simplify 32over23 please​

In the given table to determine if the relation is a function we need to check if each input (x) maps to exactly one output (y).

In other words, if the x-values are not repeated then it is a function.

In the table there is not x-values repeated, so, the table define y as a function of x.

The answer is yes.

In designing the waterskiing ramp using direct variation the vertical supports, y will be related to the horizontal distance, x by a constant k,  as in the relation

k = y/x

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and shrink at the same rate, they are directly proportional.

When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

In the problem, the distances between the vertical supports is x while the height of the support is y. To have a direct proportionality this relationship between x and y must be a constant say k.

Hence we say k = y / x

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Using Linear Approximation, the estimate of cos(62°) - cos(60°) is approximately 0.530153 - 0.5 = 0.030153 (rounded to six decimal places).

To use Linear Approximation to estimate cos(62°) - cos(60°), we'll follow these steps:

1. Choose a point near 62° where the cosine function is easier to compute, such as 60° (which is in radians, π/3).
2. Find the derivative of the cosine function: d/dx(cos(x)) = -sin(x).
3. Evaluate the derivative at the chosen point (60°): -sin(60°) = -sin(π/3) = -√3/2.
4. Use the linear approximation formula: Δy ≈ f'(x0)Δx, where Δy is the change in y (cosine values), f'(x0) is the derivative at the chosen point, and Δx is the change in x (angle).
5. Compute Δx: 62° - 60° = 2° (convert to radians: 2° * π/180 ≈ 0.0349 radians).
6. Plug the values into the linear approximation formula: Δy ≈ (-√3/2)(0.0349) ≈ -0.030153.
7. Now, subtract the linear approximation from the original cosine value at 60°: cos(60°) - Δy = cos(π/3) - (-0.030153) = 1/2 + 0.030153 ≈ 0.530153.

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Answer:

Dimensions are 20 + 20 + 40 + 40

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer: Hi there! X = 7 would be your answer

Step-by-step explanation:

Simplify both sides of the equation.

2(3x − 6) = 3(x + 3)

(2) (3x) + (2) (−6)= (3) (x) + (3) (3)

6x + −12 = 3x + 9

6x − 12 = 3x + 9

Subtract 3x from both sides.

6x − 12−3x = 3x + 9−3x

3x − 12 = 9

Add 12 to both sides.

3x − 12+12 = 9+12

3x=21

Divide both sides by 3.

3x/3=21/3

x=7

I hope this helps!!

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Answer:

First you need to know how many feet are in a mile (5280 ft) and so you would multiply this by 3 and to show your work because teachers need that now sadly you do this

\(3x5280=\)

15820

:)

The two equations for this system are C = 0.60f + 15 and C = 0.80f + 13.

The number of fish for which the cost is the same is 10 fishes.

The cost of this fish is equal to $21.

In order to write a system of linear equations to model and describe this situation, we would assign variables to the number of fish and the cost of fish respectively, and then translate the word problem into algebraic equation as follows:

Note: 1 dollar is equal to 100 cents.

Since the starter aquarium kit costs $15 plus 60 cents per fish at wet pets, we have:

C = 0.60f + 15     ........equation 1.

Since the starter aquarium kit costs $13 plus 80 cents per fish at gills and frills, we have:

C = 0.80f + 13          ........equation 2.

Next, we would solve the system of equations as follows:

0.80f + 13 = 0.60f + 15

0.80f -0.60f = 15 - 13

0.20f = 2

Number of fish, f = 2/0.20

Number of fish, f = 10 fishes.

From equation 1, we have:

Cost of fish, C = 0.60f + 15

Cost of fish, C = 0.60(10) + 15

Cost of fish, C = 6 + 15

Cost of fish, C = 21 dollars.

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Answer:

Step-by-step explanation:

x + 8 < - 28

x < - 28 - 8

x < - 36

Option A is the correct answer

Let's denote the unknown number as 'x'. The equation can be set up as x + (1/2)x = 45. Solving this equation, we find that the number is 30.

The problem states that the sum of a number and its half is equal to 45. To find the number, we can set up an equation and solve for it.

Let's represent the number as "x". The problem states that the sum of the number and its half is equal to 45. Mathematically, this can be written as:

x + (1/2)x = 45

To simplify the equation, we can combine the like terms:

(3/2)x = 45

To isolate the variable x, we can multiply both sides of the equation by the reciprocal of (3/2), which is (2/3):

x = 45 * (2/3)

Simplifying the right side of the equation:

x = 30

Therefore, the number is 30.

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The parallel lines in the given figure are;

o || p, m || n

The congruent angles are;

Corresponding angles theorem;

Alternate exterior angles theorem;

Alternate interior angles theorem;

Vertical angles theorem;

Parallel lines are lines that do not intersect.

The details of theorem used to find the congruent angles are as follows;

Corresponding angles theorem;

Alternate interior angles theorem;

Alternate exterior angles theorem;

Vertical angles theorem;

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The given data is,

→ the ratio of cups of water to cups of milk in a recipe is 1 to 5

Now we have to,

→ find three ratios equivalent to the ratio

Then the ratios will be,

→ 1 (×2) : 5 (×2)

= 2 : 10

→ 1 (×3) : 5 (×3)

= 3 : 15

→ 1 (×4) : 5 (×4)

= 4 : 20

Thus, 2 : 10, 3 : 15 & 4 : 20 are the ratios.

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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If the observed t-value exceeds the critical t-value, then the difference between the sample means is most likely statistically significant.

In other words, the difference between the sample means is unlikely to have occurred by chance and is likely due to a real difference in the population means. The direction and magnitude of the difference must be further examined using effect size measures and confidence intervals.

Therefore, the most suitable value to be fit in the blank space of the given incomplete statement is, statistically significant.

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Answer:

y = -1/8

Step-by-step explanation:

3 + 3y = 1 -13y

add 13y to both sides:

3 +3y + 13y = 1

subtract 3 from both sides:

3y + 13y = 1 - 3

16y = -2

divide both sides by 16:

y = -2/16

simplify:

y = -1/8

Answer: 20 kg

Step-by-step explanation:

You follow the line of best fit until 50cm

Then you trace across and look at the x-axis.

There you will find that the dog will be 20kg at 50cm using the line of best fit.

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

48 ÷8=6-15=-9

99÷-9=-11

Answer:

\(\fbox {See below} \downarrow\)

Step-by-step explanation:

Question 1

Part (a) :

⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ

⇒ 6⁷ = 6ˣ

⇒ x = 7

Part (b) :

⇒ y² = 169

⇒ √y² = √169

⇒ y = ± 13

⇒ y = 13, y = -13

Question 2

Part (a) :

⇒ (√5)² × (√3)²

⇒ 5 × 3

⇒ 15

Part (b) :

⇒ (∛9)³ × (√30)²

⇒ 9 × 30

⇒ 270

The correct significant figure of 0.0879/0.98 is 0.08989796. (rounded to six significant figures)

The meaningful digits in a measured or computed number are known as significant figures. They are used to convey the degree of uncertainty in a value and represent the accuracy of the measurement. You must first establish the number of significant figures in each value being utilized before you can execute a computation with significant figures. When doing the computation, use the same number of decimal places as the value with the fewest significant figures. The final step is to round the result to the appropriate number of significant digits.

According to the question

Both numbers in the calculation 0.0879/0.98 have four significant digits. The result, after performing the calculation, is 0.08989796. We look at the final digit (7) in the response to determine the right amount of significant digits to round to. The preceding digit (9) is rounded up if the digit is 5 or above. In this instance, the solution, rounded to six significant numbers, is 0.0899.

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Answer:3

Step-by-step explanation: .03 X 10

The robot moves in the positive direction along a straight line so that after t minutes its distance is s=6t^4 feet from the origin. (a) Find the average velocity of the robot over intervals 2, 4. We have the following data: Initial time, t₁ = 2 min.

Final time, t₂ = 4 min.The distance from the origin is given by s = 6t^4Therefore, s₁ = s(2) = 6(2^4) = 6(16) = 96 feet s₂ = s(4) = 6(4^4) = 6(256) = 1536 feet

We can find the average velocity of the robot over the interval 2, 4 as follows: Average velocity = (s₂ - s₁) / (t₂ - t₁)Average velocity = (1536 - 96) / (4 - 2)Average velocity = 1440 / 2Average velocity = 720 feet per minute(b) Find the instantaneous velocity at t=2.To find the instantaneous velocity at t = 2 min, we need to take the derivative of the distance function with respect to time. We have the distance function as:s = 6t^4 Taking derivative of s with respect to t gives the velocity function:v = ds / dt Therefore,v = 24t³At t = 2, the instantaneous velocity is:v(2) = 24(2)³v(2) = 24(8)v(2) = 192 feet per minute Therefore, the instantaneous velocity at t = 2 min is 192 feet per minute.

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The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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The linear approximation error when using the linear approximation to estimate the cube root of 8.25 is 0.0593.

When we want to find the linear approximation error, we can use the formula

Error = f(x) - L(x),

Where `f(x)` is the actual value of the function at `x`, and `L(x)` is the linear approximation of the function at `x`.

The linear approximation of a function f(x) near x=a is given by:

L(x) = f(a) + f'(a)(x-a)

In this case, we want to find the linear approximation of the function f(x) = cube root of x near x=8. To do so, we first need to find the value of f(8) and f'(8).

f(8) = cube root of 8 ⇒ 2

To find f'(8), we take the derivative of f(x) with respect to x:

f(x) = x^(1/3)

f'(x) = (1/3)x^(-2/3)

So, f'(8) = (1/3)(8)^(-2/3) ⇒ 1/12

Therefore, the linear approximation of f(x) near x=8 is:

L(x) = 2 + (1/12)(x-8)

Now, we want to use this linear approximation to estimate the value of the cube root of 8.25. To do so, we substitute x=8.25 into the linear approximation:

L(8.25) = 2 + (1/12)(8.25-8) ⇒ 2.0208

The actual value of the cube root of 8.25 is:

∛8.25 ⇒ 2.0801

So, the error in the linear approximation is:

2.0801 - 2.0208 ⇒ 0.0593

Therefore, the linear approximation error when using the linear approximation to estimate a cube root of 8.25 is approximately 0.0593.

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The correct answer is option (c) 2.06.  For every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets

The asset-to-debt ratio for Blaine and Lindsay McDonald can be calculated by dividing their total assets by their total debt. Using the given values, the calculation would be as follows:

Asset-to-debt ratio = Total assets / Total debt

                   = $346,000 / $168,000

The asset-to-debt ratio is a financial metric that provides insight into the financial health and leverage of an individual, company, or entity. It measures the proportion of assets to debt and is used to assess the ability to meet financial obligations and the level of risk associated with the amount of debt.

In this case, Blaine and Lindsay McDonald have total assets valued at $346,000 and total debt of $168,000. By dividing the total assets by the total debt, we obtain the asset-to-debt ratio of approximately 2.06. This means that for every dollar of debt, Blaine and Lindsay have approximately $2.06 in assets. A higher asset-to-debt ratio generally indicates a stronger financial position and lower risk, as there are more assets available to cover the debt obligations.

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Answer:

3.7018867924 × \(10^{-1}\)

Step-by-step explanation:

First you want to find what these two numbers are, then you divide, then you put that answer in scientific notation.

1.728(109) = 188.352

4.8(106) = 508.80

Now we divide :

188.352 ÷ 508.80 = 0.37018867924

That's a crazy decimal, but luckily because of scientific notation we can make it look a lot simpler.

0.37018867924 =  3.7018867924 × \(10^{-1}\)

This should be right. Please comment if you are confused and want more detail.

What is the quotient of \(1.728*10^9 and, 4.8*10^6\) expressed in scientific notation?

\(\frac{1.728*10^9}{4.8*10^6}\)  Divide

\(\frac{1.728}{4.8} * \frac{10^9}{10^6}\) Divide numbers and 10's separately.

\(0.36*10^3\) Subtract exponents.

\((3.6*10^-^1 )*10^3\) Rewrite as a number bigger than 1

\(3.6*(10^-^1*10^3)\) Associate

       The answer is

\(3.6*10^2\) Add exponents