Help me on questions 1, 2, and 3

Final answer:

Sarah will take approximately 0.6 minutes or 34 seconds to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute, after calculating the volume of the balloon and dividing by the rate.

Explanation:

How long will it take Sarah to inflate a spherical balloon with a radius of 3 inches at a rate of 200 cubic inches per minute?

To solve this problem, we first need to calculate the volume of the spherical balloon using the formula for the volume of a sphere, which is [tex]V = \(\frac{4}{3}\)\pi r^3[/tex], where r is the radius of the sphere. In this case, the radius is 3 inches. Plugging the values into the formula, we get:

[tex]V = \(\frac{4}{3}\)\pi (3)^3 = \(\frac{4}{3}\)\pi (27) = 36\pi cubic inches[/tex]

Now, given that Sarah can inflate the balloon at a rate of 200 cubic inches per minute, we can calculate the time it takes to inflate the balloon by dividing the total volume by the rate:

[tex]Time = \(\frac{Volume}{Rate}\) = \(\frac{36\pi}{200}\) minutes[/tex]

Using the approximation \(\pi = 3.14\), this results in:

[tex]Time = \(\frac{36 \times 3.14}{200}\) = \(\frac{113.04}{200}\) ≈ 0.565 minutes[/tex] or about 33.9 seconds, rounded to the nearest tenth.

Therefore, it will take Sarah approximately 0.6 minutes or 34 seconds to inflate the balloon.

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.

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.

Zoe's Fish tank holds 27 L of water, so this is the capacity of the tank. On the other hand, Zoe uses a 3L container in order to fill the tank, so the question is  how many times does she have to fill the three litter container in order to fill the fish tank? Let's solve this as follows:

First time:

She pours 3L

Second time:

She pours another 3L, but she previously poured 3L, so she has poured 6L

Third time:

She pours another 3L, but she previously poured 6L, so she has poured 9L

Fourth time:

She pours another 3L, but she previously poured 9L, so she has poured 12L

Fifth time:

She pours another 3L, but she previously poured 12L, so she has poured 15L

Sixth time:

She pours another 3L, but she previously poured 15L, so she has poured 18L

Seventh time:

She pours another 3L, but she previously poured 18L, so she has poured 21L

Eighth time:

She pours another 3L, but she previously poured 21L, so she has poured 24L

Ninth time:

She pours another 3L, but she previously poured 24L, so she has poured 27L

According to this, she needs to pours the 3L container nine times in order to fill the fish tank. This can also be solved dividing 27L/3L= 9

The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. So, the correct options are B and C.

Given:

The given expression is:

[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]

To find:

The equivalent expressions.

Explanation:

We have,

[tex]-\dfrac{2}{5}(15-20d+5c)[/tex]

Using the distributive property, we get

[tex]=-\dfrac{2}{5}(15)-\dfrac{2}{5}(-20d)-\dfrac{2}{5}(5c)[/tex]

[tex]=-6+8d-2c[/tex]

It can be rewritten as:

[tex]=-2c+8d-6[/tex]

The equivalent expressions are [tex]-6+8d-2c[/tex] and [tex]-2c+8d-6[/tex]. Therefore, the correct options are B and C.

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Upon applying the distributive property, the given expression, –25(15 – 20d + 5c), simplifies to –375 + 500d – 125c. None of the options provided match this expression, making the correct answer 'None of the above'.

The student is asked to find an expression equivalent to –25(15 – 20d + 5c). To do this, we will apply the distributive property to multiply –25 by each term inside the brackets. This gives us:

Combining these we get the expression –375 + 500d – 125c. When we look at the options provided, none are equivalent to the expression we derived. Therefore, the correct answer is:

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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.

The answer is not A because T would be flipped,  the answer is not D because T can not be reflected in that area without translations, and the answer is not B because T cannot (once again) be reflected in such locations without translations, Therefore, that leaves us with our best bet being the answer C.

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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Answer:

147

Step-by-step explanation: