The fraction of the voters who voted in favor of the measure will be 1/5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.
The fraction of the voters who voted in favor of the measure will be given as,
⇒ 20%
⇒ 20 / 100
⇒ 1 / 5
The fraction of the voters who voted in favor of the measure will be 1/5.
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What is the formula for directed line segment?
The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.
A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.
For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.
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Is there a triangle whose sides have length 10.2 cm 5.8 cm and 4.5 cm justify the answer?
Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.
As we know if these sides form a triangle, then
the sum of two sides > the third side
Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm
The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm
The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm
Here the sum of the two sides is greater than the third side in all three cases.
Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.
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A population of 210,000 people is increasing by 15% each year. How much will the population be in 5 years?
According to the compound interest formula, the population is 5 years is 422,385.
The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Here we have given that the population of 210,000 people is increasing by 15% each year.
And then while looking into the given question, we have identified that the value of
interest rate = 15%
principal count = 210,000
time period = 5
Here we have to convert R as a percent to r as a decimal, then we get
=> r = R/100
=> r = 15/100
=> r = 0.15 rate per year,
Now, we have to solve the equation for A
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Apply the values on it , then we get,
[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]
When we simplify this one then we get
[tex]A = 210,000.00(1 + 0.15)^5[/tex]
Therefore, the value of A is 422,385.
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what is f for 1/8f = 3
Answer:
F = 24
Step-by-step explanation:
simplify 1/8
(1/8 x F) - 3 = 0
3 = 3/1 = 3 x 8/ 8
F x (3 x 8) / 8 F - 24/ 8
F - 24/ 8 = 0
F - 24/ 8 = 0 x 8
Answer:
24
Step-by-step explanation:
You want to know f for 1/8f = 3.
UndoMultiply the given equation by 8 to undo the multiplication by 1/8:
8(1/8f) = 8(3)
f = 24 . . . . . . . . simplify
The value of f is 24.
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A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.016 in., with a tolerance of 0.004 in.
0.016 in.
(a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate. (Use h for
the thickness.)
(b) Solve the inequality that you found in part (a). (Enter your answer using interval notation.)
An inequality involving absolute values that describes the range of possible thickness for the laminate.
|h - 0.016| <= 0.004The range of possible thickness for the laminate is given by the interval (0.012, 0.02).What is inequality?(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:
|h - 0.016| <= 0.004
(b) To solve the inequality, we need to consider two cases:
Case 1: h - 0.016 <= 0.004
h <= 0.02
Case 2: h - 0.016 >= -0.004
h >= 0.012
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1/4 + 3/8 (i would love a explanation)
How do you find the 3rd side of a triangle?
The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)
To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.
Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.
For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:
c² = 42 + 62 - 2(4)(6)cos(75)
Solving for c yields a third side length of 8.4.
To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.
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Which angle measures are correct? Select three options.
O m 2= 125°
m 3 = 55°
O m 8= 55°
O m 12= 100°
O m14 = 100°
Answer:
Step-by-step explanation:
analyze the graph, we found ∠1=∠5,∠2=∠6,
one.because ∠5+∠6=180, so ∠2=∠6=180-∠5=180-55=125
two.∠3=∠2=125
three.∠8=∠5=55
four.∠12=∠9=80
five.∠14=∠10=180-∠9=100
so, the three options are ∠2,∠8,∠14
The diagram shows an isosceles triangle. All the measurements are in cm, work out the perimeter of the triangle.
the normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees. which inequality could be used to determine the range of body temperature?
The requried inequality to determine the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees.
Let x be the average temperature of the horse,
100 - 1.2 ≤ x ≤ 100 + 1.2
98.8 ≤ x ≤ 101.2
Thus, the requried inequality determines the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
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2x + 2y = -10
What is the slope and y intercept?
Answer:
Slope: -1; y-intercept: -5
Step-by-step explanation:
Given:
2x + 2y = -10
Question:
What is the slope and y intercept?
Work:
The "template" for the slope of a line is: y = mx + b. "m" is the slope, "x" is a variable, and "y" is the y-intercept.
2x + 2y = -10 (We need to get 2x on the other side so lets subtract 2x on both sides since subtraction is the inverse of addition)2y = -2x - 10 2y = -2x - 10 (We are almost done. Now, all we need to do is get rid of the 2 that is the coefficient of the variable "y" and we are done.)y = -x - 5y = -x - 5 (The y-intercept is -5 and the slope is -1)Answer: Slope = -1; y-intercept = -5Hope this helped! :D
Shelby is creating a budget for the week. At her job, she earns $15. 50 per hour. Her rent costs $300. Shelby wants to have at least $280 left over after paying rent. Which inequality shows how many hours, h, Shelby should work?
PLEASEEE ANSWERR LOL
The inequality which shows that Shelby should work for h hours is given by 15.5 h - 300 ≥ 280.
Given that,
Rent = 300 dollars
Shelby wants to have at least $280 left over after paying rent.
The total earnings of Shelby calculated in a week are given as, 15.5 h
where,
h is the number of hours
To that we have to substract the rent amount, and we'll get how much does she have left after paying rent,
15.5 h - 300
And she wants this amount to be at least 280 dollars. The inequality can therefore be expressed as follows,
15.5 h - 300 ≥ 280
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Find the distance between the two points rounding to the nearest
(if necessary)
tenth
(1, -6) and (-8, -4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]
Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 81 cm2
At the rate of 126cm/s is the area of the square increasing when the area of the square is 81cm2.
If each side of a square is increasing at a rate of 7 cm/s.
The area of the square increasing rate,
Area, A = s2
each side of the square is increasing at the rate of 7cm / s (= dx / dt).
s is the side length
=> dA/dt = 2s. ds/ dt
ds/dt = 7cm/s
Area of the square = 81 cm2
81 cm2 = s2
s = 9 cm
so, dA /dt = 2. 9. 7
= 126 cm2/s
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A taxicab company charges $2.30 plus $0.80 per mile. Carmen paid a fare of $11.90. Enter and solve an equation to find the number of miles she traveled. Use m as your variable.
The number of miles the taxicab traveled is 12.
The area of mathematics known as algebra aids in the representation of circumstances or problems into mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
Given that,
The fixed charges = $ 2.30
Additional charges per miles = $ 0.80,
Thus, the additional charges for x number of miles = $ 0.80x
So, the total charges for x number of miles = Fixed charges + additional charges
=> 2.30 + 0.80x
According to the question,
2.30 + 0.80x = 11.90 (this is the required equation)
Subtracting 2.30 from both sides,
0.80x = 9.6
Dividing both sides by 0.80
x = 12
Hence, the taxicab traveled 12 miles.
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A 64 acre coconut farm is arranged in an 8 by 8 array. Mika wants to know the average number of coconut palms on each acre of land. The number in each cell tells how many coconut palms grow on that particular acre
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
Specify median.The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 48 + 38 + 47 + 48+ 43+ 34+ 64+ 54 + 53+ 67 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The solution of the given problem of median comes out to be
option (A) 44.3.
What is median?
The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 34 + 51 + 43 + 35 + 52 + 35 + 62 + 38 + 34 + 59 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The complete question is:
A 64‐acre coconut farm is arranged in an 8‐by‐8 array. Mika wants to know the average number of coconut palms on each acre. Each cell in the table represents an acre of land. The number in each cell tells how many coconut palms grow on that particular acre.
45 54 40 34 44 66 32 65 66 33 42 36 33 51 50 35 51 45 66 33 47 43 66 61 46 35 48 67 60 59 52 67 46 32 64 35 55 47 61 59 45 48 53 62 55 58 51 41 48 38 47 48 43 34 64 54 53 67 44 59 58 48 62 45
The numbers in green represent Mika's random sample of 10 acres. What is the average number of coconut palms on the randomly selected acres? Round your answer to the nearest tenth. The average number of coconut palms is
A. 44.3
B. 49.3
Is there an AAA similarity?
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that "If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or percentage) and consequently the two triangles are similar".
A triangle is a closed two-dimensional shape or polygon with the fewest sides in mathematics. A triangle is made up of three sides and three angles. The most significant attribute of a triangle is that the sum of its internal angles equals 180°.
Conditions for Triangle Similarity
If the corresponding angles of two triangles are identical, they are said to be comparable triangles.
If their respective sides have the same proportion/ratio.
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Tree+snowman+tree=17
Answer:
tree = 8
snowman = 1
deer = 4
snowflake = 4
Step-by-step explanation:
say t = tree, s = snowman, d = deer, f = snowflake
1. For 2d + f, since you know d is equal to f, replace the snowflake with a deer, turning the equation into 3d = 12. To find the value of d divide by 3 on both sides. This will result in 4. So, the value of deer = 4.
2. Now, find the value of the snowman using the value of the deer.
4-3 = 1. This means the value of the snowman = 1.
3. Plug in the value of the snowman into 2t + s = 17.
2t + 1 = 17
Subtract on both sides to get 2t by itself and then simplify
2t = 17 -1 --> 2t = 16
Divide by 2 on both sides to find the value of the tree
2t/2 = 16/2 --> t = 8
Hello good morning do anyone think they could help please
Answer:
1. 15
2. 15
3. 13
4. 11
5. 14
6. 11
7. 18
8. 19
9. 18
10. 14
Step-by-step explanation:
HELP PLEASEEEEEEEEEEEEEEEE
Answer: The answer is $1,317.50
Step-by-step explanation:
First, Find how much they earn in the goods sale.
Make $1,700, their goal to earn, into 1,700/1 and set it to multiply that by 2/5, the fractional amount of money earnt at the goods sale proportional to how much they have to earn.
Simplify that by crossing 1,700 and 5 into a 340 and 1.
Multiply 340/1 by 2/1 to get 680/1.
Make that into a whole number ($680) to show how much money earnt from the goods sale.
Secondly, find how much money they earn by the Bingo Night
Make 1,700, like last time, into 1,700/1 and set it to multiply 3/8, the fractional amount of money earnt from the Bingo Night proportional to how much they have to earn
You can't simplify, so just multiply the amount.
If you multiply, you will get 5,100/8.
Divide 5,100 by 8 (the divisor by the dividend).
Make sure to also add the 0 after the tenths place after you get your quotient, which is supposed to be 637.5 (or $637.50)
Lastly, You have to add them up.
Add $637.50+$680.
You shall get $1,317.50
2x + 4y = -16
solve for y
Answer: y = -1/2x -4
Step-by-step explanation:
To solve for y, subtract 2x on both sides
2x-2x + 4y = -16 - 2x
Simplify
4y = -16 - 2x
Divide by 4 on both sides to get y by itself
4y/4 = -16 - 2x/4
Simplify
y = -4 - 1/2x
Switch the right-side terms to write them in slope-intercept form
y = -1/2x -4
xy^4 Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.
How to determine the concavity?(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]
To find f'(x), we can use the product rule and the given differential equation:
[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]
Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).
In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.
A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.
(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.
The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]
Integrating both sides gives:
[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]
Using the initial condition f(4) = -1, we can find the value of C:
[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]
So the particular solution is:
[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]
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Complete question is: Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
Write an equation of the line that passes through the points (-7,-3) and (8, -3)
y=
Answer:
y = - 3
Step-by-step explanation:
Call the line y = a + bx (d)
Since d go through (-7;-3) so -7 = a - 3b (1)
Since d go through (8;-3) so 8 = a - 3b (2)
From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]
Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]
Can u help me with this
Answer:
D) (6.6, 7.4)
Step-by-step explanation:
Begin by finding the margin of error based on the given information.
[tex]\boxed{\begin{minipage}{7.3cm}\underline{Margin of Error formula}\\\\$\textsf{Margin of Error}= Z \times \dfrac{S}{\sqrt{n}}$\\\\where:\\\phantom{ww} $\bullet$ $Z =$ $Z$ score\\\phantom{ww} $\bullet$ $S =$ Standard Deviation of a population\\\phantom{ww} $\bullet$ $n =$ Sample Size\\\end{minipage}}[/tex]
Given:
S = 1.3n = 50The z-score for 95% confidence level is 1.96.
Therefore, to find the margin of error, substitute the values into the formula:
[tex]\implies \textsf{Margin of Error}= 1.96 \times \dfrac{1.3}{\sqrt{50}}[/tex]
[tex]\implies \textsf{Margin of Error}=0.360341...[/tex]
To find a reasonable range for the true mean number of hours a teenage spend on their phone, subtract and add the margin of error to the given mean of 7 hours:
[tex]\begin{aligned}\implies \textsf{Lower bound}&=7-0.360341...\\&=6.63965...\\&=6.6\;\; \sf (1\;d.p.)\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Upper bound}&=7+0.360341...\\&=7.360341...\\&=7.4\;\; \sf (1\;d.p.)\end{aligned}[/tex]
Therefore, the reasonable range for the true mean is:
(6.6, 7.4)You have $9 to spend on lip balm and hand sanitizer. The equation $1.5x+2.5y=9$ represents this situation, where x is tubes of lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand sanitizer?
Answer:
6 tubes of lip balm
Step-by-step explanation:
We can start solving this problem by isolating the variable x.
Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:
1.5x + 2.5(0) = 9
Simplifying this, we get:
1.5x = 9
To solve for x, we can divide both sides of the equation by 1.5:
x = 9/1.5
x = 6
So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer
4
Drag each option to the correct location on the image.
Match the expenses to their respective categories.
Need
tuition and fees
staple foods
Want
Lamborghini
vacation
lavish wedding
Answer:
NEED:
Tuition and Feesstaple foodsWANT:
VacationLamborghini Lavish WeddingStep-by-step explanation:
Right on Plato! <3
Have a wonderful day!
The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.
The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.
On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.
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Which linear graph represents a proportional relationship?
A graph of a straight line that passes through the points 0 comma 2 and 1 comma 2.
A graph of a straight line that passes through the points negative 1 comma 0 and negative 1 comma 1.
A graph of a straight line that passes through the points 0 comma 0 and 1 comma negative 2.
A graph of a straight line that passes through the points 0 comma 2 and 2 comma 3.
Answer: The answer is C
Step-by-step explanation: i took the test and got it right
What is an unsolvable equation?
1. The Riemann Hypothesis Equation
2. Rabbit Problem
When rabbits were first brought to Australia last
century, they had no natural enemies so their numbers increased
rapidly. Assume that there were 60,000 rabbits in 1865, and that by
1867 the number had increased to 2,400,000. Assume that the num-
ber of rabbits increased exponentially with the number of years that
elapsed since 1865.
Write the particular equation for this function,
b. How many rabbits would you predict in 1870?
c. According to your model, when was the first pair of rabbits in-
troduced into Australia?
According to the exponential function,
a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ
b) The number of rabbits in 1870 is 6.5
c) According to your model, the first pair of rabbits introduced into Australia is 19th century
Here we have given that during the 19th century, here rabbits were brought to Australia.
And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.
And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.
Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.
Then the exponential function can be written as,
=> f(rabbits) = 65000(√500/13)ˣ
When we plot these on the graph then we get the graph like the following.
Through the graph we have identified that the value of rabbits in 1870 is 6.5
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Solve for x in this triangle. Round your answer to the nearest tenth. 15 42° X
Answer:
x ≈ 47.0°
Step-by-step explanation:
using the cosine ratio in the right triangle.
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{15}{22}[/tex] , then
x = [tex]cos^{-1}[/tex] ( [tex]\frac{15}{22}[/tex] ) ≈ 47.0° ( to the nearest tenth )