The population density of otter, raccoon, fox and bobcat is 0.3125, 1.66, 0.0803 and 0.0267 per acre
Total park area of the state park = 112 acres
Number of Otter = 35
Number of Raccoon = 186
Number of Fox = 9
Number of Bobcat = 3
The formula of population density is given by:
Population Density = Number of animals/Area of land
Population density of Otter in the park = 35/112 = 0.3125 Otter per acre
Population density of raccoon in the park = 186/112 = 1.66 Raccoon per acre
Population density of fox in the park = 9/112 = 0.0803 Fox per acre
Population density of bobcat in the park= 3/112 = 0.0267 bobcat per acre
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Number between 50 and 80 that has exactly 4 factors one which is 2
58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.
As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.
To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.
Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.
That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,
[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]
That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.
Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and
[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.
Factors: In mathematics, a factor "x" of a number, say "y" is such a number that, "y" when divided by "x", the division leaves no remainder.Prime Numbers: Any number greater than 1, that has only two factors, 1 and the number itself is known as a prime number.To learn more about Factors, click on the link below.
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A certain substance in an experiment was being stored at −2.4°F. It was then placed on a table where the temperature was raised by 5.3°F.
What was the new temperature of the substance?
A. 7.2.9°F
B. 2.9°F
C. −2.9°F
D. −7.7°F
what are the possible values of x such that 10[x] =2.5
There is no solution for the given equation i.e.10[x] =2.5
Equation:
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Greatest integer function:
The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function. Thus, the equation to determine the largest integer is fairly straightforward. It is symbolised by [x] where x can take on any value.
⇒10[x] =2.5
⇒[x] =[tex]\frac{2.5}{10}[/tex]
⇒[x] =0.25
⇒[x] will be always a interger.As a result there is no solution for the given equation.
Therefore,There is no solution for the given equation i.e.10[x] =2.5
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Solve for the system of equations.
Y=2x+3
2y-x=12
For the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.
We are given the system of equations:
y = 2 x + 3 … (1)
2 y - x = 12 …. (2)
We need to solve it to find the values of x and y.
Putting the value of y from equation (1) in equation (2), we get that:
2 y - x = 12
2 (2 x + 3) - x = 12
Multiplying the brackets, we get that:
4 x + 6 - x = 12
3 x + 6 = 12
Subtract 6 from both the sides, we get that:
3 x + 6 - 6 = 12 - 6
3 x = 6
Divide both sides by 3. we get that:
3 x / 3 = 6 / 3
x = 2
y = 2 x + 3
y = 2 (2) + 3
y = 4 + 3
y = 7
Therefore, we get that, for the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.
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Question Collapse ^ Given slope (gradient) of a line is 3 and two points that lie on that line are N(-2,3) and D(3, d). Find the value of d.
The value of d is 18.
Given, the slope of the line is 3.
Slope equals a height change (Change in width) You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y: Slope is equal to (y-change)/ (Change in x)
Two points which lie are N(₋2 , 3) and D(3,d)
slope of the line = y₂ ₋ y₁/x₂ ₋ x₁
let the points N(₋2 , 3) be (x₁ , y₁)
and D(3,d) be (x₂ , y₂)
therefore, 3 = d ₋ 3/3 ₋ (₋2)
3 = d ₋ 3/3 ₊ 2
3 = d ₋ 3 / 5
15 = d ₋ 3
d = 15₊3
d = 18
Hence we get the value of d as 18.
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if f(x)=2x2+5 then f(-3)=
The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).
We are given the function:
f ( x ) = 2 x² + 5
We need to find the value of f ( -3 ).
We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.
Putting x = -3 in the function, we get that:
f ( x = - 3 ) = 2 (- 3)² + 5
Solving the square, we get that:
f (- 3) = 2 ( 9 ) + 5
Simplifying the expression, we get that:
f (- 3) = 18 + 5
f (- 3) = 23
Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).
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Which expression is equivalent to the given expression [tex]\sqrt{45}[/tex]
Answer:
6.7
Step-by-step explanation:
√45 = 6.7
.................
What raw score best corresponds to the top 20% for each distribution?
What raw score best corresponds to the 30th percentile for each distribution?
Major Hours ZHours
1 15 -1.59248
1 24 .42616
1 25 .65045
1 18 -.91960
1 30 1.77192
1 18 -.91960
1 22 -.02243
1 23 .20186
1 26 .87474
1 20 -.47102
2 21 1.95475
2 12 -.71082
2 13 -.41464
2 10 -1.30317
2 17 .77005
2 12 -.71082
2 12 -.71082
2 20 1.65858
2 12 -.71082
2 12 -.71082
2 15 .17770
2 12 -.71082
2 15 .17770
2 14 -.11847
2 19 1.36240
The raw score from the given table that corresponds with the 20th and 30th percentiles are;
First distribution;
20th percentile; 1830th percentile; 22Second distribution;
20th percentile; 1230th percentile; 14How can percentile values be found from Z–Score?The Z–Score percentile normal distribution table can be used to find the Z–Score that gives the percentile value of a raw score.
The Z–Score, also known as the standard score, gives the number of standard deviations, a raw score is far from the mean.
The mathematical equation for the Z–Score is as following; [tex]Z = \frac{x - \mu}{ \sigma} [/tex]
Therefore, a positive value of Z is obtained when the raw score, x, is larger than the mean, [tex] \mu[/tex]
and negative Z value is given by raw scores lower than the mean.
Using the standard normal distribution table, raw score corresponds to the 1th percentile when the Z–Score = -2.326, while the Z–Score for the 99th percentile is 2.326.
The Z–Score of the 20th percentile is -0.842, while for the 30th percentile it is -0.524
Comparing the standard values with the values in the given table, we have;
First distribution;
The raw score that corresponds with the 20th percentile in the first distribution is 18, given that the Z-Hours for 18 is -0.91960, and we have;-0.91960-(-0.842) = -0.0776
-0.71082 -(-0.842) = 0.13118
The smaller difference is given by -0.91960.
Similarly;
The raw score that corresponds to the 30th percentile is 22.Second distribution;
The raw score that corresponds with the 20th percentile in the second distribution is 12While;
The raw score that corresponds to the 30th percentile is 14Learn more about the Z–Score of a normal distribution here:
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Find the angle in degrees between the two planes
x − 10y − 8z = 11
and
2x + 5y + 8z = 1.
(Round your answer to two decimal places.)
The angle in degrees between the two planes is approximately 159.460°.
What is the angle between two planes?
The equation of the plane, whose form is a · x + b · y + c · z = d is equivalent to this vectorial form (a, b, c) • (x, y, z) = d, where (a, b, c) is the vector of coefficients. The angle between the two planes:
θ = cos⁻¹ [[(a₁, b₁, c₁) • (a₂, b₂, c₂)] / [||(a₁, b₁, c₁)|| · ||(a₁, b₁, c₁)||]]
If we know that (a₁, b₁, c₁) = (1, - 10, - 8) and (a₂, b₂, c₂) = (2, 5, 8), then the angle between the two planes is:
θ = cos⁻¹ [[(1, - 10, - 8) • (2, 5, 8)] / [√165 · √93]]
θ = cos⁻¹ [(-2 - 50 - 64) / √15345]
θ = cos⁻¹ (- 116 / √15345)
θ ≈ 159.460°
The angle in degrees between the two planes is approximately 159.460°.
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Sep 20, 8:10:23 AM
The sum of three consecutive integers is 51. Find the value of the greatest of the
three.
The first integer is 16 and the next two integers are 17 and 18. The largest one is 18
What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Three categories of integers exist: Zero (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers)The first integer will be called x. Consequently, the second integer is x+1 and the third is x+2 (this is because they are consecutive integers). The total of these three numbers is 51, so build up the following equation and answer it.
x+(x+1)+(x+2)=51
3x+3=51
3x=48
x=16
Therefore, the first integer is 16 and the next two integers are 17 and 18. The largest one is 18 and this is the answer.
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5, 32, 229, 1016, 3133, 7780, 16,757 whats the next term
Answer: 32604
Step-by-step explanation:
Determine the interval(s) for which f(x) ≥ 0. f(x) = x − 2
The interval(s) for which f(x) ≥ 0. is x ≥ 2
How to determine the interval(s)?The function is given as:
f(x) = x - 2
Also, we have:
f(x) ≥ 0
This means that
x − 2 ≥ 0
Add 2 to both sides of the inequality
x ≥ 2
Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2
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Can someone tell me if this is right if it’s not can you tell me where I messed up at
Using translation concepts, the vertices of the triangle after the rotation are given as follows:
G'(2,-2), E'(5,-4), F'(5,-1).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a 90º counterclockwise rotation around the origin is:
(x,y) -> (-y,x).
Hence the vertices should be given by:
G': (-2,-2) -> (2,-2).E': (-4,-5) -> (5,-4). (here you committed a mistake, should be one left and one up to where you positioned).F': (-1,-5) -> (5,-1). (here you committed a mistake).The correct translation is graphed at the end of the question. You are doing a good job, just there was two small mistakes on the rule :).
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3. The lip balm costs about $16 to make. What is
the cost per ounce?
Using proportions, it is found that the cost per ounce is of $0.8.
What is the missing information?The missing information is the number of ounces in the balm, that is of 20.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The cost per ounce is given by the proportion of the cost by the number of ounces, hence:
Cost: $16.Number of ounces: 20.Then:
$16/20 = $0.8.
The cost per ounce is of $0.8.
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Which angles of rotation will map the figure onto itself? Explain your reasoning and/or show your work.
The angles of rotation will map the figure onto itself are 60, 120, 180....
How to deternine which angles of rotation will map the figure onto itselfIn geometry, transformation involves changing the angle, position and/or size of a shape.
The figure that completes the question is added as an attachment
The given parameter is the shape in the figure
From the figure, we can see that the shape has 6 congruent sides
This means that the shape is a regular hexagon
The angle of rotation will map the figure onto itself is calculated as
Angle = 360/Number of sides
So, we have
Angle = 360/6
Evaluate
Angle = 60
The other angles must be a multiple of 60
i.e. 60, 120, 180....
Hence, the angles of rotation will map the figure onto itself are 60, 120, 180....
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X over 3 = 6
Solve for X
Answer if you know your right, bur dont answer just for the points
Answer: 6.7% 0.67 6
-
9
Step-by-step explanation:
Answer:
[tex]\sf 6.7\% < 6/9 < 0.67[/tex]
Explanation:
You would think 6.7% is a lot bigger than both, but it is not. Remember 6.7 is a percentage out of 100, thus, 6.7% actually is 0.067.
the perimeter P. of any rectangle is given by the formula P = 21 + 2w, where I represents the length if the rectangle and w represents the width. let the length of a rectangle equal 3 ft more than 3 times its width and the perimeter equal 54 ft
Answer:
width = 6 ft
length = 21 ft
Step-by-step explanation:
Forming algebraic expressions and finding the dimensions of a rectangle:
Width = w ft
length = 3*w + 3 = (3w + 3) ft
2l +2w = P
2(3w + 3) + 2w = 54
Use distributive property to open the brackets,
2*3w + 2*3 + 2w = 54
6w + 6 + 2w = 54
Combine like terms,
6w + 2w + 6 = 54
8w + 6 = 54
Subtract 6 from both sides,
8w = 54 - 6
8w = 48
Divide both sides by 8
w = 48 ÷ 8
[tex]\sf \boxed{\bf w = 6 \ ft}[/tex]
l = 3w + 3
= 3*6 + 3
= 18 + 3
l = 21 ft
Which is the equation of the given line?
Question options:
A. x = –2
B. y = –2x
C. x = 2
D. y = –2
Answer:
Option D: [tex]y=-2[/tex]
Step-by-step explanation:
The line is horizontal, which means the slope is 0. The line also crosses the y-axis at (0,-2). Thus y at 0 is equal to 2.
Apply the indicated series of transformation to the triangle image and draw its final placement on the graph: *(x,y)—>(x+6,y-2) *reflect across y=2 (this part confuses me)
Please tell me in steps
(Photo attached)
Answer:
See the answer below
Step-by-step explanation:
can someone tell me what the asnwer is thanks (geometry)
what number is 1/10th of 8,000,000
Answer:
800,000
Step-by-step explanation:
To do this, simply divide the number by 10. 8000000/10 = 800,000.
999,999 + 1=1,000,000 show work
Answer:
use a calculator
Step-by-step explanation: the calculator doesn't lie I used a calculator
Answer:
1,000,000
Step-by-step explanation:
find the value of the variable and the measure of each labeled angle
value=
measure=
How do you write 14 programming errors for every 56 programmers as a rational number? Select the simplified rational number that represents this scenario.(1 point)
14
56
14/56
1/4
The simplified rational number that represents this scenario is 1/4
How to determine the simplified rational number that represents this scenario?The given parameters are:
14 programming errors for every 56 programmers
The above means:
Error : Actual = 14 : 56
Express as fraction
Error/Actual = 14/56
Simplify the ratio
Error/Actual = 1/4
Hence, the simplified rational number that represents this scenario is 1/4
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Solve the equation. 7x=35 x=
Answer:
x=
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
What is the mean of the data set rounded to the nearest tenth
0.7,1.1,0.8,1.6,2.2,1.1
Answer:
1.3 is the correct answer
Step-by-step explanation:
Aida starts the week with $18.00. The table below shows the change in the amount of money she has each day.
Day Change in Amount ($)
Monday -5.15
Tuesday +12.40
Wednesday -11.20
Thursday +2.50
Friday x
Aida declares that she ended the week with the same amount of money with which she started the week. Determine the value of x for which Aida's statement is true.
Answer:
+ 1.45
Step-by-step explanation:
the end result is 16.55, therefore you add 1.45 to get $18 again.
Find the measures of the central tendency of the data: (Round the answer to 2 decimal places)
7 14 9 10 10 7 13
Mode:
(Enter DNE if there are no modes)
Mean:
Median:
There are 2 numbers with a sum of 43. The first number is 2 less than twice the second. What is the SECOND number?
The value of the number is 15.
How to compute the value?Let the first number be represented by x.
The second number will be:
(2 × x) - 2 = 2x - 2
Therefore, the addition of the numbers will be:
= x + 2x - 2 = 43
3x - 2 = 43
3x = 43 + 2
3x = 45
Divide
x = 45/3
x = 15.
Therefore, the number is 15
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