What type of triangle is this triangle?acute scaleneacute isoscelesright isoscelesright scalene

The estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%). The correct option is A

The range of values that is most likely to include the true population parameter is known as the margin of error. The standard error, a gauge of the sample statistic's variability, is used to determine the margin of error.

Option A in this situation has the most margin of error of the four, at 24%. In comparison to the other options, this indicates that the true population parameter is probably within 24% of the sample statistic. This implies that option A's sample size is smaller than that of the other options.

Therefore, the estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%).

Learn more about margin of error here : brainly.com/question/30760332

#SPJ1

Option A, "Yes, because every x-value corresponds to exactly one y-value," accurately describes the situation presented in the table. Option A is the proper response, so.

The table represents a function.

A mathematical relationship known as a function is one in which every input (x-value) has exactly one corresponding output (y-value). In the given table:

xy

3 1

4 3

5 2

6 5

6 6

Every x-value in the table corresponds to exactly one y-value. There are no repeated x-values, and for each x-value, there is only one corresponding y-value. The definition of a function is met by this.

The answer given in Option A, "Yes, because every x-value corresponds to exactly one y-value," appropriately sums up the situation shown in the table. Option A is the proper response, so.

for such more question on function

https://brainly.com/question/13473114

#SPJ8

The wall area that needs to be painted, excluding the doorway, is 125 square feet.

The total area of the wall is obtained by multiplying its length and width:

Total area = 11 ft * 13 ft = 143 square feet.

The area of the doorway is given by multiplying its length and width:

Doorway area = 6 ft * 3 ft = 18 square feet.

To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:

Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.

Therefore, you will need 125 square feet of paint to cover the wall only.

Learn more about rectangles here: brainly.com/question/29123947

#SPJ11

Given the cost of the video game is $39.99, Mark gets a discount of 30%.Content loaded means there's enough information available to solve the problem. Here's how to find out the final cost of the video game. First, calculate the discount on the cost of the video game:$39.99 × 30/100 = $11.997

This gives us the discount that Mark gets on the video game. So, the cost of the video game after discount will be: Cost of the video game = $39.99 - $11.997 = $27.993Now, let's add the sales tax. The sales tax is 5%. Thus, the sales tax will be: Sales tax = $27.993 × 5/100 = $1.39965So, the final cost of the video game will be :Final cost = $27.993 + $1.39965 = $29.39265Thus, the final cost of the video game after the discount and the sales tax is $29.39.

Learn more about discount here:

https://brainly.com/question/2730006

#SPJ11

To find the x-values that are solutions of the equation

[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3)[/tex], we first need to simplify the equation and find the zeros.

By subtracting x^2 + 6x + 3 from both sides of the equation, we get:

[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3) = 0[/tex]

[tex]x^3 + 5x^2 - x - 7 - x^2 - 6x - 3 = 0\\x^3 + 4x^2 - 7x - 10 = 0[/tex]

Now, to find the zeros of this polynomial, we set it equal to zero and factor it if possible:

[tex]x^3 + 4x^2 - 7x - 10 = 0[/tex]

By trying different values, we can find that x = -2 is a zero of the polynomial. Therefore, (x + 2) is a factor of the polynomial.

Using synthetic division or long division, we can divide the polynomial [tex]x^3 + 4x^2 - 7x - 10 = 0[/tex] by (x + 2):

[tex]| (x^3 + 4x^2 - 7x - 10) ÷ (x + 2) |= x^2 + 2x - 5[/tex]

Now, we can factor the quadratic equation x^2 + 2x - 5:

(x + 2)(x - 1) = 0

Setting each factor equal to zero and solving for x, we get:

x + 2 = 0 --> x = -2

x - 1 = 0 --> x = 1

Therefore, the x-values that are solutions to the equation x^3 + 5x^2 - x - 7 = x^2 + 6x + 3 are x = -2 and x = 1. The intersection points of the two polynomials occur at these x-values.

To know more about equation visit:

https://brainly.com/question/29538993

#SPJ11

An angle is a geometric figure formed by two rays or lines that share a common endpoint called the vertex.

If Jen noticed that the angle formed at the corner of the soccer field was similar to her math lesson, we can explore the different types of angles she might be referring to.

Right Angle: A right angle measures exactly 90 degrees and forms a square corner. It is a common angle found in everyday life, such as the corners of buildings or the intersection of two perpendicular lines. Right angles are often studied in geometry due to their properties and applications in various mathematical concepts.

Acute Angle: An acute angle measures less than 90 degrees. It is a smaller angle that appears sharp and pointed. Examples of acute angles can be found in triangles, where all three angles are acute.

Obtuse Angle: An obtuse angle measures more than 90 degrees but less than 180 degrees. It is a wider angle that appears larger and open. Examples of obtuse angles can be found in shapes like rectangles or triangles with one angle greater than 90 degrees.

Straight Angle: A straight angle measures exactly 180 degrees, forming a straight line. It is a flat angle that doesn't bend or deviate. Straight angles are commonly found in line segments or in shapes like straight edges of polygons.

To learn more about vertex visit;

https://brainly.com/question/32432204

#SPJ11

a) To find the value of b that makes the integral equal to 0, we need to solve the integral:

∫(1 to b) (6x - 9) dx = 0

Applying the fundamental theorem of calculus, we can find the antiderivative of the integrand and evaluate it at the limits of integration:

[3x² - 9x] (from 1 to b) = 0

Substituting the limits, we have:

(3b² - 9b) - (3(1)² - 9(1)) = 0

Simplifying further:

3b² - 9b - 6 = 0

Now we can solve this quadratic equation for b using the quadratic formula or factoring:

b² - 3b - 2 = 0

Factoring the quadratic equation, we get:

(b - 2)(b + 1) = 0

Setting each factor to zero, we find two possible values for b:

b = 2 or b = -1.

However, since b cannot equal 1 (as stated in the problem), the only valid solution is b = 2.

b) To verify our answer, we can sketch a graph of y = 6x - 9 on the interval from x = 1 to x = b = 2. The graph will be a straight line with a slope of 6 and y-intercept at -9.

On the interval [1, 2], the line starts at the point (1, -3) and ends at the point (2, 3). By calculating the area under this line, we find that the integral from 1 to 2 of (6x - 9) equals 0, confirming our previous result.

To learn more about fundamental theorem of calculus visit

brainly.com/question/30761130

#SPJ11

The statement that is true about this comparison is that they differ in the thousandths place, with 0.739 being greater than 0.7380.

The statement that is true about the comparison

0.739 > 0.7380

is that they differ in the thousandths place. The difference between the two numbers is

0.001 or 1/1000,

which is why we can say that they differ in the thousandths place. This difference is very small, but it is enough to make

0.739 greater than 0.7380.

The comparison between

0.739 and 0.7380

is true in that the former is greater than the latter by a small margin. The two numbers differ in the thousandths place, with 0.739 having a value of

0.739 and 0.7380

having a value of 0.738.

The difference between the two values is

0.001 or 1/1000,

which is very small.

However, this difference is enough to make 0.739 greater than 0.7380.

Therefore, the statement that is true about this comparison is that they differ in the thousandths place, with

0.739 being greater than 0.7380.

To know more about thousandths visit:

https://brainly.com/question/297733

#SPJ11

Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.

To determine the number of live Blorgs the Mad Professor has at 4:05 PM, we need to understand the pattern of Blorg reproduction and lifespan.

From the given information, we know that one hour after a Blorg is born, it gives birth to a new Blorg. Two hours after birth, it gives birth to two more new Blorgs and then immediately dies.

Let's break down the timeline:

At noon, the Professor has one newborn Blorg.

One hour later, at 1 PM, the initial Blorg gives birth to a new Blorg. So, there are two Blorgs now.

Two hours after birth, at 2 PM, the initial Blorg dies, but the newborn Blorg from 1 PM gives birth to two more Blorgs. So, there are four Blorgs now.

At 3 PM, the two newborn Blorgs from 1 PM give birth to two more Blorgs each, resulting in a total of eight Blorgs.

At 4 PM, the four Blorgs that were born at 2 PM die, while the four Blorgs born at 3 PM are still alive. The four living Blorgs are from the second generation.

Now, let's calculate the number of live Blorgs at 4:05 PM:

At 4 PM, there are four living Blorgs.

Since each Blorg lives for two hours, at 4:05 PM, it has been 5 minutes past their lifespan, and all the living Blorgs from the 3 PM generation would have died.

Therefore, at 4:05 PM, the Mad Professor would have zero live Blorgs.

It is important to note that Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.

Learn more about reproductive cycle here

https://brainly.com/question/729890

#SPJ11

To calculate the area of the shape made up of three similar right-angled triangles, we need additional information about the scale factor or proportions of the triangles. Without that information, we cannot determine the exact area of the shape.

The given information states that the shape is composed of three similar right-angled triangles, and the smallest triangle has two sides of side-length 2. While we know the dimensions of the smallest triangle, we do not have any information about the scale factor or proportions of the other two triangles. Since the shape is formed by three similar triangles, the areas of the triangles would be proportional, but we cannot determine the exact proportions without additional information. Consequently, we cannot calculate the area of the shape accurately based solely on the given information.

To learn more about right-angled triangles; -brainly.com/question/30381855

#SPJ11

Hence, Eva's average speed overall is 35.29 miles per hour

The given information can be tabulated as follows: Distance, Time, Speed

Eva drove to work30 miles1 hour 18 minutes1.18 hours

Eva drove to work30 miles1.18 hours

Eva left work31 minutes0.52 hours

Eva left work30 miles0.52 hours

It is given that Eva drove to work in rush hour traffic, going just 30 miles in 1 hour and 18 minutes, i.e. 1.18 hours.

Her speed during this time can be calculated as follows:

Speed = Distance / Time

Speed = 30 / 1.18 = 25.42 miles per hour

Similarly, when Eva left work early to avoid the rush and was able to take the same route home in 31 minutes, i.e. 0.52 hours.

Her speed during this time can be calculated as follows:

Speed = Distance / Time

Speed = 30 / 0.52 = 57.69 miles per hour

Therefore, Eva's average speed overall can be calculated as follows:

Average speed = Total distance / Total time

Total distance = 30 + 30 = 60 miles

Total time = 1.18 + 0.52 = 1.7 hours

Average speed = 60 / 1.7 = 35.29 miles per hour

to know more about average speed visit:

https://brainly.com/question/17661499

#SPJ11

To solve this problem, we can set up an equation based on the volume of lemon juice in the mixture:

Let's assume Milo needs to add x gallons of 100% lemon juice.

The total volume of the final mixture is given as 4 gallons, and it should be a 50% lemon juice and 50% lime juice mixture.

The initial mixture contains 20% lemon juice, which means it contains 20% of 4 gallons = 0.2 * 4 = 0.8 gallons of lemon juice.

So, the equation becomes:

0.8 gallons (initial lemon juice) + x gallons (additional 100% lemon juice) = 0.5 * 4 gallons (final lemon juice)

Simplifying the equation:

0.8 + x = 2

Subtracting 0.8 from both sides:

x = 2 - 0.8

x = 1.2

Therefore, Milo needs to add 1.2 gallons of 100% lemon juice to make 4 gallons of the 50% lemon/50% lime juice mixture.

#SPJ11

The coordinates of the fourth vertex are (1.1, -3.1).

We know that a rectangular piece of material has two pairs of parallel sides and four right angles. Therefore, we can calculate the distance between two opposite sides by using the distance formula. The two sides that are parallel to the x-axis have the same y-coordinate, and the two sides parallel to the y-axis have the same x-coordinate.

Thus, the distance between opposite sides is given by the difference between the x-coordinates or the difference between the y-coordinates. The x-coordinates of the vertices are −1.3, −1.3, and 1.1. So the difference between them is 1.1 − (−1.3) = 2.4. The y-coordinates of the vertices are −3.1, 1.2, and 1.2. So the difference between them is 1.2 − (−3.1) = 4.3. The fourth vertex is located at the point with an x-coordinate of 1.1 and a y-coordinate of −3.1. Therefore, the coordinates of the fourth vertex are (1.1, -3.1).

Learn more about distance formula here:

https://brainly.com/question/25841655

#SPJ11

The given expression is an equation containing fractions.

Given expression is:

[tex]$$\frac{2x}{x+7} - \frac{x}{x+3} = 1 + \frac{1}{x^2+10x+21}$$[/tex]

We can rewrite the given expression as follows:

[tex]$$\frac{2x(x+3)-x(x+7)}{(x+7)(x+3)}=\frac{x^2+10x+22}{(x+3)(x+7)}$$[/tex]

Simplifying the numerator and denominator of the above expression,

we get:[tex]$$\frac{x^2-4x-21}{(x+7)(x+3)} = \frac{x^2+10x+22}{(x+7)(x+3)}$$[/tex]

On simplifying, we get the following equation:

[tex]$$x^2-4x-21=x^2+10x+22$$[/tex]

Simplifying the above equation, we get:

$$14x=-43$$

On dividing by 14 on both sides,

we get:[tex]$${x=-\frac{43}{14}}$$[/tex]

To know more about denominator visit:

https://brainly.com/question/32621096

#SPJ11

The given restrictions can be written as follows:Maximum weight carried by Josh: 2p + 1a ≤ 50Maximum number of plates per day: p ≤ 3his objective function would be:Profit = 12a + 25pWe need to find the values of a and p which can maximize his profit.

Thus, the linear inequalities to represent the number of pots p and plates a that Josh may bring to the fair is:2p + 1a ≤ 50, a ≤ 5 and p ≤ 3.b) The feasible region can be found by plotting the given constraints on the coordinate plane. Here is the graph for the same:From the graph, we can see that the vertices of the feasible region are (0,0), (3,5), (8,0), and (16,0).c) Josh wants to maximize his profit.

Therefore,  To do so, we can substitute the vertices of the feasible region and calculate the profit to identify the combination of pots and plates that gives the maximum profit.

To know more about profit visit:

https://brainly.com/question/32381738

#SPJ11

The fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction. In this fact family, when we subtract 3 from 4, the result is 1. If we then add 2 to 1, we get 3. Furthermore, when we subtract 2 from 9, the result is 7. If we add 7 and 2 together, the sum is 9.



In the given fact family, the numbers 4 and 3 are related through subtraction. When we subtract 3 from 4, we get 1. This is represented by the equation 4 - 3 = 1.

On the other hand, the numbers 2 and 1 are related through addition. If we add 2 to 1, the sum is 3. This is represented by the equation 1 + 2 = 3.

Similarly, the numbers 9 and 2 are related through subtraction and addition. When we subtract 2 from 9, we get 7, represented by the equation 9 - 2 = 7. By adding 7 and 2 together, the sum is 9, represented by the equation 7 + 2 = 9.

Therefore, the fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction within the given numbers.

Learn more about addition here : brainly.com/question/29464370

#SPJ11

Histograms visualize the distribution and spread of data. A higher standard deviation implies greater variability in the data points. In a histogram, a wider shape indicates a larger spread of data and thus a higher standard deviation. Therefore, the histogram with a broader shape depicts a higher standard deviation.

To determine which histogram depicts a higher standard deviation, we need to look for the histogram with a greater spread or dispersion of data. In a histogram, a higher standard deviation indicates that the data points are more spread out or have a larger variability. This means that the values are more scattered from the mean. Therefore, the histogram with a wider and more spread-out shape would depict a higher standard deviation, as it indicates a greater variability in the data.

learn more about histograms here:
https://brainly.com/question/16819077

#SPJ11

Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8

In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.

In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.

In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.

Learn more about variable here:

https://brainly.com/question/29696241

#SPJ11

To calculate Elizabeth's finance charge using the previous balance method, we need to determine the average daily balance and then apply the APR (Annual Percentage Rate) to calculate the finance charge.

First, let's calculate the average daily balance:

Beginning Balance: $969.26

Days until payment: 2 (from July 1st to July 3rd)

Payment: $45.00

Days until purchase: 7 (from July 3rd to July 10th)

Purchase: $67.48

Days until payment: 2 (from July 10th to July 12th)

Payment: $20.00

Days until payment: 16 (from July 12th to July 28th)

Payment: $85.00

To calculate the average daily balance, we sum up the balances for each day and divide it by the total number of days in the billing cycle (30 days).

Average Daily Balance = (969.26 × 2 + 0 × 7 + 67.48 × 2 + 0 × 16) / 30 = $85.95

Next, we can calculate the finance charge using the APR:

Finance Charge = Average Daily Balance × (APR / 365) × Number of Days in the Billing Cycle

Finance Charge = 85.95 × (0.1461 / 365) × 30 ≈ $9.97

Therefore, Elizabeth's July finance charge will be approximately $9.97. The correct answer is option a.

Learn more about Annual Percentage Rate here -: brainly.com/question/30774234

#SPJ11

The following expressions are equivalent to 8.9 x 6.28.7: 9 x 6; 6.28.7; 8.9 x 6.2. The product of two numbers, in general, is the outcome when we multiply the numbers together.

It means, when we take two quantities and multiply them, we get the result as a product. Let us understand how the multiplication of numbers works with an example. When we multiply 3 and 4, we get:3 × 4 = 12Here, 3 and 4 are called factors, and the result, 12, is called the product. Equivalent expressions are the expressions that have the same value, but their structures may differ. The expressions can be equivalent if they have the same value, but their format is different .Let's list the expressions that are equivalent to 8.9 x 6.28.7:The product of 9 and 6 is equal to 54. The product of 8.9 and 6.2 is equal to 55.18.The expression 6.28.7 is the same as 55.18. The product of 8.9 and 6.2 is the same as 6.28.7.Therefore, the following expressions are equivalent to 8.9 x 6.28.7:9 x 66.28.78.9 x 6.2.

Learn more about equivalent here:

https://brainly.com/question/28804962

#SPJ11

The time it would take for the bag to infuse at the maximum time would be the value of 1. 5 hours.

The maximum rate of infusion for an IV bag is 250 ml/hour. This means that the maximum time it would take for the bag to infuse is:

= Quantity in bag / Maximum rate of infusion

Therefore, it will take:

= 376 ml / 250 ml/hour

= 1. 5 hours to infuse the entire bag

In conclusion, the time it would take for the bag to infuse at the maximum time is 1. 5 hours.

Find out more on Blood administration at https://brainly.com/question/30748600

#SPJ4

n = 45 satisfies the equation, and it is the value that makes 3/5 of n equal to 27. The value of n can be determined by setting up an equation based on the given information that 3/5 of n is equal to 27.

By solving the equation, we can find the value of n. Let's set up the equation based on the given information:

(3/5) * n = 27

To solve for n, we need to isolate n on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 3/5, which is 5/3:

n = 27 * (5/3)

Simplifying the right side of the equation:

n = (27 * 5) / 3

n = 135 / 3

n = 45

Therefore, the value of n is 45. We can confirm this by substituting n = 45 back into the equation:

(3/5) * 45 = 27

(3/5) * 45 = 135/5 = 27

Learn more about reciprocal here:

https://brainly.com/question/15590281

#SPJ11

The cost of a 12-minute phone call is $4.20.

The cost of a nine-minute phone call is $3.15. To find the cost of a 12-minute phone call, we must first determine the cost per minute. We can do this by dividing the cost of a nine-minute call by 9 minutes, which gives us the cost per minute.

3.15 ÷ 9 = $0.35 (cost per minute) Now that we know the cost per minute, we can find the cost of a 12-minute phone call by multiplying the cost per minute by the number of minutes. 12 × $0.35 = $4.20 Therefore, the price of a 12-minute phone call is $4.20.

To know more about cost visit:-

https://brainly.com/question/32660686

#SPJ11

The solution to the equation is x is less than 1.

Let's assume the number as "x".

The given statement can be translated into an equation as follows:

3 - 11x > 21 - 5x

To solve this equation, we can start by simplifying both sides:

3 - 11x > 21 - 5x

Next, let's gather the terms with x on one side and the constant terms on the other side by adding 11x and subtracting 21 from both sides:

3 - 11x + 11x - 5x > 21 - 5x + 11x - 21

Simplifying further, we get:

-16x > -x

Now, we can divide both sides by -16, but since we are dividing by a negative number, we need to reverse the inequality sign:

-16x / -16 < -x / -16

x < 1

Therefore, the solution to the equation is x is less than 1.

Visit here to learn more about inequality brainly.com/question/20383699

#SPJ11

option B is the correct answer.

The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b

Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².

To know more about Perimeter visit:

https://brainly.com/question/7486523

#SPJ11

The vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.

To determine how many bushels of corn the vendor can afford to buy, we need to consider the cost of each bushel of corn and the fixed delivery fee. Here's how we can calculate it:

Subtract the fixed delivery fee from the total amount of money the vendor has:

$22.00 - $5.50 = $16.50

Divide the remaining amount of money by the cost per bushel of corn to find the maximum number of bushels the vendor can buy:

$16.50 ÷ $3.00 = 5.5 bushels

Since the vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.

Please note that in this calculation, we assumed that the vendor would spend all of the available money on purchasing corn, without considering any additional expenses or constraints.

Learn more about vendor here

https://brainly.com/question/29157067

#SPJ11

The explicit formula for the given sequence 4, -12, 36, -108,... is D. tn = 4(-3)n. Option D

In the given sequence, each term is obtained by multiplying the previous term by -3. This indicates an exponential decay pattern with a common ratio of -3.

To derive the explicit formula, we start with the initial term 4 and observe that each subsequent term can be obtained by multiplying the previous term by -3:

Term 1: 4

Term 2: -3 × 4 = -12

Term 3: -3 ×(-12) = 36

Term 4: -3 × 36 = -108

We can generalize this pattern by using the formula tn = ar^(n-1), where tn represents the nth term, a is the initial term, and r is the common ratio. In this case, a = 4 and r = -3. Thus, the explicit formula for the sequence is tn = 4(-3)n which matches option D.

learn more about explicit formula here:

https://brainly.com/question/25094536

#SPJ11

The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.

To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.

To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.

Converting the fractions to have a denominator of 12, we get:

James: 2/3 = 8/12

Gilbert: 11/12 (already in terms of 12)

Matthew: 5/6 = 10/12

Simon: 7/12 (already in terms of 12)

Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).

To find the difference between these two times, we subtract the slowest time from the fastest time:

8/12 - 11/12 = -3/12 = -1/4

Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.

To learn more about fractions: -brainly.com/question/10354322

#SPJ11

9 kilograms of cashews were in the mixture the grocer sold.

To solve the given problem, let x represent the number of kilograms of cashews.

Hence, the number of kilograms of Brazil nuts would be (12 - x) as the grocer sold 12 kg of the mixture.

Therefore, the cost of the cashews at $8 per kilogram is 8(x)

and the cost of the Brazil nuts at $10 per kilogram is 10(12 - x).

Hence, the cost of the mixture at $8.50 per kilogram is:

8.5*(12) = 8(x) + 10(12 - x)

We solve this equation for x:

102 = 8(x) + 120 - 10(x)

2(x)= 18

x = 9

To know more about cashews,visit:

https://brainly.com/question/32799716

#SPJ11

The scatter plot shows a comparison between the amount of television watched by students (in hours per week) and their GPA. a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.

Based on the scatter plot, we can observe the general trend of the data points. If the points on the plot are more closely clustered around a straight line, it indicates a stronger correlation between the two variables. Conversely, if the points are more spread out and do not follow a clear pattern, it suggests a weaker correlation. To determine the correlation coefficient, we need to assess the direction and strength of the relationship.

If the data points on the scatter plot exhibit a clear upward or downward trend, it indicates a positive or negative correlation, respectively. The correlation coefficient ranges between -1 and 1, with values closer to -1 or 1 indicating a stronger correlation. A correlation coefficient of 0 indicates no linear relationship. Given that the scatter plot does not show a clear pattern or trend, it suggests a weak or no correlation between the amount of television watched and GPA. Therefore, a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.

Learn more about coefficient here:

https://brainly.com/question/1594145

#SPJ11