[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]
a certain forest covers an area of 1700km^(2). Suppose that each year this area descreases by 7.5%. What will the area be after 11 years?
round your answer to the nearest square kilometer.
The area of the forest after 11 years will be 298 km².
To calculate the area of the forest after 11 years, we need to decrease the initial area of 1700 km² by 7.5% each year for 11 years.
First, let's calculate the decrease in area for one year:
Decrease in area for one year = 7.5% of 1700 km²
7.5% of 1700 km² = (7.5/100) × 1700 km²
= 127.5 km²
Now, we can calculate the total decrease in area over 11 years:
Total decrease in area over 11 years = 11 × 127.5 km² = 1402.5 km²
Finally, we can subtract the total decrease in area from the initial area to get the area of the forest after 11 years;
Area of the forest after 11 years = Initial area - Total decrease in area
= 1700 km² - 1402.5 km²
= 297.5 km²
Therefore, Rounding to the nearest square kilometer, the area of the forest after 11 years will be approximately 298 km².
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A bushel of apples costs $15.00 in the U.S. The same apples cost 1,600 yen in Japan. If the exchange rate is 80 yen per dollar, what is the real exchange rate? Is there a possibility for arbitrage? Explain and defend your answer.
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
We have,
To find the real exchange rate, we need to compare the price of apples in the two countries in terms of their respective currencies.
In the U.S., a bushel of apples costs $15.00.
In Japan, the same apples cost 1,600 yen.
Using the exchange rate of 80 yen per dollar, we can convert the cost in yen to dollars:
1,600 yen / 80 yen per dollar
= $20.00
So, the price of a bushel of apples in Japan is equivalent to $20.00 in the U.S.
The real exchange rate is the ratio of the prices of the same goods in two different countries, taking into account the exchange rate.
In this case, the real exchange rate is:
Real exchange rate = Price in U.S. / Price in Japan
= $15.00 / $20.00
= 0.75
This means that it takes 0.75 U.S. dollars to buy the same goods in Japan which would cost 1 Japanese yen.
To determine if there is an arbitrage opportunity, we need to compare the real exchange rate with the actual exchange rate.
If the real exchange rate is greater than the actual exchange rate, there is an arbitrage opportunity for someone to buy the good in one country and sell it in another country for a profit.
However, if the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
In this case,
The real exchange rate is 0.75, while the actual exchange rate is 80 yen per dollar, or 0.0125.
Since the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
Therefore,
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
5 15 two and a half
7
At this rate, how much sauce and oregano will be needed to make 7 servings?
The recipe will need 17 cups of sauce and three and a half teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and 5 teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.
The recipe will need 17 cups of sauce and 5 teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings. The correct option is C.
How to calculate the valueThe sauce to oregano ratio for five servings is equal to 15 cups and 2.5 teaspoons, respectively. For a single portion of the recipe, this computes to 3 cups and 0.5 teaspoons.
It should be noted that to attain the correct amount needed for seven servings, simply multiply each part of the ratio by seven. Consequently, you should use 21 cups of sauce and three and one-half teaspoons of oregano. All together, this recipe requires 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.
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What is the meaning of "there is some [tex]k \in I[/tex] such that [tex]D_{i}\subseteq D_{k}[/tex] and [tex]D_{j}\subseteq D_{k}[/tex]?
The given statement "there is some k∈I such that [tex]D_{i}[/tex]⊆[tex]D_{k}[/tex] and [tex]D_{j}[/tex]⊆[tex]D_{k}[/tex]means that there is a set [tex]D_{k}[/tex] in a collection of sets I that contains all the elements of both sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex].
For example, let's say we have a collection of sets I that includes sets A, B, C, D, E, and F. If we have two sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex], where [tex]D_{i}[/tex] is the set of all even numbers, and [tex]D_{j}[/tex] is the set of all positive integers less than or equal to 10, then we can say that there exists a set [tex]D_{k}[/tex] in I that contains both [tex]D_{i}[/tex]and [tex]D_{j}[/tex] as subsets.
In this case, the set [tex]D_{k}[/tex] could be the set of all even positive integers less than or equal to 10. This set contains all the elements of [tex]D_{i}[/tex] and [tex]D_{j}[/tex], making them both subsets of [tex]D_{k}[/tex]. The statement "there is some k belongs I such that [tex]D_{i}[/tex] is a subset of [tex]D_{k}[/tex] and [tex]D_{j}[/tex] is a subset of [tex]D_{k}[/tex]" is a way to express this relationship between the sets.
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A painter needs 3/8 gallon of green paint to finish a job. He has 5/8 gallon of red paint. He has 1/2 gallon more red paint than green paint. Can he finish the job?
Answer: 17/24 for both jobs
Step-by-step explanation:
y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)
Answer:(6, −2), (6, 0.5) I’m pretty sure
What is the slope of the line that passes through
the points (2,-4) and (2, 4)?
A. -3 B.0. C.8. D. Undefined
The line is a vertical line, then the correct option is D, the slope is undefined.
How to find the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope, b is the y-intercept, and x is the variable.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the two points are (2, -4) and (2, 4)
Replacing that we would have a problem, that is because we have the same x-value in both points.
Then we have a vertical line at x = 2.
That line has no defined slope, thus, the correct option is D.
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Office Services An auto mechanic has total receipts of $1861.16 for a certain day. He determines that $1240 of this is labor. The remaining amount is for parts plus 6% sales tax on the parts only. Find the amount of the sales tax he collected.
The amount of sales tax he collected from the office services would be =$658.43
How to calculate the amount of sales tax?To calculate the amount of sales tax,the percentage tax amount should be determined as follows.
The total receipts from the office services = $1861.16
The amount that is for labor = $1240
The amount for parts = 1861.16-1240
= $621.16
The tax amount = 6/100 × 621.16
= 3726.96/100
= $37.27
Therefore the amount sale tax = 621.16+37.27 = $658.43
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quadratic equations. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 48.
geometry pls helpppppp
A graph of triangle TOW is shown below.
A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.
The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (-x, y)
T (-5, 6) → (-(-5), 6) = T' (5, 6)
O (1, 8) → (-(-1), 8) = O' (-1, 8)
W (-4, -2) → (-(-4), -2) = W' (4, -2)
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Please please help me with my work thank you
The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.
We are given that;
The four equations to match from
Now,
Using the slope-intercept form, we can plug in m = 3/2 and b = -8:
y = (3/2)x - 8
This equation matches with y = 3/2x - 5 if we multiply both sides by 2:
2y = 3x - 16
Therefore, the correct equation is 2y - x = -16.
A line that contains the points (0,-2) and (4,0)
m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2
Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:
-2 = (1/2)(0) + b -2 = b
Therefore, the equation is:
y = (1/2)x - 2
This equation matches with -5x - 3y = -12 if we multiply both sides by -6:
6y = -3x + 12
Therefore, the correct equation is -5x - 3y = -12.
A line that contains the y-intercept (0-2) and the slope of -3/4
Using the slope-intercept form, we can plug in m = -3/4 and b = -2:
y = (-3/4)x - 2
This equation matches with y = -3/4x - 2.
A line that has a slope of 5/3 and a y-intercept of 4
Using the slope-intercept form, we can plug in m = 5/3 and b = 4:
y = (5/3)x + 4
This equation matches with 2y - x = -4 if we multiply both sides by 3:
3y = (5/3)x + 12
Therefore, the correct equation is 2y - x = -4.
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What is the equation for the line of reflection?
On a coordinate plane, triangle A B C has points (6, 3.7), (5.4, 2), (1, 3). Triangle A prime B prime C prime has points (3.7, 6), (2, 5.4), (3, 1).
The equation of line of reflection of the coordinates is
y = x
What is line of reflection?Mathematics gives the concept of a line of reflection, otherwise known as a line of symmetry. This line acts as a mirror for any figure, where when shown through its reflection, the image becomes congruent to the initial shape.
In simpler words, the line of reflection is like an invisible partition that accurately segments a figure into two identical halves, each resembling the other in more ways than one.
The image is attached and upon investigation shows that the equation of y = x matches the equation of line of reflection
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Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR 6% of . How much should you deposit monthly to accumulate $ 85,000 in 18 years?
Monthly you should deposit approximately $241 to accumulate $ 85,000 in 18 years.
Given that,
f = 85000
r = 6% = 0.06/12 = 0.005
n = 17×12 = 204
We know that, a = (f×r)/((1+r)ⁿ⁻¹)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.
Here,
a = (85000×0.005)/((1.005)²⁰⁴⁻¹)
a = 240.6356536
a ≈ $241
Therefore, monthly you should deposit approximately $241 to accumulate $ 85,000 in 18 years.
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You have 979,584 grams of a radioactive kind of argon. If its half-life is 2 hours, how much
will be left after 10 hours?
Answer:
Step-by-step explanation:
Find the interquartile range using the following.
Minimum: 1
Q1: 3
Median: 5
Q3: 7
Maximum: 9
A. 8
B. 4
C. 5
D. 10
Answer: B. 4
Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.
What function is represented in the graph?
Select one:
У = 3(4^x)
y = 4(3^x)
y = 4(.25)^x
y = 2(.25^x)
Answer:
The correct function is y = 4(.25^x).
Drag the tiles to the boxes to form correct pairs.
Find the sum of each pair of vectors and match it with the magnitude of the resultant vector.
The dragging of the tiles to the appropriate places is given below.
How to explain the information1. 5.83 m/s > magnitude 4.5 m/s, direction angle 55˚ magnitude 3m/s, direction angle 135°
2. 4.05 m/s > magnitude 3.5 m/s, direction angle 35˚ magnitude 4 m/s, direction angle 150˚
3. 5.29 m/s > magnitude 6 m/s, direction angle 120˚ magnitude 2 m/s, direction angle 240˚
4. 3.32 m/s > magnitude 3 m/s, direction angle 70° magnitude 5 m/s, direction angle 210˚
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Molly has four t-shirts in her closet that she plans to wear over the next four days without wearing the same one twice. She has a blue, green, yellow, and black shirt. What are the chances that she will wear the black shirt the first day?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.
Step-by-step explanation:
∠A and ∠ � ∠B are vertical angles. If m ∠ � = ( 2 � − 2 ) ∘ ∠A=(2x−2) ∘ and m ∠ � = ( 3 � − 15 ) ∘ ∠B=(3x−15) ∘ , then find the value of x.
The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
∠A = (2x − 2)
∠B = (3x − 15)
Since the ∠A and ∠B are vertical angles, then they are congruent angles
So, we have
3x - 15 = 2x - 2
Evaluate the like terms
So, we have
x = 13
Hence, the solution is x = 13
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Tan(x) times cos(x) simplify it to single trig
Using trigonometric identities, the given expression, tan(x) × cos(x), simplified to a single trigonometry is sin(x)
Simplifying trigonometric identitiesFrom the question, we are to simplify the given trigonometric expression
From the given information
The given expression is
tan(x) × cos(x)
From trigonometric identities, we know that
tan(x) = sin(x) / cos(x)
Now,
Substituting this value in the given expression
tan(x) × cos(x)
We get
sin(x) / cos(x) × cos(x)
Simplifying further
sin(x) / cos(x) × cos(x) = sin(x)
Hence,
The simplified expression is sin(x)
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107/103 X 101/100 =
What is 107 over 103 times 101 over 100
107 over 103 times 101 over 100 would result in 10807/10300.
Mathematical operationsIn order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:
(107/103) x (101/100) = (107 x 101) / (103 x 100)
Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:
(107 x 101) / (103 x 100) = 10807 / 10300
Therefore, 107/103 times 101/100 simplifies to 10807/10300.
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Solve please! A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.
1. The diagram below shows the net of a pyramid with all its labeled sides.
2. The surface area; S = L + B
3. The total surface area = 22.44 cm².
How do we solve for the total surface area?To calculate the total surface area, we use the formula to find Area = (1/2) x b x h.
After we've found the area, we say
Total surface area = 1/2 x 2.24 x (3 x 4) + (3)²
= 22.44 cm²
The above answers are based on the full questions below;
A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.
1. Draw a net for the pyramid. Label all sides with measurement?
2. Write an expression for the surface area of the pyramid and then find the total surface area
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Select the correct answer.
Which graph represents the solution to this system of inequalities?
x+y<4
2x-3y²12
O A.
-10
y 10
-5
10
The two inequalities that the graph represents are:
y < -x + 4
y ≤ ²/₃x - 4
How to interpret the Inequality Graph?An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The first inequality is the one with the dashed line and a y-intercept of 4 and so since shaded below line, we will use the symbol <.
The slope from two coordinates on the line (0, 4) and (4, 0) is:
(0 - 4)/(4 - 0) = -1
Thus, inequality is:
y < -x + 4
The first inequality is the one with the solid line and a y-intercept of -4 and so since shaded below line, we will use the symbol ≤.
The slope from two coordinates on the line (0, -4) and (6, 0) is:
(0 + 4)/(6 - 0) = 2/3
Thus, inequality is:
y ≤ ²/₃x - 4
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use your knowledge of transformations to find matching graph f (x) = ½ √x - 1
Answer:
Step-by-step explanation:
down 1
compress 1/2
Find the measure of the exterior angle 1
WILL mark as brainliest if you get correct
Answer: C: 144
Step-by-step explanation:
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
thats the meaure of the exterior angle!
Answer:144
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
1. Find the area. 15 cm summ · 12 cm 20 cm
It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.
PLEASE HELP ME !!! I NEED THIS TO GRADUATE
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. Group of answer choices
The probability of getting two numbers whose sum is greater than 9 = 5/36
We know that the probability is nothing but the number of favourable outcomes divided by the total number of outcomes.
Here, a single die is rolled twice.
and we get the set of 36 equally likely outcomes.
so, the total number of outcomes n(S) = 36
Let us assume that event A: getting two numbers whose sum is greater than 9
A = {(4, 6), (5,5), (5, 6), (6, 4), (6, 5)}
n(A) = 5
Using above formula of probability,
P(A) = n(A)/n(S)
P(A) = 5/36
Thus the required probability = 5/36
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2. Solve 4.3(n + 6) > 47.3. Then graph the solution.
Answer: n>5
Step-by-step explanation: