Describe a time you needed to use an equation or an inequality in your everyday life.
How did you apply it?
What were the results of your calculations?
How could you help a friend with a similar situation to find success with their problem using equations or inequalities?

The correct option for the approximate value of [tex]\sf -12 + \sqrt{32}[/tex]  is -6.3 to the nearest tenth.

An approximation is anything that is similar, but not exactly equal, to something else.

The given expression is:

[tex]\sf -12 + \sqrt{32}[/tex]

The value of [tex]\sqrt{32}[/tex] is given as 5.656

Since, after decimal 6 to the right of 5 is greater than 5

To the nearest tenth, we can write as 5.66

[tex]\sf \therefore \sqrt{32} = 5.66[/tex]

For the required value of the expression we can write,

[tex]\sf -12 + \sqrt{32}[/tex]

Put the value of [tex]\sf \sqrt{32} = 5.66[/tex]

Putting values in expression we have,

[tex]\sf -12 + \sqrt{32} = -12 + 5.66[/tex]

Solving them

[tex]\sf \rightarrow -12 + \sqrt{32} = -6.34[/tex]

Hence, the approximate value of [tex]\sf -12 + \sqrt{32}[/tex] is -6.3 to the nearest tenth.

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The value of x is 3 / 2.

The side length of the triangle are 11, 11 and 14 units.

The triangle above is an isosceles triangle. Therefore, two sides of the triangles are equal and the base angles are equal.

Therefore, let's find the value of x in the triangle and the length of the three sides as follows;

Hence,

8x - 1 = 4x + 5

8x - 4x = 5 + 1

4x = 6

x = 6 / 4

x = 3 / 2

Therefore,

8x - 1 = 8(3 / 2) - 1 = 12 - 1 = 11 units

4x + 5 = 4(3 / 2) + 5 = 11 units

2x + 11 = 2(3 / 2) + 11 = 3 + 11 = 14 units

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The two functions f and g are f(x) = 5/x² and g(x) = 9x + 6

From the question, we have the following parameters that can be used in our computation:

(f o g)(x) = 5/(9x + 6)²

The function (f o g)(x) can be calculated using

(f o g)(x) = f(g(x))

This means that we can set the denominator of (f o g)(x) = 5/(9x + 6)² to g(x)

So, we have

g(x) = 9x + 6

Using the above as a guide, we have the following:

(f o g)(x) = 5/(g(x))²

So, we have

f(x) = 5/x²

Hence, the two functions f and g are f(x) = 5/x² and g(x) = 9x + 6

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In Container B, there are roughly 1.7643 kg of sand.

Compared to Container B, Container C had about 0.7057 kg less sand.

Let's say that Container B contains 'x' kilogrammes of sand.

The amount of sand in Container A is 2x kg since it has twice as much as Container B does.

The amount of sand in Container C grew by 20% after 15% of the sand from Container A and 20% of the sand from Container B were transferred there.

Let's figure out how much sand is in Container C:

Sand moved from Container A to Container C weighed 0.15 x 2 x kg.

The amount of sand moved from Container B to Container C is equal to 0.20 * x kg.

After the transfer, Container C now contains 20% more sand overall. Sand in Container C therefore contains 1.2 times as much as it did initially.

After the transfer, the total amount of sand in Container C is equal to 1.2 * (0.3x + 0.2x) = 1.2 * 0.5x = 0.6x kg.

Therefore, we can conclude that Container C held 2.47 kg more sand than Container A. Thus, we can construct the following equation:

0.6x - 2x = 2.47

Simplifying the equation:

-1.4x = 2.47

Dividing both sides by -1.4:

x = -2.47 / -1.4 ≈ 1.7643

So there is roughly 1.7643 kg of sand in Container B.

To determine the variation in sand content between Containers C and B:

Sand in Container C less Sand in Container B equals the difference.

Difference = 0.6x - x

Difference = -0.4x

Substituting the value of x:

Difference = -0.4 * 1.7643 ≈ -0.7057

Container C therefore contained around 0.7057 kg less sand than Container B.

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Answer:

-8r^6y^5.

Step-by-step explanation:

In order to find the product, we multiply the coefficients and then add the powers of the same variable.

Coefficient of -2r^5y^2: -2

Coefficient of 4ry^3: 4

Power of r: 5 + 1 = 6

Power of y: 2 + 3 = 5

Product: -2 * 4 = -8

r^6 * y^5 = -8r^6y^5

Therefore, the product of -2r^5y^2 and 4ry^3 is -8r^6y^5.

The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer: 0.03125

Step-by-step explanation:

To find how much each of the students received, we must divide 1/8 by the amount of students (4). If it's asking for an answer in the form of a fraction you should try googling 0.03 as a fraction.

In the diagram, the correct option is

angle DAB = angle DCB

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a geometric postulate used in proving the congruence of triangles.

According to CPCTC, if two triangles are proven to be congruent (having all corresponding angles and sides congruent), then their corresponding parts, including angles and sides, are also congruent.

The two triangles in the figure are congruent by the SAS congruence theorem and hence applying the CPCTC we have that

angle DAB = angle DCB

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Answer:

6(4c-3), 9w-1

Step-by-step explanation:

GCF is the biggest thing you can divide both 24c and 18 by.

you can see that you can divide both 24c and 18 by 6, and when you do that you get 4c and 3. That means that the answer for that question is

6(4c-3)   (which is A)

The next question all you need to do first is distribute the 3/4 to the 12w and 8.

3/4 * 12w = 9w

3/4 * 8 = 6

so you get

9w -6 + 5

you combine like terms to get

9w - 1  (B)

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =[tex]3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54[/tex] centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =[tex](1/2) * 54 * 56 = 1512[/tex] square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Answer:

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sofiapenaloza

05/31/2023

Mathematics

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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Step-by-step explanation:

The Range of the total number of travelers constraint (x + y ≥ 100), it is feasible.the maximum number of first-class tickets they can sell is 100 (at the point (100, 80)).The maximum profit they can achieve is $38,500 when they sell 100 first-class tickets and 80 coach tickets.

(a) Let's create a system of constraints based on the given situation:

1. First-class ticket constraint: First-class ticket sales must be at least 20.

  x ≥ 20

2. Coach ticket constraint: Coach ticket sales must be at least 45.

  y ≥ 45

3. Total number of travelers constraint: The plane must have at least 100 travelers.

  x + y ≥ 100

4. Maximum capacity constraint: The plane has a maximum capacity of 180 travelers.

  x + y ≤ 180

(b) To graph the system of constraints, we plot the inequalities on a coordinate plane:

The first-class ticket constraint (x ≥ 20) is a vertical line passing through (20, 0).

The coach ticket constraint (y ≥ 45) is a horizontal line passing through (0, 45).

The total number of travelers constraint (x + y ≥ 100) is a line passing through (100, 0) and (0, 100).

The maximum capacity constraint (x + y ≤ 180) is a line passing through (180, 0) and (0, 180).

(c) The feasible region is the shaded area where all constraints are satisfied.

   |

180 +--------------------------------------------------+

   |       /|\

   |      / | \

   |     /  |  \

   |    /   |   \

   |   /    |    \

   |  /     |     \

   | /      |      \

100 +--------------------------------------------------+

   |_________________________________________________

       20    45   100   180

The corner points of the feasible region are (20, 45), (20, 100), (80, 100), and (100, 80).

(d) To determine if it is feasible to sell 150 coach tickets and 25 first-class tickets, we check if these values satisfy the constraints.

150 coach tickets and 25 first-class tickets would give us a total of 175 travelers (150 + 25). Since this is within the range of the total number of travelers constraint (x + y ≥ 100), it is feasible.

(e) From the graph, we can observe that the maximum number of coach tickets they can sell is 80 (at the point (80, 100)), and the maximum number of first-class tickets they can sell is 100 (at the point (100, 80)).

(f) To maximize profits, we need to determine the corner point within the feasible region that gives the highest profit. We calculate the profit for each corner point and select the maximum.

For (20, 45): Profit = (225 * 45) + (200 * 20) = 10,125 + 4,000 = $14,125

For (20, 100): Profit = (225 * 100) + (200 * 20) = 22,500 + 4,000 = $26,500

For (80, 100): Profit = (225 * 100) + (200 * 80) = 22,500 + 16,000 = $38,500

For (100, 80): Profit = (225 * 80) + (200 * 100) = 18,000 + 20,000 = $38,000

The maximum profit they can achieve is $38,500 when they sell 100 first-class tickets and 80 coach tickets.

(g) The minimum profit they can achieve from the flight is $0 if they don't sell any tickets or if the number of travelers is below the minimum required for profitability.

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We have shown that AC:BC is indeed in the ratio 2:1 or 2:3. The ratio is 2:3 because AC is twice the length of AB, and BC is one-third the length of AB.

To show that AC:BC is in the ratio 2:3, we need to compare the lengths of AC and BC in terms of their respective expressions.

Given AB:AC = 1:2, we can represent the lengths of AB and AC as follows:

AB = 3x - 4

AC = 2(3x - 4) = 6x - 8

Next, we need to find the length of BC. Since AB and BC are segments of the same line, we can express BC in terms of AB and AC using the fact that the sum of two segments is equal to the length of the whole line. Therefore:

AB + BC = AC

Substituting the expressions we have for AB and AC:

(3x - 4) + BC = 6x - 8

Now, let's solve this equation for BC:

BC = 6x - 8 - (3x - 4)

BC = 6x - 8 - 3x + 4

BC = 3x - 4

We have found the length of BC, which is 3x - 4. Now we can compare the ratios of AC:BC:

AC:BC = (6x - 8):(3x - 4)

To simplify the ratio, we can factor out a common factor of 2:

AC:BC = 2(3x - 4):(3x - 4)

Notice that we have a common factor of (3x - 4) in the numerator and denominator. We can cancel out this common factor, resulting in:

AC:BC = 2:1

Therefore, we have shown that AC:BC is indeed in the ratio 2:1 or 2:3. The ratio is 2:3 because AC is twice the length of AB, and BC is one-third the length of AB.

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The calculated value of x is 3/2

The lengths of all three sides of the triangle are 11, 11 and 14

From the question, we have the following parameters that can be used in our computation:

The triangle

The triangle is an isosceles triangle

So, we have

8x - 1 = 4x + 5

Evaluate

4x = 6

So, we have

x = 3/2

Recall that

x = 3/2

So, we have

4x + 5 = 4 * 3/2 + 5

4x + 5 = 11

Also, we have

2x + 11 = 2 * 3/2 + 11

2x + 11 = 14

Hence, the lengths of all three sides of the triangle are 11, 11 and 14

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The probability that exactly 9 of the chosen apartments are on the ground floor is approximately 0.3088 or 30.88%.

The number of favourable outcomes and the total number of possible outcomes must be determined in order to determine the likelihood that precisely 9 of the chosen flats are on the ground floor.

The total number of outcomes is the number of ways to select 14 of the 17 available flats. You can compute this using the following combination formula:

C(n, r) = (n!/(n-r)!)

In this instance, the total number of flats is 17 and the number of units that were selected is 14. In other words, C(17, 14) = 17! / (14!(17-14)!) = 17! / (14!* 3!) = (17 * 16 * 15) / (3 * 2 * 1) = 680.

Let's now count the number of successful results. From the 10 flats on the ground floor that are available, we must select 9 and from the 7

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The value of the variable x that helps us to find  the lengths of the triangle is: x = 3/2

We know that when we have an Isosceless triangle, that we have two equal sides and two equal base angles and as such we can easily see that the given triangle is an Isosceles Triangle.

We are given the two equal sides to be represented by the lengths:

(8x - 1) and (4x + 5)

Thus:

8x - 1 = 4x + 5

8x - 4x = 5 + 1

4x = 6

x = 6/4

x = 3/2

Thus, that is the value of x to solve for the lengths of the triangle.

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Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = [tex]Pe^(^r^t^)[/tex]

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = [tex]Pe^(^0^.^0^3^5^*^9^)[/tex]

640 = Pe^0.315

P =[tex]640/e^0^.^3^1^5[/tex]

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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The profit after selling 300 cappuccinos is $1000.

The equation p = xc - 500 can be used to calculate the profit after selling c cappuccinos. In this equation, p is the profit, x is the price per cappuccino, and c is the number of cappuccinos sold.

To calculate the profit after selling 300 cappuccinos, we need to know the price per cappuccino. Let's assume that the price per cappuccino is $5.00. Plugging these values into the equation, we get:

p = 5.00 * 300 - 500

= 1500 - 500

= 1000

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The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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The solution to the given system of equations is x = 0 and y = 5.

To find the solution of the system of equations:

Let's write the given system of equations:

Equation 1: 4x + 3y = 15

Equation 2: x - 3y = -15

We can solve this system using the method of substitution or elimination. Let's use the method of elimination in this case.

To eliminate the variable 'y', let's multiply Equation 2 by 3:

Equation 2: 3(x - 3y) = 3(-15)

3x - 9y = -45

Now, we can add Equation 1 and Equation 2 together to eliminate the 'y' variable:

(4x + 3y) + (3x - 9y) = 15 + (-45)

4x + 3x + 3y - 9y = -30

7x - 6y = -30

Rearrange the equation to isolate 'x':

7x - 6y = -30

7x = 6y - 30

x = (6y - 30)/7

Substitute the expression for 'x' into either Equation 1 or Equation 2. Let's substitute it into Equation 1:

4x + 3y = 15

4((6y - 30)/7) + 3y = 15

(24y - 120)/7 + 3y = 15

Simplify the equation and solve for 'y':

(24y - 120 + 21y)/7 = 15

45y - 120 = 105

45y = 225

y = 5

Substitute the value of 'y' back into the expression for 'x':

x = (6y - 30)/7

x = (6(5) - 30)/7

x = 0

The solution to the system of equations is x = 0 and y = 5.

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To find the mean of the population based on the given data, we need to calculate the sum of all the responses and divide it by the total number of campers.

The given responses are: 3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1

Sum of the responses = 3 + 2 + 0 + 1 + 0 + 2 + 3 + 4 + 1 + 2 + 2 + 1 = 21

Total number of campers = 48

Mean of the population = Sum of the responses / Total number of campers = 21 / 48 ≈ 0.4375

Rounded to the nearest unit, the mean number of siblings for the population is 0.

To find mean, first add everything together.

3 + 2 + 0 + 1 + 0 + 2 + 3 + 4 + 1 + 2 + 2 + 1

This equals to 21.

Then, divide the total by the amount of campers there are.

21 ÷ 48 ≈ 0.4375

Round this to the nearest whole number.

The mean number of siblings is 0.

The value of x, considering the similar triangles in this problem, is given as follows:

x = 3.6.

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

3/20 = x/24

Applying cross multiplication, the value of x is obtained as follows:

20x = 72

x = 72/20

x = 3.6.

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For 18.) The total mileage that was covered by the new vehicle for a whole year would be = 13,800miles.

From the table given above, the total mileage can be calculated using the following steps below as follows:

For 2 months the mileage = 2300

Therefore for a month the mileage = 2300/2 = 1150

If 1150 miles = 1 month,

X miles = 12 months

make X miles the subject of formula;

X miles = 1150×12 = 13,800miles.

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Answer:

156 cm²

Step-by-step explanation:

The surface area of a square pyramid is a² + 2al if a = the length of the side of the base of the pyramid and l = the height of each triangle. a would be equal to 6 in this case, since it is the length of the side of the base, and l would be 10 because it is the height of each triangle.

So, here's our expression:

6² + 2(6)(10) =

36 + 12(10) =

36 + 120 =

156

The surface area of the square pyramid is 156 cm². If this process doesn't make sense to you or if you'd like some further clarification, please let me know! :)

The method that determines the volume of the prism is simply multiply the area of the base by the height, and the result is 12.5 cm³. (option-a)

To determine the volume of the prism shown in the diagram, we need to multiply the area of the base by the height.

The base of the prism is a rectangle with dimensions 5 cm by 2 cm. Therefore, the area of the base is:

A = length x width = 5 cm x 2 cm = 10 cm²

The height of the prism is 2-¹ cm, which is equivalent to 5/4 cm.

Therefore, the volume of the prism is:

V = A x h = 10 cm² x 5/4 cm = 12.5 cm³

The expressions involving unit cubes and one-quarter cubes are not relevant to this problem and do not provide a method for finding the volume of the prism.

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Answer:

Step-by-step explanation:

Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

The total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

If you have a credit card with an annual percentage rate (APR) of 30% and a minimum payment requirement of 8% of the balance, and you have a balance of $400 on the credit card, you decide to stop charging and pay it off by making the minimum monthly payment each month, here's how it would work:

The minimum monthly payment would be 8% of the balance, which is 0.08 x $400 = $32.

Each month, you would make a payment of $32 towards your credit card balance. However, keep in mind that the interest will continue to accrue on the remaining balance.

Since the APR is 30%, the monthly interest rate would be 30% / 12 = 2.5%.

To calculate the interest charged each month, you multiply the remaining balance by the monthly interest rate. For example, after the first payment, the remaining balance is $400 - $32 = $368. The interest charged for that month would be 2.5% x $368 = $9.20.

Therefore, the total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

Each month, you would continue making the minimum payment, and the interest charged would be based on the remaining balance. The process would continue until the balance is paid off in full.

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Based on the fact that Nan and Santo are designing a coffee table using 4 inch tiles, they used a total of 45 tiles.

Nan uses 30 tiles, and Santo uses half as many as Nan.

To know the amount of tiles Santo uses, one need to divide the number of tiles Nan uses by 2:

30 tiles / 2 = 15 tiles

Hence, Santo uses 15 tiles.

To be able to calculate the total number of tiles used, one need to add the number of tiles used by Nan and Santo and so:

30 tiles + 15 tiles = 45 tiles

Therefore, in the case above, they used a total of 45 tiles.

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Answer:

The given correlation is a strong positive correlation, and it is not likely causal.

We have given that,

The correlation coefficient relating the two variables is 0.74.

What is the correlation coefficient?

The correlation coefficient value is used to determine the strength of the linear relationship between two variables. The value ranges from - 1 to +1.

The correlation coefficient value is used to determine the strength of the linear relationship between two variables. The value ranges from - 1 to +1.

with negative values depicting a negative relationship and positive values showing a positive relationship.

The value of 0 implies that no relationship exists.

The closer the correlation coefficient value is to +1 or - 1, the greater the strength of the relationship between them.

Also, correlation does not mean causation.

Hence, a correlation coefficient of 0.74 depicts a strong positive relationship.

However, it doesn't imply causation.

We have the given correlation coefficient relating the two variables is 0.74 and it is near +1

Therefore, the given correlation is a strong positive correlation, and it is not likely causal.

Step-by-step explanation: