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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

\( \frac{6 {x}^{2} - 12x - 48 }{3 {x}^{2} - 12x - 36 } = \frac{6( {x}^{2} - 2x - 8)}{3( {x}^{2} - 4x - 12)} = \frac{6(x + 2)(x - 4)}{3(x + 2)(x - 6)} = \frac{2(x - 4)}{x - 6} = \frac{2x - 8 }{x - 6} \)

The solution is 440 ft² because the overall size of the image is 528 sq ft, which in itself is closest approaching 440 square feet.

Parallel forms are defined as having at least two even more parallel lines. If two lines never cross, they are considered to be parallel. There are different parallel shapes, however any parallel sides require an equitable distribution of sides in the shape.

Sum of the measurements of the two main sides divided by height equals the area of a trapezoid.

Let's refer to the longer parallel side's length as "L." The figure's height is 22 feet, while the shorter parallel side's length is 16 feet.

Area = (L + 16) / 2 * 22

We also knows that the distance between a point and the vertical line formed by two studs is 4 feet and the distance between a vertex and the opposing height is 8 feet. The Pythagorean theorem may be used to determine the length of the greater parallel side, L, since these two lengths create a right triangle.

L² = (8 + 4)² = 64

L = 8

We can now calculate the overall area using the formula for a trapezoid's area.

Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528

The solution is 440 ft² because the overall size of the figures is 528 sq ft, that is closest towards 440 sq ft.

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Answer:

Let's denote:

- S = number of student tickets sold

- A = number of adult tickets sold

From the problem, we know:

1. S + A = 700 (total number of tickets sold)

2. 5S + 10A = 4500 (total amount of money collected)

Now, let's solve these equations. The most straightforward method would be substitution or elimination. Let's use substitution:

From equation 1, we can express S as 700 - A. Substitute this into equation 2:

5(700 - A) + 10A = 4500

3500 - 5A + 10A = 4500

5A = 1000

A = 200

Substitute A = 200 into equation 1 to find S:

S + 200 = 700

S = 500

So, 500 student tickets and 200 adult tickets were sold.

Now, let's calculate how much more money would have been collected if the ticket booth charged $15 for both student and adult tickets:

Total revenue = $15 * (S + A)

Total revenue = $15 * (500 + 200) = $15 * 700 = $10,500

Therefore, the amount of additional revenue would be $10,500 - $4500 = $6,000.

a multiple regression model, the error term `e’ is assumed to be a random variable with a mean of is A) zero. This means that in a multiple regression model, the errors are assumed to have a mean of zero. This assumption is necessary to ensure that the model is unbiased and accurate in predicting the outcome variable.

this assumption is that the error term represents the unexplained variation in the outcome variable that is not accounted for by the predictor variables. If the error term had a mean value other than zero, this would indicate that there is a systematic bias or error in the model, which would affect the accuracy of the predictions.

the assumption of a zero mean error term is a critical aspect of multiple regression modeling and helps to ensure that the model is reliable and valid for predicting the outcome variable.

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7 test scores are 85 or greater according to the given scenario.

The third quartile (Q3) is a measure of central tendency that represents the value separating the lower 75% of a dataset from the upper 25%. In this case, the third quartile has a value of 85, meaning that 75% of the test scores are 85 or lower.

Since there are 30 exams in total, 30 x 0.75 = 22.5 exams have scores of 85 or lower. To find the number of exams with scores of 85 or greater, we subtract the number of exams with scores of 85 or lower from the total number of exams, which is 30 - 22.5 = 7. This means that 7 exams have scores of 85 or greater.

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Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer:

98 cats and 19 dogs

Step-by-step explanation:

cat = c

dog = d

The animal shelter currently has a total of 117 animals

c + d = 117

c = 117 - d

the number of cats is 3 more than 5 times the number of dogs

c = 3 + 5d

subtitute c

117 - d = 3 + 5d

117 - 3 = 5d + d

114 = 6d

6d = 114

d = 114/6 = 19

so, the cat is 117-19 = 98

Answer:

The square root must be between the square roots of the perfect squares just above and just below your number.

For example the square root of 89 must be between 9 and 10.

Step-by-step explanation:

Answer:

55°

Step-by-step explanation:

50+75=125. 180-125=55

55+90=145. 180-145=35

90-35=55

Angle ABC (B) is 55°

Method I used:

All lines need to add to 180° so I found the 3rd angle for C. Then I drew an imaginary line perpendicular to lines n and m that intersects line m at point B. The angles of that triangle need to add to 180° so I added 90° (right angle) with the 3rd angle of C (55°) then subtracted that value from 180 to get angle B. Then i found ABC (B).

Answer:

2,304in^3

Step-by-step explanation:

The formula for volume is [ b * l * h ]. We can use the values we are given to find the volume of both rectangles then add them both together.

12 * 12 * 6 = 864in^3

18 * 10 * 8 = 1,440in^3

Add them both together.

864 + 1440 = 2,304in^3

Best of Luck!

The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

In the given kite ABCD, we know that sides AB and BC are congruent, and the length of AB is 14 units. Additionally, sides CD and AD are congruent, and the length of CD is 22 units.

To find the length of BC, we can use the properties of a kite. Since AB and BC are congruent, we can conclude that BC is also 14 units long.

This is because a kite has two pairs of congruent adjacent sides. Therefore, the length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

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Answer:

The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

Step-by-step explanation:

just took test

Answer:

16b^5

Step-by-step explanation:

8b^2×2b^3

= 16b^2+3

= 16b^5

Answer:

D)16b5

Step-by-step explanation:

8b2×2b3

= 16b2+3

= 16b5

The total area of water that will that sprayed by four nozzles is π v⁴/g² total length of the fountain side that well get wet.

Let us consider the velocity of water, which is v m/sec, and the g acceleration due to gravity.

The time of flight of projectiles is 2vcosx/g.

horizontal speed (r) = v cos x

horizontal range R = uₓT = v²(2 sin x cosx)/g v²sin2x /g

maximum horizontal range is sin2x = 90° => 2x = 90° => x = 45°

So, maximum range = v² sin 90° /g = v² /g

Area of water that will be sprayed by four nozzles when the fountain is on and fountain's side get wet π × (Rₘₐₓ)²

=> Aₘₐₓ = π v⁴ / g²

complete question:

A water fountain sprinkles water all around it. If the speed of water coming out of the fountain is v, find the total area around the fountain that gets wet, in terms of π, g and v.

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Answer:

97.92 m³ (nearest hundredth)

Step-by-step explanation:

The composite solid is a cube with a cone cut out.

Therefore, to find the volume of the solid, subtract the volume of the cone from the volume of the cube.

\(\textsf{Volume of a cube}=\sf s^3 \quad\textsf{(where s is the side length)}\)

Given:

Substitute given value into the formula:

\(\begin{aligned}\implies \sf V_{cube} & = \sf 5.1^3\\& = \sf 132.651\: m^3\end{aligned}\)

\(\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}\)

Given:

Substitute given values into the formula:

\(\begin{aligned}\sf \implies V_{cone} & = \sf \dfrac{1}{3} \pi (2.55^2)(5.1)\\& = \sf 11.05425 \pi \: m^3\end{aligned}\)

\(\begin{aligned}\sf V_{solid} & = \sf V_{cube}-V_{cone}\\& = \sf 132.651-11.05425 \pi \\& = \sf 97.92304941...\\& = \sf 97.92 \: m^3 \: (nearest\:hundredth)\end{aligned}\)

Volume of the cube

For the cone

Volume

Total volume of the figure

Answer:

Step-by-step explanation:

The most likely quantity is centimetres.

The second option can be inches.

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A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Inequalities are used to represent unequal expressions

The interpretation of the inequality is all values between 0 and 5

The inequality is given as:

0 < x <5

The above means that x is any number between 0 and 5

Note that the term "between" means that the values of x are exclusive of 0 and 5

Hence, the interpretation of the inequality is all values between 0 and 5

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The slant height of the triangular pyramid is 8.7 feet.

Given a triangular pyramid.

The surface area of the triangular pyramid = 174 square feet

A triangular pyramid consists of 4 triangular faces.

Given that all the triangular faces are equilateral triangle with a length of side as 10 feet.

We have to find the slant height of the pyramid.

The formula to find the surface area of the triangular pyramid is,

Surface area = base area + 1/2 (perimeter × slant height)

Base area = 1/2 × 10 × √(10² - 5²) = 5√75 feet²

Perimeter = 3 × 10 = 30 feet

Substituting,

174 = 5√75 + 1/2 (30h)

174 = 5√75 + 15h

h = (174 - 5√75) / 15

h = 8.7 feet

Hence the slant height is 8.7 feet.

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1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer:

x - 3 = 6

Step-by-step explanation:

In all of the other equations... when you solve for x... you get x = 6.

x -3 = 6 does not end up with x = 6... rather x = 9 in that equation

Answer:

the 2nd one

Step-by-step explanation:

1. 6-2=4

2.9-3=6

3.6-5=1

4.6-6=0

all 6's except 2nd

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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Answer:

6 and 8

Step-by-step explanation:

A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 \(mi.^{3}\)

A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;

The volume of a cone = \(\frac{1}{3}\) \(\pi\)\(r^{2}\)h

where r is the radius of its flat surface, and h is its height.

From the given question, we have to determine the value of h using the Pythagoras theorem.

Such that;

\(/Hyp/^{2}\) = \(/Adj 1/^{2}\) + \(/Adj 2/^{2}\)

\(4^{2}\) = \(h^{2}\) + \(1^{2}\)

16 = \(h^{2}\) + 1

\(h^{2}\) = 15

h = \(\sqrt{15}\)

Thus the volume of the cone = \(\frac{1}{3}\) \(\pi\)\(r^{2}\)h

                             =  \(\frac{1}{3}\)x \(\frac{22}{7}\) x \(1^{2}\)x    \(\sqrt{15}\)

                             = 4.0574

Therefore the volume of the given cone is 4.1 \(mi.^{3}\)

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Answer:

f(g(x)) = 9x² - 6x - 4

Step-by-step explanation:

f(g(x) )

= f(3x - 1)

= (3x - 1)² - 5 ← expand factor using FOIL

= 9x² - 6x + 1 - 5

= 9x² - 6x - 4

The equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation is passing through the points  (−5,5) and (8,5). The equation of the line will be written below,

Y = mx + c

Slope = m  = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = m  =( 5 -5  ) / ( 8 + 5)

Slope = m  = 0

The y-intercept will be calculated as,

Y = 0x + c

5 = 0 + c

C = 5

The equation of the line is,

Y = mx + c

Y = 0x + 5

Therefore, the equation of the line passing through the points (−5,5) and (8,5) will be y = 0x + 5

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Answer:

7

Step-by-step explanation:

26-2 = 24. 24/6 = 4. 53-4=49. The square root of 49 is 7.

Answer:

angle 9 measures 105 degrees

Step-by-step explanation:

measure of angle 8 is congruent to measure of angle 11 (alternate-interior angles are congruent)

measure of angle 11 is congruent to measure of angle 9 (corresponding angles are congruent)

therefore, measure of angle 8 = measure of angle 9

(a) The general solution to the differential equation is: y = 3 + 1 / (sin(t) + \(\sqrt{C_1}\). (b) The general solution to the differential equation is: y = (±√(arctan(t)) + \(\sqrt{C_2}\). (c) The solution to the initial value problem is: y = (√(arctan(t)) + 4). (d) The solution to the initial value problem is: y = (-√(arctan(t)) + 9).

(a) To solve the differential equation y' = (y - 3)² cos(t) using separation of variables:

First, rewrite the equation as:

dy / (y - 3)² = cos(t) dt

Now, integrate both sides:

integration of 1 / (y - 3)²dy = integration of cos(t) dt

Integrating the left side:

(-1) / (y - 3) = sin(t) + \(\sqrt{C_1}\)

Solving for y:

1 / (y - 3) = -sin(t) - \(\sqrt{C_1}\)

(y - 3) = (-1) / (-sin(t) - \(\sqrt{C_1}\))

Simplifying:

y = 3 - 1 / (-sin(t) -\(\sqrt{C_1}\))

y = 3 + 1 / (sin(t) + \(\sqrt{C_1}\))

So the general solution to the differential equation is

y = 3 + 1 / (sin(t) + \(\sqrt{C_1}\))

(b) To solve the differential equation dy / dt = 1 / (2y(1 + t²)) using separation of variables:

Separate the variables:

2ydy = 1 / (1 + t²}) dt

Integrate both sides:

integration of 2dy = ∫ 1 / (1 + t²) dt

Integrating the left side:

y² = arctan(t) + \(\sqrt{C_2}\)

Solving for y:

y = (± \(\sqrt{(arctan(t)) }\)+ C₂)

So the general solution to the differential equation is

y =( ±\(\sqrt{(arctan(t)) }\) + \(C_2\)

(c) To solve the differential equation dy / dt = 1 / (2y(1 + t²)) with the initial condition y₀ = 2

Using the general solution from part (b), substitute t = 0 and y = 2:

2 =( ±s\(\sqrt{(arctan(0)) }\) )+ \(C_2\)

2 = (±\(\sqrt{C__2}\))

Taking the positive square root:

2 =( \(\sqrt{C_2}\))

4 = \(C_2\)

Substituting the value of C₂ back into the general solution:

y = (\(\sqrt{(arctan(t))}\) + 4)

So the solution to the initial value problem is:

\(y = \sqrt{(arctan(t)} + 4)\)

(d) To solve the differential equation dy / dt = 1 / (2y(1 + t²})) with the initial condition \(y_0 =( -3)\)

Using the general solution from part (b), substitute t = 0 and y = (-3):

(-3) = ±\(\sqrt{(arctan(0)}\) + \(C_2\)

(-3) = ±\(\sqrt{C_2}\)

Taking the negative square root:

(-3) =\(\sqrt{C_2}\)

9 = \(C_2\)

Substituting the value of \(\sqrt{C_2}\) back into the general solution:

y = (-√(arctan(t) + 9))

So the solution to the initial value problem is

\(y = \sqrt{arctan(t) + 9))}\)

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