How do I find the constant of proportionality in an equation

Answer:

Step-by-step explanation:

the diagonal of a square splits the square into 2 right triangles. So we can use Pythagorean's theorem.

where c is the hypotenuse. So the diagonal is the hypotenuse here, and thus c = 10. Now, since we are dealing with a square, all the sides are the same length, so a = b. So we have:

a² + a² = c²

2a² = 100

a² = 50

a = √50

a = 5 × √2 or 7,071067811865475

--------------------------

Answer: 50

Step-by-step explanation  :<

Answer: 0.05

Step-by-step explanation:

1) Re-arrange the formula given to find the rate (r)

I = Prt

becomes r = I / Pt

Now we add in the values we know

P = 3000, t = 3 years, I = 450

r = 450 / ( 3000 × 3 )

r = 0.05 or 5% / year

Answer:

Step-by-step explanation:

To find the surface area of the surface generated by revolving the curve defined by the parametric equations x = 6t^3 + 5t, y = t, 0 ≤ t < 5, around the x-axis, we can use the formula:

S = ∫_a^b 2πy √(1 + (dx/dt)^2) dt

where y = f(t) is the equation of the curve and dx/dt is the derivative of x with respect to t.

In this case, we have:

y = t

dx/dt = 18t^2 + 5

√(1 + (dx/dt)^2) = √(1 + (18t^2 + 5)^2)

So the surface area is:

S = ∫_0^5 2πt √(1 + (18t^2 + 5)^2) dt

This integral can be evaluated numerically using numerical integration methods, such as Simpson's rule or the trapezoidal rule, or by using a computer algebra system. The result is approximately 1035.38 square units.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

Base = ( Volume / Height )

. = 150/ 20 = 7.5 cm

. = 7.5

Then answer is

OPTION D) 7.5 cm

The expected value of this gamble is $1.

The expected value of this gamble is the weighted average of all possible outcomes where the weights are the probabilities of each outcome happening.

The formula for expected value (EV) is as follows:

          Expected Value = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost)

Hence, substituting the values:

          Expected Value = (0.5 × $10) − (0.5 × $8)

          Expected Value = $5 - $4

          Expected Value = $1

Therefore, the expected value of this gamble is $1.

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Given the set of values, you have to determine the y-intercept, slope, and the equation that corresponds to de relationship on the table.

The slope-intercept form is

Where

m represents the slope

b represents the y-intercept (is the y-coordinate of the point corresponding to the y-intercept)

The y-intercept of any function in the coordinate system is the point where the line intercepts the y-axis, at this point the x-coordinate is equal to zero. You can determine this value directly from the table, the ordered pair (0,6) corresponds to the y-intercept coordinates.

So "b = 6"

To determine the slope of the line, m, you need to use two points of the line and the following formula:

Where

(x₁,y₁) are the coordinates of one point on the line

(x₂,y₂) are the coordinates of a second point on the line

You can use any two points of the line to calculate the slope, I will use (2,14) and (1,10)

The slope of the line is m=4

Finally, you have to replace the values of the slope and y-intercept in the formula to determine the equation of the line in slope-intercept form:

For b=6 and m=4

The triangle similar to ΔABC is ΔSTU, in which m∠S = 87° and m∠U = 70°. Option C

We have,

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

In ΔABC, we know that m∠A = 87° and m∠B = 23°.

The angle m∠C must therefore be 70°,

since the sum of the angles in a triangle is always 180°.

now, we have,

In ΔSTU, we are given that m∠S = 87°, which corresponds to ∠A in ΔABC.

We are also given that m∠U = 70°, which corresponds to ∠C in ΔABC.

so, we get,

as, This is because two triangles are similar if their corresponding angles are congruent.

Therefore, ΔSTU is similar to ΔABC.

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The above answer is in response to the full question below

In Δ ABC, m∠A = 87° and m∠B = 23°.

Select the triangle that is similar to ΔABC.

A. ΔXYZ, in which m∠X= 87° and m∠z = 50°

B. ΔLMN, in which m∠M=20° and m∠N=87°

C. ΔSTU, in which m∠s = 87° and m∠U=70°

D. ΔPQR, in which m∠P= 110° and m∠R = 23°

Answer:

(x-6)3

hope it helps

Answer:

C

Step-by-step explanation:

The triangles are not similar. Option E

Similar triangles are those triangles that may not be of the same size but a related in the sense of the proportionality in the following ways;

Looking at the two triangles as shown, we can see that they are not related in any of the ways by which we define proportionality of two triangles as such, the triangles are not similar. Option E

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Answer: B. 1,356.48cm³

Step-by-step explanation:

Formula:V=πr²·h

V=(3.14) · (6cm)² · (12cm)

V=(3.14) · (36 cm²) · (12cm)

V=1, 356.48 cm³

Answer:

figure it out urself

Step-by-step explanation:

No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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After 6 years with a 4% annual interest rate, the amount of money in your bank account would be approximately $125.06.

To calculate the amount of money in your bank account after 6 years with a 4% annual interest rate, we can use the formula for compound interest:

A = P(1 + r/100)^t

Where:

A = Final amount in the account

P = Initial amount (starting balance)

r = Annual interest rate

t = Number of years

In this case, the initial amount (P) is $100, the annual interest rate (r) is 4%, and the number of years (t) is 6.

Plugging these values into the formula:

A = 100(1 + 4/100)^6

Simplifying the equation:

A = 100(1.04)^6

A = 125.06

Therefore, after 6 years with a 4% annual interest rate, the amount of money in your bank account would be approximately $125.06.

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Answer:

2 · x² - 20

Step-by-step explanation:

2x - 5 · x + 4

2x · x - 20

2x² - 20

2 · x² - 20

Answer:

X = 5

Step-by-step explanation:

Answer: x = 5

Step-by-step explanation:

Solve for x given the equation 2(x - 2)² = (2x - 1)(x - 3).

Simplify the equation.

2(x - 2)(x - 2) = (2x - 1)(x - 3)

2(x² - 4x + 4) = (2x² - 7x + 3)

2x² - 8x + 8 = 2x² - 7x + 3

Solve for x.

2x² - 8x + 8 = 2x² - 7x + 3

              -8                  - 8

2x² - 8x = 2x² - 7x - 5

       +8x         + 8x

2x² = 2x² + x - 5

 -x              - x

2x² - x = 2x² - 5

-2x²      - 2x²

- x = - 5

- 5 ÷ - 1 = 5

x is equal to 5.

Answer:

B

Step-by-step explanation:

It's where the line goes over the x line

Answer:

B,

Step-by-step explanation:

The zeros are the x values  where the graph crosses the horizontal x-axis.

These are at x = 0 and x = 5.

If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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If P=$10, MPL= $25 and APL=$ 40, then the value of marginal product of labor is $250

The marginal product of labor (MPL) is the change in output that results from employing an added unit of labor.

The average product of labor (APL) is the total product of labor divided by the number of units of labor employed.

Here,

P= $10

The marginal product of labor (MPL)= $25

The average product of labor (APL)= $40

The value of marginal product of labor= P × The marginal product of labor (MPL)

The value of marginal product of labor= 10×25=$250

Hence, If P=$10, MPL= $25 and APL=$ 40, then the value of marginal product of labor is $250

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Part(a),

The average rate of change in annual sales between 2001 and 2002 was $14$ million per year.

Part(b),

The average rate of change in annual sales between 2001 and 2004 was a decrease of $3.33$ million per year.

a) Compute the difference in sales between 2001 and 2002 and divide it by the total number of years in order to determine the rate of change between those two years:

Rate of change = (Sales in 2002 - Sales in 2001) / (2002 - 2001)

Rate of change = (255 - 241) / 1 = 14 million/year

Therefore, the average rate of change in annual sales between 2001 and 2002 was $14$ million per year.

b) Calculate the difference in sales between 2001 and 2004 and divide it by the total number of years to determine the rate of change between those two years:

Rate of change = (Sales in 2004 - Sales in 2001) / (2004 - 2001)

Rate of change = (231 - 241) / 3 = -3.33 million/year

Therefore, the average rate of change of annual sales between 2001 and 2004 was a decrease of $3.33$ million per year.

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Answer:

2,1,4,3,6,5,8,7

Step-by-step explanation:

Given:

2,1,4,3,6,5,8,___

Pairing the sequence in twos

2,1

4,3

6,5

It can be seen that each pair of the sequence is arranged in descending order (from highest to lowest)

1, 2 is written as 2,1

3, 4 is written as 4,3

5, 6 is written as 6, 5

Then the next two numbers

7, 8 will be written as 8,7

2,1,4,3,6,5,8,7

Answer:

-12/6 or -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Gradient = slop

(-3,6)

(3,-6)

\(gradient \: = \frac{difference \: of \: y \: }{difference \: of \: x} \)

\(gradient \: = \frac{6 - ( - 6)}{ - 3 - 3} \)

= 12/-6

= - 2

Answer:

5,386,830

Step-by-step explanation:

1 pound is equal to approximately 453.59 grams. you can multiply the weight in pounds by 453.59 to get the weight in grams.

The pound and the gram are both units of measurement for mass. The pound is commonly used in the United States and other countries that follow the imperial system of measurement, while the gram is used in most other countries that follow the metric system.

To convert pounds to grams, you need to use a conversion factor. The conversion factor between pounds and grams is:

1 pound = 453.59 grams

Therefore, to convert pounds to grams, you simply multiply the weight in pounds by 453.59. For example, if you have a weight of 2 pounds and want to convert it to grams, you would use the following formula:

2 pounds x 453.59 grams/pound = 907.18 grams

So, 2 pounds is equal to approximately 907.18 grams. Similarly, to convert any weight in pounds to grams, you can multiply the weight in pounds by 453.59 to get the weight in grams.

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The axis of symmetry of the quadratic function for this problem is given as follows:

x = -1.

Considering a quadratic function with equation y = ax² + bc + c, the line of symmetry is defined as follows:

L: x = -b/2a.

The line of symmetry is the x-coordinate of the vertex of the function (turning point on the graph).

The coordinates of the vertex are given as follows:

(-1, -1).

Hence the line of symmetry is given as follows:

x = -1.

The problem asks for the axis of symmetry of the quadratic function.

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