How many cubic centimeters are there in 2.11 yards^3? express your answer in cubic centimeters to three significant figures?

Answer:

10°

Step-by-step explanation:

To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.

AB is opposite ∠C and AC is adjacent to ∠C.

The ratio of opposite/adjacent is the ratio of tangent.  This gives us the equation

tan C = 2/11

To solve this for C, we take the inverse tangent of each side:

tan⁻¹(tan C) = tan⁻¹(2/11)

C = 10.305 ≈ 10°

The measure of the angle ∠c will be 10°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.

AB is opposite ∠C and AC is adjacent to ∠C.

The ratio of opposite/adjacent is the ratio of a tangent.  This gives us the equation

tan C = 2/11

To solve this for C, we take the inverse tangent of each side:

tan⁻¹(tan C) = tan⁻¹(2/11)

C = 10.305 ≈ 10°

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The required simplified value of the g(h(3)) is given as 59.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
g(x) = x³ - 5 and h(x) = 2x - 2

h(3) = 2(3) - 2
h(3) = 4

g(h(3)) = 4³ - 5
         = 64 - 5
         = 59

Thus, the required simplified value of the g(h(3)) is given as 59.

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complete question:

A dentist orders 15 boxes of floss and 20 boxes of toothbrushes each month. Floss is sold 70 to a box and toothbrushes are sold 50 to a box . how many items does the dentist order each month.

Answer:

The dentist orders 1050 number of floss and 1000 number of toothbrushes. The items are 2 different items namely floss and toothbrushes.

Step-by-step explanation:

The dentist orders 15 boxes of floss and 20 boxes of toothbrushes each month.

The floss is sold 70 to a box, this means about 70 numbers of floss occupies each box of floss.  To get the total number of floss items in the 15 boxes of floss, we have to multiply the number of boxes of floss by the number of floss present in each box. Mathematically,

70 × 15 = 1050  items of floss

The boxes of toothbrushes is 20 . For each box the number of toothbrushes is 50 . To get the total number of tooth brushes  we multiply the number of boxes by the total number of toothbrushes in each box.

50 × 20 = 1000  items of toothbrushes.

The dentist orders 1050 number of floss and 1000 number of toothbrushes. The items are 2 different items namely floss and toothbrushes.

The probability that your flight will arrive on time is 0.6, or 60%.

To calculate the probability that your flight will arrive on time, we can use the concept of conditional probability. Let A represent the event of good weather and B represent the event of the flight arriving on time. We know P(A) = 0.6, P(B|A) = 0.8, and P(B|A') = 0.3 (where A' represents bad weather). We can use the formula for conditional probability: P(B) = P(A) * P(B|A) + P(A') * P(B|A'). Substituting the given values, we have P(B) = 0.6 * 0.8 + 0.4 * 0.3 = 0.48 + 0.12 = 0.6. Therefore, the probability that your flight will arrive on time is 0.6, or 60%.

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The x-coordinate of the point is changing at a rate of [tex]\( 6 \text{ cm/s} \)[/tex].

To determine how fast the x-coordinate of the particle is changing at the instant it reaches the point (4, 2), we start with the equation of the hyperbola and apply the related rates method.

Given:

[tex]\[ xy = 8 \][/tex]

Differentiate both sides of the equation with respect to time [tex]\( t \)[/tex]:

[tex]\[ \frac{d}{dt}(xy) = \frac{d}{dt}(8) \][/tex]

Using the product rule on the left side:

[tex]\[ x \frac{dy}{dt} + y \frac{dx}{dt} = 0 \][/tex]

We need to find [tex]\(\frac{dx}{dt}\)[/tex] when the particle is at the point [tex]\((4, 2)\)[/tex] and [tex]\( \frac{dy}{dt} = -3 \text{ cm/s} \)[/tex] (since the y-coordinate is decreasing).

Substitute [tex]\( x = 4 \)[/tex], [tex]\( y = 2 \)[/tex], and [tex]\( \frac{dy}{dt} = -3 \)[/tex] into the differentiated equation:

[tex]\[ 4 \left( -3 \right) + 2 \frac{dx}{dt} = 0 \][/tex]

Simplify and solve for [tex]\( \frac{dx}{dt} \)[/tex]:

[tex]\[ -12 + 2 \frac{dx}{dt} = 0 \][/tex]

[tex]\[ 2 \frac{dx}{dt} = 12 \][/tex]

[tex]\[ \frac{dx}{dt} = 6 \][/tex]

Answer:

92/27 and 58/27 for n=3 and 13/4 and 9/4 for n=4

Step-by-step explanation:

n = 3: First let’s find ∆x:

∆x = (b − a)/n = 1 − (−1)3 = 2/3

We will have three intervals: −1 ≤ x ≤ −1/3, −1/3 ≤ x ≤1/3, 1/3 ≤ x ≤ 1.

Upper sum: On the first interval, the highest point occurs at f(−1) = 2. On the second interval, the highest point occurs at f(1/3) = f(−1/3) = 1 + ( 1/3)^2=1 + 1/9 = 10/9

On the third interval, the highest point occurs at f(1) = 2. So A ≈ A upper = 3Σ i=1 f(xi)∆x = [f(−1) + f (1/3)+ f(1)]∆x = (2 +10/9+ 2)*2/3 = 92/27

Lower sum: On the first interval, the lowest point occurs at f(−1/3) = 10/9

On the second interval, the lowest point occurs at f(0) = 1. On the third interval, the lowest point occurs at f(1/3) = 10/9. SoA ≈ A lower =3Σ i=1 f(xi)∆x = f(−1/3) + f(0) + f(1/3) . ∆x = (10/9+ 1 +10/9)· 2/3= 58/27

Apply the same technique for n=4

The original volume equation looks like this: V = 1/3 * h * (x^2) 
After the side is reduced by 0.002, the new volume would look like V1 = 1/3 * h * (x-0.002) ^ 2 

Then we have: 
V-V1 = 1/3*h*(x^2) - 1/3*h*(x – 0.002) ^2 

= 1/3 * h *(x^2 - (x – 0.002) ^2) 

= 1/3 * h * (0.004x - 0.00004) 

The rate of decreasing is computed by:

(V-V1)/V * 100% = [1/3 * h *(0.004x - 0.00004)] / [1/3 * h * (x ^ 2)] * 100% this would be equal to (0.004x - 0.00004) / (x^2) * 100% 

So replace x by 200, you’ll get:

(0.004(200) - 0.00004) / (200^2) * 100% 

= 0.001999% is the rate of decreasing.

85 divided by 5 equals 17.

To find the answer to 85 divided by 5 using the distributive property, we break 85 into simpler numbers that are easier to divide by 5. For example:

Step 1: Write 85 as a sum of numbers that can easily be divided by 5:
85 = 50 + 35

Step 2: Divide each part by 5:
50 ÷ 5 = 10
35 ÷ 5 = 7

Step 3: Add the results:
10 + 7 = 17

Therefore, 85 divided by 5 equals 17.

The speed of thirty-four thousand centimeters per second in scientific notation is 3.4  x 10^2 meters per second, after converting centimeters to meters.

The speed of thirty-four thousand centimeters per second can be expressed in scientific notation by first converting it to the base unit of meters per second (since one meter is equal to one hundred centimeters) and then expressing it in the form of a significant figure followed by the power of 10.

First, convert centimeters to meters:

Now, express this in scientific notation:

This shows the speed in scientific notation with the unit meters per second, which is a combination of two SI units.

To find the inverse of f(x) = -6x + 6, swap the variables and solve for y, yielding the inverse function f^-1(x) = 1 - (x/6).

To find the inverse function, f-1(x), of the given function f(x) = -6x + 6, you need to follow a series of steps. First, swap the 'x' and 'y', so it becomes x = -6y + 6. Next, solve this equation for 'y' to find the inverse function. Add 6x to both sides to get x + 6y = 6, then subtract x from both sides to have 6y = 6 - x. Dividing both sides by 6 results in y = 1 - (x/6). Therefore, the inverse function is f-1(x) = 1 - (x/6).

Answer:

30

Step-by-step explanation:

A bundle of 3 adult tickets and 1 child ticket sells for $32.80, so there were ...

... $984/$32.80 = 30 . . . . bundles sold.

The number of child tickets sold was 30.

_____

Using an equation

Let c represent the number of child tickets sold. Then 3c is the number of adult tickets sold. The total revenue is ...

... 5.80c + 9.00·(3c) = 984.00

... 32.80c = 984.00 . . . . . . . . . . simplify

... c = 984.00/32.80 = 30 . . . . . divide by the coefficient of c

The value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x is 9/4. This is because a line is tangent to a curve when it touches the curve at exactly one point, hence the slope of the given line (9/4) will be equal to the value of c, which is the slope of the curve.

The problem asks us to find the value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x. A line is tangent to a curve when it touches the curve at exactly one point. In this context, the slope of the given line (9/4) will be equal to the value of c since in the line equation y = c x, c is the slope. So the value of c is 9/4.

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Final answer:

The numerical value of n for the 5d orbitals is 5, which indicates that the d subshell in question is located in the fifth principal energy level of an atom.

Explanation:

The numerical value of n corresponding to the 5d orbitals is 5. In the context of atomic and quantum physics, the principal quantum number, denoted as n, signifies the principal electronic shell of an atom. Since the question refers to 5d, it means we are discussing the d subshell in the fifth principal energy level (n=5).

For a d subshell, which is represented by the azimuthal quantum number (l) having a value of 2, the first principal shell where a d subshell appears is when n=3. Therefore, the 5d subshell is present in the fifth principal energy level. As for the ml values of the d orbitals, which represent the magnetic quantum number, they can be -2, -1, 0, +1, or +2 for any d subshell.

Answer:2/3

Step-by-step explanation: