Arturo builds a cube that measures 5 in on each side. What is the volume of Arturo's cube?

The sum of the shortest distance a student ran and the longest distance a student ran is 11/8

A fraction represents equal parts of a whole, by dividing it up into equal partitions. Each fraction has a numerator and denominator. The denominator represents the total number of parts the whole has been divided into.

Given is a line plot, describing the distances that is a fraction of a mile, 13 students ran during their fitness test, we need to find the sum of the shortest distance a student ran and the longest distance a student ran,

Here, according to the graph, the shortest distance = 3/8 of a mile

And the longest distance = 8/8 of a mile

So, the sum = 8/8 + 3/8 = 11/8

Hence, the sum of the shortest distance a student ran and the longest distance a student ran is 11/8

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The sales price of the camera is $46.4

The given parameters are:

Discount = 20%

Price = $58

The sales price is calculated using:

Sales price = Price * (1 - discount)

This gives

Sales price = $58* (1 - 20%)

Evaluate

Sales price = $46.4

Hence, the sales price of the camera is $46.4

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The correct statements are:

- B. The rocket reached a maximum height of 59 feet.

- C. It took the rocket 3.5 seconds to reach its maximum height.

- E. The equation that represents the rocket’s height over time has two solutions.

To determine which statements about the rocket's flight are true, analyze the given graph.

1. Statement B: The rocket reached a maximum height of 59 feet.

  - This statement is true. The highest point on the graph is marked as (3.5, 59), indicating that the maximum height of the rocket was 59 feet.

2. Statement C: It took the rocket 3.5 seconds to reach its maximum height.

  - This statement is true. The coordinates (3.5, 59) show that the rocket reached its maximum height at 3.5 seconds.

3. Statement E: The equation that represents the rocket’s height over time has two solutions.

  - This statement is true. The parabolic path of the rocket implies a quadratic equation. A quadratic equation typically has two solutions, which correspond to the times when the rocket is at ground level (height = 0). From the graph, we see the rocket starts at (0, 0) and lands at (6.9, 0), confirming two solutions.

Verifying the incorrect statements:

1. Statement A: The rocket was launched from a platform 4.9 feet above the ground.

  - This statement is false. The graph shows that the rocket was launched from the origin point (0, 0), meaning it was launched from ground level, not 4.9 feet above the ground.

2. Statement D: The rocket landed after 34 seconds.

  - This statement is false. The graph indicates the rocket landed at 6.9 seconds, not 34 seconds.

The correct options are:

A. The rocket was launched from a platform 4.9 feet above the ground.

B. The rocket reached a maximum height of 59 feet.

C. It took the rocket 3.5 seconds to reach its maximum height.

D. The rocket landed after 34 seconds.

E. The equation that represents the rocket's height over time has two solutions.

To determine the validity of each statement, we must analyze the graph of the rocket's height over time. Here is the logical reasoning behind each option:

A. The rocket was launched from a platform 4.9 feet above the ground.

This statement is true if the graph's vertical intercept (the height at time zero) is 4.9 feet. The vertical intercept is the starting height of the rocket before it is launched.

B. The rocket reached a maximum height of 59 feet.

This statement is true if the graph reaches a maximum value of 59 feet at some point in time. This would be the peak of the graph, where the height is greatest.

C. It took the rocket 3.5 seconds to reach its maximum height.

This statement is true if the time at which the graph reaches its maximum height is 3.5 seconds. This is the horizontal coordinate of the peak of the graph.

D. The rocket landed after 34 seconds.

This statement is true if the graph returns to the horizontal axis (height of zero) at 34 seconds. This would indicate that the rocket has returned to the ground.

E. The equation that represents the rocket's height over time has two solutions.

This statement is true if the graph intersects the horizontal axis at two distinct points. The first intersection represents the launch point (time zero), and the second intersection represents the landing point. The fact that there are two intersections implies that the equation has two solutions.

The point (2, 8) lies on the line  y = 5x - 2 which is correct option(B).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To determine the point lie on line or not we have to put points in equation if it satisfy then it lie otherwise not.

(A) Point (0, 4)

y = 5x - 2

Substitute x = 0 and y = 4,

4 = 5(0) - 2

4 = -2

Point (0, 4) does not lie on the line.

(B) Point (2, 8)

y = 5x - 2

Substitute x = 2 and y = 8,

8 = 5(2) - 2

8 = 10 - 2

8 = 8 True

Point (2, 8) lies on the line.

(C) Point (-1,2)

y = 5x - 2

Substitute x = -1 and y = 2,

2 = 5(-1) - 2

2 = -7

Point (-1,2) does not lie on the line.

(D) Point (4,10)

y = 5x - 2

Substitute x = 4 and y = 10,

10 = 5(4) - 2

10 = 18

Point (4,10) does not lie on the line.

Hence, the point (2, 8) lies on the line.

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Answer:

[tex]Cos^{-1}(0.9455)[/tex] = 19 degree.

Step-by-step explanation:

Given: [tex]Cos^{-1}(0.9455)[/tex].

To find : values of  [tex]Cos^{-1}(0.9455)[/tex].

Solution : We have given that  [tex]Cos^{-1}(0.9455)[/tex].

[tex]Cos^{-1}(0.9455)[/tex].  =0.33166 radians

In form of degree

0.33166 radians =  19 degree.

Therefore,   [tex]Cos^{-1}(0.9455)[/tex] = 19 degree.

Answer:

Step-by-step explanation:

To obtain the graph of a parabola, three data are necessary: ​​the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values ​​of x for which the expression is 0. Graphically,  the roots correspond to the abscissa of the points where the parabola  cuts the x-axis.) and the concavity.

Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:

In this way, the graph shown in the attached image is obtained.

When the function f(x)=25[tex]x^2[/tex]−2 is vertically stretched by a factor of 2 to create the function g(x), the resulting equation is g(x) = 50[tex]x^2[/tex]−4.

The equation of g(x) can be found by vertically stretching f(x) by a factor of 2. Since f(x) = 25[tex]x^2[/tex] - 2, we can multiply the function by 2 to get g(x) the equation:

The function g(x) is described as a vertical stretch of the function f(x) by a factor of 2. If f(x)=25[tex]x^2[/tex]−2, a vertical stretch implies that we multiply all y-coordinates by the given factor, which is 2 in this case. Therefore, g(x) will be 2*f(x).

This gives us:

g(x) = 2*(25[tex]x^2[/tex] −2)

Expand this:

g(x) = 50[tex]x^2[/tex]−4

So, the equation of g(x) after the vertical stretch of f(x) by a factor of 2 is g(x) = 50[tex]x^2[/tex] −4.

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The equation of g(x), which is a vertical stretch of f(x) = 25x² - 2 by a factor of 2, is g(x) = 50x² - 4.

To solve this, we need to apply a vertical stretch to the function f(x).

A vertical stretch by a factor of 2 means multiplying the entire function f(x) by 2.

Given :

f(x) = 25x² - 2

we multiply it by 2:

g(x) = 2 * (25x² - 2)

g(x) = 50x² - 4

So, the equation of g(x) is g(x) = 50x² - 4.

Final answer:

Nicole will need 2 1/4 cups of vinegar to make 3/4 of her salad dressing recipe, as you multiply the total amount (3 cups) by 3/4.

Explanation:

Nicole uses 3 cups of vinegar for her full salad dressing recipe. To make 3/4 of the recipe, you would calculate three-quarters of the total amount of vinegar used. Simply multiply 3 cups by 3/4 to find out how much vinegar Nicole would need.

The calculation is as follows:

Thus, Nicole will need 2 1/4 cups of vinegar to make three-quarters of her salad dressing recipe.

Answer:

The sign of the product is negative because a negative multiplied by a positive is a negative.

Step-by-step explanation:

Without multiplying, determine the sign of the product (−247,634)(183,758).

The sign of the product is positive because a negative multiplied by a positive is a positive.

The sign of the product is negative because a negative multiplied by a positive is a negative.

The sign of the product is negative because the first number is negative.

The sign of the product is positive because the second number is positive.

This is correct because  The sign of the product is negative because a negative multiplied by a positive is a negative.

Final answer:

Pythagorean triples are sets of three whole numbers that form the sides of a right triangle and satisfy the Pythagorean theorem, a² + b² = c².

Explanation:

Pythagorean triples are unique because they consist of three whole numbers that satisfy the Pythagorean theorem.

Specifically, the squares of the two shorter sides (a and b), when added together, equal the square of the longest side (the hypotenuse, c). That is, a² + b² = c² holds true for these numbers.

Answering the student's question, the characteristic that is unique about Pythagorean triples is: C) The length of each side is a whole number.

This means that all three sides of the right triangle are integers, which is helpful in various mathematical and practical applications. Examples of Pythagorean triples include (3, 4, 5) and (5, 12, 13).

Answer:

706.5

Step-by-step explanation: