Dennis is growing tomatoes in his backyard. In one row of his garden, he has 8 plants. Each plant is separated from the next plant by 1.5 feet of space. Ignoring the width of each plant stem, what is the distance from the first plant to the last plant, in feet?

The surface area of the square pyramid is 89.4 ft² as the lateral area is  80.4 ft².

The surface area of a square pyramid is calculated by the formula

SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.

In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.

The slant height of a square pyramid is calculated by the formula

s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.

In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is

s = √(3² + (3/2)²)

= √(9 + 2.25)

= √11.25

= 3.35 ft.

The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is

4ℓ = 4 x 3.35 ft x 6 ft

= 80.4 ft².

The surface area of the square pyramid is then

SA = B + 4ℓ

= 9 ft² + 80.4 ft²

= 89.4 ft².

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Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.

To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.

The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.

For Taste, the weighted score is 0.30 * 8.6 = 2.58

For Presentation, the weighted score is 0.35 * 9.8 = 3.43

For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93

For Practicality, the weighted score is 0.10 * 4.1 = 0.41

To find the final score, we add up the weighted scores for all categories:

2.58 + 3.43 + 1.93 + 0.41 = 8.35

Therefore, Gretchen's final score is 8.35 out of 10.

The question is incomplete, below is the complete question given -

Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.

Table -
Category                   Weight      Score

Taste                             30%          8.6

Presentation                 35%          9.8

Use of Ingredients       25%           7.7

Practicality                    10%            4.1

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The equation is 84= h₀ -16t² and

Solving the equation we get the time taken by the object will be √6 seconds.

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be  at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get  x = 8.

When an object is dropped vertically from a platform, its height after

seconds can be estimated with the formula shown.

ℎ=ℎ₀−16t²

where ℎ is the height of the object in feet.

and ℎ₀ is the initial height of the object in feet.

t is the time in seconds after the drop.

If the object reach the height 84 feet then the equation will be,

                     84= h₀ -16t²

If the initial height is 180 feet then the equation will be

                        84 = 180- 16t²

Solving the equation we get,

                       ⇒ 16t² = 180- 84

                        ⇒ 16t² = 96

                       ⇒ t² = 6

                      ⇒ t= ±√6

As time can't be negative so t= √6

Hence solving the equation we get the time taken by the object will be √6 seconds.

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Step-by-step explanation:

To solve for d in the equation d/11 = 14, we can multiply both sides by 11 to isolate d on one side of the equation.

d/11 = 14 (multiply both sides by 11)

d = 11 x 14

Simplifying, we get:

d = 154

Therefore, the solution for d is 154.

The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.

Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.

The expression is (3/125) times something, but the value of that something is missing.

To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:

(3/125) = (3/5³)

Now, let's look at each of the answer choices:

125

If we multiply (3/5³) by 125, we get:

(3/5^3) * 125 = 3/5

Therefore, 125 is not equivalent to (3/125) times something.

1/3 × 125

If we multiply (3/5³) by (1/3 × 125), we get:

(3/5^3) * (1/3 × 125) = 1/5

Therefore, 1/3 × 125 is not equivalent to (3/125) times something.

125 1/3 ×

If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:

125 1/3 = 376/3

If we multiply (3/5³) by 376/3, we get:

(3/5³) ×(376/3) = 2256/125 = 18.048

Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.

125× 3x

If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:

125 ×3x = 375x

Therefore, 125 3x is not equivalent to (3/125) times something.

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According to the table, the complete sentence would be: 96 students chose art as their favorite subject.

To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:

96 students chose art as their favorite subject.

According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.

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Answer:

27 18*3=2*r18/2*3=r9*3=rr=27

Step-by-step explanation:

The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.

To find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.

Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...

To get from the 1st term to the 2nd term, we multiply by 1.

To get from the 2nd term to the 3rd term, we multiply by 1.

To get from the 3rd term to the 4th term, we multiply by 2.

To get from the 4th term to the 5th term, we multiply by 4.

To get from the 5th term to the 6th term, we multiply by 4.

The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.

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every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

How to solve ratio?

To find the ratio of 4 inches to 3 yards, we need to convert both measurements to a common unit of measurement.

Firstly, let's convert the 3 yards to inches, since inches are already given. There are 36 inches in a yard (3 feet in a yard, and 12 inches in a foot), so:

3 yards = 3 x 36 inches = 108 inches

Now we can compare the two measurements:

Ratio of 4 inches to 108 inches = 4/108

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case:

4/108 = 1/27

So, the ratio of 4 inches to 3 yards is 1:27.

This means that for every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

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Answer: What do you mean where is the arc?

Step-by-step explanation:

Answer:

x = 6;

y = 3√3

Step-by-step explanation:

Use trigonometry:

[tex] \ \cos(60°) = \frac{3}{x} [/tex]

Use the property of proportion to find x:

[tex]x = \frac{3}{ \cos(60°) } = \frac{3}{0.5} = 6[/tex]

Use the Pythagorean theorem to find y:

[tex] {y}^{2} = {x}^{2} - {3}^{2} [/tex]

[tex] {y}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]

[tex]y > 0[/tex]

[tex]y = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]

The machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

The cost of a tangible asset is spread out throughout the course of depreciation. It symbolises the asset's value dropping over time as a result of damage, obsolescence, or other circumstances. Depreciation is crucial because it enables firms to account for an asset's cost over the course of its useful life rather than just in the year it was purchased.

Depreciation can be calculated using a number of different approaches, such as the straight-line method, the decreasing balance method, and the sum-of-years' digits method.

The annual depreciation expense is:

Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life in Units

Annual Depreciation Expense = ($84,600 - $6,000) / 393,000

Annual Depreciation Expense = $0.20 per unit

For second year we have:

Second-Year Depreciation = Annual Depreciation Expense x Units Produced in Second Year

Second-Year Depreciation = $0.20 x 33,300

Second-Year Depreciation = $6,660

Now, the year-end book value is:

Accumulated Depreciation = Annual Depreciation Expense x Number of Years

Accumulated Depreciation = $0.20 x 2

Accumulated Depreciation = $0.40 per unit

For:

Accumulated Depreciation = $0.40 x 33,300

Accumulated Depreciation = $13,320

Also,

Book Value = Cost of Asset - Accumulated Depreciation - Salvage Value

Book Value = $84,600 - $13,320 - $6,000

Book Value = $65,280

Hence, the machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

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Answer: w = -13

Step-by-step explanation:

    To solve, we will isolate the variable with inverse operations.

Given:

   4 + w = -9

Subtract 4 from both sides of the equation:

   w = -13

No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.

We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.

The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:

Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6

Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):

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Therefore, the correct option is B. ∠EGF with the angle measure of 138°.

A quadrilateral is a four-sided polygon with four vertices and four angles. It is a closed figure with four straight sides that do not intersect. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. The sum of the interior angles of a quadrilateral is always 360 degrees.

Here,

In an inscribed quadrilateral, opposite angles are supplementary. That is, the sum of the measures of any two opposite angles is 180 degrees. Therefore, to find the angle that has the same measure as ∠EDF, we need to look for the angle that is also opposite ∠EDF in the inscribed quadrilateral.

In the inscribed quadrilateral with points D, E, F, and G, we know that ∠EDF has a measure of 42 degrees. We also know that the opposite angle to ∠EDF is ∠EGF, because they share side EF.

Since opposite angles in an inscribed quadrilateral are supplementary, we can find the measure of ∠EGF by subtracting 42 degrees from 180 degrees:

∠EGF = 180° - ∠EDF

= 180° - 42°

= 138°

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* The probability that Ahmad has to stop at both P and Q is: 7/40

* The probability that Ahmad has to stop at least once is: 27/50

* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.

What is probability ?

The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.

given

We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:

Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10

= 49/200

P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50

The chance that he likewise stopped at P must be determined if he had stopped at Q.

Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.

Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.

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If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2  sin(θ) = οppοsite/hypοtenuse = 2√21/29.

The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.

We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".

Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:

c² = a² + b²

29² = a² + (-5√29)²

29² = a² + 725

a² = 29² - 725

a² = 84

a = √84 = 2√21

Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:

sin(θ) = οppοsite/hypοtenuse = 2√21/29

Therefοre,  sin(θ) equals 2√21/29.

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Complete Question:

Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.

The number of bald eagles in the state during the winter of 1999 would be 34.

The coordinates of the matrix A with the given base S are:

<1, 2, 0, 2>

The coordinates will be a vector of the form:

<x, y, z, k>

Such that these four values are each of the coefficients that affect each one of the matrices in the base respectively.

Then we can write a system of equations like:

x + y + z + k = 5

x - y - z  = 3

x + y = 3

x = 1

We can replace the last equation in the third one to get:

1 + y = 3

y = 3 - 1

y = 2

Now we can replace x and y in the second equation:

1 + 2 - z = 3

z = 1 + 2 - 3

z = 0

And the with the first equation:

1 + 2 + 0 + k = 5

3 + k = 5

k = 5 - 3 = 2

Then the coordinates of the matrix A are:

<1, 2, 0, 2>

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The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.

A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.

To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:

Population after n years = Population before ×(1 + r/100)²

where r is the annual growth rate and n is the number of years.

Substituting the given values, we get:

Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3

Population after 7.3 years = 26,190 * 1.037^7.3

Population after 7.3 years = 26,190 * 1.301

Population after 7.3 years = 34,052.9

Rounding to the nearest hundredth, we get:

Population after 7.3 years = 34,052.90 ≈ 34,052.89

Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

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Answer:

the answer is b

Step-by-step explanation:

Answer:

a. A linear equation would best represent the total cost a shopper will pay for an order.

b. y = .7x + 5 would model this situation.

Answer:

x = [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

8x = [tex]\frac{2}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

24x = 2 ( divide both sides by 24 )

x = [tex]\frac{2}{24}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

I think the answer is B?

Step-by-step explanation:

Answer:

Step-by-step explanation:

just guess if not use the internet

Answer:

w = 6 ft.; l = 9 ft.

Step-by-step explanation:

We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.

Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3

To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.

This gives us 54 = (2w - 3)*w

If we rewrite the equation, we'll see that its quadratic:

[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]

Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.

(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)

Positive:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]

Negative:

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]

We know that we can't have a negative measure, so the width is 6 ft.

Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.

Answer:

awnser is 288 seriously  15 x 12 = 180

and 9 x12 =108 add together is 288

The solution is : (-2,7) is the point of intersection.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

To solve the equations by graphing, use the form y=mx + b to find the slope and y-intercept of each equation. Graph the line and find their intersection point.

y = −2x + 3                                     y = −4x − 1

Slope: -2                                        Slope: -4

Y-int: (0,3)                                      Y-int: (0,-1)

Start at (0,3) and go down            Start at (0,-1) and go down 4 units

2 units and 1 to the right.               and 1 to the right. Connect the points.

Connect the points.

Continue this pattern in either direction for both lines until they intersect each point. The point of intersection (x,y) is the solution to the system of equations.

See attached graph.

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Complete question:

A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically?