36 push ups to 2 minutes unit rate

Answer:

Step-by-step explanation:

The speed is:

Covert to inches / min:

Answer:

The formula you are referring to is the quadratic formula, which is used to solve quadratic equations of the form ax^2 + bx + c = 0. The formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are coefficients of the quadratic equation.

Answer:

Step-by-step explanation:

pattern by pattern

\(2) \: 2(9 + 3) = 2(12) = 24\)

Answer: 24

Ok done. Thank to me :>

hope this was fast enough!!

Answer:

9.9 gallons

Step-by-step explanation:

250 mi/9 gas = 27.7777 miles per gallon of gas

275 mi/ (27.77 mi/gal) = 9.9 gallons

Answer:

second option, it represents the y-intercept before the rocket is propelled

Step-by-step explanation:

Answer:

maximum- median

80-50=30

The correct option is D. Behavioral economics studies the influence of cognitive biases and irrational decision-making on consumer behavior.

Behavioral economics combines insights from psychology and economics to understand how individuals make choices that deviate from the assumptions of classical economics. It recognizes that human behavior is often influenced by emotions, cognitive biases, and heuristics.

leading to deviations from rational decision-making. Behavioral economists study these behavioral patterns to develop more realistic models and theories that better capture the complexities of decision-making in real-world situations.

By incorporating psychological factors into economic analysis, behavioral economics provides a broader understanding of human behavior and its implications for economic outcomes.

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Answer:

4.4 < x < 18.8

Step-by-step explanation:

11.6 - 7.2 = 4.4

11.6 + 7.2 =18.8



1. P-adic Numbers:

P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.

2. Nonstandard Analysis:

Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.

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The solution set of the trigonometric equation is x = 60° or x = 180°

A trigonometric equation is an equation that contains trigonometric ratios

Given the trigonometric equation sin(x/2) = cosx, we desire to find the solution set. We proceed as follows.

Using the half angle formula for sine, we have that

Sin(x/2) = √[(1 - cosx)/2]

So, substituting this into the equation, we have that

sin(x/2) = cosx,

√[(1 - cosx)/2] = cosx

Squaring both sides, we have that

√[(1 - cosx)/2]² = (cosx)²

(1 - cosx)/2 = cos²x

1 - cosx = 2cos²x

Re-arranging the equation, we have that

2cos²x + cos - 1 = 0

Let cosx = y

So,we have that

2y² + y - 1 = 0

Factorizing, we have

2y² + 2y - y - 1 = 0

2y(y + 1) - (y + 1) = 0

(2y - 1)(y + 1) = 0

⇒ 2y - 1 = 0 or y + 1 = 0

⇒ 2y = 1 or y = -1

⇒ y = 1/2 or y = -1

Since cosx = y, we have that

cosx = 1/2 or cosx = -1

Taking innverse cosine of both sides, we have that

x = cos⁻¹(1/2) or x = cos⁻¹(-1)

x = 60° or x = 180°

So, the solution set is x = 60° or x = 180°

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Thus, the Fourier series of the given function simplifies to Sf(t) = π/4.

To determine the Fourier series of the 2π-periodic function f(t) = |t|, we need to find the coefficients of the trigonometric terms in its Fourier series representation.

The Fourier series representation of f(t) can be written as:

f(t) = a₀ + Σ(aₙcos(nt) + bₙsin(nt))

where a₀, aₙ, and bₙ are the Fourier coefficients to be determined.To find these coefficients, we will calculate the integrals involving f(t) multiplied by the trigonometric functions:

₀ = (1/2π) ∫[π,-π] |t| dt

To find the integral of |t| over the interval [-π, π], we split the integral into two parts:

₀ = (1/2π) ∫[0,π] t dt + (1/2π) ∫[-π,0] -t dt

= (1/2π) ([(t²/2)] from 0 to π + [(-t²/2)] from -π to 0)

= (1/2π) ([(π²/2) - (0)] + [(0) - (π²/2)])

= (1/2π) (π² - π²/2)

= (1/2π) (π²/2)

= π/4

Next, we calculate the coefficients for the sine terms:

= (1/π) ∫[π,-π] |t|sin(nt) dt

Since the function |t| is symmetric around the y-axis, the integral of |t| multiplied by an odd function (such as sin(nt)) over a symmetric interval is zero. Therefore, bₙ = 0 for all n.

Finally, we calculate the coefficients for the cosine terms:

aₙ = (1/π) ∫[π,-π] |t|cos(nt) dt

We can split the integral into two parts similar to before:

= (1/π) ∫[0,π] t cos(nt) dt + (1/π) ∫[-π,0] -t cos(nt) dt

the integrals, we have:

aₙ = (1/π) ([(t/n)sin(nt)] from 0 to π + [(t/n)sin(nt)] from -π to 0)

= (1/π) ([(π/n)sin(nπ) - (0)] + [(0) - (-π/n)sin(-nπ)])

= (1/π) ([(π/n)sin(nπ)] - [(π/n)sin(nπ)])

= 0

Therefore, aₙ = 0 for all n.

In summary, the Fourier series representation Sf(t) of the function f(t) = |t| is:

Sf(t) = a₀ + Σ(aₙcos(nt) + bₙsin(nt))

= (π/4) + 0

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As the sample size gets larger, the z value increases therefore we will more likely to  less likely to fail to reject the null hypothesis, thus the power of the test increases.

Statistical tests provide a mechanism for making quantitative decisions about one or more processes. The intent is to determine whether there is sufficient evidence to "reject" speculations or hypotheses about the process. If you want to keep pretending that you "believe" the null hypothesis is true, then not rejecting it can do you good. Alternatively, it may indicate that there is not yet enough data to "prove" something by rejecting the null hypothesis. A classic application of statistical testing is process control studies. Suppose a manufacturing process is interested in  a photomask with an average linewidth of 500 microns. The null hypothesis in this case is that the average linewidth is 500 microns. This statement implies the need to characterize photomasks with average linewidths much larger or  smaller than 500 microns. This leads to the alternative hypothesis that the average linewidth is not equal to 500 microns. This is a two-way substitution as it protects against substitution in the opposite direction. In other words, the line width is either too small or too large.

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The maximum value of B is 80.

1. We are given the expression B = 5xy² and the constraint x + y² = 8.

2. We need to find the maximum value of B by optimizing the variables x and y.

3. To solve this problem, we can use the method of Lagrange multipliers.

4. Let's define the Lagrange function L(x, y, λ) as L(x, y, λ) = B - λ(x + y² - 8).

5. Taking the partial derivatives of L concerning x, y, and λ, we have:

  ∂L/∂x = 5y² - λ

  ∂L/∂y = 10xy - 2λy

  ∂L/∂λ = -(x + y² - 8)

6. Setting the partial derivatives equal to zero, we get the following equations:

  5y² - λ = 0    ...(1)

  10xy - 2λy = 0  ...(2)

  x + y² = 8     ...(3)

7. From equation (1), we can solve for λ in terms of y:

  λ = 5y²    ...(4)

8. Substituting equation (4) into equation (2), we have:

  10xy - 2(5y²)y = 0

  10xy - 10y³ = 0

  10y(x - y²) = 0

9. From the above equation, we have two possibilities:

  i) 10y = 0, which implies y = 0.

  ii) x - y² = 0, which implies x = y².

10. If y = 0, then from equation (3), we get x = 8.

11. If x = y², then substituting this into equation (3), we have:

   y² + y² = 8

   2y² = 8

   y² = 4

   y = ±2

   If y = 2, then x = (2)² = 4.

   If y = -2, then x = (-2)² = 4.

12. We have three potential solutions: (x, y) = (8, 0), (4, 2), and (4, -2).

13. Finally, substitute each of these solutions into the expression B = 5xy² and find the maximum value of B:

   B = 5(8)(0)² = 0

   B = 5(4)(2)² = 80

   B = 5(4)(-2)² = 80

14. Therefore, the maximum value of B is 80.

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      We will plug-in the value and see if it falls upon our line. Coordinate points are written in terms of (x, y).

y = 5/3x - 8

(-3) = 5/3(-9) - 8

-3 ≠ -23

                      (-9,-3) is not on the line / slope of y = 5/3x - 8.

Answer:

8.4 grams

Step-by-step explanation:

We have $70 to start and someone us another $30 for a total of $100.  We pay $100 for 28 grams of seeds.  If we assume the peron giving us $30 wants a fair share of the seeds, we would calculate an average cost per gram and use that to determine the grams of seeds that the $30 would have covered.

($100/28 grams) = $3.57/gram

($30/$3.57/gram) = 8.4 grams

Answer:

28 grams of seeds

Step-by-step explanation:

(This question is a little tricky)

Note that:

{28 grams of seeds = $100}

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

You have $70 already, and then someone gives you $30.

It means $70 + $30 = $100

So you have $100 now, you can buy 28 grams of seeds and give the person that gave you $30.

Hope this helps :)

We will find the area of the triangle as follows:

So, the area of the triangle is approximately 425.5 square units.

Answer:

c is actually correct lol

Step-by-step explanation:

g(x) = (x-4)(x+2)

set both (x-4) and (x+2) equal to zero

x-4=0

x=4

& bx+2=0

x=-2

c has 4 and -2 as x values

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

Slope= 15

Hope this helps! :)

Answer: D, x < 8

Step-by-step explanation: Subtract 18 from both sides.

Simplify the expression

Subtract the numbers

Subtract the numbers

Divide both sides by the same factor, and flip the relation because the factor is negative

Cancel terms that are in both the numerator and denominator

Divide the numbers

−6x+18−18>−30−18=

=x<8

Answer:

134/5

Step-by-step explanation:

First you do 26 times 5 which is 130. And then you add 4, which is equal to 134/5

The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).

Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.

We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:

P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4

Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:

P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563

P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015

P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159

P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747

P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340

P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824

Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.

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hello

determine the amount each of them have, let's write an equation to represent thier total amount

let x represent the amount Jason have

let y represent the amount Jeff has

now, we know that Jason has 3 more than 4 times the amount Jeff has

x = 4y + 3 .... equation 1

x + y = 72 .... equation 2

from equation 2,

make x the subject of formula

x = 72 - y .....equation 3

put equation 3 into equation 1

x = 4y + 3

72 - y = 4y + 3

solve for y

we know y = 13.8

we can simply substitute the value into equation 2 and solve for x

therefore, Jason has $58.2 and Jeff has $13.8

Answer:

Yes SAS

Step-by-step explanation:

2 sides are the same

1 90 degree angle for each triangle

Hence the Answer Side-Angle-Side

The population of Fairview will reach 1,600,800 in 22.80 years.

Since the population of the city of Fairview is given by the model function y = 780,500(1.032)ˣ.

To find the the number of years, we can say solve for x when y = 1,600,800. That is:

y = 780,500(1.032)ˣ

1,600,800 = 780,500(1.032)ˣ

1,600,800/780,500 = (1.032)ˣ

(1.032)ˣ = 16008/7805

ln(1.032)ˣ  = ln(16008/7805)

x ln(1.032) = ln(16008/7805)

x =  [ln(16008/7805)]/ [ln(1.032)]

x = 22.80 years

Thus, in 22.80 years the population of Fairview will reach 1,600,800.

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To get 8 heads in 16 throws of a fair coin there are 12870n different ways and we get by combination

We have 16 throws, and we want to select 8 of those throws to be heads (assuming a fair coin).

The remaining 16 - 8 = 8 throws will be tails.

The number of ways to choose 8 heads out of 16 throws can be calculated using the binomial coefficient formula:

C(n, k) = n! / (k!(n - k)!)

where C(n, k) represents the number of combinations of n items taken k at a time, and n! denotes the factorial of n.

Applying this formula to our situation, we have:

C(16, 8) = 16! / (8!(16 - 8)!)

Calculating the factorial values:

16! = 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 20922789888000

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320

(16 - 8)! = 8! = 40320

Substituting these values into the formula:

C(16, 8) = 20922789888000 / (40320 × 40320) = 12870

Therefore, there are 12,870 different ways to get 8 heads in 16 throws of a fair coin.

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Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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1) Las situaciones en que la variable y es función de x

como y =x , son aquellas en que y es la variable dependente y x es la variable independente

Como por ejemplo,

y=x

y=3x +4

y =(5x +3)/2

etc.

Así, todos valores de y depende de las cantidades, de x. Por eso, decimos que están en funcion de x.