What is the percent of decrease from 100 to 57?

Answer:

\(x = -3\)

Step-by-step explanation:

\(\frac{-3(2x + 1)}4 = 3(x + 4) + \frac34 \text{ // Distribute}\\\\\frac{-6x - 3}4 = 3x + 12 + \frac34 \text{ // Multiply by 4}\\\\-6x - 3 = 12x + 48 + 3\\-6x - 3 = 12x + 51 \text{ // Add 6x and subtract 51}\\-54 = 18x \text{ // Divide by 18}\\-3 = x\)

Answer: x=-3

\(\frac{-3(3x+1)}{4} = 3(x+4) +3/4\\\frac{-3x-3}{4} = 3x+12+3/4\\\frac{-3x-3}{4}=3x+15/4\\4*\frac{-3x-3}{4}= 3x+15/4\\ *4\\-3x-3= 3x+15\\+3 +3\\-3x=3x+18\\-3x -3x\\-6x=18\\/-6 -/6 \\x= -3 \\\\\)

I think i did this right for you, hopefully this helped

Answer: 5.4545 ounces

Step-by-step explanation:

Given the following :

Acid solution required = 75% acid solution

Let the number of ounces of 20% acid solution required = s

Then total ounces acid required can be expressed as :

=0.20s + 0.90 x 20

= 0.20s + 18

While the total ounces required is :

s + 20

Hence, (total ounces of acid / total ounces) = 75% acid solution

= (0.2 + 18) / (s + 20) = 0.75

= 0.2s + 18 = 0.75( s + 20)

0.2s + 18 = 0.75s + 15

18 - 15 = 0.75s - 0.2s

0.55s = 3

S = 3 / 0.55

= 5.4545 ounces

Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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Answer:

a) t (α)  =  30 * tan α

b) α =  75 °  is not possible because

Step-by-step explanation:

The vertical cliff  (y),  the observing partner ( 150 ft ) from the point o ( the common point for the cliff and the ground ) between the cliff, and the line of sight from the observer and the climber, shape a right triangle. Hypothenuse is the distance between the partners, the cliff, and distance of the observer to the cliff are the legs.

Then

α is the elevation angle

tan α  =  y / 150           (1)

y(t)  = elevation of the climber

y(t) = speed * time

y(t)  =  5 * t

tan α  =  5 *t / 150

tan α  =  t / 30

t (α)  =  30 * tan α

b) α =  75 °  is not possible because:

tan α  =  y / 150              tan 75°  =  3.73

Then     y  =  3.73 * 150  =  559 ft and the cliff is only 500 ft

Therefore , the solution of the given problem of fraction comes out to be   0.25 inches per hour average rainfall per hour.

To represent a whole, any number of equal sums or decimals can be utilized. The quantity of a particular size is expression as a fraction in standard English. 8, 3/4. Fractions are included in wholes. In mathematics, the fraction to numerator ratio is used to represent numbers. All of these fractions of integers are simple fractions. A challenging fraction has a percent in the denominator. because actual fractions have different calculations, numerators, and numerators.

Here,

Given :

=> 6 1/2 hours or 13/2 hours

=> 6.5 hours

7/8 pf an inches.

So,

the average rainfall per hour is :

=> 7/8 / 3.5

=> 0.25 inches per hour

Therefore , the solution of the given problem of fraction comes out to be   0.25 inches per hour average rainfall per hour.

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Answer:

247cm^2

Step-by-step explanation:

Construct a formula to find the total area of the figure. To do that first figure out what shapes are in the given figure. In this case there are 2 triangles each with a height of 4cm and a base of 10cm, 1 sqaure with a width of 9cm and a length of 5cm, 1 square with a width of 9cm and a length of 8cm and one last square with a width of 9cm and length of 10cm.

The formula for the area of a triangle is A=(1/2)(b)(h) and the fromula for the area of a sqaure is A =  L*W.

The total area: A = (4)(10)+(9)(5)+(9)(8)+(10)(9) = 247cm^2

Answer: 378

Step-by-step explanation:

439 minus 78 equals 378.

The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.

To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.

First, let's rewrite the equation in a standard form:

\(4x^2 - 16y^2 + z^2 = 16\)

By rearranging terms, we have:

\((x^2/4) - (y^2/1) + (z^2/16) = 1\)

Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.

The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).

When y = 0, the equation becomes:

\(4x^2 + z^2 = 16\)

This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.

When z = 0, the equation becomes:

\(4x^2 - 16y^2 = 16\)

This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.

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identify the surface from the following equation \(4x^2-16y^2 z^2=16\)

The value of the element in row 1, column 1 of matrix x is; y.

According to the task content, it follows that matrix x is defined as; x= [y 4].

In essence, it follows that the matrix x contains one row and 2 columns. Therefore, the element in row 1, column 1 of matrix x is; y.

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Answer: A

Step-by-step explanation:

Answer: 40º

Step-by-step explanation:

To find angle c, not give 2 angles at least, we must use a trigonometric function. With respect to angle c, we can see that we have the opposite and adjacent sides.

The trigonometric function that relates opposite and adjacent sides is tangent.

\(tan=\frac{opposite}{adjacent}\)

\(tan=\frac{21}{25}\)

\(tan^-^1=40\)

To find the radian measure of a central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches.

In a circle, the relationship between the central angle (θ) and the arc length (s) is given by the formula s = rθ, where r is the radius of the circle. In this case, the radius (r) is 17 inches, and the arc length (s) is 12 inches.

To find the radian measure of the central angle (θ), we rearrange the formula as follows:

s = rθ  (Divide both sides by r)

θ = s/r

Substituting the given values:

θ = 12/17

Therefore, the radian measure of the central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches is approximately 0.7059 radians.

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Hence, a cylinder with height h and base area \(\pi r^{2}\) may be proven to have the same volume as a triangular prism.

Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.

When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.

A cylinder's volume may be calculated using the formula V = \(r^{2}\)h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.

Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.

Let's consider the given triangular prism with base area  \(\pi\)\(r^2\) and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:

\(A(y) = \pi r^2 + (2r)(y) / 2\)

Simplifying, we get:

\(A(y) = \pi r^2 + ry\)

Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:

\(A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh\)

By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:

\(\pi r^² + ry = \pi r^² + 2rh\)

\(ry = 2rh\)

\(y = 2r\)

So, we see that the areas are equal for all y between 0 and h, except at \(y = 2r.\) However, this is just a single point and has no effect on the volume,

Therefore,  the cylinder with base area \(\pi\)\(r²\) and height h has the same volume as the triangular prism, with base area \(\pi\)r² and height h.

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Answer:

its 135

Step-by-step explanation:

Answer:

C. his conclusion represent correlation and causation

Answer:

6.5 × 10^-3

Step-by-step explanation:

there 3 decimal points to make it 6.5 so it makes it -3

Answer:

106.25

Step-by-step explanation:

Answer: The answer is 106.25

Step-by-step explanation: I used a calculator and just multiplied them both.

This means that the rate of change of I with respect to W remains constant at the rate given by k (0.088). (a) The differential equation that describes the change of the evapotranspiration index

I with respect to the amount of water available W can be written as:

dI/dW = k

where k is the constant rate of increase, which is given as 8.8% or 0.088.

(ii) To analyze the differential equation, we can examine its critical values, stability, and phase plot.

Critical value(s):

The critical value of I occurs when dI/dW = 0. In this case, since dI/dW = k, the critical value of I is 0.

Stability:

Since the rate of change of I with respect to W is a constant positive value (k = 0.088), the system is stable. This means that as the amount of water available increases, the evapotranspiration index I will also increase.

Phase plot:

A phase plot can be used to visualize the behavior of the system. In this case, the phase plot would show the relationship between I and W. However, since the equation is linear and the rate of change is constant, the phase plot would simply be a straight line with a positive slope.

(iii) According to the article, when W = 0, I has a value of 1. We can solve the initial value problem using the given initial condition.

Integrating both sides of the differential equation:

∫dI = ∫k dW

I = kW + C

Using the initial condition I = 1 when W = 0:

1 = k(0) + C

C = 1

So the solution to the initial value problem is:

I = kW + 1

(iv) As W becomes larger and larger, the evapotranspiration index I will also increase linearly with a slope of k. This means that the rate of change of I with respect to W remains constant at the rate given by k (0.088). Therefore, as W increases, I will continue to increase at a constant rate, reflecting the relationship between soil moisture (I) and the amount of water available (W).

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Answer:

44 is the answer for the question

Answer:

44

Step-by-step explanation:

5x8= 40

40+4=44

Answer:

20 toonies and 1 loonie

a. The replacement free cash flows is $255,000

b.  The Payback Period time required to recover the initial investment is 2.7778 years.

d. By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

a. To calculate the replacement free cash flows, we need to consider the cash flows associated with the new fleet of trucks. Here's the calculation:

Initial cash outflow: Purchase cost of new trucks + Shipping cost

= $350,000 + $50,000

= $400,000

Annual cash flows:

Operating cost savings:

Diesel fuel savings: $250,000 - $150,000 = $100,000

Maintenance cost savings: $35,000 - $10,000 = $25,000

Net operating working capital reduction: $20,000

Total operating cost savings per year: $100,000 + $25,000 + $20,000 = $145,000

Revenue increase:

Revenue growth rate: 10%

Year 1 revenue increase: $800,000 * 10% = $80,000

Year 2 revenue increase: $800,000 * 10% = $80,000

Year 3 revenue increase: $800,000 * 10% = $80,000

Year 4 revenue increase: $800,000 * 10% = $80,000

Year 5 revenue increase: $800,000 * 10% = $80,000

Salvage value: Market value of the new trucks at the end of 5 years = $30,000

Free cash flows:

Year 0: Initial cash outflow = -$400,000

Year 1: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 2: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 3: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 4: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 5: Cash flow = Operating cost savings + Revenue increase + Salvage value = $145,000 + $80,000 + $30,000 = $255,000

b. The Payback Period is the time required to recover the initial investment. To calculate it, we sum the cash flows until they equal or exceed the initial investment. Here's the calculation:

Payback Period = Number of years to recover initial investment

= 2 years (Year 1 cash flow + Year 2 cash flow)

+ (Remaining investment / Year 3 cash flow)

= 2 years + ($400,000 - $225,000) / $225,000

= 2 years + 0.7778 years

= 2.7778 years

c. To calculate the Net Present Value (NPV) and Profitability Index (PI), we need to discount the cash flows using the given discount rate of 15%. Here's the calculation:

Discount rate: 15%

Present value factor for each year:

Year 0: 1 / (1 + Discount rate)^0 = 1

Year 1: 1 / (1 + Discount rate)^1 = 0.8696

Year 2: 1 / (1 + Discount rate)^2 = 0.7561

Year 3: 1 / (1 + Discount rate)^3 = 0.6575

Year 4: 1 / (1 + Discount rate)^4 = 0.5718

Year 5: 1 / (1 + Discount rate)^5 = 0.4972

NPV calculation:

NPV = (Year 0 cash flow) + (Year 1 cash flow * Present value factor) + (Year 2 cash flow * Present value factor) + ...

= -$400,000 + ($225,000 * 0.8696) + ($225,000 * 0.7561) + ($225,000 * 0.6575) + ($225,000 * 0.5718) + ($255,000 * 0.4972)

Profitability Index calculation:

PI = NPV / Initial investment

= NPV / $400,000

d. To calculate the Internal Rate of Return (IRR), we find the discount rate that makes the NPV equal to zero. Here's the calculation:

IRR = Discount rate that makes NPV equal to zero

By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

e. Based on the information provided, we can determine if the fleet should be replaced by considering the Payback Period, NPV, Profitability Index, and IRR.

If the Payback Period is within the company's acceptable timeframe and the NPV is positive, or the Profitability Index is greater than 1, and the IRR exceeds the company's required rate of return, then replacing the fleet would be financially favorable. If any of these criteria are not met, it would indicate that the replacement may not be the best option.

Please note that the calculation of IRR requires further information, and the final decision should consider additional factors such as qualitative aspects, operational requirements, and strategic considerations.

Without the specific values for cash flows in each year, it is not possible to provide a definitive answer to whether the fleet should be replaced based on the given information.

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The slope of the tangent is -2/3, hence the derivative of the function f(x) at x = 3 is:f'(3) = -2/3. Hence, option B is correct.

Given function is:

x cos (818 x)

Find the limit of the given function:

lim x → ∞ x cos (818 x)

Now, let us apply the following limit formula, i.e.,

lim x → ∞ [f(x) / g(x)] = 0,

if degree of f(x) is smaller than degree of g(x)

lim x → ∞ [f(x) / g(x)] = ∞,

if degree of f(x) is greater than degree of g(x)

lim x → ∞ [f(x) / g(x)] = c,

if degree of f(x) is same as degree of g(x)

where c is a constant

Therefore, applying the formula: We have

f(x) = x and g(x) = 1 / cos (818x)

Degree of f(x) is 1

Degree of g(x) is zero (no x)

Hence, degree of f(x) is greater than degree of g(x)

Therefore,

lim x → ∞ x cos (818 x) = ∞

Hence, option A is correct.

Tangent to the curve at x = 3 passes through (-2, 3) and (4, -1).

The slope of the tangent can be found using the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (-1 - 3) / (4 - (-2)) = -4/6 = -2/3

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In conclusion, 9 blarsfs and 6 crobs on Shm'lort correspond to approximately 200 seconds in Earth time.

Let's start by finding the conversion rates between Shm'lort time and Earth time. From the given information, we know that 3 blarsfs and 18 crobs correspond to 1 minute on Shm'lort. This means that 1 blarsf is equivalent to 20 seconds (60 seconds / 3 blarsfs) and 1 crob is equivalent to 3.33 seconds (60 seconds / 18 crobs).

Next, we can use the conversion rates to calculate the Earth time for 9 blarsfs and 6 crobs:

9 blarsfs = 9 blarsfs * 20 seconds/blarsf = 180 seconds

6 crobs = 6 crobs * 3.33 seconds/crob = 19.98 seconds (approximately 20 seconds)

Therefore, the total Earth time elapsed for 9 blarsfs and 6 crobs on Shm'lort is 180 seconds (blarsfs) + 20 seconds (crobs) = 200 seconds.

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The probability that a basketball player with a 71% free throw shooting accuracy does not make his next free throw shot is 29%.

The probability that a basketball player with a 71% free throw shooting accuracy does not make his next free throw shot.
To calculate the probability of missing a free throw shot, we need to subtract the shooting accuracy percentage from 100%.

In this case, the probability of making a free throw is 71%, which means the probability of missing the free throw is 29%.

Therefore, the probability that the basketball player does not make his next free throw shot is 29%.
It is important to note that free throw shooting accuracy can vary depending on the player's physical and mental condition, as well as external factors such as the audience's noise, the game's pressure, and the distance from the basket.

Thus, it is crucial for basketball players to train and practice regularly to improve their shooting skills and increase their chances of making free throw shots.
To answer this, we need to consider the complement of the success probability.

Since the player has a 71% chance of making the free throw, it means there is a 29% chance that he will not make it (100% - 71% = 29%).

The probability can also be expressed as a decimal, which is 0.29 (29/100 = 0.29).

Therefore, the probability that your favorite basketball player does not make his next free throw shot is 29% or 0.29.
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Answer:

\(d=\sqrt(x2-x1)^{2} + (y2-y1)^{2}\)

Step-by-step explanation:

1- Identify the x and  the y

x1= 3

x2=7

y1= 2

y2= 9

2- solve the equation:

d=\(\sqrt\\)(7-3))\(^{2}\)  + (9-2)\(^{2}\)

d= \(\sqrt\)(4)\(^{2}\)        + (7)\(^{2}\)

= \(\sqrt\)16        + 49

= \(\sqrt\)65

d=8.06 answer rounded to the nearest hundredth

In   linear equation, 2 hours and 45 minutes, the temperature of the pork roast is 165 ° F.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The temperature of the pork roast is greater at 3 hours than at 2 hours and 45 minutes.

After 2 hours and 45 minutes, the temperature of the pork roast is 165 ° F.

    f(a) = 67  the temperature of the pork roast is 67° F. When it is placed in the over .

     f( 2.45 ) = the temperature  of pork roast is 65° F when its done cooking.

 f( 2.45 ) = the temperature  of pork roast decrease between 2 hours and                        

                          45 min and 3 hours .

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The length of one drama is 47.4 minutes.

Given that a drama club is showing two videos from 4:00pm to 6:05pm having a 1/2 hours of break in between two of them,

We need to find the length of the dramas,

So,

Total time = 4:00 to 6:05 = 2 hours and 5 minutes.

Subtracting the break length = 2.083 hours - 0.5 hours = 1.58 hours.

Now the length of one drama = 1.58/2 = 0.79 hours.

= 47.4 minutes

Hence the length of one drama is 47.4 minutes.

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Answer:

Step-by-step explanation:

3x + 2 = 7(3 - x)

3x + 2 = 21 - 7x

3x + 7x = 21 - 2

10x = 19

 x = 1.9

\(26-x-4 = 26 - 1.9 -4 = 20.1\)

The remaining amount of water will be  \(\dfrac{\pi}{3}\) cubic meters.

We must determine the volume difference between the tank and the water already there in order to determine how much additional water might be accommodated in the tank. Here is the procedure in detail:

Utilising the formula for a cone's volume, determine the tank's volume:

\(\rm V= \dfrac{1}{3} \times \pi \times r^2 \times h\)

\(\rm V= \dfrac{1}{3} \times \pi \times (5)^2 \times 11\)

Use the same formula to get the tank's water volume:

\(V_w= \dfrac{1}{3} \times \pi \times 3^2 \times 6\)

To determine the tank's remaining capacity, subtract the volume of the water from the tank's volume.

Remaining capacity = Volume of the tank - Volume of the water

Simplifying the equation, we have:

\(\rm Rc= [\dfrac{1}{3} \times \pi \times 5^2 \times 11] - [\dfrac{1}{3} \times \pi \times 3^2 \times 6]\\\\Rc = \dfrac{1}{3} \times \pi \times [5^2 \times 11 - 3^2 \times 6]\\\\Rc = \dfrac{1}{3} \times \pi \times [55 - 54]\\\\Rc= \dfrac{1}{3} \times \pi \times 1\\\\Rc= \dfrac{\pi} {3} \rm \ cubic\ meters\)

Therefore, more water might fit in the tank by \(\dfrac{\pi}{3}\) cubic metres or around 1.047 cubic metres.

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