A rectangle's width is one-fifth it's length, and it's perimeter is 180m. Find the dimensions of the rectangle. The length is M and the width is m

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

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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The area of the region bounded by the parabola[tex]y=2x^2[/tex]angent line at (5,50), and the x-axis is found by integrating the function of the parabola, finding the x-intercept of the tangent line, and subtracting the area under the tangent line from the area under the parabola between x=0 and x=5.

The area of the region bounded by the parabola , the tangent line at the point (5,50), and the x-axis can be found using integral calculus. First, we find the equation of the tangent line to the parabola at (5,50). The derivative of y with respect to x is given by [tex]y=2x^2[/tex]= 4x. At x=5, the slope of the tangent line is 20. Thus, the equation of the tangent line is y - 50 = 20(x - 5). To find the bounded area, we integrate the area under the parabola from the x-intercept of the tangent line to x=5, and subtract the area under the tangent line in the same interval.

Let's call the x-intercept of the tangent line x1. To find x1, we set the y-value of the tangent line equation to 0 and solve for x. The integration itself uses the antiderivative of  which is [tex]2x^2,[/tex] and the antiderivative of the linear tangent line equation. Subtracting the integral of the tangent line from the integral of the parabola gives us the exact area under the parabola.

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.

4N-7 = 35

4N = 42

N = 42/4 = 10.5

10.5 = 21/2

B 21/2  is the answer

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.

Answer:

transcript

Step-by-step explanation:

dividing by a polinomial

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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(450-210)/4+50=110

 hope this helps

Answer:

Option B is correct

x= 3, At level 3, 27  number of people contacted

Step-by-step explanation:

As per the given statement:

The number of people contacted at each level of a phone tree can be represented by:

[tex]f(x) = 3^x[/tex]

where, x represents the level.

We have to find the value of x when f(x) = 27.

⇒27 = 3^x

We can write 27 as:

[tex]27 = 3 \times 3 \times 3 = 3^3[/tex]

then;

[tex]3^3 = 3^x[/tex]

on comparing we have;

3 = x

or

x = 3

Therefore, the value of x is, 3.

Function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function by its name and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input.

To evaluate a function using function notation, we simply substitute the input value into the function's expression. For example, if the function is f(x) = x^2, then to evaluate f(2), we would substitute 2 into the function's expression:

f(2) = 2^2 = 4

This means that the ordered pair solution (2, 4) is a solution of the function f(x) = x^2.

In general, any ordered pair solution of a function can be evaluated using function notation. For example, if the function is g(x) = 2x + 1, and the ordered pair solution is (3, 7), then we can evaluate g(3) as follows:

g(3) = 2(3) + 1 = 6 + 1 = 7

This confirms that the ordered pair solution (3, 7) is a solution of the function g(x) = 2x + 1.

Conversely, any function value can be represented as an ordered pair solution of the function. For example, if the function is h(x) = x^3, and the function value is 8, then we can represent this as the ordered pair solution (2, 8), since h(2) = 8.

In general, any function value can be represented as an ordered pair solution of the function by writing the input value as the first coordinate and the function value as the second coordinate.

Therefore, function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input. Any function value can be evaluated using function notation, and any ordered pair solution of a function can be represented as a function value.

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The following question may be like this:

What is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the​ function?

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:788

Step-by-step explanation: