The area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b[tex])^x[/tex], where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Here initial area a = 3500[tex]km^2[/tex] ,
Rate of decay = 4.25%= 4.25/100 = 0.0425
Now using exponential decay formula then,
=> [tex]y=a(1-b)^x[/tex] where x=13 years .
=> y = [tex]3500(1-0.0425)^{13}[/tex]
=> y = [tex]3500(0.9575)^{13}[/tex]
=> y = 1990.08 [tex]km^2[/tex]
Hence the area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
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Scores on the GRE (graduate record examination) are normally distributed with a mean of 553 and a standard deviation of 112. Use the 68-95-99.7 rule to find
the percentage of people taking the test who score between 421 and 645
The percentages of people taking the test who scores between 421 and 645 is__%
The percentages of people taking the test who scores between 421 and 645 is: 68 %
How to use the empirical rule of statistics?The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
We are given:
Sample mean: x' = 553
standard deviation; s = 112
Thus:
x' - ns = 421
x' + ns = 645
Where n is the number of standard deviations from the mean. Thus:
553 - 112s = 421
112s = 553 - 421
112s = 132
s = 132/112
s ≈ 1
So 1 standard deviation from the means indicates a percentage of 68%
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Simplify the expression.
2e + tr + 4y + e - y + tr
Answer:
3e + 3y + 2tr
Step-by-step explanation:
2e + tr + 4y + e - y + tr
=> (2e + e) + (tr + tr) + (4y - y)
=> 3e + 2tr + 3y
=> 3e + 3y + 2tr
Answer: The answer is 3e + 3y - 2tr
Step-by-step explanation:
2e + tr + 4y + e - y + tr
=(2e + e) + (tr + tr) + (4y- y)
=3e + 2tr + 3y
=3e + 3y +2tr
Help please -A special safe lets you choose from 5 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there?
Answer:
125
Step-by-step explanation:
the statement " 5 symbols for a 3-symbols- long pass code" in mathematics simply means 5 has a power of 3 or 5^3 = 5×5×5= 125
A student claims that all squares are congruent to each other. is this true or false?
Answer: False.
Step-by-step explanation:
Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. ... This means that they have the same shape, although not necessarily the same size.
There are 19 Keurig pods in the green basket next to the Keurig machine. Maddy, Charlie, and Ben each want coffee. There are five Donut Shop, six Swiss Miss hot chocolate, and 7 Breakfast Blend flavors. Maddy and Charlie each grabbed one Donut Shop pod and two Swiss Miss pods. What is the probability that Ben will get the Donut Shop pod after Maddy or Charlie’s selection?
The probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
There are 5 Donut Shop pods and Maddy and Charlie each took 2, leaving 3 Donut Shop pods in the green basket.
There are 17 pods left in the basket after Maddy and Charlie's selection (5 Donut Shop, 6 Swiss Miss, and 6 Breakfast Blend), so the probability that Ben will get the Donut Shop pod is 3/17.
Therefore, the probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.
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Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton.
Answer:
The probability of choosing a brown egg from the carton is 2/12 or 1/6. This is because there are two brown eggs in the carton and a total of twelve eggs, so the probability of choosing a brown egg is 2/12 or 1/6.
Angles in a Triangle
Answer:
No
Step-by-step explanation:
The angles of a triangle must add up to 180. 140+15+15 = 140 +30 = 170. This is not 170, so no. Hope this helps!
Answer:
It is not possible to draw a triangle with these angles because 140 + 15 + 15 = 170, triangle angles must add up to 180 and 180=170 is a false statement.
Step-by-step explanation:
what is the break even points in coming year?
Help now please math will briain list
According to the given information, the one angle on the straight line inside a circle is 135 then the value of the x = 4 as both angles are supplementary angles.
What are supplementary angles?Supplementary angles are two angles whose sum is 180 degrees. In other words, if we add the measures of two supplementary angles, the result is always 180 degrees.
When two lines intersect, they form four angles at the intersection point. If two of these angles are supplementary, they are called adjacent supplementary angles. In this case, they share a common side and a common vertex, and their non-shared sides form a straight line.
For example, if angle A and angle B are adjacent angles, and angle A measures 120 degrees, then angle B must measure 60 degrees, since 120 + 60 = 180.
According to the given informationIf the two angles are on a straight line, then they are supplementary, meaning their sum is 180 degrees. Therefore, we can set up the equation:
135 + (11x + 1) = 180
Simplifying the left side, we get:
136 + 11x = 180
Subtracting 136 from both sides, we get:
11x = 44
Dividing both sides by 11, we get:
x = 4
Therefore, the value of x is 4.
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i start with y, add 5 and then, double the result
Answer:
2y + 10Step-by-step explanation:
i start with y, add 5 and then, double the result
y add 5
y + 5 double the result
(y + 5) × 2 solve
2y + 10
or
(y + 5) × 2 =
2y + 10
6th grade math whats the surface area
Answer:
416
Step-by-step explanation:
The front and back are triangles
a = 1/2 bh
a = 1/2(12)(8)
a = 48
We times this by 2 to find the front and the back.
96
Bottom
a = lw
a = 10 x 12
a = 12
120
Right and left sides
a = lw
a = 10 x10 = 100
Multiply this by 2 to find the right and the left sides.
200
Add the numbers together:
96 + 120 + 200 = 416
Helping in the name of Jesus.
To find the surface area of a three-dimensional object, you need to add up the area of all its faces.
This can be done using formulas specific to the shape of the object. For example, the surface area of a rectangular prism (a box) can be found using the formula SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Other common three-dimensional shapes include spheres, cones, and cylinders, each with their own unique formulas for finding surface area. So, to answer your question, I would need to know what specific object you are referring to in order to provide an accurate answer about its surface area.
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which ones is a function and not a function
Answer:
No,No,No,Yes,No,Yes
Step-by-step explanation:
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
The purchase price of the anitque dresser purchased by Danielle is $120 and the advertised price is $ 300 after which it was sold on profit of $255. Correct answer:optionA
What is profit?
The extra money is left after paying your business expenses is your profit. Gross profit, operating profit, and net profit are the three primary types of profit. The cost foundation for determining profit or loss when selling a product is the price the buyer pays at the time of purchase, known as the purchase price. The price of a product as advertised for marketing purposes is known as the marketed price.
Let us consider the purchase price of antique dresser with mirror= p
Given that the advertised price= 250% of her purchase price
=[tex]\frac{250}{100}[/tex] of p
=[tex]\frac{250}{100}[/tex] p
=[tex]\frac{250 p}{100}[/tex]
Also given that the selling price which was 15% less than advertised price= $255
advertised price - 15% of advertised price =$255
[tex]\frac{250 p}{100}[/tex] - 15% of [tex]\frac{250 p}{100}[/tex] =$255
[tex]\frac{250p}{100} - \frac{15}{100} of \frac{250p}{100}[/tex] =$255
[tex]\frac{250p}{100} - \frac{3750p}{10000}[/tex] =$255
[tex]\frac{250p}{100} - \frac{375p}{1000}[/tex] =$255
[tex]\frac{2500p - 375p}{1000}[/tex] =$255
[tex]\frac{2125p}{1000}[/tex] =$255
p = [tex]\frac{255 (1000)}{2125}[/tex]
p = $120
The purchasing price is $120
Advertised price =[tex]\frac{250 p}{100}[/tex]
= [tex]\frac{250(120)}{100}[/tex]
= 25 x 12
= $ 300
The Advertised price is $ 300
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School pictures come in 8 in. by 10 in., 5 in. by 7 in., and wallet size 2¼ in. by 3¼ in. Are the pictures similar to each other? Why?
The three sizes of school pictures may feature the same subject, but they are not similar to each other in terms of size and aspect ratio.
The 8 in. by 10 in. size has an aspect ratio of 5:4, which is wider than the 5 in. by 7 in. size that has an aspect ratio of 7:5. The wallet size 2¼ in. by 3¼ in. has an aspect ratio of 9:13, making it even more elongated. This means that the relative proportions of the images are different.
Furthermore, the larger sizes such as 8 in. by 10 in. and 5 in. by 7 in. provide a lot more detail than the wallet size, which is smaller and often used as a miniature version of the larger sizes. The larger sizes also have a higher resolution, making them more suitable for framing and displaying.
Therefore, while the school pictures may depict the same subject, they are not similar in size, aspect ratio, and level of detail.
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Can someone please help me
The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
How to solveThe height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.
Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.
Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:
h_A = radius + center's height
h_A = 85 + 100
h_A = 185 feet
So, the height of point A off the ground is 185 feet.
To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:
h_A = radius * sin(0)
h_A = 85 * 0
h_A = 0
So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
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5. Jack sold the laptop that he ka vong for his business, He purchased It in 2012 for 64,000. The current book value ing of the laptop IS 18,000 Jack Gold it for 28,000- Compte Gain in sale of the laptop. 48 000
The gain on sale of the laptop which Jack purchased in 2012 for $64,000 with a current book value of $18,000 but sold for $28,000 is $10,000.
What is the book value of an asset?The book value of an asset is the difference between the original value or purchase cost and the accumulated depreciation.
Accumulated depreciation represents the depreciation from the purchase date to the current period. It can be determined as the difference between the purchase price and the current value.
The purchase price of the laptop in 2012 = $64,000
Current book value = $18,000
Accumulated depreciation = $46,000 ($64,000 - $18,000)
Sales price = $28,000
Gain on sale = $10,000 ($28,000 - $18,000)
Thus, when the laptop is sold by Jack, he realized a gain of $10,000 because the sales price exceeded the current book value.
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Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 5 comma 3, negative 5 comma negative 2, and 7 comma negative 2
The perimeter of the right triangle is 30 units.
What is perimeter?
In geometry, perimeter refers to the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the sum of the lengths of all the sides of the shape.
To find the perimeter of the right triangle, we need to determine the lengths of its sides first.
Using the distance formula, we can find the lengths of the three sides of the triangle:
Side 1: From (-5, 3) to (-5, -2)
[tex]Length = \sqrt{[(3 - (-2))^2 + (-5 - (-5))^2]} = \sqrt{[5^2]} = 5[/tex]
Side 2: From (-5, -2) to (7, -2)
[tex]Length = \sqrt{[(7 - (-5))^2 + (-2 - (-2))^2]} = \sqrt{[12^2]} = 12[/tex]
Side 3: From (7, -2) to (-5, 3)
[tex]Length = \sqrt{[(-5 - 7)^2 + (3 - (-2))^2]} = \sqrt{[144 + 25]} = \sqrt{[169]} = 13[/tex]
We know that the triangle is a right triangle because two of its sides (Side 2 and Side 3) form a straight line along the x-axis, and the third side (Side 1) is perpendicular to this line.
Therefore, Side 1 is the hypotenuse, and Sides 2 and 3 are the legs of the right triangle.
To find the perimeter, we add up the lengths of all three sides:
Perimeter = Side 1 + Side 2 + Side 3 = 5 + 12 + 13 = 30
Therefore, the perimeter of the right triangle is 30 units.
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Please answer this question, I’ll give brainliest and no chatgpt please!!
Q5. If you heat a 0.45 kg sample of an unknown substance to a temperature of 80 °C then quickly transfer it into a beaker that contains 0.70 kg of water at 15 °C (the specific heat capacity of the water is 4200 J/kg: C), the highest temperature that the sample and water will attain is 21 °C. What is the heat capacity of the sample? [4 marks]
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Answer:
The correct frequency table is table c.
The distance between Eilat and Jerusalem is 292 kilometers. Give this distance in miles. Round the answer to the nearest tenth.
The distance between Eilat and Jerusalem is 181.4 miles.
To convert kilometers to miles, we need to multiply the number of kilometers by 0.621371, which is the conversion factor from kilometers to miles. Therefore, to convert the distance between Eilat and Jerusalem from kilometers to miles, we can use the following formula:
distance in miles = distance in kilometers × 0.621371
Substituting the given distance of 292 kilometers into the formula, we get:
distance in miles = 292 km × 0.621371 = 181.417852 miles
Rounding this answer to the nearest tenth, we get:
distance in miles ≈ 181.4 miles
Therefore, the distance between Eilat and Jerusalem is approximately 181.4 miles.
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Jordan, Jessica, Eloise, and James travel to Europe. They see many famous places.
\
The friends hiked on a trail in the Austrian Alps. They hiked 1.08 kilometers on Monday and 0.94 kilometer on Tuesday.
How many kilometers did they hike in all? Describe how to use the grids to solve the problem. Then use the grids to find the solution.
The total number of kilometers that the friends hiked in all would be 2. 02 km.
How to solve for the total distance ?The total distance that Jordan, Jessica, Eloise, and James hiked in the Austrian Alps, can be found to be :
= Distance on Monday + Distance on Tuesday
= 1. 08 + 0. 94
= 2. 02 km
Using grids, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.
Add them up and you will get 202 cubes which would be 2.02 km.
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You deposited $5,000 in your account earning 2.5 simple interest how long would it take for the balance of the account to earn $1,500 in interest?
To solve this problem, we can use the formula for simple interest:
I = P * r * t
where I is the interest earned, P is the principal amount (the initial deposit), r is the interest rate as a decimal, and t is the time in years.
We want to find how long it will take for the account balance to earn $1,500 in interest, so we can set up the equation:
$1,500 = $5,000 * 0.025 * t
where t is the time in years.
Simplifying this equation, we get:
t = $1,500 / ($5,000 * 0.025)
t = 12 years
Therefore, it will take 12 years for the balance of the account to earn $1,500 in interest
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The probabilities for this problem are given as follows:
Purchase price less than $20,000, repair cost less than $10,000: 45.74% -> about 46%.Repair costs less than $10,000, purchase cost more than $40,000: 20.3 -> about 20%.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of cars with purchase prices less than $20,000 is given as follows:
86 + 67 + 35 = 188.
Of those 188 cars, 86 had repair costs less than $10,000, hence the probability is given as follows:
p = 86/188
p = 0.4574.
The number of cars with repair costs less than $10,000 is given as follows:
86 + 71 + 40 = 197.
Of those, 40 had a purchase price of more than $40,000, hence the probability is given as follows:
p = 40/197
p = 0.203.
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The final counts are:
58 students interested in athletics but not academic clubs, 118 students interested in academic clubs but not athletics, 96 students not interested in academic clubs, 156 students not interested in athletics.How to solveGiven a survey of 240 students, 35% of students were interested in athletics, which is equal to 84 students.
3/5 of students were interested in academic clubs, which is equal to 144 students.
26 students were interested in both athletics and academic clubs.
Using this information, we can fill in the remaining cells of a table to show the number of students in each category.
The final counts are:
58 students interested in athletics but not academic clubs, 118 students interested in academic clubs but not athletics, 96 students not interested in academic clubs, 156 students not interested in athletics.Read more about samples here:
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Help me please, I need help! Thanks
Answer:
5w² + 4
Step-by-step explanation:
there's no like terms, so just write the expression again
nangle
In order to justify your general statement above (to give a reason why it is true), construct the angles A, B
and C of triangle 1 around point M as in the diagram below.
H
Are [MN] and [ML] on the same straight line?
Answer:
MN and ML are on the same straight line.
P = $5000
r = 6.25%
Compounded daily for 5 years
Answer:
Account balance = $6,834.01
Interest accrued = $1,834.01
Step-by-step explanation:
To find the account balance of an initial investment of $5,000 at 6.25% compounded daily for 5 years, use the Compound Interest Formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).As the interest is compounded daily, n = 365.
Therefore, the values to substitute into the formula are:
P = $5,000r = 6.25% = 0.0625n = 365t = 5Substitute the values into the formula and solve for A:
[tex]\implies A=5000\left(1+\dfrac{0.0625}{365}\right)^{365 \cdot 5}[/tex]
[tex]\implies A=5000\left(1.000171232...\right)^{1825}[/tex]
[tex]\implies A=5000\left(1.3668013759...\right)[/tex]
[tex]\implies A=6834.0068795...[/tex]
[tex]\implies A=6834.01\; \sf (2\;d.p.)[/tex]
Therefore, the account balance after 5 years is $6,834.01, and the total amount of interest earned is $1,834.01.
Solve for x.
A) 6
B) 9
9)
D)
15
4
3
5
The value of x in the given chords is determined as 9.
What is the measure of x?
The measure of length x is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
3 (3 + x ) = 4 ( 4 + 5 )
9 + 3x = 36
collect similar terms ang solve for x;
3x = 36 - 9
3x = 27
divide both sides of the equation by 3;
3x/3 = 27/3
x = 9
Thus, the value of x in the given chords is determined by applying chord theorem.
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The figure on the right is a scaled copy of the
figure on the left.
V
U
W
T
H
I
G
J
The side GJ in the big one corresponds to the side WT in the small one.
It's not possible to find the scale factor between the two drawings, because there's no numerical information given to show us the relationship between any pair of corresponding sides. (This information is probably there in the book or on the homework sheet you copied the problem from, but for some strange reason, you didn't include it in what you decided to show us.)
x²+x-72=0 rewrite the equation by completing the square
The solution of the equation written by completing square is (x + 1/2)² = 289/4.
What is completing square?In algebra, the process of "completing the square" is used to transform a quadratic expression into a perfect square trinomial. Using this method, a constant term is either added or subtracted from the quadratic expression to produce a perfect square trinomial that may be factored as the square of a binomial. Solving quadratic equations, locating the vertex of a parabola, and simplifying formulas with square roots all involve the completion of the square.
The value of the equation x² + x = 72 can be written as a completer square by taking half of the coefficient of the x-term.
(1/2)² = 1/4
Add this to both sides of the equation:
x² + x + 1/4 = 72 + 1/4
Now, the LHS is:
(x + 1/2)² = 289/4
x = -1/2 ± (17/2)
Hence, the solution of the equation written by completing square is (x + 1/2)² = 289/4.
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