if one rectangular lot with 1350' of frontage contains 25 acres, how many acres would the lot next to it contain if it has a 900' frontage and is the same width as the first lot? select one: a. 1.67 acres b. 16.67 acres c. 26.00 acres d. 14.67 acres

Answer:

252

Step-by-step explanation:

(5+22) x (35-27) +\(6^{2}\)

27 x 8 + \(6^{2}\)

27 x 8 + 36

216 + 36

252

Answer: I fixed my answer

252

Hope this helped<3

The value of the trigonometric identities are:

Sin Ф = 20/29

Cos Ф = 21/29

Tan Ф = 20/21

We have,

Sin x = Perpendicular / Hypotenuse

Cos x = Base / Hypotenuse

Tan x = Perpendicular / Base

So,

Sin Ф = 20/29

Cos Ф = 21/29

Tan Ф = 20/21

Thus,

Sin Ф = 20/29

Cos Ф = 21/29

Tan Ф = 20/21

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The desired fuel efficiency of a car two years from now would ideally be improved compared to the current fuel efficiency.

There are several reasons why we would want the fuel efficiency of a car to be better in the future:

Environmental Concerns: Improving fuel efficiency helps reduce carbon emissions and minimize the environmental impact of vehicles. As the world becomes more conscious of climate change and the need to reduce greenhouse gas emissions, enhancing fuel efficiency plays a vital role in mitigating environmental damage.

Energy Conservation: Better fuel efficiency means using less fuel to travel the same distance. With finite energy resources and the need to conserve them, improving fuel efficiency helps reduce the overall energy consumption in transportation, leading to better resource management.

Cost Savings: Increasing fuel efficiency directly translates to lower fuel consumption and reduced expenses for car owners. With rising fuel prices, having a more fuel-efficient car can significantly cut down on fuel costs, saving money for individuals and businesses.

Technological Advancements: As technology progresses, advancements in engine design, aerodynamics, lightweight materials, and alternative energy sources enable the development of more fuel-efficient vehicles. Striving for improved fuel efficiency encourages innovation in the automotive industry, leading to the creation of more sustainable and eco-friendly transportation options.

Government Regulations: Many governments worldwide have implemented fuel efficiency standards and regulations to reduce fuel consumption and emissions. By meeting or exceeding these standards, car manufacturers contribute to a cleaner and more sustainable transportation sector.

Ultimately, aiming for improved fuel efficiency two years from now aligns with the global push for environmental sustainability, energy conservation, cost savings, technological advancements, and adherence to regulatory standards. It benefits both individuals and society as a whole by promoting a greener and more efficient approach to transportation.

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Answer:

x = 5

Step-by-step explanation:

there are 4,200 possible distributions of the 10 different types of cookies among Anthony, Misha, and Lizard, considering the given conditions.

To determine the number of possible distributions of the 10 different types of cookies among Anthony, Misha, and Lizard, we can use combinatorial analysis.

First, let's consider the distribution of 3 cookies to Anthony. Since there are 10 cookies to choose from, the number of ways to select 3 cookies for Anthony is given by the combination formula:

C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = 10 * 9 * 8 / (3 * 2 * 1) = 120

Next, we consider the distribution of 3 cookies to Misha. Since there are 7 remaining cookies after Anthony's selection, the number of ways to select 3 cookies for Misha is:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Finally, the remaining 4 cookies are automatically assigned to Lizard.

To find the total number of possible distributions, we multiply the number of ways to distribute the cookies to Anthony, Misha, and Lizard:

Total number of possible distributions = 120 * 35 = 4,200

Therefore, there are 4,200 possible distributions of the 10 different types of cookies among Anthony, Misha, and Lizard, considering the given conditions.

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Answer:

The value of c² - b² is 352.

Step-by-step explanation:

Given that a, b and c are consecutive odd number. In a simplier way, you can make an expression of b and c in terms of a, as b and c are consecutive numbers which are connected to a :

\(let \: a = a \\ let \: b = a + 2 \\ let \: c = a + 2 + 2 = a + 4\)

e.g

Let a = 1,

b = a + 2

= 1 + 2

= 3 (odd number)

c = a + 4

= 1 + 4

= 5 (odd number)

Then, substitite the expression of a and b into b² - a² = 344, in order to find a :

\( {b}^{2} - {a}^{2} = 344\)

\( {(a + 2)}^{2} - {a}^{2} = 344\)

\( {a}^{2} + 4a + 4 - {a}^{2} = 344\)

\(4a + 4 = 344\)

\(4a = 340\)

\(a = 85\)

Next, we have to substitute the value of a into the expression c² - b² :

\( {(a + 4)}^{2} - {(a + 2)}^{2} \)

\( = {(85 + 4)}^{2} - {(85 + 2)}^{2} \)

\( = {89}^{2} - {87}^{2} \)

\( = 352\)

The coordinate of point k is (-5,0) with the given transformation and the coordinate of point P is (9,-2).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

14)

The K'(-8,6) is become by the rule x - 3 and y + 6

So, x - 3 = -8 → x = -8 + 3 = -5

y + 6 = 6 → y = 0

So the coordinate of point K is (-5,0).

15)

The point P'(1,-2) is translated along the vector {-8,0} so -8 means x - 8 and 0 mean y - 0.

Therefore, x - 8 = 1 → x = 1 + 8 = 9

y - 0 = -2 → y = -2 so coordinate is (9,-2).

Hence "The coordinate of point k is (-5,0) with the given transformation and the coordinate of point P is (9,-2)".

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Answer:

73

Step-by-step explanation:

The total cost of materials and labor for the office space, considering a tile unit cost of P300 and labor cost equal to the materials cost, amounts to P63,000.

To calculate the total cost of materials and labor, we first need to determine the cost of the tiles. Given that the unit cost of a certain tile is P300, we can multiply this by the area of the office space to find the total cost of the tiles. The office space has an area of 63 sqm, so the total cost of the tiles is P300 * 63 = P18,900.

Next, we need to calculate the labor cost, which is 100% of the materials cost. Since the materials cost is P18,900, the labor cost will be equal to P18,900. Therefore, the total cost of labor is also P18,900.

To find the total cost of materials and labor, we add the cost of the tiles (P18,900) and the labor cost (P18,900): P18,900 + P18,900 = P37,800.

Therefore, the total cost of materials and labor for the office space is P37,800.

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The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality among those the student whose first step was incorrect is Luis.

Luis started by subtracting 4.8b from both sides to get 2.4b - 6.5 < -8.1. However, the correct step would be to subtract 4.8b from both sides and keep the inequality sign the same, resulting in 2.4b - 6.5 > -8.1.

Luis made an error by flipping the inequality sign, which is not allowed when subtracting a variable term from both sides of an inequality. The correct approach would have been to subtract 4.8b from both sides while maintaining the original inequality sign.

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Answer:

j = -4/(k - h)

Step-by-step explanation:

h - 4/j = k

use inverse operation

h - 4/j = k

-h         -h

-4/j = k - h

*j      *j

-4 = j( k - h )

/( k - h )  /( k - h )

-4/( k - h ) = j

The coordinates of m with respect to the basis b are  x = [x1 x2 x3]T = [−7/3 −1/3 −1/2]T

To find the coordinates of m = [5 −8 01] with respect to this basis, we must first write the basis elements as matrices.

Therefore, we have b = {[−1 −3 0],[0 −1 1],[0 0 −2]}

The given matrix is  m = [5 −8 01]

To obtain the coordinates of m with respect to the basis b, we perform the following steps. In this context, we are trying to represent the given matrix in terms of the basis matrices.

As a result, we have to utilize the solution for the linear system that is formed by combining the basis matrices and the given matrix.

We set up a linear system of equations with the basis matrices as coefficients and the given matrix as a constant vector.

In this case, we have [b1 b2 b3][x1 x2 x3]T = m

This can be expressed in the following matrix equation form.

[−1 −3 0 0 −1 1 0 0 −2][x1 x2 x3]T = [5 −8 01]

Rearranging the equation, we have

−x1 − 3x2 + 5 = 0

− x2 − 8x3 − 8 = 0

x2 + x3 = 1 − 2x3 = 0

Solving the system of equations, we get

x1 = −7/3

x2 = −1/3

x3 = −1/2

Thus, the coordinates of m with respect to the basis b are  x = [x1 x2 x3]T = [−7/3 −1/3 −1/2]T

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Answer: It is B. RuthAnn will meet her annual goal of $32,523 for retirement with an excess of $20,791.60.

Step-by-step explanation:

Answer:

-17.6,-13.8,-9.4,-3.6,-3.2,13.8

From number line the closer a decimal number is to zero the greater it is

The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.

To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula

z = ( x- μ)/ σ

where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get

z = ( 42,000- 40,000)/ 3,000 = 0.67

Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.

thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.

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The correct question is given below-

A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?

Answer:

it should be either a or b

Answer:

1

Step-by-step explanation:

Anything raised to the power of 0 is 1

If

(2 sin(x) - 1) (2 cos²(x) - 1) = 0

then either

2 sin(x) - 1 = 0   or   2 cos²(x) - 1 = 0

sin(x) = 1/2   or   cos(2x) = 0

The first equation gives two families of solutions,

x = arcsin(1/2) + 2nπ = π/6 + 2nπ

x = π - arcsin(1/2) + 2nπ = 5π/6 + 2nπ

where n is any integer; we get the solutions x = π/6 and x = 5π/6 in the interval 0 ≤ x < 2π when n = 0.

The second equation also gives two families of solutions,

2x = arccos(0) + 2nπ = π/2 + 2nπ

2x = -arccos(0) + 2nπ = -π/2 + 2nπ

Divide both sides by 2 :

x = π/4 + nπ

x = -π/4 + nπ

Then the solutions we want are x = π/4 and x = 5π/4 (when n = 0 and 1 in the first family, respectively) and x = 3π/4 and x = 7π/4 (when n = 1 and 2 in the second family).

We have 6 solutions, so A is the correct choice.

Surface area of the cone is 1589.625 feet²

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called an apex or vertex. A cone is formed by a series of line segments, half-lines, or lines connecting apex that is common to all  points on the base that lie in a plane that does not contain the apex.

Given,

Slant height of the cone l = 24 feet

Radius of the cone r = 13.5 feet

Surface area of cone

= πr² + πrl

= 3.14(13.5)² + 3.14×13.5×24

= 3.14(182.25) + 3.14(324)

= 572.265 + 1017.36

= 1589.625 feet²

Hence,  1589.625 feet² is the surface area of the cone.

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Answer:

d) 1 11/16

Step-by-step explanation:

Given problem,

→ 12 ÷ (2 + 2/3)²

Let's solve the problem,

→ 12 ÷ (2 + 2/3)²

→ 12 ÷ ((6 + 2)/3)²

→ 12 ÷ (8/3)²

→ 12 ÷ (64/9)

→ 12 × (9/64)

→ 108/64

→ 27/16 = 1 11/16

Hence, answer is 1 11/16.

Accοrding tο the prοvided assertiοn, the value οf x is 4.5.

An equilateral triangle has three edges that are all the same length.

In ΔABC

∠B = 90

ABC represents a right angle triangle.

Nοw, apply Pythagοras' theοrem;

(AC)² = (AB)² + (BC) (BC)

(2+x)² = (AB)² +(BC) (BC)

Nοw, in ABCD,

∠D = 90

ABCD is a right-angled triangle.

(AB)² = (AD)² + (BD)².

(AB)² = (2)² + (3) (3)

(AB)² = 4+9

(AB)² = 13..............(2) (2)

Currently, in a BDC;

∠D = 90

(BC)² = (BD)² + (CD)²

(BC)² = (3)² + (x) (x)

(BC)² = x² +9............(3) (3)

Nοw enter the equatiοn (1)

(AB)² = 13

(BC)² = x² + 9

∴ (2 + x) ² = (AB)² + (BC)²

(2 + x)² = 13 + x² + 9

4 + x² + 4x = 13 + x² +9

4x = 18

x = 4.5

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To minimize the use of framing, the rectangular frame should have dimensions of around 9.3 inches by 2.9 inches.

Let's assume the length and width of the rectangular frame be L and W, respectively. The total area of the frame can be expressed as:

Total Area = (L + 3W) * (W + 3L) [adding 1.5 inch of framing to each side]

The opening of the frame is given as 27 square inches:

L * W = 27

We can substitute the value of L from the second equation into the first equation and simplify:

Expanding the brackets and simplifying:

Total Area = 3W² + 27*3 + 81/W + 27/W²

We can now take the derivative of this expression with respect to W and set it to zero to find the value of W that minimizes the total area:

Substituting the value of W back into the equation L * W = 27:

Therefore, the dimensions of the frame should be approximately 9.3 inches by 2.9 inches to minimize the amount of framing used.

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Answer:

You still need to wait two hours.

Step-by-step explanation:

So first of all we need to calculate the total volume.

Which is b.h.d.

so here it's:

1m.2m.0,6m= 1,2m³

+

(1m.2m.(1,4m-0,6m))/2=(2m.1m.0,8m)/2=(1,6m³)/2=0,8m³

=2m³

Then it goes down 20cm in 30 min. so that means it cleared

1m.2m.0,2m=0,4m³

2m³/0,4m³=5

So you need 5 times 30 min to clear up the whole volume.

Since you have already cleared it once now you need to do it 4 more times.

4.30min.=2h

Answer:

x = 11

Step-by-step explanation:

\(x + \frac{10}{5} + 7 = 20\\x + 2 + 7 = 20\\x+9=20\\x=11\)

Espero que estaba fuera de ayuda! #Difundir El Amor <3

Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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Answer:

\(V=\pi r^2h=\pi *6^2*19\) ≈ \(2148.8\)

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