lindsey earn $70 for working 5 hours. how much does she earn for working 12 lawns?
Answer $ 168
as per the question,
money earned for working 5 hours = 70
money earned for working 1 hour = 70/5= 14
money earned for working 12 hours = 12 * 14
money earned for working 12 hours = $168
A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?
Final answer:
The farmer needs to buy 320 linear feet of fence to enclose the rectangular area behind his barn.
Explanation:
Let's represent the width of the rectangle as x. Since the length is three times the width, we can represent the length as 3x. The perimeter of a rectangle is calculated by adding up all four sides, so we have the equation:
2(x + 3x) = 320
Simplifying, we get:
2(4x) = 320
8x = 320
x = 40
So the width of the rectangle is 40 feet, and the length is 3 times that, which is 120 feet. The perimeter is calculated by adding up all four sides: 40 + 120 + 40 + 120 = 320 feet. Therefore, the farmer needs to buy 320 linear feet of fence.
Need the rate of change!!!
Two points: (30, 14) and (34, 17)
What is the equation of this circle in general form?
x² + y² + 8x + 10y + 25 = 0
x2+y2−8x−10y+25=0
x2+y2−8x−10y+37=0
x² + y² + 8x + 10y + 37 = 0
Tis the actual answer :)
A class has 50 students. use the third row of digits in the random number table below to select a simple random sample of three students. if the students are numbered 01 to 50, what are the numbers of the three students selected
To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would use the digits in the third row to determine the numbers of the selected students.
Explanation:To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would start by numbering the students from 01 to 50.
Then, you would use the digits in the third row of the random number table to select the students.
For example, if the digits in the third row are 579362814, you would select the students with the corresponding numbers: 05, 79, and 36.
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Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65. Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket. $$
Answer:
4 Lawns
Step-by-step explanation:
Jenny wants to buy a concert ticket that costs = $65.00
Jenny has $25.00.
She needs more to buy a concert ticket = 65 - 25 = $40.00
For each lawn that she mows she earns = $10.00
For $40 she needs to mow = 40 ÷ 10 = 4 lawns
Jenny needs to mow 4 lawns to be able to buy the concert tickets.
suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is pi/3. what is the length of the third side of the triangle
The length of the third side of the triangle will be 2.65 units.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:
a² + b² – 2ab cos(C) = c²
A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.
Then the length of the third side of the triangle will be
c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)
c² = 4 + 9 – 12 x (1/2)
c² = 13 – 6
c² = 7
c = √7
c = 2.65 units
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A plumbing contractor receives proceeds of $4,713.54 on a 12.5% simple discount note with a face value of $5,000. Find the time of the note in days. (Assume a 360-day year.) Do not round intermediate calculations!
The time of the note in days is calculated using the simple discount formula, and by substituting the values of proceeds, face value, and discount rate, the result is 164.99856 days.
The question involves finding the time in days for which a simple discount note is held, given the proceeds, face value, and discount rate. The note's face value is $5,000 and the proceeds received are $4,713.54. The simple discount rate is 12.5%. Assuming a 360-day year, we need to calculate the time period for the note.
Firstly, we need to determine the amount of the discount, which is the difference between the face value and the proceeds: $5,000 - $4,713.54 = $286.46. The discount, given the simple discount formula, is equal to the face value multiplied by the discount rate and the time (in years). The simple discount formula can be expressed as: Discount = Face Value × Discount Rate × Time. Rearranging this formula to solve for time, we get: Time = Discount ÷ (Face Value × Discount Rate).
Substituting the known values we have: Time = $286.46 ÷ ($5,000 × 0.125) = $286.46 ÷ $625 = 0.458336 years. To convert years to days, we multiply the time in years by the number of days in a year (assuming a 360-day year): 0.458336 years × 360 days/year = 164.99856 days. Since we're instructed not to round intermediate calculations, the time of the note is 164.99856 days.
The sun is 25 degrees above the horizon. find the length of a shadow cast by a building that is 100 feet tall. round your answer to two decimal places. the length of the shadow is ____ feet.
Answer:
214.45 feet.
Step-by-step explanation:
Please find the attachment.
Let x be the length of building's shadow.
We have been given that the sun is 25 degrees above the horizon. The length of the building is 100 feet tall.
We can see from our attachment that the length of the building is opposite side and the length of the shadow is adjacent side for the angle of 25 degrees.
Since tangent relates the opposite side of right triangle with adjacent side, so we can set an equation to find the length of building's shadow as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(25^{\circ})=\frac{100}{x}[/tex]
[tex]x=\frac{100}{\text{tan}(25^{\circ})}[/tex]
[tex]x=\frac{100}{0.466307658155}[/tex]
[tex]x=214.45069\approx 214.45[/tex]
Therefore, the length of shadow cast by the building is 214.45 feet.
Jimmy is a partner in an internet-based coffee supplier. The company offers gourmet coffee beans for $14 per pound and regular coffee beans for $7 per pound. Jimmy is creating a medium-price product that will sell for $9 per pound. The first thing to go into mixing bin was 18 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?
To create a blend that sells for $9 per pound, when Jimmy has already added 18 pounds of the gourmet beans, he needs to add approximately 36 pounds of the regular coffee beans.
Explanation:This is a problem of mixtures in mathematics. Jimmy is attempting to create a new blend of coffee for his business that will have a price point between the regular beans and the gourmet beans.
First, let's understand the goal: A new blend worth $9 per pound. He has already added 18 pounds of gourmet beans which costs $14 per pound. To bring the overall cost down to $9 per pound, we need to add cheaper beans, worth $7 per pound.
Let's denote the weight of the regular beans needed as 'x'. We set up the equation based on weights and costs:
(18*$14 + x*$7) / (18 + x) = $9
Solving this equation, we find x to be around 36 pounds. So, Jimmy should add approximately 36 pounds of the regular beans to his mixture to reach the target price of $9 per pound.
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Factorise x^2 + 3x -40
Which shows a correct order to solve this story problem? Kent and Curtis went to the state fair. They had to pay a total of $7.18 sales tax on everything they bought. They spent $22.50 for each admission ticket and $35.50 altogether for food. They split all the costs evenly. How much did each boy pay? A. Step 1: Calculate the price of 2 admission tickets. Step 2: Add that amount to the amount spent on food and the tax. Step 3: Divide by 2. B. Step 1: Double the amount for 1 admission ticket. Step 2: Take half of the amount spent on food and add the total from Step 1 plus the tax. Step 3: Divide by 2. C. Step 1: Add $22.50 and $35.50. Step 2: Divide the total by 2. Step 3: Add the amount of the tax.
Math question
Algebra 2, Fundamental Theorem of Algebra, Stste the number of complex roots and the possible number of real and imaginary roots for each equation. Then find all roots. One root has been given.
x^6 - 3x^5 + 2x^4 - 6x^3 - 15x^2 + 45x = 0; 3
(if possible please provide work)
Equipment was acquired at the beginning of the year at a cost of $75,720. The equipment was depreciated using the straight-line method based on an estimated useful life of six years and an estimated residual value of $7,920. What was the depreciation expense for the first year?
Final answer:
The annual depreciation expense for the equipment is calculated by subtracting the estimated residual value from the cost to find the depreciable base, and then dividing by the useful life. The first-year depreciation expense is $11,300.
Explanation:
To calculate the depreciation expense for the first year using the straight-line method, we first need to determine the depreciable base of the equipment. The depreciable base is the cost of the asset minus its estimated residual value. For the equipment mentioned, the cost is $75,720 and the estimated residual value is $7,920.
Depreciable base = Cost - Residual Value
= $75,720 - $7,920
= $67,800
Next, we divide the depreciable base by the useful life of the asset to calculate the annual depreciation expense:
Depreciation Expense = Depreciable base / Useful life
= $67,800 / 6 years
= $11,300 per year
Therefore, the depreciation expense for the first year is $11,300.
Hazel has an assortment of red, blue, and green balls. The number of red balls is the number of blue balls. The number of green balls is more than the number of blue balls. In total, she has balls.
An equation created to find the number of blue balls will have?
When finding the number of blue balls in the scenario described, the equation will have x + x + x + 1 = 9, where x represents the number of blue balls.
An equation created to find the number of blue balls will have:
Let x be the number of blue balls.
The equation will be x + x + x + 1 = 9.
Solving the equation, we get x = 2.67.
A trading token is in the shape of a trapezoid and has an area of 25 square centimeters. If the bases are 3 and 7 centimeters, What is the height of the token
Answer:
5 cm
Step-by-step explanation:
The formula for the area of a trapezoid gives a relation that can be used to find the height.
A = 1/2(b1 +b2)h . . . . b1, b2 are base lengths, h is the height
__
Filling in the given information, we have ...
25 cm² = 1/2(3 cm +7 cm)h
25 cm²/(5 cm) = h = 5 cm . . . . . . . divide by the coefficient of h
The height of the token is 5 cm.
Lamar purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Lamar paid.
A jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30o east of north (or 30o ne). how far is he from his house after running 8 miles
We want to find how far is the jogger from his house after he runs a total of 8 miles, we will see that the distance is equal to 7 miles.
So we need to define a coordinate axis, the point (0, 0) will be the jogger's house (where he/she starts). North is the positive y-axis and East is the positive x-axis.
Then the jogger starts at (0, 0).
Then he ran 3 miles due East, so the new position is:
(0, 0) + (3mi, 0) = (3mi, 0)
Then he ran 5 miles at 30° East of North (or 60° North of East).
The components are:
x-component = 5mi*cos(60°) = 2.5 miy-component = 5mi*sin(60°) = 4.33 miThen the new position is:
(3mi, 0) + (2.5mi, 4.33 mi) = (5.5mi, 4.33 mi)
The distance to the jogger's house is just the magnitude of that final vector, which is:
|| (5.5mi, 4.33 mi) || = √( (5.5mi)^2 + (4.33mi)^2) = 7mi
So the jogger is at 7 miles from his/her house.
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The jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast after running 8 miles.
Explanation:To find how far the jogger is from his house after running 8 miles, we need to calculate the resultant displacement. The jogger ran 3 miles due east, so his displacement in the east direction is 3 miles. Then, he ran 5 miles at a heading of 30° east of north (or 30° NE). We can split this displacement into the north and east components. The east component can be calculated as 5 miles * cos(30°) = 5 miles * 0.866 = 4.33 miles. The north component can be calculated as 5 miles * sin(30°) = 5 miles * 0.5 = 2.5 miles.
To calculate the resultant displacement, we can use the Pythagorean theorem. The east and north components form a right triangle, with the resultant displacement as the hypotenuse. The magnitude of the resultant displacement can be found as √(3^2 + 4.33^2 + 2.5^2) = √(9 + 18.7489 + 6.25) = √33.9989 = 5.83 miles. The direction of the resultant displacement can be found using trigonometry. tan(θ) = opposite/adjacent = (2.5 miles + 3 miles)/(4.33 miles) = 5.5/4.33. Taking the arctan of both sides, θ = arctan(5.5/4.33) = 51.83°. Therefore, the jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast.
Why do the functions f(x) = sin−1(x) and g(x) = cos−1(x) have different ranges?
In this exercise we want to explain why two more similar functions have different ranges, like this:
the values of the range are different because the domain in which the inverse function exists are different .
In this exercise we know that we are dealing with two distinct functions, like this:
What is the function of sine?The sine function is considered an odd function, as there is a symmetry in the graph with respect to the bisector of the odd quadrants. When a function is considered odd, we have that f (x) = -f (x), that is, sin (-x) = -sin (x).
What is the function of cosine?Cosine is a trigonometric function, used in a right triangle to define the ratio of the side adjacent to and the hypotenuse of this triangle.
So we can see that the reason the two functions have different ranges is associated with them having different domains.
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when is a rectangle a square?
a) when its sides are parallel
b) when its angles are right angles
c) when its sides are congruent
d) when its angles are convex angles
A rectangle becomes a square when all of its sides are congruent, which is the defining characteristic that differentiates it from a rectangle. While rectangles do share other attributes such as parallel sides, right angles, and convex angles, these do not specifically define a square.
A rectangle becomes a square when all of its sides are congruent. This by definition means that all four sides of the shape are of equal length. While rectangles do have parallel sides and right angles, these characteristics alone do not suffice to differentiate a square from a rectangle, as rectangles also have these attributes. In the case of convex angles, both squares and rectangles have angles that are convex, so this also cannot be used to distinguish a square from a rectangle.
To specifically address the options provided:
a) when its sides are parallel: This is true for both rectangles and squares, but it doesn't make a rectangle a square.b) when its angles are right angles: Again, both shapes share this characteristic so it doesn't define a square specifically.c) when its sides are congruent: This is the defining characteristic of a square compared to a rectangle.d) when its angles are convex angles: Both rectangles and squares have convex angles, so this does not define a square.Therefore, the most accurate answer is (c) when its sides are congruent.
The lines shown below are parallel. If the green line has a slope of -2, what is the slope of the red line?
what is the perimeter of a right trianglr whose hypotenuse is the line segment A(-6,4) B(2,-1)
A coyote 43 mph while rabbit can man up to 35 mph right to equivalent expressions in then find how many more miles a coyote can run in six hours then a rabbit these rates
Answer:
(6x43)+(6x35)
6•43+6•35
48 miles
Step-by-step explanation:
Find equations for the tangent plane and the normal line at point upper p 0(3 comma 5 comma 0) on the surface negative 7 cosine left parenthesis pi x right parenthesis plus 3 x squared y plus 5 e superscript xz baseline plus yz equals 147.
Jaws made his figure from six congruent squares the edge of each square was 8 inches which figure did Josh construct what is the surface area of his figure
Will someone please do number 8 for me ?
In 33,294 how is the value of the 3 in the ten thousands place related to the value of the 3 in the thousands place ?
The value of the 3 in the ten thousands place is 30,000, while the value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number.
Explanation:The value of the 3 in the ten thousands place in 33,294 is 30,000. The value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number. In this case, the 3 in the ten thousands place is ten times greater than the 3 in the thousands place.
A building in san fransico is shaped like a square pyramid. It has a slant height of 856.1 feet and each side of its base is 145 feet long. Find the lateral area of the building.
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
find the mean and median of these numbers 14, 3, 15, 4, 3, 11