Renee hiked for 3 and 3/ 4 miles. After resting, Renee hiked back along the same route for 2 and 1 /4 miles. How many more miles does Renee need to hike to return to the place where she started? Represent your answer as a simplified mixed number, if necessary.

The surface area of the disco ball is approximately 804 square inches.

To find the surface area of a sphere, we can use the formula: 4πr², where r is the radius of the sphere. Since the diameter of the disco ball is given as 16 inches, we can find the radius by dividing the diameter by 2. So, the radius will be 8 inches. Plugging this value into the formula, we get:

Surface area = 4π(8)² = 4π(64) = 256π inches². To the nearest square inch, the surface area of the disco ball is approximately 804 square inches.

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The problem involves understanding relationships between functions F(x) and G(x), achieved by creating new functions P(x) as their product and Q(x) as their quotient, and studying their behavior for different values of x.

The subject of the question deals with understanding the relationship between two functions, F(x) and G(x), through creating new functions P(x) and Q(x). P(x) is defined as the product of F(x) and G(x), while Q(x) represents the division of F(x) by G(x).

One way to explore the nature of these new functions would be to take particular values of x, calculate the corresponding outputs for F and G, and then apply the definitions of P and Q. For instance, if F(1)=2 and G(1)=3, then P(1)=F(1)G(1)=2*3=6 and Q(1)=F(1)/G(1)=2/3. Through these examples we can get a grasp of how these functions behave. Comparing P(x) and Q(x) across a number of x-values also provides insight into their relative behavior and interplay.

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On comparison 9 x 10⁴ is a larger number than 3 x 10².

To compare 9 x 10⁴ and 3 x 10², we can compare the coefficients (9 and 3) and the powers of 10 (10⁴ and 10²) separately.

Comparing the coefficients: 9 vs. 3

The coefficient 9 is greater than the coefficient 3. Therefore, 9 x 10⁴ is greater than 3 x 10² in terms of the actual value of the numbers themselves.

Comparing the powers of 10: 10⁴ vs. 10²

The power of 10 in 10⁴ is greater than the power of 10 in 10². A larger power of 10 means the number has more zeros. In this case, 10⁴ has four zeros (10,000), while 10² has two zeros (100).

Since 10⁴ has more zeros than 10², it represents a larger value.

Combining both comparisons:

When comparing the entire numbers, 9 x 10⁴ is greater than 3 x 10². The larger coefficient (9) and the larger power of 10 (10⁴) contribute to its greater value.

In summary, 9 x 10⁴ is a larger number than 3 x 10².

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Answer:

transcript

Step-by-step explanation:

dividing by a polinomial

Answer:

Line plot

Step-by-step explanation:

Consider the provided information.

I am a graph that records each piece of data above a number line

Line plot is a graph that uses marks to record each piece of  given data above the number line.

It shows the frequency of data along a number line. Remember it is different from line graph.

The example of line plot is shown in figure below.

Final answer:

To find the average cost per radio of producing the first 30 radios, divide the total cost of producing the first 30 radios by 30. The average cost per radio is $10.67.

Explanation:

To find the average cost per radio of producing the first 30 radios, we need to divide the total cost of producing the first 30 radios by 30. The total cost function is given as c(x) = 200 + 10x - 0.2x^2, where x represents the number of radios produced. Plugging in x = 30 into the function, we get c(30) = 200 + 10(30) - 0.2(30^2) = 200 + 300 - 180 = 320.

Therefore, the total cost of producing the first 30 radios is $320. To find the average cost per radio, we divide the total cost by the number of radios: $320 / 30 = $10.67.

Solving this problem is pretty straight forward.

We simply use the formula:

z-score = (x – u) / s

where,

x = sample value = 48 minutes

u = mean value = 30 minutes

s = standard deviation = 7 minutes

Therefore,

z-score = (48 minutes – 30 minutes) / 7 minutes

z-score = 2.57

Final answer:

To calculate Nolan's z-score for playing time against Fairview, use the given formula. Nolan's z-score for this game is 2.57.

Explanation:

A: To calculate the z-score for Nolan's playing time against Fairview, use the formula: z = (x - μ) / σ, where x is Nolan's playing time, μ is the average time, and σ is the standard deviation.

B: Substituting the values, z = (48 - 30) / 7 = 2.57. Therefore, Nolan's z-score for playing time against Fairview is 2.57.

To know how much Marty pours into each bottle, divide the total juice amount by the number of bottles. His total of 2 4/5 quarts became 14/5 when turned into fifths for easier calculation. Dividing 14/5 by 2, we find that Marty pours 1 2/5 quarts into each bottle.

Marty has 2 4/5 quarts of juice. He is trying to equally distribute this juice into 2 bottles. To find out how much juice each bottle will contain, we divide the total amount of juice by the number of bottles.

Given that 1 full quart is made up of 5 fifths, 2 quarts are equivalent to 2x5=10 fifths. Marty has 2 full quarts and 4/5 of a quart, which amounts to 10+4=14 fifths of a quart. So, Marty has 14/5 quarts of juice in total.

If he pours the same amount into 2 bottles, then each bottle will contain half of the total amount. To find this out, we divide the total amount by 2, which gives us 14/5 ÷ 2 = 7/5 quarts. Therefore, Marty pours 7/5 quarts or 1 2/5 quarts of juice into each bottle.

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The standard form of the given expression is 70,418,539.

Given that, 70,000,000+400,000+10,000+8,000+500+30+9.

We need to write the given expanded form in word form and standard form.

Standard form is the usual way of writing numbers. One example is 756. This is how we see numbers every day in the grocery, on our phones, on computers, etc.

Expanded form is breaking down the numbers in such a way that you see the value of each number. So, the expanded form of 756 is 700 + 50 + 6.

Word form is when you write a number the way that you read it. When you see the number 756, you write it as “seven hundred fifty-six”.

Now, standard form of the given expression is 70,418,539.

Word form of the given expression is sevety million, four hundred and eighteen thousand, five hundred and thirty nine.

Therefore, the standard form of the given expression is 70,418,539.

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Answer:788

Step-by-step explanation:

4N-7 = 35

4N = 42

N = 42/4 = 10.5

10.5 = 21/2

B 21/2  is the answer

When a body is said to be in a state of free fall, therefore this means that the only force associated with it is gravity. Gravity imposes an acceleration of about 9.81 m/s^2. Therefore we do not need to calculate for a, since a = g. (g = acceleration due to gravity)

a = 9.81 m/s^2