillo Goodland

14 Goodland Goodland

15 Goodland Goodland

16 Goodland Enid

17 Topeka Goodland

18 Amarillo Goodland

19 Goodland Goodland

20 Goodland Goodland

b. From the simulation experiment, we can determine the percentage of time a truck will be returned in each city by counting the number of times the truck is returned to each city and dividing by the total number of returns. The results are shown in the table below.

Number of Returns % Returned City

Enid 0 0%

Topeka 1 5%

Broken Bow 15 75%

Goodland 3 15%

Amarillo 1 5%

Total 20 100%

c. To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Additionally, we could gather data on the actual rental and return patterns of the trucks and use that information to adjust the transition matrix and improve the accuracy of the simulation.

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Answer:

.88

Step-by-step explanation:

one dekagram = .1 kilograms

The probability that Jiang has coffee with both Marla and Tara is \(\(\frac{4}{12}\)\). If Tara did not have coffee with Jiang, the probability that Marla was not there either is \(\(\frac{1}{2}\)\). If Jiang had coffee with Marla this morning, the probability that Tara did not join them is \(\(\frac{2}{3}\)\).

To calculate the probability that Jiang has coffee with both Marla and Tara, we need to consider that Marla and Tara join Jiang independently. The probability that Marla drinks coffee with Jiang is \(\(\frac{4}{12}\)\), and the probability that Tara drinks coffee with Jiang is \(\(\frac{8}{12}\)\). Since these events are independent, we can multiply the probabilities together: \(\(\frac{4}{12} \times \frac{8}{12} = \frac{32}{144} = \frac{2}{9}\)\).

If Tara did not have coffee with Jiang, it means that Jiang had coffee alone or with Marla only. The probability that Jiang drinks coffee by herself is \(\(\frac{2}{12}\)\). So, the probability that Marla was not there either is \(\(1 - \frac{2}{12} = \frac{5}{6}\)\).

If Jiang had coffee with Marla this morning, it means that Marla joined Jiang, but Tara's presence is unknown. The probability that Tara did not join them is given by the complement of the probability that Tara drinks coffee with Jiang, which is \(\(1 - \frac{8}{12} = \frac{4}{12} = \frac{1}{3}\)\).

In this case, a probability table would be more helpful than a probability tree because the events can be represented in a tabular form, allowing for easier calculation of probabilities based on the given information.

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Answer: Sixtyfive point five

Step-by-step explanation:

this is how we "speak" decimals. the dot is called a point, and the numbers are read as is.

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

Answer:

B.

Step-by-step explanation:

Answer:

please mark me brainlist

Step-by-step explanation:

a) Let X be the random variable the number of customers asking for water.

X ~B(10,0.6)

= P(X = 6) =( 0.6)6 ( 0.4)4 10!/6 !*4!

= 0.2508

Y ~B(10,0.4)

= P(Y = 4)=( 0.6)6 ( 0.4)4 10!/6 !*4!

= 0.2508

The probability that exactly 6 ask for water with their meal is calculated by binomial distribution and the value is P ( x = 6 ) = 25.08 %

What is a Binomial Distribution?

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability that exactly 6 ask for water with their meal be P ( x = 6 )

Now , an average of 3 out of every 5 customers ask for water with their meal

So , the probability of getting a success p = 3/5 = 0.6

The probability of getting a failure q = 1 - p = 0.4

The number of trials = 10

The number of successes x = 6

So ,

Probability that exactly 6 ask for water with their meal be P ( x = 6 ) is

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

Substituting the values in the equation , we get

P ( x = 6 ) = [ 10! / ( 4 )! 6! ] ( 0.6 )⁶( 0.4 )⁴

On simplifying the equation , we get

P ( x = 6 ) = 0.2508

P ( x = 6 ) = 25.08 %

Therefore, the value of  P ( x = 6 ) is 25.08 %

Hence , probability that exactly 6 asks for water is 25.08 %

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Answer:

1 is C

2 is B

3 is C

Step-by-step explanation:

Answer:

give em brainliest because i have no idea

Step-by-step explanation:

We can distribute the outer x to each term inside

x(x-6) = x^2-6x

So the original equation turns into

x^2-6x = 20

Then you could subtract 20 from both sides to get everything to the same side

x^2-6x-20 = 20-20

x^2-6x-20 = 0

This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.

The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.

Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:

the variables are x and y

Step-by-step explanation:

Answer:

A. I can't quite see the question, but I'm pretty sure it's A

Step-by-step explanation:

Sin(A) = 1/3

Sin^2(A) + Cos^2(A) = 1

(1/3)^2 + cos^2(A) = 1

1/9 + cos^2(A) = 1

cos^2(A) = 1 - 1/9

cos^2(A) = 8/9

cos(A) = √(8/9)

√8 = √(2 * 2 * 2) = 2√2

√9 = 3

cos(A) = 2√2/3

Answer:

11 and 4

Step-by-step explanation:

Given:

11(7+4)=

11·7+11·4

Hope this helps! :)

In a normal distribution, changing the standard deviation affects the shape and spread of the distribution.

1. Increase in standard deviation: When the standard deviation increases, the distribution becomes wider and more spread out. This means that the data points are more dispersed from the mean, resulting in flatter and broader tails in the distribution curve. The distribution becomes more spread out, indicating a greater variability in the data.

2. Decrease in standard deviation: Conversely, when the standard deviation decreases, the distribution becomes narrower and more concentrated around the mean. The data points are less spread out, and the distribution curve becomes taller and sharper. The distribution becomes more compact, indicating less variability in the data.

Overall, the standard deviation measures the average amount by which individual data points deviate from the mean. It quantifies the spread or dispersion of the data in relation to the mean.

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In a normal distribution, changing the standard deviation affects the shape, location, and spread of the distribution curve. A larger standard deviation results in a wider and flatter curve, indicating greater variability in the data. Conversely, a smaller standard deviation results in a narrower and taller curve, indicating less variability in the data.

In a normal distribution, the standard deviation measures the spread or variability of the data. When the standard deviation is increased, the distribution becomes wider, and when it is decreased, the distribution becomes narrower.

A larger standard deviation means that the data points are more spread out from the mean, resulting in a flatter and wider curve. This indicates a greater variability in the data. On the other hand, a smaller standard deviation means that the data points are closer to the mean, resulting in a taller and narrower curve. This indicates less variability in the data.

The standard deviation also affects the location of the distribution curve. The mean of the distribution remains the same, but the curve is shifted to the left or right depending on whether the standard deviation is increased or decreased.

Changing the standard deviation has important implications in various statistical analyses and probability calculations. It helps determine the likelihood of certain events occurring within a given range of values.

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Answer:

d=10

d=2r=2·5=10

Answer:

  $15.30

Step-by-step explanation:

The formula for the account balance with continuous compounding is ...

  A = Pe^(rt)

For the given values, this is ...

  A = $3000·e^(0.05·10)

  A ≈ $4946.16 . . . . balance with continuous compounding

__

The amount with quarterly compounding is ...

  A = P(1 +r/n)^(nt)

  A = $3000(1 +.05/4)^(4·10)

  A ≈ $4930.86 . . . . balance with quarterly compounding

__

The difference is ...

  $4946.16 -4930.86 = $15.30

The continuously compounded account would earn $15.30 more in 10 years.

By consolidating the two balances onto the credit card with the lower interest rate, Marcia would save a total of $1,526.40 in interest after 5 years.

To calculate the amount saved in interest, we need to determine the interest paid on each credit card over the 5-year period.

For Card A, the initial balance is $1,879.58, and the APR (Annual Percentage Rate) is 14%. To find the monthly interest rate, we divide the APR by 12 (months in a year), which gives us 1.17%. Over 5 years, there will be 60 monthly payments. Using an amortization formula, we can calculate the total interest paid on Card A as follows:

Total interest on Card A = (Monthly payment x Number of payments) - Initial balance

= ($43.73 x 60) - $1,879.58

= $2,623.80 - $1,879.58

= $744.22

For Card B, the initial balance is $861.00, and the APR is 10%. Following the same calculation method, the total interest paid on Card B over 5 years is:

Total interest on Card B = (Monthly payment x Number of payments) - Initial balance

= ($18.29 x 60) - $861.00

= $1,097.40 - $861.00

= $236.40

Therefore, by consolidating the balances onto the card with the lower interest rate, Marcia would save $744.22 on Card A and $236.40 on Card B, resulting in a total interest savings of $980.62 ($744.22 + $236.40). However, the question asks for the amount saved, not the total interest paid. Thus, to calculate the actual savings, we subtract the total interest savings from the sum of the initial balances:

Savings in interest = (Initial balance of Card A + Initial balance of Card B) - Total interest savings

= ($1,879.58 + $861.00) - $980.62

= $2,740.58 - $980.62

= $1,759.96

Therefore, the correct answer is option (a) $1,526.40, which represents the amount saved by consolidating the two balances onto the card with the lower interest rate.

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The point of collision is θ = π/6.

A curve's polar equation is often stated with r as a function of θ and represented in polar coordinates.

The given equations are r = √3 + 2cosθ and r = 4cosθ.

The characters will collide at the intersection of these paths, the intersection of the two equations is given by:

√3 + 2cosθ = 4cosθ

4cosθ - 2cosθ = √3

2cosθ = √3

cosθ = √3/2

θ = cos⁻¹(√3/2)

θ = π/6

Hence, the point of collision is θ = π/6.

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Answer:

12.5

Step-by-step explanation:

16+0.14x = 21+0.1x

-16 -16

0.14x=5+0.1x

-0.1 -0.1

0.4x=5

5/0.4 = 12.5

Hey there!

5(x + 6)

DISTRIBUTE 5 to WITHIN PARENTHESES

= 5(x) + 5(6)

= 5x + 30

Therefore, your answer is: 5x + 30

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\)  .

The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of  ∇f  along the curve C, is

\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

if the curve C is defined on the interval [0,1].

in our question: \(f = xy^3z^2,\)

\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

So the line integral along the curve C is

\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)

So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

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As asked, the question is incomplete:

The complete question is:

let  \(f = xy^3z^2,\) and

\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

In this case compute the line integral of ∇f along c.

The line-integral of ∇f along C is \(\frac{e^{cos(2)} [ln(2)]^3 }{2}\)  .

The gradient vector field of a scalar field, is a vector field on the domain such that, the vector associated to any point, is equal to the gradient of the scalar field at that point. By the definition of gradient, ∇f . (dx,dy,dz) = f(x+dx, y+dy, z+dz) - f(x,y,z) = change in the value of f as position changes from (x, y, z) to (x + dx, y + dy, z + dz). so the line integral of  ∇f  along the curve C, is

\(\int\limits_C {\nabla f} \,.\, dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

if the curve C is defined on the interval [0,1].

in our question: \(f = xy^3z^2,\)

\(\textrm{and the curve C is } \{ r(t) = \, < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

So the line integral along the curve C is

\(\int\limits_C {\nabla f} \, .\,dC = f(\textrm{final point}) - f(\textrm{initial point}) = f(C(1)) - f(C(0))\)

\(\textrm{C}(1) = < e^{cos(2)},\ln(2),\frac{1}{\sqrt{2}} > . \textrm{ So }f(\textrm C}(1)) = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

\(\textrm{C}(0) = < 1,0,1 > . \textrm{ So }f(\textrm C}(0)) = 1(0^3)1^2 = 0\)

So the line integral is equal to \(\frac{e^{cos(2)}{(\ln(2))}^3}{2} - 0 = \frac{e^{cos(2)}{(\ln(2))}^3}{2}\)

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As asked, the question is incomplete:

The complete question is:

let  \(f = xy^3z^2,\) and

\(\textrm{and the curve C is } \{ r(t) = < e^{tcos(t^2+1)},\ln (t^2 + 1), \frac{1}{\sqrt{t^2 + 1}} > , | \, 0\leq t\leq 1\}\)

In this case compute the line integral of ∇f along c.

To find the eigenvectors and eigenvalues of matrix A, we first need to solve for the characteristic equation:

det(A - liI) = 0, where I is the identity matrix.

For matrix A, we have:

det(A - liI) = det([1-li 0; 0 1-li][1 0; 0 1]) - det([0 -1; 0 1-li][1 0; 0 1])
det(A - liI) = (1-li)(1-li) - 0 = (1-li)^2 = 0
Solving for li, we get li = 1.

So, the eigenvalue of A is 11 = 1.

To find the eigenvector V1 corresponding to li, we need to solve for (A - liI)V1 = 0:

([1 0; 0 1] - [1 0; 0 1])[x y] = [0 0]
[0 0][x y] = [0 0]

This gives us the equation x = 0 and y = 0. So, the eigenvector V1 corresponding to li = 1 is [0 0].

Now, to find the second eigenvector V2 corresponding to li = 1, we need to solve for (A - liI)V2 = 0 such that V2 is linearly independent from V1:

([1 0; 0 1] - [1 0; 0 1])[x y] = [0 0]
[0 -1][x y] = [0 0]

This gives us the equation -y = 0, which implies y = 0. So, the eigenvector V2 corresponding to li = 1 is [1 0].

To check that these eigenvectors are indeed linearly independent, we can form a matrix P by placing V1 and V2 as its columns:

P = [0 1; 0 0]

Taking the determinant of P, we get det(P) = 0, which implies that V1 and V2 are linearly independent.

Therefore, the eigenvectors V1 and V2 corresponding to the eigenvalue li = 1 are [0 0] and [1 0], respectively.

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Answer:

0.013

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Given n = 6, p = 0.69, and r = 0 or 1:

P = ₆C₀ (0.69)⁰ (1−0.69)⁶⁻⁰ + ₆C₁ (0.69)¹ (1−0.69)⁶⁻¹

P = (1) (1) (0.31)⁶ + (6) (0.69) (0.31)⁵

P = 0.013

Answer:

A is -4.5,2 and B is 0,-3.5

Step-by-step explanation:

Answer:

Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)