£9.60:£12 as a ratio in its simplest form

Answer:  9/10

=======================================================

Explanation:

Imagine a pizza split into 5 equal slices. Then imagine that you split each slice in half. This means we now have 5*2 = 10 slices.

Eating 3 out of the original 5 is equivalent to eating 6 smaller slices out of the now 10 total.

In other words:  The fraction 3/5 is the same as 6/10

Put another way: Multiply top and bottom of 3/5 by 2 to get 6/10.

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

Gary painted 3/10 of the fence in the morning, and then 3/5 of it in the afternoon. We can replace the "3/5" with "6/10".

3/10 + 6/10 = (3+6)/10 = 9/10 total

Going back to the pizza scenario, we can imagine 3/10 as eating 3 slices out of 10 total. Then 6/10 adds 6 more slices to get 3+6 = 9 slices total. That's how we end up with 9/10 as the answer.

Answer:

45.5cm

Step-by-step explanation:

70/20 = 3.5cm per book

20- 7 = 13

13 x 3.5 = 45.5cm

The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

A Markov chain model, also known as a Markov process or simply a Markov model, is a mathematical framework used to describe and analyze systems that evolve over time.

To create a Markov chain model for a rat wandering through the maze, we need to consider the different states the rat can be in and the probabilities of transitioning between these states.

In this maze, the rat can be in different rooms. Let's say there are three rooms: A, B, and the center room (C). The center room is an absorbing state, which means that once the rat enters this room, it will stay there and not move to any other room.

To create the Markov chain, we need to define the transition probabilities between the different rooms. Since the rat is equally likely to leave its current room through any of the doorways, the transition probabilities for each room will be 1/3.

Here is an example of the transition probabilities:

1. From room A:
  - Probability of transitioning to room B: 1/3
  - Probability of transitioning to the center room C: 1/3
  - Probability of staying in room A: 1/3

2. From room B:
  - Probability of transitioning to room A: 1/3
  - Probability of transitioning to the center room C: 1/3
  - Probability of staying in room B: 1/3

3. From the center room C:
  - Probability of staying in room C: 1

Once the transition probabilities are defined, we can represent the Markov chain using a transition matrix. In this case, the transition matrix will be a 3x3 matrix, where each row represents the current room and each column represents the next possible room. The values in the matrix will correspond to the transition probabilities.

Transition matrix:
```
| 1/3   1/3   1/3 |
| 1/3   1/3   1/3 |
|   0     0     1   |
```

Note that the last row of the matrix represents the absorbing state (center room C), where the probability of transitioning to any other room is 0, and the probability of staying in the center room is 1.

By using this Markov chain model, we can analyze the rat's behavior and calculate probabilities of different events, such as the number of periods it takes for the rat to reach the center room or the probability of the rat being in a specific room after a certain number of periods.

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Answer:

D) y= -2X+1

Step-by-step explanation:

All of the lines are perpendicular to the line 2x+y=6 except for D) y= -2X+1.

To paint 70 ornaments, he will need 70 bottles of paint.

To find the total surface area of one ornament, we need to find the lateral area of each cone and add them together.

The lateral area of a cone can be found using the formula:

L = πrℓ

where L is the lateral area, r is the radius, and ℓ is the slant height.

Since the two cones are identical, we only need to find the lateral area of one cone and then multiply it by two.

For each cone, we have:

r = 3.9 cm

ℓ = 8.4 cm

Using the formula, we get:

L = π(3.9)(8.4) ≈ 103.45 cm²

So the lateral area of both cones is:

2L = 2(103.45) = 206.9 cm²

The total surface area of one ornament is the sum of the lateral area and the area of the circular base:

A = πr² + 2L

A = π(3.9)² + 2(103.45)

A ≈ 235 cm²

Since one bottle of paint covers an area of 235 cm², Tim will need one bottle of paint for each ornament.

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The complete question is given in the attached image.

The least amount of money she needs to deposit to avoid a fee is;  $16.62

We are given;

Amount Keisha has in her checking account = $585.43

Minimum balance to be maintained = $300

Check written = $302.05

Now, if x represents the variable, that would be used for the least amount of money she needs to deposit to avoid a fee, then the inequality is;  $585.43 - $302.05 + x ≥ $300

$283.38 + x ≥ $300

Subtract 283.38 from both sides to get;

x ≥ $16.62

Thus, the least amount of money she needs to deposit to avoid a fee is;  $16.62

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The original price of the television was $240.

Let's denote the original price of the television by "x".

From the first sentence, the website applies a 4.5% processing fee and charges $6.00 for shipping. Therefore, the cost of the television with these fees is:

x + 0.045x + 6.00 = 1.045x + 6.00

From the second sentence, the customer uses a coupon that takes 15% off of the final price. Therefore, the price after the discount is:

0.85(1.045x + 6.00) = 0.88825x + 5.10

The problem states that the customer paid $218.28 for the order. Therefore, we can set up the following equation:

0.88825x + 5.10 = 218.28

Solving for x, we get:

0.88825x = 213.18

x = 240

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Answer: 4,875.05

Step-by-step explanation:

I took the quiz

Answer:

d

Step-by-step explanation:

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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We need to write the equation for the expression "nine less than a number n":

Answer:

The median of the scores in this stem-and-leaf plot is 78

Step-by-step explanation:

The total data set represented by Stem and leaf in order from the least to the greatest are as following:

58, 59, 64, 64 , 66, 68, 72, 74, 75, 76, 78, 79, 83, 84, 86, 87, 88, 91, 93, 93, 95

The number of data is 21

The median of the data at the place number 11

So, median = 78

Answer:

D

Step-by-step explanation:

The result of the integral \(\int\limits^2_0 {(2\cdot x + 3)\cdot f''(x)} \, dx\) based on the incomplete graph of \(f'\) is approximately 35.943. (Choice C)

Based on the information given on the figure, we have a set of points which resembles a second order polynomial, whose expression can be found by the fact that coefficients can be found by know three distinct points: \((x_{1}, y_{1}) = (0, 1)\), \((x_{2}, y_{2}) = (1, 2.718)\), \((x_{3}, y_{3}) = (2, 7.389)\)

Then, we form the following system of linear equations:

\(c = 1\) (1)

\(a + b + c = 2.718\) (2)

\(4\cdot a + 2\cdot b + c = 7.389\) (3)

The solution of this system is: \(a = 1.4765\), \(b = 0.2415\), \(c = 1\). Then, the expression of the first derivative is:

\(f'(x) = 1.4765\cdot x^{2} + 0.2415\cdot x + 1\) (4)

And the second derivative is:

\(f''(x) = 2.953\cdot x + 0.2415\) (5)

Then, we have the following integral equation:

\(I = \int\limits^{2}_{0} {(2\cdot x + 3)\cdot (2.953\cdot x + 0.2415)} \, dx\)

\(I = \int\limits^{2}_{0} {(5.906\cdot x^{2}+9.342\cdot x +0.7245)} \, dx\)

\(I = 5.906\int\limits^{2}_{0} {x^{2}} \, dx + 9.342\int\limits^{2}_{0} {x} \, dx + 0.7245\int\limits^{2}_{0} \, dx\)

\(I = \frac{5.906}{3}\cdot (2^{3}-0^{3}) + \frac{9.342}{2}\cdot (2^{2}-0^{2}) + 0.7245\cdot (2-0)\)

\(I = 35.882\)

This choice that is closest to this result is C. \(\blacksquare\)

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Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

Answer:

C

Step-by-step explanation:

if you draw a line between the points then draw vertical lines they dont cross more than one dot

Answer:

the answer is 6 just do the math and it's pretty easy

Steps to solve:

4 + (9 * 2) / (4 - 1) - 4

~Simplify what is in parenthesis

4 + (18) / (3) - 4

~Divide

4 + 6 - 4

~Add

10 - 4

~Subtract

6

Best of Luck!

Answer:

Yes

Step-by-step explanation:

The rule side,angle,side can be applied to these triangles

So... option 4 (SAS)

Answer:

They are congruent by SAS criteriorn.

This is because the two sides of both triangles with the angle between those sides are congruent in both triangles, therefore, congruent by SAS (SIDE-ANGLE-SIDE) criterion

Step-by-step explanation:

In hypothesis testing, the tentative assumption about the population parameter is either the null hypothesis or the alternative hypothesis. The null hypothesis (denoted as H₀) represents the statement that there is no significant difference or effect between the variables being studied, while the alternative hypothesis (denoted as H₁) asserts that there is a significant difference or effect.

Hypothesis testing involves comparing observed data against these hypotheses to determine which one is more likely to be true. Researchers aim to either reject or fail to reject the null hypothesis, based on the evidence provided by the data. If the null hypothesis is rejected, it suggests that the alternative hypothesis is more likely to be true.

To make this decision, a significance level (usually denoted as α) is chosen to quantify the risk of making a Type I error, which is rejecting the null hypothesis when it is actually true. Common significance levels are 0.05 or 0.01. If the probability of observing the data (or more extreme) under the null hypothesis, called the p-value, is less than the chosen significance level, the null hypothesis is rejected in favor of the alternative hypothesis.

In summary, hypothesis testing involves evaluating the tentative assumptions about the population parameter using the null and alternative hypotheses to draw conclusions based on the observed data.

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Answer:

33 oz

Step-by-step explanation:

63x1/3=21

63x1/7=9

21+9=30

63-30=33

33 oz of powdered sanitizer is left in the bag.

I took 1/3 of 63 first, to show how much he used on the pool. Then I took 1/7 of 63 to show how much he used on the hot tub. I added the amount he used, and subtracted them from 63 to see how much was left. He had 33 oz left in the bag. Hope this helps! Good luck! :)

Answer:

Step-by-step explanation:

If the coordinates of A are (3,-6) then the coordinates if A after dilation by a factor 1/3 then the coordinates will be (9,-18).

The dilation is the action or condition of becoming or being made wider, larger,or more open, point or figure. The area of shape will be area/ factor after dilation.

We have been given point A whose coordinates are (3,-6). We have to plot the point A after dilation with factor 1/3,

The x value after dilation will be 3/1/3=9

The y value after dilation will be -6/1/3=-18.

Hence the coordinates of A after dilation are (9,-18).

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Answer:

19 miles

Step-by-step explanation:

Length of new road - Length of old road = Change in length = 23 - 4 = 19

The correct statement regarding the mode of the sample is given as follows:

a. can be larger, smaller or equal to the mode of the population.

The mode of a data-set is the observation that appears the most often in the data-set.

The mode of the sample is simply the most frequently occurring value in the sample. It is not necessarily expected to be the same as the mode of the population, which is the most frequently occurring value in the entire population.

As a sample is a group taken from an entire population, the observation that appears the most in the sample can be different from the more common observation in the population,

Hence, option (a) is correct.

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Answer:

The answer is 8.27×10^4

Answer: 8.27×10^4

Step-by-step explanation:

The structure of an expression to identify ways to rewrite it is Distributive Property, Commutative and Associative Properties, Exponent Rules and Factoring.

Interpreting the structure of expressions is a key aspect of algebraic understanding. By analyzing the structure, we can identify patterns, operations, and relationships within the expression, allowing us to make simplifications or rewrite the expression in a more concise or equivalent form. Here are some common ways to interpret the structure of expressions and identify ways to rewrite them:

Distributive Property: If you have an expression with a common factor multiplied by multiple terms within parentheses, you can apply the distributive property to distribute the factor to each term. For example:

\(3(x + y)\) can be rewritten as \(3x + 3y\).

Grouping: If you notice terms with similar factors or variables, you can group them together using parentheses or factoring out common factors. For example:

\(x + 2x + 3x\) can be rewritten as \((1 + 2 + 3)x\) or 6x.

Commutative and Associative Properties: The commutative property allows us to change the order of addition or multiplication, while the associative property allows us to change the grouping of terms without changing the result. For example:

2 + 3 + 4 can be rewritten as 4 + 3 + 2 (commutative property) or (2 + 3) + 4 (associative property).

Simplifying Operations: If you have expressions involving addition, subtraction, multiplication, or division of like terms, you can simplify or combine them. For example:

\(2x + 3x\) can be rewritten as 5x (combining like terms).

Factoring: If you have a polynomial expression, you can factor out common factors or use factoring techniques to simplify the expression. For example:

\(x^2 + 4x + 4\) can be factored as \((x + 2)^2\).

Exponent Rules: If your expression contains exponents, you can apply exponent rules to simplify or rewrite the expression. For example:

\((x^2)^3\)can be rewritten as x^6 (applying the rule for exponentiation of a power).These are just a few examples of how you can interpret the structure of expressions to identify ways to rewrite them. By analyzing the patterns, operations, and relationships within the expression, you can apply appropriate algebraic techniques to simplify, combine, or transform the expression into a more manageable or equivalent form.

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The required return for a stock with a beta of 2.20, a risk-free rate of 2%, and a market risk premium of 6% is 14.39%.  The correct option is c.

To calculate the required return, we can use the Capital Asset Pricing Model (CAPM), which relates the expected return of a stock to its beta, the risk-free rate, and the market risk premium. The formula for CAPM is as follows:

Required Return = Risk-Free Rate + (Beta × Market Risk Premium)

In this case, the risk-free rate is 2% and the market risk premium is 6%. The beta of the stock is given as 2.20. Plugging these values into the formula, we get:

Required Return = 2% + (2.20 × 6%) = 2% + 13.2% = 15.2%

Therefore, the correct answer is option C: 14.39%.

The CAPM is a widely used model in finance to estimate the required return on an investment. It takes into account the risk-free rate, which represents the return on a risk-free investment such as government bonds, and the market risk premium, which represents the additional return investors expect to receive for taking on the risk of investing in the overall market.

The beta of a stock measures its sensitivity to market movements, and multiplying it by the market risk premium gives us an estimate of the stock's additional required return. By summing this additional return with the risk-free rate, we obtain the required return for the stock.

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Answer:

honestly idc use a calculator

Step-by-step explanation:

Answer:

78.5

Step-by-step explanation:

πr²

= π×5²

= 25π

= 78.5