qwerty
2.8% the answer is 2.8% and b is 2.8%
Mary bought 8 blouses and 3 skirts for a total of $120.00. Kristy bought 5 blouses and 5 skirts at the same prices for a total of $112.50. What is the cost of each blouse and each skirt?
After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the cost of each blouse and skirt:
x be the price of one blouse and y is the price of one skirt.
For a total of $215, Carol purchased 3 skirts and 5 blouses.
5x + 3y = 215
For a total of $135, Ellen purchased 2 skirts and 3 blouses.
3x + 2y = 135
By resolving the equations in the system:
5x + 3y = 215
3x + 2y = 135
We will obtain:
x = $25
y = $30
Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
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Correct question:
Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?
(2)
Each hemisphere has three basic wind systems. The first, at 30( latitude north and south,
is known as the (3).
There, air sinks, warms, and moves toward the
equator from northeast to southwest in the northern hemisphere and from southeast to
northwest in the southern hemisphere. When the air reaches the equator, it rises, then moves
back toward 30( to start the cycle again. These winds from both hemispheres converge at the
equator. They are forced upward, creating an area of (4)
This area
near the equator is called the (5).
The second wind system, called the (6)
flows between 300 and
60 Latitude north and south of the equator. Its circulation pattern is opposite that of the
wind system discussed above. These winds are responsible for the movement of many
weather systems across much of (7)
The third wind system, the (8).
Latitude. In the northern hemisphere, these winds flow from the (9)
to the (10)
lies between the poles and 60(
They flow in the opposite direction in the southern
hemisphere.
Narrow bands of fast, high-altitude, westerly winds called (11)
flow at the boundaries between wind zones in the middle latitudes. These bands of
wind steer weather systems in the middle latitudes. The most important one, the
(12)
separates the polar easterlies from the prevailing westerlies.
(Picture included)
The table shows the results for spinning the spinner 50 times. What
is the relative frequency for the event "spin a 2"?
Experiment Table
Outcome 1 2 3 4
Frequency 12 10 10 18
Number of Trials
50
The relative frequency for the event "spin a 2" is:
(Simplify your answer)
The relative frequency for the event "spin a 2" is 1/5.
What is the relative frequency?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
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Profit is the money made when a business' income is more than its expenditure. Loss is the money lost when a business' expenditure is more than its income. For each of the businesses below, state whether they made a profit or a loss. Business A B C Income £100 £49.85 £21,357 Expenditure £200 £71.24 £7,028
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)
What is percent?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.
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christina's pizza sells pizza by the slice for lunch. today, they sold 76 slices, including 20 slices of pepperoni pizza. what is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?
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
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Which graph shows the line that passes through (21) and is parallel
to a line with a slope of ?
++
o
o
*
+
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.
How to determine an equation of this line?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:
m represent the slope.x and y represent the points.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
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Calculate the Value of x.
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]
suppose you have 4 pairs of socks and 4 pairs of shoes. if you can wear any combination of socks and shoes, including mismatched pairs, how many different possible footwear choices can you make
There are a total of 32 different possible footwear choices that we can make.
Given, The number of pairs of socks = 4
The number of pairs of shoes = 4
We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.
So, We can wear any pair of socks with any pair of shoes including a mismatch.
Thus, for each pair of socks, there are 4 possible pairs of shoes.
And for each pair of shoes, there are 4 possible pairs of socks.
Therefore, we can form,
Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.
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Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
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."
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Find the value of M.
A) 20,
B)10,
C)36,
D)100
In the given parallelogram, The value of M is option B) 10 , so values of given angles is 50°.
What is parallelogram?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°
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3.- cual es la máxima distancia que pueden recorrer sin cambiar de dirección en una pista de patinaje en forma de rombo, si cada lado mide 26 mts y ka diagonal menor 40 mts ?
Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.
what is perimeter ?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.
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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?
What is the value of m ?
Answer:
Step-by-step explanation:
90-28=62
62 is the answer
Three and seven tenths times five
Answer:
6.5
Step-by-step explanation:
3 + (and) 7/10 x 5 = 6.5
Hope this helps!
The prices of petrol in a British and an American
petrol station are shown below.
The conversion rate is $1 = £0.80
What is the price of 1 litre of petrol in the cheaper
petrol station?
Give your answer in pounds (£).
British petrol station
£13.20 for 12 litres
of petrol
American petrol station
$17 for 20 litres
of petrol
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.
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a regular hexagon is truncated to form a regular dodecagon (12-gon) by removing identical isosceles triangles from its six corners. what percent of the area of the original hexagon was removed? express your answer to the nearest tenth.
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%.
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The surface area of the right triangular prism is 376.8 cm²
What is the value of x? Show your work.
In response to the stated question, we may state that As a result, the prism value of x is around 6.432 cm.
what is prism?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.
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7th grade math questions pls help me as soon as possible will give brainlist thingy
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:
1.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.
2.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.
3.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
Interpreting data (Box & Whisker & Histogram) & Review Systems
For questions 1-4 use the graph below to answer the following questions/problems.
1. What is the value of the third quartile shown on the box-and-whisker plot?
2. Determine the interquartile range? Determine the range?
3. How many people were surveyed?
12
4. What is the type of average you can find? Find that average.
The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.
What is value ?Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.
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Please help
What is the value of x?
Enter your answer in the box.
X =
F
E
L
24
25
1
2 3 4 5
x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.
Give a brief account on 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
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5. Use the digits 3, 4, 5, 6, 7 and 8 to complete the statement.
Answer:
Step-by-step explanation:
i don't see a statement but use 7 i guess
Select the true statements. Select the two correct answers. A. 1 . 01 < 0 . 99 1 . 01 < 0 . 99 B. 4 . 5 = 4 . 50 4 . 5 = 4 . 50 C. 3 . 5 < 3 . 39 3 . 5 < 3 . 39 D. 1 . 51 > 1 . 15 1 . 51 > 1 . 15 E. 2 . 09 = 2 . 9
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.
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_____ percent of women in a study reported in the Dove consumer insight perceived their actual beauty to fall short of their ideal.
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.
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A company records the value of a machine used for production at $25,000. As the machine ages, its value depreciates, that is, decreases in value. If the depreciation is estimated to be 20% of the value of the machine at the end of each year, what is the expected value of the machine after 6 years?
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
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Franklin is an ecologist monitoring the catfish population in Athena Lake each year. When he first started monitoring the population one year ago, he estimated that there were 800 catfish in the lake. Today, Franklin estimates the population has decreased to 760 and it will continue decreasing each year.
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).
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A plane is 148 mi north and 167 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the nearest tenth of a degree
Therefore, the pilot should turn by approximately 41.8 degrees to fly directly to the airport.
What is trigonometry?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)
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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°
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A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
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:
the sum of two rational numbers is 85. if one number is 5 more than the other, then what are the numbers?
Answer:
40 and 45
Step-by-step explanation:
let the 2 numbers be x and y with y the larger of the two, then
x + y = 85 → (1)
x = y + 5 → (2)
substitute x = y + 5 into (1)
y + 5 + y = 85
2y + 5 = 85 ( subtract 5 from both sides )
2y = 80 ( divide both sides by 2 )
y = 40
substitute y = 40 into (2)
x = 40 + 5 = 45
the two numbers are 40 and 45
7/3+21/5+7/6=.? How do you solve this?
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.
SOMEONE HELP PLEASE
Kiki runs 4 3/7 miles during the first week of track practice she runs 6 2/3 miles during the second week of track practice. How much longer does kiki run during the second week of track practice than the first week of track practice
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].
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in 2005 the population of a district was 35,700 with a continuous annual growth rate of approximately 4%, what will the population be in 2030 according to the exponential growth function?
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.
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Answer: I got 97,042.7
Step-by-step explanation: