what is the solution set for this inequality -8x + 40 > -16

Answer:

To add these fractions, we need to find a common denominator. The least common multiple of 3, 5, and 6 is 30, so we can convert each fraction to an equivalent fraction with a denominator of 30:

7/3 = 70/30

21/5 = 126/30

7/6 = 35/30

Now we can add the fractions:

7/3 + 21/5 + 7/6 = 70/30 + 126/30 + 35/30

Combining the numerators, we get:

= (70 + 126 + 35) / 30

= 231 / 30

Simplifying this fraction by dividing the numerator and denominator by their greatest common factor, which is 3, we get:

= 77 / 10

Therefore, the sum of the fractions 7/3, 21/5, and 7/6 is equal to 77/10.

0%.

The area of a regular hexagon is given by A = (3√3/2)s2, where s is the length of one side of the hexagon. To calculate the percent of the area of the original hexagon that was removed, we need to calculate the area of the dodecagon and subtract it from the area of the hexagon.

The area of a regular dodecagon is given by A = 3(3 + 2√3)s2, where s is the length of one side of the dodecagon.

Let's assume that the side length of the original hexagon is s, and the side length of the resulting dodecagon is sd. Since each of the isosceles triangles removed has base length of s and height of s/2, we can find the side length of the dodecagon as sd = √3s.

Substituting this into the area formula for the dodecagon, we get:
Ad = 3(3 + 2√3)sd2

Ad = 3(3 + 2√3) (√3s)2

Ad = 3(3 + 2√3)(3s2)

Ad = 27s2

Therefore, the area of the dodecagon is 27 times the area of the original hexagon.

The percent of the area of the original hexagon that was removed is given by the following formula:
Percent removed = 100 x (Ahex - Adod) / Ahex

Percent removed = 100 x (Ahex - 27Ahex) / Ahex

Percent removed = 100 x (1 - 27) / 1

Percent removed = 100 x (-26) / 1

Percent removed = -2600 / 1

Percent removed = -2600%

Since the percent of the area of the original hexagon that was removed cannot be negative, the correct answer is 0%.

Learn more about hexagon

brainly.com/question/3295271

#SPJ11

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.

given

The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.

Given that the sides are each 26 metres long, the rhombus's perimeter would be:

Perimeter: (4 x 26) = 104 metres

But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.

Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.

To know more about perimeter visit:

https://brainly.com/question/6465134

#SPJ1

The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?

The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

What is variability?

To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.

To calculate the range, we subtract the smallest value from the largest value:

Largest value: 58

Smallest value: 10

Range = Largest value - Smallest value = 58 - 10 = 48

Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

To know more about variability, visit:

https://brainly.com/question/17344045

#SPJ1

Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.

We have, a runner Kiki and she runs on track for practice. In first week,

Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]

which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,

Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]

After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].

taking least common multiple of (3,7)= 21

=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]

[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].

Hence, required distance value is

[tex]3\frac{2}{21} [/tex].

For more information about distance, visit :

https://brainly.com/question/28551043

#SPJ4

Answer:

[tex]\large\boxed{\mathtt{x=44^{\circ}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of x.}[/tex]

[tex]\textsf{We should know that} \ \angle \textsf{CAB is an Interior Angle.}[/tex]

[tex]\large\underline{\textsf{What is an Interior Angle?}}[/tex]

[tex]\textsf{An Interior Angle is any angle that is inside of a circle. It's formed by 2 Chords.}[/tex]

[tex]\large\underline{\textsf{What is a Chord?}}[/tex]

[tex]\textsf{A Chord is any line segment inside of a circle. Its' endpoints are on the circumference.}[/tex]

[tex]\textsf{Because Interior Angles are formed by Chords, the arc within its endpoints is}[/tex]

[tex]\textsf{half of the measurement of the Interior Angle.}[/tex]

[tex]\large\underline{\textsf{For this problem;}}[/tex]

[tex]\mathtt{x=\frac{1}{2} \widehat{BC}}[/tex]

[tex]\textsf{We can't find x right away. We should find} \ \mathtt{ \widehat{BC}} \ \textsf{first.}[/tex]

[tex]\textsf{We are given} \ \mathtt{\widehat{AC} = 92^{\circ}.}[/tex]

[tex]\textsf{The Arcs around a circle add up to 360}^{\circ}.[/tex]

[tex]\overline{AB} \ \textsf{is a diameter. The arc will equal 180}^{\circ}.[/tex]

[tex]\large\underline{\textsf{Solve for BC;}}[/tex]

[tex]\mathtt{92^{\circ}+180^{\circ}+\widehat{BC} = 360^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]

[tex]\mathtt{272^{\circ}+\widehat{BC} = 360^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 272 from both sides of the equation:}}[/tex]

[tex]\mathtt{\widehat{BC} = 88^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Remember that;}}[/tex]

[tex]\mathtt{x=\frac{1}{2} \widehat{BC}}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{x=\frac{1}{2} (88^{\circ})}[/tex]

[tex]\large\underline{\textsf{Multiply:}}[/tex]

[tex]\large\boxed{\mathtt{x=44^{\circ}}}[/tex]

Answer:

6.5

Step-by-step explanation:

3 + (and) 7/10 x 5 = 6.5

Hope this helps!

To word his guarantee for free replacement of tires, the mechanic needs to determine the minimum life expectancy that the tires must meet in order to replace approximately 10% of them.

Since the life expectancy of the tires is normally distributed, we can use the standard normal distribution and the z-score formula to determine the minimum life expectancy that corresponds to a probability of 10%:

z = (x - μ) / σ

where z is the z-score, x is the minimum life expectancy, μ is the mean life expectancy of 24,000 miles, and σ is the standard deviation of 2700 miles.

Solving for x, we get:

x = zσ + μ

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a probability of 10%, which is approximately -1.28. Plugging this into the formula, we get:

x = (-1.28) * 2700 + 24000

x ≈ 20,856 miles

Therefore, the mechanic should guarantee free replacement of tires that wear out before reaching a mileage of approximately 20,856 miles, in order to replace approximately 10% of the tires.

To learn more about distribution click on,

https://brainly.com/question/17135573

#SPJ4

In response to the stated question, we may state that As a result, the prism value of x is around 6.432 cm.

A prism is a polyhedron with either an n-sided polygonal basis, a second base that is a shifted copy of the original base, and n extra faces (essentially all parallelograms), with two connecting the corresponding sides of the base. Any cross sections those are parallel to the base are translations of it. A prism is a three separate, solid, three-dimensional object with two faces. It has the same merge, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with out any bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by planes that are obliquely oriented to one another. A typical prism has two triangular faces and parallel square faces. They are made of either glass or metal.

Two congruent triangles and three rectangular faces make up the right triangular prism.

L is the length of the rectangular faces.

W is the width of the rectangular faces.

H is the height of the rectangular faces and the prism.

B is the triangle's base.

x is the height of the triangles.

SA = 2B + PH

B = 1/2 * base * height

B = 1/2 * 13 cm * x = 6.5x cm²

P = 13 cm + 5 cm + x = 18 cm + x

SA = 2B + PH

376.8 cm² = 2(6.5x cm²) + (18 cm + x)(12 cm)

376.8 cm² = 13x cm² + (18 cm)(12 cm) + 12x cm²

376.8 cm² = 25x cm² + 216 cm²

25x cm² = 376.8 cm² - 216 cm²

25x cm² = 160.8 cm²

x = 6.432 cm

As a result, the value of x is around 6.432 cm.

To know more about prism visit:

https://brainly.com/question/27914026

#SPJ1

The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

Learn more about Experimental probability here

brainly.com/question/30694293

#SPJ4

The circumference of a gazebo is 47.1 ft

To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).

Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft

To know more on the topic of circumference, click here:

https://brainly.com/question/28757341

#SPJ11

For each of the businesses below:

Business A: Loss (Income £100 - Expenditure £200 = -£100)

Business B: Loss (Income £49.85 - Expenditure £71.24 = -£21.39)

Business C: Profit (Income £21,357 - Expenditure £7,028 = £14,329)

Percent is a term used to describe a fraction or ratio as a portion of 100. It is commonly denoted by the symbol %, which means "per hundred." For example, the percentage 50% means 50 out of 100 or 0.5 as a fraction. Percentages are often used to express change, growth, or comparison between different quantities. Percentages are commonly used in many fields, including finance, science, and statistics, to express values in a more convenient and easily interpretable way.

Here,

Business A:

Income = £100

Expenditure = £200

Profit/Loss = Income - Expenditure = £100 - £200 = -£100

Since the result is negative, the business made a loss.

Business B:

Income = £49.85

Expenditure = £71.24

Profit/Loss = Income - Expenditure = £49.85 - £71.24 = -£21.39

Since the result is negative, the business made a loss.

Business C:

Income = £21,357

Expenditure = £7,028

Profit/Loss = Income - Expenditure = £21,357 - £7,028 = £14,329

Since the result is positive, the business made a profit.

To know more about percent,

https://brainly.com/question/29172752

#SPJ1

Answer:

Step-by-step explanation:

90-28=62

62 is the answer

The true statements are:

B. 4.5 = 4.50 (both sides are equal to 4.5, with the same number of significant figures)

D. 1.51 > 1.15 (1.51 is greater than 1.15)

What is system of inequalities ?

A system of inequalities is a set of two or more inequalities with one or more variables. The solution to a system of inequalities is the set of all possible values of the variables that satisfy all the inequalities in the system simultaneously. In other words, it is the intersection of the solution sets of each individual inequality in the system.

According to the question:
The two correct statements are B and D.

B is true because trailing zeros after a decimal point do not change the value of a number, so 4.5 is equal to 4.50.

D is true because 1.51 is greater than 1.15, as the digits to the right of the decimal point represent fractions of a whole number, so 0.51 is greater than 0.15.

A is false because 1.01 is greater than 0.99.

C is false because 3.5 is greater than 3.39.

E is false because 2.09 is not equal to 2.9.

To know more about inequalities visit:

brainly.com/question/29785389

#SPJ1

A graph that shows the line that passes through (-8, 1) and is parallel to a line with a slope of 1/2 is: B. graph B.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-8, 1), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 1/2(x - (-8))

y - 1 = 1/2(x + 8)

y - 1 = x/2 + 4

y = x/2 + 5

Read more on slope here: brainly.com/question/23086745

#SPJ1

The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

for such more question on population

https://brainly.com/question/25630111

#SPJ11

Answer: I got 97,042.7

Step-by-step explanation:

Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It has applications in various fields, such as engineering, physics, architecture, and astronomy. Trigonometry is based on the use of six fundamental trigonometric functions, which are sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the ratios of the sides of a right triangle. In a right triangle, one angle is a right angle, which measures 90 degrees, and the other two angles are acute angles, which are less than 90 degrees. The three sides of a right triangle are called the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the longest side, and it is always opposite to the right angle. The adjacent side is the side that is adjacent to the angle of interest, and the opposite side is the side that is opposite to the angle of interest.

Here,

We can use trigonometry to find the angle x that the pilot should turn in order to fly directly to the airport.

First, let's draw a diagram of the situation:

A(airport)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

|        \

|         \

|          \

P         x mi

In the diagram, P represents the position of the plane, which is 148 miles north and 167 miles east of the airport A. The line labeled "x mi" represents the distance that the plane needs to fly in order to reach the airport, and the angle x is the angle between the line x mi and the line representing the eastward direction.

To find x, we can use the trigonometric ratio for tangent (tan):

tan(x) = opposite/adjacent

In this case, the opposite side is 148 miles (the distance north of the airport) and the adjacent side is 167 miles (the distance east of the airport). Therefore:

tan(x) = 148/167

Using a calculator, we can find that:

tan(x) ≈ 0.8868

To find x, we need to take the arctangent (tan⁻¹) of both sides:

x = tan⁻¹(0.8868)

Using a calculator, we find that:

x ≈ 41.8°

To know more about trigonometry,

https://brainly.com/question/26719838

#SPJ1

The exponential model for the population of catfish in Athena Lake is:

P(t) = 800 × e^{-0.0513t}

What is exponential ?

an exponential function is a function of the form:

f(x) = a^{x}

where a is a positive constant called the base, and x is the exponent. The base represents the factor being repeatedly multiplied, while the exponent represents the number of times the base is being multiplied by itself.

To model the decreasing population of catfish in Athena Lake, we can use an exponential function of the form:

P(t) = P0 × e^{-rt}

where:

P(t) is the population at time t

P0 is the initial population

r is the annual growth rate (in this case, a negative value representing a decreasing population)

e is the mathematical constant e (approximately 2.71828...)

t is the time elapsed (measured in years)

In this case, we know that the initial population P0 is 800, and that the current population P(1) is 760 (since Franklin started monitoring one year ago and estimates the population has decreased to 760). So we can use these values to solve for the annual growth rate r:

760 = 800 × e^{-r}

Dividing both sides by 800, we get:

0.95 = e^{-r}

Taking the natural logarithm (ln) of both sides, we get:

ln(0.95) = -r

Solving for r, we get:

r ≈ 0.0513

So the exponential model for the population of catfish in Athena Lake is:

P(t) = 800 × e^{-0.0513t}

where t is the time elapsed (measured in years).

To learn more about exponential visit the link:

https://brainly.com/question/11975096

#SPJ9

Answer:

A = 21 units²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height between parallel sides )

here b = 7 and h = 3 , then

A = 7 × 3 = 21 units²

The price of 1 liter of petrol at the cheaper petrol station is £0.68.

What is the conversion rate?

Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. Your conversion rate would be 5%, for instance, if you had 50 conversions out of 1,000 interactions, as 50 divided by 1,000 equals 5%.

Here, we have

Given: The prices of petrol in a British and an American petrol station are shown below. The conversion rate is $1 = £0.80.

We have to find the price of 1 liter of petrol in the cheaper petrol station.

$1 = £0.80

= £13.20×($1/£0.80)

= $16.5

For British petrol station

12 liter of petrol = $16.5

1 liter = $16.5/12

1 liter = $1.375

For American petrol station

20 liters of petrol = $17

1 liter = $17/20

1 liter = $0.85

The price of cheaper petrol from American petrol stations = $0.85× (£0.80/$1)

= £0.68

Hence, the price of 1 liter of petrol at the cheaper petrol station is £0.68.

To learn more about the conversion rate from the given link

https://brainly.com/question/29895939

#SPJ1

We can use the fact that the ratio of the corresponding lengths in two similar shapes is equal to the ratio of their corresponding surface areas. Since we are looking for the surface area of a similar cone with radius 9 inches, we need to find the ratio of the surface area of that cone to the surface area of the original cone with radius 3 inches.

The surface area of a cone is given by:

surface area = πr(r + l)

where r is the radius and l is the slant height.

For the original cone with radius 3 inches and slant height 12 inches, we have:

surface area of original cone = π(3)(3 + 12) = 45π

For the similar cone with radius 9 inches, we can find the slant height using the fact that the slant height and radius are proportional in similar cones. Specifically, the ratio of the slant heights is equal to the ratio of the radii. Therefore:

slant height of similar cone = (9/3)(12) = 36 inches

Using this slant height and the radius of 9 inches, we can find the surface area of the similar cone:

surface area of similar cone = π(9)(9 + 36) = 405π

Finally, we can find the ratio of the surface areas:

ratio of surface areas = surface area of similar cone / surface area of original cone

= (405π) / (45π)

= 9

Therefore, the surface area of the similar cone is 9 times the surface area of the original cone. The exact surface area of the similar cone is 9 times the surface area of the original cone, or:

9 × 45π = 405π square inches

Answer:405pi in^2

Step-by-step explanation:

The percentage of women in a study reported in the Dove consumer insight perceived their actual beauty to fall short of their ideal is 96%.

Explanation:

The percentage of women in a study reported in the Dove consumer insight perceived their actual beauty to fall short of their ideal is 96%. There is a prevalent stereotype in society that women should look a certain way, such as being thin and having flawless skin, which can cause women to feel self-conscious and dissatisfied with their appearance. Dove's mission is to help women feel more confident and happy in their skin, regardless of their size or skin type.

To that aim, they conducted a study where 96% of women perceived their actual beauty to fall short of their ideal. Dove's Real Beauty campaign has been very popular in recent years, encouraging women to embrace their natural beauty and feel proud of who they are.

To learn more about percentage  visit:https://brainly.com/question/29306119

#SPJ11

The relative frequency for the event "spin a 2" is 1/5.

Relative frequency measures how often a value appears relative to the sum of the total values.

In order to determine the relative frequency of spinning a 2, divide the frequency of spinning a two by the total number of trials.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign that is used to represent division is ÷.

Relative frequency = number of times a two was spun / total number of trials

= 10 / 50 = 1/5

To learn more about relative frequency, please check: https://brainly.com/question/26577861

#SPJ1

Answer:

Step-by-step explanation:

i don't see a statement but use 7 i guess

Answer:

There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).

Step-by-step explanation:

In the given parallelogram, The value of M is option B) 10 , so values of given angles is 50°.

Parallelogram is type of quadrilateral with two pairs of parallel sides.

The opposite sides of  parallelogram are congruent in length.

The opposite angles of parallelogram are congruent in measure.

The adjacent angles of parallelogram are supplementary (add up to 180 degrees).

The area of parallelogram can be calculated by multiplying the length of its base by its height.

Since ABCD is  parallelogram, then opposite angles are congruent. Therefore, we have:

∠ABD = ∠ABC = 5M° (opposite angles in a parallelogram)

∠ABD = ∠CBD (alternate interior angles formed by transversal BD)

∠CBD = ∠BCD = 3M+20° (opposite angles in a parallelogram)

Thus, we have:

5M° = ∠ABD = ∠CBD = 3M+20°

Solving for M, we get:

5M° - 3M - 20° = 0

2M = 20°

M = 10°

To know more about alternate interior angles visit:

https://brainly.com/question/29114209

#SPJ1

x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.

The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².

It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.

Given,

DF = 24

DE = 25

Using Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

25² = x² + 24²

x² = 25² - 24²

x² = 625 - 576

x² = 49

x = √49

x = 7

To know more about Pythagoras theorem, visit:

https://brainly.com/question/343682

#SPJ1

Answer:r=25

Step-by-step explanation: he spends 96$ on 12 pairs of gloves and 25 dollars per 1 rake.  thus r equals 25

Answer:

See below answer of each.

Step-by-step explanation:

Let's assume the cost of one small popcorn to be 'x'.

Each friend bought one ticket and one small popcorn, so the cost of one ticket and one small popcorn is $7.50 + x.

The total amount spent by 8 friends is $83.60.

Therefore, we can set up the following equation:

8(7.50 + x) = 83.60

Simplifying the equation, we get:

60 + 8x = 83.60

8x = 23.60

x = 2.95

Therefore, the cost of one small popcorn is $2.95.

The equation to represent the situation is:

Total cost = Initial cost + (Cost per mile x Number of miles)

$24.25 = $3.00 + ($2.50 x m)

where m represents the number of miles to Jeremiah's house.

Let's start by setting up the equation for the total cost of the gloves:

12 pairs of gloves x $8 per pair = $96

We know that the gardener spent a total of $300 on both rakes and gloves, so we can set up an equation:

12r + $96 = $300

Now we can solve for r:

12r = $204

r = $17

Therefore, the cost of 1 rake is $17.

The equation that models the situation is:

12($17) + $96 = $300

The expected value of the machine after 6 years is approximately $4086.

To find the value of the machine after each year, we can use the formula:

Vn = V0 x (1 - r)ⁿ

where Vn is the value of the machine at the end of year n, V0 is the initial value of the machine, r is the depreciation rate (0.20 in this case), and n is the number of years.

For the first year, we have:

V1 = 25000 x (1 - 0.20)¹ = 20000

For the second year, we have:

V2 = 25000 x (1 - 0.20)² = 16000

Continuing this pattern, we find that the value of the machine at the end of the sixth year is:

V6 = 25000 x (1 - 0.20)⁶ = 4085.76

Find out more about depreciation rates

brainly.com/question/28734384

#SPJ4