Ben is showing his work in simplifying (3.9 − 9.4) − 0.6 + 6.1. Identify any error in his work or reasoning.
Step 1: (3.9 − 9.4) − 0.6 + 6.1
Step 2: 3.9 + (−9.4 − 0.6) + 6.1 (associative property) Step 3: 3.9 − 10 + 6.1
Step 4: 3.9 + 6.1 − 10 (identity property)
Step 5: 10 − 10 = 0
A. He wrote identity instead of commutative in step 4.
B. He wrote associative instead of commutative in step 2.
C. He wrote identity instead of distributive in step 4.
D. He wrote associative instead of distributive in step 2.

Answer:

The correct option is 3.

Step-by-step explanation:

In ΔACT and ΔDGO.

[tex]\angle A=\angle D[/tex]               (Given)

[tex]\angle AC=\angle DG[/tex]               (Given)

[tex]\angle C=\angle G[/tex]                 (Given)

By ASA property of congruent triangles.

[tex]\triangle ACT\cong \triangle DGO[/tex]

The congruent part of congruent triangles are congruent.

[tex]TA=OD[/tex]                               (CPCTC)

The side TA is corresponding to OD.

Therefore the correct option is 3.

Final answer:

The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance after both cars have traveled in opposite directions for the same amount of time. The second car's average speed is found to be 70 mph.

Explanation:

To find the average speed of the second car, we first need to establish the total distance covered by both cars. Since they are moving in opposite directions, we can add their distances together to determine the total distance.

Let's designate the distance the first car travels as D1 and the distance the second car travels as D2. The average speed of the first car is given as 30 mph, and both cars travel for 4 hours. Therefore, D1 can be calculated as follows:

D1 = average speed of first car × time = 30 mph × 4 h = 120 miles

Since we know that the combined distance D1 + D2 is 400 miles, we can find D2 by subtracting D1 from the total distance:

D2 = total distance - D1 = 400 miles - 120 miles = 280 miles

Now, to find the average speed of the second car, we divide D2 by the time, which is 4 hours:

Average speed of the second car = D2 / time = 280 miles / 4 h = 70 mph

Therefore, the average speed of the second car is 70 mph.

4:4

Alice and Cori have the same amount of cookies

Answer:

d 15

Easy. As that

Answer:

They cannot. They have to be obtuse and acute.

We would expect the height of women at age 4 and their height as women at age 18 to be the highest correlation since it is rational to think taller children to turn out to be taller adults and shorter children to become shorter adults. The next highest would be the correlation between the father and their adult sons. Tall fathers be likely to have tall sons, but naturally not as tall, and similarly for shorter fathers. The lowest correlation would be between husbands and their wives.  Husbands may be taller than their wives in common, but there is no purpose to expect anything more than a  weak positive correlation.

The heights of fathers and their adult sons have the highest correlation due to genetics, followed by the heights of husbands and wives influenced by assortative mating. Lastly, the correlation between the heights of women at age 4 and their heights at age 18 is weaker due to the intervening growth factors.

To rank the correlation between these pairs of variables, we should consider how closely related they are likely to be based on genetic, environmental, and social factors. Genetics plays a significant role in the height of fathers and their adult sons because height is a highly heritable trait. Therefore, we can expect a high correlation here. Social factors influence the heights of husbands and their wives since people may choose partners similar to themselves in height, a phenomenon known as assortative mating, but the correlation is likely to be weaker than genetic influence. Lastly, for the heights of women at age 4 and their heights at age 18, while early childhood height can be an indicator of adult height, there's substantial growth and development between these ages, affected by environmental and genetic factors, resulting in a lower correlation compared to the direct genetic link between fathers and sons.

If we were to rank the correlation from largest to smallest, it would be:

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The statement which best describes the resulting three-dimensional figure is:

We know that when a rectangle is rotated about a line then the resulting figure so obtained is a cylinder.

Also, the breadth of the rectangle will be the radius of the cylinder.

Here the perimeter of the rectangle is: 76 cm.

Also the length of the rectangle is: 24 cm.

Let b be the breadth of the rectangle.

We know that the perimeter of rectangle is given by the formula:

               [tex]Perimeter=2(l+b)[/tex]

where l is the length of the rectangle and b is the breadth of the rectangle.

Here we have: l=24 cm

Hence,

[tex]76=2(24+b)\\\\i.e.\\\\24+b=\dfrac{76}{2}\\\\i.e.\\\\24+b=38\\\\i.e.\\\\b=38-24\\\\i.e.\\\\b=14\ cm[/tex]

see attached picture for the answers:

Velocity is the rate of change of distance over time.

The ball's approximate vertical speed when it hits the ground is 19.8m/s

The maximum height of an object, thrown up is calculated as:

[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]

Where:

[tex]\mathbf{h_{max} = 20m}[/tex] --- the maximum height

[tex]\mathbf{v = ??}[/tex] --- final velocity

[tex]\mathbf{g = 9.8ms^{-2}}[/tex] --- acceleration due to gravity

So, we have:

[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]

[tex]\mathbf{20 = \frac{v^2}{2 \times 9.8}}[/tex]

Solve for v^2

[tex]\mathbf{v^2 = 2 \times 9.8 \times 20}[/tex]

[tex]\mathbf{v^2 = 392}[/tex]

Take square roots of both sides

[tex]\mathbf{v = 19.8ms^{-1}}[/tex]

Hence, the ball's approximate vertical speed when it hits the ground is 19.8m/s

Read more about velocity at:

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When a softball is thrown straight up and reaches a maximum height of 20 meters, the approximate vertical speed when it hits the ground can be determined by taking into account the initial vertical velocity and the time it takes to reach the maximum height and fall back down. Using the given information, the initial vertical velocity is calculated using the equation v0y = sqrt(2gh), where g is the acceleration due to gravity and h is the maximum height. Substituting the values, the approximate vertical speed is 19.80 m/s.

When a softball is thrown straight up and reaches a maximum height of 20 meters, its approximate vertical speed when it hits the ground can be determined using the principles of projectile motion. The vertical speed of the ball when it hits the ground can be calculated by taking into account the initial vertical velocity and the time it takes for the ball to reach its maximum height and then fall back down. In this case, since the ball is thrown straight up, the vertical speed when it hits the ground will be equal to the initial vertical speed.

Using the given information, we know that the ball reaches a maximum height of 20 meters. We can calculate the time it takes for the ball to reach this height using the equation for vertical displacement:

h = v0yt + (1/2)gt2

Where:

Since we know the maximum height and the acceleration due to gravity, we can rearrange the equation to solve for the initial vertical velocity:

v0y = sqrt(2gh)

where:

Substituting the values into the equation, we get:

v0y = sqrt(2 * 9.8 * 20)

Simplifying further:

v0y = sqrt(392)

v0y ≈ 19.80 m/s

Therefore, the approximate vertical speed of the ball when it hits the ground is 19.80 m/s.

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Answer:

50 ft²

Step-by-step explanation:

As you can see the polygon on the grid is not a regular polygon, so to calculate the area would be very complicated without having the right tools, what we can doo is to draw a squre that covers the whole height but not the total length, that way we can take a close estimate of the area, the closest square that can be formed would be a 6x9 square, and the estimated area would be 54, that would be the maximun area, so the answer would be 50 squared feet.

The answer is $1932.15

3,513+351.30=3864.30

3864.30÷2=1932.15

Hope this helps!

Answer-

Correlation coefficient for the data in the table was found to be 0.93.

Solution-

Taking the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable or output variable as the amount of the bill.

We know that,

[tex]r=\frac{n(\sum xy)-\sum x \sum y}{\sqrt{[n\sum x^{2} -({\sum x})^{2}]\times [n\sum y^{2} -({\sum y})^{2}]}}[/tex]

Calculating the values from the table, then putting it in the formula

[tex]r=\frac{4 \times 3130.9 \ - \ 6.45 \times 1473}{\sqrt{[4\times 12.3725 \ - \ 6.45^{2}][4 \times 877475 \ - \ 1473^2]}}[/tex]

[tex]\Rightarrow r=0.929720561 \approx 0.93[/tex]

∴  Correlation coefficient for the data is 0.93.

The correlation coefficient for the data in the table would be 0.93. So, the correct option is A.

The correlation coefficient is used to measure the strong relationship between the two variables.

It is given that the first column is labeled time spent at the dentist (in hours) with entries 1.4, 2.7, 0.75, and 1.6.

The second column is labeled bill amount (in dollars) with entries 235, 867, 156, and 215.

The numbers between -1 and 1 should be one of the values related to the bill amount.

By assuming the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable as the amount of the bill.

Hence, The correlation coefficient for the data in the table was found to be 0.93.

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The value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.

Simplified form of an equation is the simplest way of expression the equation, which is obtained by applying the required operations of mathematics.

A polynomial expression is shown below.

[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)[/tex]

The expression is simplified to the following expression,

[tex]8x^3 + 6x^2 + 15x + 6[/tex]

As the equation is a simplified expression of the given polynomial. Thus, both the equation are same.

[tex](mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)=8x^3 + 6x^2 + 15x + 6[/tex]

Open the brackets and simplify it further,

[tex]2mx^5+5mx^4+2mx^3+6x^2+15x+6-8x^5-20x^4=8x^3 + 6x^2 + 15x + 6\\2mx^5+5mx^4+2mx^3=8x^3+6x^2+15x+6-6x^2-15x-6+ 8x^5+20x^4\\m(2x^5+5x^4+2x^3)= 8x^5+20x^4+8x^3 \\m(2x^5+5x^4+2x^3)=4(2x^5+5x^4+2x^3)[/tex]

On comparing both side of the equation, the value of m we get is,

[tex]m=4[/tex]

Thus, the value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.

Learn more about the simplified form here;

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