Find three rational numbers such that their product is 210. The second number is 5 less than the first. The third number is 1 more than twice the first.

With the bottom of the Ferris Wheel being 5 meters off the ground, and a radius of, r = 7.5 meters, the center of the Ferris Wheel is 12.5 meters off the ground.

A horizontal  line through the center of the Ferris Wheel is 12.5 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 14 meters.

The distance from the horizontal to 14 meters is 1.5 meters (14 - 12.5), and angle between the horizontal and a radius to 14 meters is sin(θ) = 1.5/7.5 or θ = sin-1(1.5/7.5) = 11.54o. This angle height is on both sides of the Ferris Wheel and therefore 180o + 2*11.54o = 203.07o is always under 14 meters. What is above 14 meters is 360o - 203.07o = 156.93o.

Since it takes 8 minutes for 1 revolution, (156.93o/360o)*8 min ≈ 3.5 min, the amount of time the Ferris Wheel is above 14 meters.

I do hope this is helpful! :)

Answer:

358.62

Step-by-step explanation:

Answer:

358.62

Step-by-step explanation:

Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

Answer:

[tex]x {}^{ \frac{19}{15} } [/tex]

Step-by-step explanation:

Hope that's helps

Answer:

answer is 8

Step-by-step explanation:

Answer: [tex]x=8[/tex]

Step-by-step explanation:

[tex]3x+13=37\\\\3x=24\\\\x=8[/tex]

Answer:

  30 feet

Step-by-step explanation:

You want to know the distance between the first and last of 10 stakes evenly spaced, such that the first and fourth are 10 feet apart.

Between stakes 1 and 4 are 3 gaps. Between stakes 1 and 10 are 9 gaps, which is 3 times as many.

The distance from the 1st to 10th stakes will be 3 times the 10 ft distance from the 1st to 4th stakes.

  3 · 10 ft = 30 ft

The first and tenth stakes are 30 feet apart.

Answer:

20%

Step-by-step explanation:

[tex]\frac{2}{10}[/tex] x 100 = [tex]\frac{200}{10}[/tex] = 20%    

When selecting the ply of the mat which we will use for an image, what we choose is the thickness of the mat. The correct answer is option A.

The width of our mat really influences how our art is showed. A perfect rule of thumb is to select a mat which is at least 1 inch wider than our moulding. Many mats are 2-4 inches wide; usually, larger artwork can use a wider mat, and smaller artwork should be paired with a narrower mat.

Mats available in 4 ply (0.040 to 0.052″) and 8 ply (0.125″); but it does not mean all ply are the same. For instance, there are 0.052″ 4 ply and 0.040″ 4 ply. Double or triple 4 ply mats are possible also to be used in area of 8 ply mats to produce a similar effect.

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When use the graphs of f and g to graph then, we find that

Now, h(x) = (f + g)(x)

As you know that different x values that must be taken into consideration so that the graph h (x).

At first, h (0) = f (0) + g (0) = 2 - 1 = 1

Now,

If h (1) = f (1) + g (1) =

3 + 0 = 3

Then, after proper calculation, now

Later as we know, hence

finally the answer is h (3) = f (3) + g (3)

= 2 + 0 = 2

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Answer:

b) The stock is 5.5 less than the original value, and the absolute value is 5.5.

Step-by-step explanation:

First of all, let's make our number line. The question says you need it to start at -9, so we can assume that it will go until 10. It also wants us to make half-tick marks. (There is an image attached of the number line.)

It says that -5.5 is labeled, so do that on your number line.

Next, it explains that 0 is the original price. 0 is where the stock is starting at. This does not mean that the value of the stock is 0!!! (It means that NO MATTER what the price of the stock is, that is now considered 0.)  

Now for the multiple choice, here's why all the answers are incorrect/correct.

a) If something is -5.5 less, it's the same as subtracting a negative number- which makes it positive!! SO this would mean that it added value.

b) Correct! Since it value is lower by 5.5, it's 5.5 less than the og value.

c) Since it's -5.5 greater, that's like adding a negative number: it's the same as subtracting. I suppose this is technically correct, but it's weird.

d) This one says's it's 5.5 greater, which is totally wrong. The value is decreasing, not increasing!

All of them say the absolute value is 5.5. This is correct. Absolute value is the distance from 0, and -5.5 is 5.5 units away from 0. (put simply, absolute value is just making the number positive.

hopefully this makes sense and helps you!!

The amount of tax that Eric and Maria will pay on their dividend income is 24% so 24% * $3,000 = $720. This amount will then be added to their taxable income of $88,910, and the resulting amount will be used to calculate the total tax they owe for the year.

The amount of tax that Eric and Maria will pay on their dividend income will depend on their marginal tax rate. In 2021, the federal tax rate is progressive, meaning that the higher their taxable income, the higher their marginal tax rate. For a taxable income between $80,251 and $171,050, the marginal tax rate is 24%. Therefore, the tax that Eric and Maria will pay on their dividend income will be 24% of the amount of dividend income they received. This amount will then be added to their taxable income of $88,910, and the resulting amount will be used to calculate the total tax they owe for the year.

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To make x the subject of the equation q^2 = x - m^2, we can start by adding m^2 to both sides of the equation:

q^2 + m^2 = x

We can then rearrange the terms to get x on the left side:

x = q^2 + m^2

This is the equation with x as the subject.

welcome to the site

The Corner Points are (-6.529, -10.235), (0, -2.4), (2, 0), (-2.143, 0), (0, 5)

What is Linear Inequality?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.

Solution:

Please refer to the Graph

So, we plotted the graph using the basic point method in which we found two point of the equation to draw a straight line.

And once we drawn the lines for the Inequalities we shaded the respective region

The Corner Points are (-6.529, -10.235), (0, -2.4), (2, 0), (-2.143, 0), (0, 5)

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To determine Mary's required speed, we need to first understand the relationship between speed and time.

If Mary's speed is inversely related to her drive home, then this means that as her speed increases, her drive time decreases, and vice versa. In other words, the drive time is inversely proportional to the speed. We can represent this relationship using the equation t = k/s, where t is the drive time, s is the speed, and k is a constant. If we plug in the given values, we get t = 40 minutes = k/55 mph.

Now, if Mary wants to arrive home 15 minutes earlier, we can set the desired drive time equal to 25 minutes (40 minutes - 15 minutes) and solve for the required speed. Substituting this value into the equation above, we get s = k/(25 minutes) = (55 mph)/(25 minutes) = 2.2 mph.

Therefore, Mary needs to drive at a speed of 2.2 mph in order to arrive home 15 minutes earlier. Note that this answer is not realistic, as it is much lower than the speed limit on most roads. This suggests that it may not be possible for Mary to arrive home 15 minutes earlier without breaking the law or increasing her risk of an accident.

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Complete Question:

Mary's speed is inversely related to her drive home. Mary drives home from work in 40 minutes driving 55mph. If Mary needs to get home 15 minutes earlier, how fast dose she need to drive?

The excretion  Superscript one-eighth Beeline is

[tex]\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right)=12[/tex]

What is exponential identity?

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

To find, the possible value of x = ?

[tex]\begin{aligned}& \therefore\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right)=12 \\& \Rightarrow x^{\frac{1}{8}}+\frac{3}{8}=12\end{aligned}[/tex]

Using the exponential identity

,[tex]\begin{aligned}& a^m a^n=a^{m+n} \\& \Rightarrow x^{\frac{1+3}{8}}=12 \\& \Rightarrow x^{\frac{4}{8}}=12 \\& \Rightarrow x^{\frac{1}{2}}=12\end{aligned}[/tex]

Squaring both sides, we get

[tex]\begin{aligned}& \left(x^{\frac{1}{2}}\right)^2=(12)^2 \\& \Rightarrow x^{\frac{1}{2} \times 2}=144 \\& \Rightarrow x=144\end{aligned}\therefore The possible value of x=144[/tex]

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Answer:

125

Step-by-step explanation:

alternate interior

Answer:

x^2-10x-9+9/x-6

quotient:x^2-10x-9

remainder:9

Step-by-step explanation:

Answer:

t=180-2x46=88 degrees

u=1/2(180-114)=33 degrees

The amount produced is the independent variable and the number of truckers is the dependent variable. So, option 2 is the correct answer.

Independent variables are those variables that do not require any other quantity/variable in order to determine their value. On the other hand, dependent variables do require another such variable.

In the given problem, the amount of product does not depend on any other factor. This means it is independent of any other variable. Meanwhile, the number of truckers depends on the amount produced. This makes it the dependent variable. So, option 2 is the answer here.

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The z-score corresponding to an observation is -1.02

From the given data μ=335

σ=50

X=284

It is a way to compare the results from a test to a “normal” population.

If X is a random variable from a normal distribution with mean (μ) and standard deviation (σ), its Z-score may be calculated by subtracting mean from X and dividing the whole by standard deviation.

Where, x = test value

μ is mean and

σ is SD (Standard Deviation)

For the average of a sample from a population ‘n’, the mean is μ and the standard deviation is σ.

X=284 now we have to find Z score

so from the formula the Z score corresponding to observation X=284 is we have

Z=X- μ/σ

=[tex]\frac{284-335}{50}[/tex]=-1.02

Therefore, the z-score is -1.02.

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Answer: 1 knife costes £5.52

Step-by-step explanation:

Let a knife costes £x and a spoon costes £y

Hence, we obtain a system of equations:

x=3y                         (1)

12x+9y=82.80         (2)

Divide both parts of the equation (2) by 3:

x=3y                    

4x+3y=27.6        (3)

We substitute the value of x=3u into equation (3):

4(3y)+3y=27.6

12y+3y=27.6

15y=27.6

Divide both parts of the equation by 15:

y=£1.84

x=3y

x=3(1.84)

x=£5.52

Answer:

32%

Step-by-step explanation:

[tex]\frac{8}{25} \times 100=32\%[/tex]

Answer:

Step-by-step explanation:

32%

The probability of drawing a red marble from the jar is 5/11 and the probability of drawing a blue marble from the jar is 6/11.

There are 22 marbles in the jar in total, 10 of which are red and 12 of which are blue. To find the probability of drawing a red marble, we can use the formula for probability:

Probability = Number of favorable outcomes / Total number of outcomes

In this case, the number of favorable outcomes is 10 (the number of red marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:

Probability of drawing a red marble = 10/22

This fraction can be reduced to 5/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a red marble from the jar is 5/11.

To find the probability of drawing a blue marble, we can use the same formula:

Probability = Number of favorable outcomes / Total number of outcomes

In this case, the number of favorable outcomes is 12 (the number of blue marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:

Probability of drawing a blue marble = 12/22

This fraction can also be reduced to 6/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a blue marble from the jar is 6/11.

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The population means may be the same

So, option D is correct.

What is meant by confidence interval?

In statistics, the probability that a population parameter will fall between a set of values a predefined percentage of the time is known as the confidence interval. Analysts typically use confidence intervals that cover 95% or 99% of the expected observations while assessing data. In frequentist statistics, an estimation range for an unknown parameter is referred to as a confidence interval. The most common confidence level for computing confidence intervals is 95%, however other levels, such 90% or 99%, are also occasionally employed. The conclusion is reached that the result is statistically significant if the confidence interval eliminates the value of zero effect.

If (μ₁- μ₂=0) is included in the confidence interval, that means this two means have the same difference that is zero.

Therefore, they may be nearly same,

So, The population means may be the same

Hence, option D is correct.

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the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

Lets take v1 = (1,0,0), v2 = (1,1,0) and v3 = (0,1,0). Neither of the vectors are a multiple of the other, however they dont generate R³ because for example the vector (0,0,1) is not a linear combination of v1, v2 and v3.

Not that, despite not being a multiple of v1 or v3, v2 is a linear combination of v1 and v3, because it is the sum of both of them. Therefore, the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

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The length, b, of the longest side of the triangle is 13.17 cm

From the question, we are to determine the length, b, of the longest side of the triangle

From the given information,

Area of the triangle = 22.4 cm²

Then, we can write that

22.4 = 1/2 × a × 3.7 sin97

44.8 = a × 3.7 sin97

44.8 = a × 3.6724

a = 44.8/3.6724

a = 12.199

a = 12.2

Given that the sides of the triangle are a, b, and c,

Then,

From the law of cosines, we can write that

b² = c² + a² - 2ac cosB

b² = 3.7² + a² - 2×a×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 173.53

b = √173.53

b = 13.17 cm

The length of b is 13.17 cm

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Only answers A, C, and D are in standard form, so we can rule B out immediately.

If you throw (5,1) into A, you get:

   5(5) - 2(1) = 23

        25 - 2 = 23

This checks, so A *might* be the answer.

If you throw (5,1) into C, you get:

  2(5)-3(1) = 9

      10 - 3 ≠ 9

This doesn't check, so it's not C.

If you throw (5,1) into D, you get:

  5(5)+2(1) = 23

     25 + 2 ≠ 23

This doesn't check, so it's not D.

The only standard form equation that (5,1) is a solution for is A.

Your answer is A.

Answer:

$43

Step-by-step explanation:

substitute x = 2.75 into f(x)

f(2.75) = 12(2.75) + 10 = 33 + 10 = 43

that is he earns $43

A mathematical model that represents the statement using a  constant of proportionality is; y = 25(x/y²)

The constant of proportionality is defined as the ratio of two proportional values that is said to be in a constant value.

We are told that P varies directly as x and inversely as the square of y.

Thus, we have;

P ∝ x/y²

We are now told that;

P = 28/3 when x = 84 and y = 15. Thus;

P = k(x/y²)

where k is constant of proportionality

Thus;

28/3 = k(84/15²)

k = (28 * 15²)/(84 * 3)

k = 25

Thus, the mathematical model is concluded as;

y = 25(x/y²)

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Complete question is;

Find a mathematical model representing the statement. (Determine the constant of proportionality.)

P varies directly as x and inversely as the square of y.

P = 28/3 when x = 84 and y = 15.

P=??