Y is directly proportional to x if x=20,when y=160,then what is the value of x when y=3. 2

Answer:

7.2 miles

Step-by-step explanation:

52-16= 36

36/5= 7.2

Answer:

О  B. Standard deviation.

Step-by-step explanation:

Standard deviation measures the dispersion of a data distribution (variability in scores).

...

Answer:

The correct answer is 0 or choice A on edge

Step-by-step explanation:

right on edge

Therefore, value of r(x) as x approaches Infinity : zero

\(\bold{\lim_{x \to \infty} r(x)=0}\)

"A function is a special relationship where for each input and their is single outputs."

"Limit is defined as the value that a function approaches for the given input value."

For given situation,

We have been given a function,

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite it as,

\(r(x)= \frac{ax^b+8}{cx^d}\) , where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit \(\lim_{x \to \infty} r(x)\)

Now, we find the value of limit for given function.

\(\lim_{x \to \infty} r(x)\)

=  \(\lim_{x \to \infty} \frac{ax^b+8}{cx^d}\)

= \(\lim_{x \to \infty} (\frac{ax^b}{cx^d} + \frac{8}{cx^d})\)

= \(\lim_{x \to \infty} \frac{a}{cx^(d-b)} + \lim_{x \to \infty} \frac{8}{cx^d}\)                          ...............(since d > b)

= \(0 + 0\)

= \(0\)

Therefore, \(\bold{\lim_{x \to \infty} r(x)=0}\)

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The fatigue exponent, m = 4

The fatigue coefficient, c = 10⁻¹¹

The geometric factor, Y = 1.27

Given Data:

Length of crack= 8mm

Length of crack to be grown = 22mm

Alternating stress = 50 MPa

Fatigue coefficients m = 4

Fatigue coefficients c = 10⁻¹¹

Y factor = 1.27

Formula Used:

Δa/2 = Y(KΔσ)m⁄c

Where, Δa/2 = half length of the crack

K = Stress Intensity Factor

Δσ = Stress Range

M = Fatigue Exponent

C = Fatigue Coefficient

Y = Geometric Factor

Calculation:

From the given question, the half length of the crack,

Δa/2 = (22 - 8) mm / 2

= 7 mm

The stress intensity factor,

K = σ √(πa)

Where,

σ = stress

= 50 MPa

= 50 N/mm²

a = length of the crack

= 8 mm/ 2

= 4 mm

K = 50 √(π × 4)

K = 251.32 MPa √mm

The Δσ is stress range and given,

Δσ = 50 MPa

The fatigue exponent, m = 4

The fatigue coefficient, c = 10⁻¹¹

The geometric factor, Y = 1.27

Substituting all the given values in the formula,

Δa/2 = Y(KΔσ)m⁄c7

= 1.27 ((251.32 × 50) / 10⁻¹¹)4

Δa/2 = 7.8 mm

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Answer:

1/3

Step-by-step explanation:

So there are 12 natural numbers in total: (113 - 102) + 1

Then there are the prime numbers: 103, 107, 109, and 113

so there are 4/12 prime numbers or 1/3

Answer:

1/3

Step-by-step explanation:

We can list all the numbers from 102 to 113:

To check if each number is prime, we simply have to check divisibility by 2, 3, 5, and 7 — if any of these numbers are not divisible by those, it will have no factors lower than its square root, and will therefore be prime.

102 - composite, multiple of 2

103 - prime

104 - composite, multiple of 2

105 - composite, multiple of 5

106 - composite, multiple of 2

107 - prime

108 - composite, multiple of 2

109 - prime

110 - composite, multiple of 2

111 - composite, multiple of 3

112 - composite, multiple of

113 - prime

4/12 or 1/3 of the numbers in this list are prime.

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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The required cycle-time is approximately 57.6 seconds.

To find the required cycle time, we need to divide the total available time by the number of units to be produced.

Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds

Number of units to be produced: 1,000 units

Required cycle time: Total available time / Number of units

Cycle time = 57,600 seconds / 1,000 units

Cycle time ≈ 57.6 seconds

Therefore, the required cycle time is approximately 57.6 seconds.

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The values of m for which\(y = e^mx\) is a solution of \(y" - 4y' - 5y = 0\) are m = -1 and 4.

The equation y" - 4y' - 5y = 0 is a second order linear homogeneous differential equation with constant coefficients. The solution of this equation is given by the general form of the solution as \(y = e^mx\), where m is the root of the characteristic equation m2 - 4m - 5 = 0, which can be solved by the quadratic formula as m = 2 and 3 or m = -2 and -3.

To solve this equation, we expand the quadratic equation as,

m2 - 4m - 5 = 0

m2 - 5m + m - 5 = 0

(m - 5)(m + 1) = 0

Therefore, the two roots of this equation are m = 5 and -1.

Now, we plug in these two roots in the solution of the differential equation, \(y = e^mx\).

For m = 5,

\(y = e^(5x)\)

For m = -1,

\(y = e^(-x)\)

Therefore, the values of m for which \(y = e^mx\) is a solution of y" - 4y' - 5y = 0 are m = -1 and 4.

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Answer:

#5 is X=63.5

#6 is X=32.9

Step-by-step explanation:

i hope it helps

have a nice day ^_^

The equation of the other line of the triangle is x + 2y - 18 = 0.

A right triangle is formed by the y-axis, the line y = 2x + 4 and another line. If the legs of the right triangle intersect at (2, 8), then the point of intersection of the legs of the right triangle is (2, 8) which is also the vertex of the right triangle.

Let the equation of the other line be y = mx + c. The slope of the line passing through the point (2, 8) and the point of intersection of line y = 2x + 4 with x-axis is -1/2.

Slope of line y = 2x + 4 is 2. Therefore, the slope of the line perpendicular to y = 2x + 4 and passing through the point (2, 8) is (-1/2). Thus, the equation of the line is y - 8 = (-1/2)(x - 2) which simplifies to 2y - 16 = - (x - 2) and further simplifies to x + 2y - 18 = 0.

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\((\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }\)

A closed under addition can be proved if the sum of any two members of the set also belongs to the set.

We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

For example,

A = {( x, y) , y = 0 }

B= { (x, y) , x+ y = 1 }

Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is  (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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Answer:

Step-by-step explanation:

it woulkd be 200 gallons

Answer: I believe the answer is 3.07 but I may be wrong so if you want you can wait for another answer :D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Using the proportional relationship, it is found that the radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

\(y = kx\)

In which k is the constant of proportionality.

If they are inverse proportional, the relationship is:

\(y = \frac{k}{x}\)

In this problem, the amount of time is inversely proportional to the square of the radius of the pipe, hence:

\(t = \frac{k}{r^2}\)

A pipe of radius 1 cm can empty a sink in 22 seconds, hence k = 22.

The radius for 14 seconds is:

\(t = \frac{k}{r^2}\)

\(14 = \frac{22}{r^2}\)

\(r^2 = \frac{22}{14}\)

\(r = \sqrt{\frac{22}{14}}\)

\(r = 1.25\)

The radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

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Answer:

The easiest ways to do this is to add, subtract, multiply, or devide 5 from a number, do that operation to x, and set that number as the equivelent.

For example

3 * 5=15

so

3x=15

The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.


In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.

Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978

Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.

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Answer:

here  is the link the.hh/g49

Step-by-step explanation:

Answer:

q = 45

Step-by-step explanation:

Since q is 30 when p is 6, we divide to find the rate.

30/6=5.

If the rate is 5 we multiply the new p, 9 by five as well.

9*5=45

45 is q ok

Answer:

105m²

Step-by-step explanation:

15+6=21

21÷2=10.5

10.5x10=105

Answer:

\(y=2x-1\)

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Being m the slope and b the y-intercept.

The question provides both the slope m=2 and the y-intercept b=-1.

Thus, substituting:

\(\boxed{y=2x-1}\)

Answer:

200020ft

Step-by-step explanation:

Step-by-step explanation:

In geometry, we have many formal definitions using defined words or terms. However, I can think of three words that are not formally defined. These words are point, line and plane. Even though these words are undefined we can describes them as follows:

1. Point. A point is an exact position or location in space.

It is important to understand that a point has no dimension (that is, actual size). So, it has no length, no width, and no height (thickness).

We usually named a point with a capital letter. In the coordinate plane, a point is named by an ordered pair, x,y .

Even though we represent a point with a dot, the dot can be very tiny or very large. Recall that a point has no size.

2. Line (Straight line)

A line has no thickness.

So, its length extends in one dimension.

The line extends in both directions without end (infinitely). A line has infinite length and has no width, no height.

We assume the line to be straight.

and can be drawn with arrowheads on both ends.

3. Plane

A plane is a flat surface with no thickness extending indefinitely in all directions and having two dimensions. So, it has infinite length, infinite width and has no height (thickness). Moreover, a plane is drawn as a four-sided figure resembling a parallelogram.

The representation of each concept is shown in the Figure below.

Answer:

a + b

Step-by-step explanation:

Answer:

a+b=ab

Step-by-step explanation:

you have to combine the two variables and multiply them by phi then divide by gamma

The required population of Florida was 5 million approximately 32.8 years after 1953, which is around 1985.

To find the population of Florida in 1953, we can use the formula:

\(P = Po*(1 + r)^t\)

where P is the population after t years, Po is the initial population, r is the annual growth rate, and t is the number of years.

Let's first find the value of Po. We know that in 1993, the population of Florida was 13 million. Using the formula, we can write:

\(13 = Po*(1 + 0.08)^{40}\)

Simplifying, we get:

\(Po = 13(million) / (1.08)^{40} = 598,402\)

Therefore, the population of Florida in 1953 was 598,402.

Now, to find the population in 1969, we can use the formula again with t = 16:

\(P = 598,402*(1 + 0.08)^{16} = 2,764,715\)

So, the population of Florida in 1969 was approximately 2.8 million.

Finally, to find when the population was 5 million, we can set P = 5 and solve for t:

\(5 = 598,402*(1 + 0.08)^t\)

Taking the logarithm of both sides, we get:

\(t = log(5/598,402) / log(1 + 0.08) = 32.8\)

So, the population of Florida was 5 million approximately 32.8 years after 1953, which is around 1985.

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Answer:

x² + x + 1

Step-by-step explanation: