Solve the proportion 8/9=r/6

The total number of individuals in the development area is 2240 kg/day.

The volume of waste produced by a single family per week is 0.91 containers/family

i) The total number of individuals in the development area is calculated as:
350 x 8 = <<350*8=2800>>2800

individuals' total waste produced by the development area is calculated as:

0.8 kg/capita/day x 2800 individuals = <<0.8*2800=2240>>2240 kg/day

Answer: 2240 kg/day

ii) Volume of waste produced by a single family per week is calculated as:

0.4 kg/person/day x 8 persons x 7 days = <<0.4*8*7=22.4>>22.

4 kg/week

The density of waste in each container is 210 kg/m3.

The volume of waste generated by each family each week is calculated as:22.4 kg/week ÷ 210 kg/m3 = 0.107 m3/family

The number of 118 L containers required for each family is calculated as:

0.107 m3/family ÷ 0.118 m3/container = <<0.107/0.118

=0.91>>0.91 containers/family (rounded to two decimal places)

Answer: 0.91 containers/family

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Answer:

3,000ft

Step-by-step explanation:

First set up the equation:

Start: 13,000 ft
Middle: 10,000 ft
End: ??

Lindsey started at 13,000ft, dropped 10,000ft, and then the remainder of it is what we are asked to find out. So all we have to do is 13,000 - 10,000 which equals 3,000.

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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The chart fits the functional equation for all values of x, according to the claim made.

The Geometric Mean (GM) in mathematics is the average or mean that, by calculating the product of the values of the collection of numbers, denotes the central trend of the numbers. In essence, we combine the numbers collectively and calculate their nth root, in which n is the entire amount of data values.

We can use the given functional equation f(x+1) = 4(f(x)) to find the values of f(x) for each value of x, given that we know f(1) = 4. We start by computing:

f(2) = 4(f(1)) = 4(4) = 16

f(3) = 4(f(2)) = 4(16) = 64

f(4) = 4(f(3)) = 4(64) = 256

f(5) = 4(f(4)) = 4(256) = 1024

Now, we have determined all the values of f(x) for x=1 to 5. Since the table has 5 rows, we can write:

x f(x)

1 4

2 16

3 64

4 256

5 1024

We can check that the table satisfies the given functional equation f(x+1) = 4(f(x)). For example, when x = 3, we have:

f(x+1) = f(4) = 256

4(f(x)) = 4(f(3)) = 4(64) = 256

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Answer: It's not a polynomial

It's not a polynomial because the exponent of -1 in the second term. The exponents for any polynomial must be nonnegative whole numbers {0,1,2,3,...}

The equation of the asymptote of the function h(x) = -2(5)^x + 4 is y = 4.

An asymptote is a line that the graph of a function approaches but never touches or crosses. In this case, we can observe that as x approaches negative or positive infinity, the exponential term (-2(5)^x) becomes extremely small, approaching zero. Therefore, the function h(x) approaches the constant term 4. This means that the horizontal line y = 4 serves as the asymptote of the function h(x).
To further understand this, we can analyze the behavior of the function as x becomes very large or very small. As x approaches negative infinity, the exponential term (5^x) becomes closer and closer to 0, and when multiplied by -2, it approaches 0 as well. Adding the constant 4 gives us y = 4. Similarly, as x approaches positive infinity, the exponential term (5^x) grows larger and larger, but when multiplied by -2, it becomes more negative and approaches 0. Again, adding the constant 4 gives us y = 4. Therefore, the equation of the asymptote of h(x) is y = 4.

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The type of manufacturing process used to create the world's largest pizza can be classified as batch processing. Considerations such as ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams were likely made during the planning stage. The process would change when planning the manufacturing process for a pizza available at Pie Craft or a pizza in the frozen section of a supermarket, with a shift towards more standardized and automated production methods.

World's Largest Pizza:

The manufacturing process for the world's largest pizza was a massive undertaking due to its size and quantity of ingredients. It involved batch processing, where a specific quantity of the product was produced at one time. During the planning stage, considerations were made regarding ingredient sourcing, logistics, equipment capacity, and coordination among multiple teams.

Pizza at Pie Craft:

If planning the manufacturing process for a pizza available at Pie Craft, a more standardized and streamlined approach would be adopted. The emphasis would be on consistency and quality. This would involve creating standardized recipes, portion control, and training staff to follow specific procedures. Some manual steps might still be involved, but automation could be introduced to streamline processes such as dough mixing and ingredient assembly.

Frozen Supermarket Pizza:

For a pizza in the frozen section of a supermarket, the manufacturing process would undergo significant changes. It would be highly automated and designed for mass production. The emphasis would be on consistency, convenience, and shelf life. The dough would be mechanically mixed, shaped, and portioned, while ingredients would be applied using automated systems. Packaging and freezing processes would also be optimized to maintain product quality.

In summary, the manufacturing process for the world's largest pizza was a massive undertaking, involving batch processing and careful planning regarding ingredient sourcing, logistics, and equipment capacity. For a pizza at Pie Craft, a more standardized approach would be adopted with a balance of manual and automated processes. In contrast, a frozen supermarket pizza would undergo a highly automated process to achieve consistency, convenience, and extended shelf life.

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As a result, the radian measure of the relevant center angle is around 3.07 radians.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference.

Here,

The formula for the length of an arc in a circle is given by:

Arc Length = (Central Angle / 2π) * Circumference

We know the Arc Length and the Radius of the circle, so we can find the Central Angle as follows:

Arc Length = (Central Angle / 2π) * 2π * Radius

66/5 * π = (Central Angle / 2π) * 2π * 22

66/5 * π = Central Angle * 22

Central Angle = (66/5 * π) / 22

The radian measure of an angle is equal to the ratio of the length of the arc that it intercepts to the radius of the circle. Hence, the radian measure of the central angle is given by:

Central Angle (in radians) = Arc Length / Radius

= (66/5 * π) / 22

So, the radian measure of the corresponding central angle is approximately 3.07 radians.

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Hello the answer is B Hope that helps!

E is the middle of [AC]

so AE = 1/2 x AC

then

4x = 1/2 * (6x + 5)

4x = 3x + 5/2

x = 5/2

x = 2,5

Answer:

\(x=\dfrac52\)

Step-by-step explanation:

In a parallelogram, the diagonals bisect each other.  This means that the diagonals are divided into 2 equal parts by the other diagonal.

Therefore,

\(\implies AE =\dfrac12 AC\)

\(\implies 4x=\dfrac12(6x+5)\)

To solve:

multiply both sides by 2:

\(\implies 8x=6x+5\)

subtract 6x from both sides:

\(\implies 2x=5\)

divide both sides by 2:

\(\implies x=\dfrac52\)

Easy Do 7x8x8x8x8=3584 hope this helps

Answer:

4

The absolute value of 4 is the same since there is no negative

Answer:

REMEMBER =

The absolute value is the positive of ANY NUMBER!

EXAMPLE =

| 6 | = 6

| -1,000,000 | = 1,000,000

| -7 | = 7

Hope this helps! <3

Answer:

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Step-by-step explanation:

The ounce is a mass unit, as we notice that the metallurgist wants to make 12 ounces of an alloy containing 45 % copper by mixing two metal with different copper proportions. We can use the following two equations:

Alloys

\(m_{R} = m_{A}+m_{B}\) (Eq. 1)

Copper

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A}+r_{B}\cdot m_{B}\) (Eq. 2)

Where:

\(m_{A}\) - Mass of the 30 % copper alloy, measured in ounces.

\(m_{B}\) - Mass of the 50 % copper alloy, measured in ounces.

\(m_{R}\) - Mass of the 45 % copper alloy, measured in ounces.

\(r_{A}\) - Proportion of copper in the 30 % copper alloy, dimensionless.

\(r_{B}\) - Proportion of copper in the 50 % copper alloy, dimensionless.

\(r_{R}\) - Proportion of copper in the 45 % copper alloy, dimensionless.

Now, the mass of the 50 % copper alloy is cleared in Eq. 1 and eliminated in Eq. 2:

\(r_{R}\cdot m_{R} = r_{A}\cdot m_{A} + r_{B}\cdot (m_{R}-m_{A})\)

\((r_{R}-r_{B})\cdot m_{R} = (r_{A}-r_{B})\cdot m_{A}\)

And we clear and calculate the mass of the 30 % copper alloy:

\(m_{A} = m_{R}\cdot \left(\frac{r_{R}-r_{B}}{r_{R}-r_{A}} \right)\)

If we know that \(m_{R} = 12\,oz\), \(r_{R} = 0.45\), \(r_{A} = 0.30\) and \(r_{B} = 0.50\), the mass of the 30 % copper alloy:

\(m_{A} = (12\,oz)\cdot \left(\frac{0.45-0.50}{0.30-0.50} \right)\)

\(m_{A} = 3\,oz\)

And the mass of the 50 % copper alloy is:

\(m_{B} = m_{R}-m_{A}\)

\(m_{B} = 12\,oz-3\,oz\)

\(m_{B} = 9\,oz\)

The metallurgist should use 3 ounces of the 30 % copper alloy and 9 ounces of the 50 % copper alloy to make 12 ounces of 45 % copper alloy.

Answer: 15%

Step-by-step explanation:  

I hope this helps,

have an wonderful Day!

The tax rate Tasha will pay on her investment income is 15%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Ordinary taxable income= $90,000

Capital gains= $12,000

Now,

The tax rate Tasha will pay on her investment income depends on her ordinary taxable income and the tax brackets for qualified dividends and long-term capital gains. Since Tasha’s ordinary taxable income is $90,000, she falls in the 15% tax bracket for her investment income.

Therefore, by the percentage the answer will be 15%.

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Answer:

80 degrees, explanation down below

Step-by-step explanation:

according to the vertical angle theorem, two vertical angles are the same angle measure. so, angle CBD and angle ABF must be the same. this is 100 degrees. now, according to the corresponding angles theorem, corresponding angles are supplementary to each other (they add up to 180 degrees), so angle ABF and angle EFB are supplementary. since angle ABF is 100 degrees, we can subtract that from 180 degrees. therefore, angle x (same thing as EFB) is 80 degrees.

Answer:

80 is the answer

Explanation: angle CD=100

                    angle CA= 180-100      (linear pair)

                                    = 80

                      angle x = 80 (because when cbd = 100°, bfh = 100; therefore angle x=180-100 = 80

Mathematical Reason: if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Answer:

P(-5) = 109

Step-by-step explanation:

     If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).

   Dividend = divisor * quotient + remainder.

   p(x) = (x-a) * q(x) + p(a)

Here, q(x) is the quotient and p(a) is the remainder.

      P(x) = 4x² - x + 4

     P(-5) = 4*(-5)² - 1*(-5) + 4

              = 4*25 + 5 + 4

              = 100 + 5 + 4

              = 109

Answer:

80 boxes of cookies

Step-by-step explanation:

First, we have to find 1% by taking

32 divided by 40 = 0.8

Then we take it times 100%

0.8 x 100 = 80 boxes of cookies

Jean want to sell 80 boxes of cookies

Answer:

(5,4)

Step-by-step explanation:

first, if you have a calculator you can put the equation into y = and just find the maximum point there

to find the x value of the maximum point you do -B/2A

-80/2(8) = 5 so the x value would be 5

then to find y just plug in 5 for x and you should get 4

Answer:

Maximum value of
\(f(x) = - 8x^2 + 80x - 196\)

is

\(\boxed{f(x) = 4}\)

Step-by-step explanation:

The maximum or minimum value of a function f(x) occurs when the first derivative equals zero

The first derivative of
\(f(x) = - 8x^2 + 80x - 196\)

\(f'(x) = \dfrac{d}{dx}\left(-8x^2+80x-196\right)\)

\(=-\dfrac{d}{dx}\left(8x^2\right)+\dfrac{d}{dx}\left(80x\right)-\dfrac{d}{dx}\left(196\right)\)

\(\dfrac{d}{dx}\left(8x^2\right) = 16x\\\\=- \dfrac{d}{dx}\left(8x^2\right) = -16x\\\\\\\dfrac{d}{dx}\left(80x\right)=80\\\\\dfrac{d}{dx}\left(196\right)=0\)

\(\dfrac{d}{dx}\left(-8x^2+80x-196\right) \\\\\\ =-16x + 80 + 0\\\\= -16x + 80\\\\\)

Set this expression equal to 0 and solve for x to find the x value which maximizes or minimizes the function

\(-16x + 80 = 0\\\\\implies -16x = -80\\\\x = -80/-16\\\\x = 5\\\\\)

Plug this value of x into the original function to get the maximum or minimum value.

\(f(5) = -8(5^2) + 80(5) - 196\\\\= -8 (25) +400 -196\\\\= -200 + 400 - 196\\\\= 4\\\\\)

So the maximum value of \(\boxed{f(x) = 4}\) ANS

and occurs at \(x = 5\)  

(Strictly speaking to find if this is a maximum or minimum, we have to find the second derivative and see if it is negative or positive. If negative, it is a maximum, if positive it is a minimum

But since the question does not ask for this, I am skipping it. In case you are interested, the second derivative of f(x) is the derivative of f'(x) which will work out to -16 so it is a maximum)

The mean absolute percent error (MAPE) is 25%.

The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.

To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:

MAPE = (MAD / Total Demand) * 100

     = (25 / 1,000) * 100

     = 2.5%

Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.

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Based on the provided information to conduct the hypothesis test the condition met are random sampling, sample size, independence. From this sample, the taxpayer calculates a sample mean of $934 and a sample standard deviation of $619.

To conduct a hypothesis test, we need to ensure certain conditions are met. These conditions are:
1. Random sampling :The taxpayer used a random sample of 32 families, which helps to ensure the sample is representative of the population.
2. Sample size: The sample size is 32, which is considered a large enough sample size for a hypothesis test (generally, a sample size of 30 or more is considered large enough).
3. Independence: Since the sample is random and the sample size is less than 10% of the population (assuming there are more than 320 families), the independence assumption can be considered as met.
4. Approximately normal distribution: With a sample size of 32 (which is considered large), the Central Limit Theorem suggests that the sampling distribution of the sample mean will be approximately normal.
With these conditions met, the taxpayer can proceed with a hypothesis test to compare their sample mean with the IRS representative's claimed average and determine whether the real figure for medical care deductions is likely to be lower than $1,250.

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The general form of an exponential function is given below:

For point (1,3); x = 1 and y = 3,

Substituting the above values into the equation, we get

Thus, the correct answer is y = 0.5(6)^x (option C)

Answer?

Step-by-step explanation:

The probability of winning $3,899 is 0.0001, which is a very small probability, but still possible.

To write the probability distribution for a player's winnings in the Pick 4 game, we need to consider all the possible outcomes and their probabilities.

There are a total of 10,000 possible four-digit numbers that can be drawn in the game. Since the player has to match the numbers in the exact order, there is only one winning combination for each four-digit number. Therefore, the probability of winning is 1/10,000.

To calculate the player's winnings, we need to subtract the $1 cost of playing from the $3,900 prize. Thus, the player's net winnings can be calculated as follows:

Net Winnings = $3,900 - $1 = $3,899

The probability distribution for the player's winnings can be summarized in the following table:

| Winnings (x) | Probability (P) |
|--------------|-----------------|
| $0           | 0.9999          |
| $3,899       | 0.0001          |

Note that the table shows the possible winnings (x) in ascending order, as requested. The probability of winning $0 is 0.9999, which means that the player is most likely to lose their $1 bet.

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Answer:

an angle greater than 180° and less than 360°.

Step-by-step explanation:

The correct value of reflex angle is,

⇒ An angle measuring 185 degrees.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

To find reflex angle.

Now, We know that;

Reflex angle is greater than 180 degree and less than 360 degree.

Thus, By options;

⇒ 185° > 180°

Hence, The correct value of reflex angle is,

⇒ An angle measuring 185 degrees.

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Check the picture below.  When will it reach its height? well, at the vertex, so

\(~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&24\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&50\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+24t+50\implies \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients}\)

\(h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+24}t\stackrel{\stackrel{c}{\downarrow }}{+50} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 24}{2(-16)}~~~~ ,~~~~ 50-\cfrac{ (24)^2}{4(-16)}\right)\implies \left( \cfrac{3}{4}~~,~~50-\cfrac{576}{64} \right)\)

\(\left(\cfrac{3}{4}~~,~~50+9 \right)\implies \stackrel{\underset{\qquad \downarrow }{\textit{how far up it went}}}{\underset{\stackrel{\uparrow \qquad ~~}{\textit{when it reached it}}}{\left( \cfrac{3}{4}~~,~~59 \right)}}\)

Answer:

After 3 years, Dakota will have $674.09 total.

Answer:

I think the answer is A. Specialty shops that offer high-quality goods have been created to address one specific need