25 Patricia bought 5 apples and 7 bananas for $12. 65. Jose bought 10 apples and 8 bananas for $18. 10 at the same grocery store. What is the cost of one apple?​

Answer:

y= 1/4x -3

Step-by-step explanation:

point-slope form: y-y1=m(x-x1)

y-2=1/4(x-4)

y-2= 1/4x - 1

y= 1/4x - 3

The equation of a line in point-slope form with slope 1/4 and point (4, 2)

is y - 2 = (1/4)(x - 4).

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

The equation of a line is point-slope form is y - y₁ = m(x - x₁).

Given, Slope is 1/4 and has point (x₁, y₁) = (4, 2).

∴ The equation of the given line is y - 2 = (1/4)(x - 4).

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The Laplace transform of the function 1 u^5/2(t)e^5tcos(πt) with respect to the variable s can be computed using the properties and formulas of Laplace transforms.  

The Laplace transform is a mathematical operation that transforms a function of time into a function of complex variable s. It is denoted as L{f(t)} = F(s), where f(t) is the original function and F(s) is its Laplace transform.

To compute the Laplace transform of the given function, we can apply the linearity property of Laplace transforms. First, we can compute the Laplace transform of each term separately. The Laplace transform of 1 is 1/s, the Laplace transform of u^5/2(t) is u^5/2/s^(5/2), and the Laplace transform of e^5tcos(πt) is (s-5)/(s-5)^2 + π^2.

Then, we can combine these individual Laplace transforms using the properties of Laplace transforms, such as the multiplication property and the linearity property. The Laplace transform of the entire function will be the product of the Laplace transforms of its individual terms.

Therefore, the Laplace transform of the function 1 u^5/2(t)e^5tcos(πt) with respect to s is (1/s) * (u^5/2/s^(5/2)) * ((s-5)/(s-5)^2 + π^2).

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Answer:

88

Step-by-step explanation:

the median is 88

the mean is 87.5

Answer:

The cost of 15 potatoes is $7.50

Step-by-step explanation:

The potatoes are sold at a rate of $0.5 per potato.

1. Given Amanda can only spend $5 on potatoes at that price, she can buy at most $5 / 0.5 = 10 potatoes.

Amanda can buy at most 10 potatoes

2. Sam wants to buy 15 potatoes at that very same price. The cost of 15 potatoes is:

15 * $0.5 = $7.50

The cost of 15 potatoes is $7.50

The statements that are true regarding function S are:

What is function?

In mathematics, a function is a rule or a relationship between two sets of values, which associates each element of the first set (called the domain) with a unique element of the second set (called the range). The domain and range can be any sets, including numbers, letters, or other objects.

The statements that are true regarding function S are:

The other statements are not necessarily true:

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% Initialize variables

delta = 1/2;

M = 100;

N = 150;

% Create a vector of particle positions

x = zeros(M, N);

% Simulate the random walk

for n = 1:N

 for i = 1:M

   x(i, n) = x(i, n - 1) + randi([-1, 1], 1, 1) * delta;

 end

end

% Plot the particle positions

figure

plot(x)

xlabel('Timestep')

ylabel('Position')

The first paragraph of the answer summarizes the code. The second paragraph explains the code in more detail.

In the first paragraph, the code first initializes the variables delta, M, and N. delta is the step size, M is the number of particles, and N is the number of timesteps. The code then creates a vector of particle positions, x, which is initialized to zero. The next part of the code simulates the random walk.

For each timestep, the code first generates a random number between -1 and 1. The random number is then used to update the position of each particle. The final part of the code plots the particle positions. The x-axis of the plot represents the timestep, and the y-axis represents the position.

The code can be modified to simulate different types of random walks. For example, the step size can be changed, or the probability of moving forward or backward can be changed. The code can also be used to simulate random walks in multiple dimensions.

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Answer:

\(the \: equation \: is \: equivalent \: to \\ 2 \: { \sin }^{2} (( \: \frac{\pi}{2}) \: {cos}^{2} x ) = \\ \: 2 \: {sin}^{2} (( \frac{\pi}{2} sin \: 2x \: ) \\ = {cos}^{2} x = sin \: 2x \\ = \: \cos \: x(cos \: x \: - \: 2 \: sin \: x) \: = \: 0 \\ = \: 1 - 2 \tan \: x = 0 \: as \: cos \: x \: ≠ 0 \\ x ≠ (2n + 1) \frac{\pi}{2} \\ = \tan(x) = \frac{1}{2} \\ = \cos(2x) = \frac{1 - {tan \: }^{2}x }{1 + {tan \: }^{2} \:x } = \frac{3}{5} \)

The estimated total time for all five pools is approximately 13.85 hours.

To estimate the time required to install the fifth pool using the learning curve, we can use the formula:

Time for nth unit = Time for first unit * (n^b)

Where:

Time for nth unit is the estimated time to install the nth pool

Time for first unit is the estimated time to build the first pool (30 hours)

n is the number of units (in this case, n = 5 for the fifth pool)

b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))

Let's calculate the estimated time for the fifth pool:

b = log(0.85) / log(2) ≈ -0.157

Time for fifth pool = Time for first pool * (5^b)

Time for fifth pool = 30 * (5^(-0.157))

Calculating this, we find:

Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours

Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.

To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:

Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))

Using this formula, let's calculate the total time for all five pools:

Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))

Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))

Calculating this, we find:

Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours

Therefore, the estimated total time for all five pools is approximately 13.85 hours.

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Answer:

A=80 square feet.

Step-by-step explanation:

First, we find the area of the model. 6*4=24. Now, due to the ratio of 1:40, we know that every inch is actually forty inches. So, you do this:

24*40=960.

So, the area of the actual living room is 960 inches. Or 80 feet.

Answer:

√89

Step-by-step explanation:

√(4+4)2+(0-5)2

√(8)2+(-5)2

√64+25

√89

Answer:

here!

Step-by-step explanation:

so graphing lines are pretty hard but this one is fairly simple. here the slope formula format is y=mx+b

m being the slope

and b being the y-intercept

so as you can see your equation has no slope meaning your line is just going to be straight

and then if you take a look to find the only other thing your equation has in it is a 6 as the y-intercept meaning in order to graph this find where 6 is on the y-axis (the vertical line on the side) and draw a line going horizontal and put a dot or a point on (0,6) to mark that you have found the y-intercept and that this is the only known point on your line graph so far with the information given. i hope this makes sense, and have a great day!

The expression for the rectangular prism's base area is 11x² + 7x + 5.

Given;

The volume of rectangular prism = 33x³ + 43x² + 29x + 10

The height of the prism = 3x + 2

We know that, the area of the prism = length * breadth

where as, volume = length * breadth * height

So, area = volume / height

Using synthetic division, dividing volume by height, we get;

3x+2  ) 33x³ + 43x² + 29x + 10 ( 11x² + 7x + 5

            33x3 + 22x2

           ---------------------------------

                        21x² + 29x

                        21x² + 14x

          ----------------------------------

                                  15x + 10

                                   15x + 10

          ----------------------------------

                                       x

Quotient is 11x² + 7x + 5 which is equal to expression for the area of the base of the rectangular prism.

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We have come to find that confidence interval is (16.802, 37.998) μg

Micrograms: This is a unit for measuring the weight of an object. It is equal to one millionth of a gram.

To find a 95% confidence interval for the difference in mean selenium intakes between the two regions, we can use the following formula:

Confidence interval = (x1 - x2) ± t * SE

where:

x1 and x2 are the sample means for region 1 and region 2, respectively.

t is the critical value from the t-distribution for a 95% confidence level.

SE is the standard error of the difference, calculated as follows:

\(\rm SE = \sqrt{((s_1^2 / n_1) + (s_2^2 / n2))\)

Let's calculate the confidence interval using the given values:

x₁ = 167.8

s₁ = 24.5 μg

n₁ = 40

x₂ = 140.9

s₂ = 17.3 μg

n₂ = 40

SE = √((24.5² / 40) + (17.3² / 40))

SE ≈ 4.982

Now, we need to determine the critical value from the t-distribution. Since both sample sizes are 40, we can assume that the degrees of freedom are approximately 40 - 1 = 39. Consulting a t-table or using a statistical software, the critical value for a 95% confidence level with 39 degrees of freedom is approximately 2.024.

Substituting the values into the confidence interval formula:

Confidence interval = (167.8 - 140.9) ± 2.024 * 4.982

Confidence interval = 26.9 ± 10.098

Rounded to three decimal places:

Confidence interval ≈ (16.802, 37.998) μg

Interpretation:

We are 95% confident that the true difference in mean selenium intakes between the two regions falls within the interval of 16.802 μg to 37.998 μg. This means that, on average, region 1 has a higher selenium intake than region 2 by at least 16.802 μg and up to 37.998 μg.

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Answer:

344 = 12*22 + 80

Step-by-step explanation:

They made the ball 22 times

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\(2 {y}^{2} - 9y - 2 + 4(y + 1) = \)

\(2 {y}^{2} - 9y - 2 + 4y + 4 = \)

\(2 {y}^{2} - 9y + 4y - 2 + 4 = \)

Collect like terms

\(2 {y}^{2} - 5y + 2 = \)

\((2y - 1 )(y - 2)\)

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Answer:

2y² - 5y + 2

Step-by-step explanation:

Original equation:

2y² - 9y - 2 + 4(y + 1) =​

Use distributive property

4 · y = 4y

4 · 1 = 4

Plug these values back into the equation:

2y² - 9y - 2 + 4y + 4 = ?

Combine like terms

2y² - 5y - 2 + 4

Combine more like terms

2y² - 5y + 2

That is the most simplified version

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Answer: In math End Behavior describes a graph at its end values. To explain, it is the high values and what the graph would like like as x values get very high and how it would look for the y values. Also, in terms of graph looks, this could be an exponential or logarithmic curve as values get very high. Think about End Behavior as the graphical patterns when the values get high. Hope this helps! Please give this a brainiest if this was helpful as I am one away from the next rank.

Step-by-step explanation:

Answer:I hope this helps

Step-by-step explanation:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

End behavior refers to the appearance of a graph as it is followed indefinitely in either horizontal direction. Leading coefficient POSITIVE: both "ends" are UP. Leading coefficient NEGATIVE: both "ends" are DOWN. Leading coefficient POSITIVE: left end is DOWN and right end is UP.

If the degree is odd and the lead coefficient is positive, then the right end of the graph will point up and the left end will point down. If the degree is odd and the lead coefficient is negative, then the right end of the graph will point down and the left end will point up

Answer:

Conversion: a change in the form of a measurement, different units, without a change in the size or amount.

for a further explanation please give us more information about the question

8. -a+b-7

9. m=(y-b)/x

Answer:

first one: C

second one: A

Step-by-step explanation:

4a - 5 + 3b - 2 - 2b - 5a

combine a terms:

-a - 5 + 3b - 2 - 2b

combine b terms:

-a - 5 + b - 2

combine numbers:

-a  + b - 7 (this is option c)

_____________________

y = mx + b, solve for m

subtract b from both sides:

y - b = mx + b - b

y - b = mx

divide both sides by x:

(y - b)/x = mx/x

m = (y - b)/x (this is option a)

The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

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Answer: Expression that is to be deducted will be (6x + 3).

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Answer:

x = 138° because they are alternate interior angles. Alternate interior angles are congruent.

Step-by-step explanation:

Answer:

Likely

Step-by-step explanation:

There are only 2 odd numbers so you’re more likely to get an even number than an odd one.

Answer:

2.24/0.16

736.434 × 0.019011

Step-by-step explanation:

The above questions have a solution of 14.

Answer:

Neither

Step-by-step explanation:

Perpendicular: Slope = -1/x

Parallel: Slope = x

Perpendicular slope is negative reciprocal of original slope. Parallel slope is equal to original slope.

Make these lines into slope-intercept form.

1)

2x+3y=1

3y=-2x+1

y=-2/3x+1/3

Slope: -2/3

2)

3x=3

x=1

Slope = undefined

Undefined ≠ -2/3

Answer:

y = 3

Step-by-step explanation:

3(2y-3) = -4y+21

6y-9 = -4y+21

10y-9 = 21

10y = 30

10y/10 = 30/10

y = 3

The sample size which is required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03 is equals to the 382.

We have provide that the state education commission wants to draw an estimate on the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Population proportion, p = 0.21

confidence level = 85%

Margin of error = 0.03,

We have to determine the sample size. For determining sample size for estimating a population propotion, using the below formula,

n = (Zα/2)² ×p×(1-p) / MOE²

where MOE is the margin of error

Using the distribution table, Zc for 85% for confidence level where α = 0.15 or α/2 = 0.075 equals to the 1.439.

Substituting all known values in formula we

n = 1.439² × 0.21( 0.79)/ (0.03)²

=> n = 382.2336 ~ 382

Hence, required sample size is 382.

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Answer:

Sometimes true. It may be true at times if x or y equal each other, but if they do not equal each other it is not true

Step-by-step explanation:

We are given two expressions:  x -3 and y  - 3

Here x and y are two different variables.

These expressions are equal, when the value of x and the value of y are equal.

x - 3 = y -3 if x = y.

Therefore, the two expressions have the same value in sometimes.

That is, when x = y, then the value of two expressions are the same.

Example.

If x = 2 and y = 2, then

x - 3 = y - 3

2 - 3 = 2 - 3

-1 = -1

If they have different values, for x =  2 and y = 3

x - 3 = y - 3

2 - 3 = 3 -3

-1 = 0

Which is not true.

Therefore, the answer is sometimes.