In 1994, the moose population in a park was
measured to be 3280. By 1997, the
population was measured again to be 4120.
If the population continues to change
linearly:
Find a formula for the moose population, P,
in terms of t, the years since 1990.
P(t)
=
What does your model predict the moose
population to be in 2006?
To answer this question we will use The Linear Programming concept
The formula for the moose population is
The moose population in 2006 would be
We use the year 1990 as the base year for creating the equation of the moose population. We could assume that:
The moose population of the year: P(x)
The moose population in year 1990: a
The year difference to 1990: x
The linear change of the moose population: b
Hence, we could make some assumption about the relationship between each elements mentioned above, where the moose population of the year would be depends on the linear change of the population added into the original moose population in year 1990. We could write this relationship into the equation (i):
P(x) = a + bx ... (i)
Using data provided from the question, we could make some other equations and find the value of b:
P(x) = a + bx
P(4) = a + 4b = 3280 ---> year 1994 ... (ii)
P(7) = a + 7b = 4120 ---> year 1997 ... (iii)
We could do some eliminations between equations (ii) and (iii)
3280 = a + 4b
4120 = a + 7b -
840 = 3b
b = 280 ... (iv)
After finding the value of b, we could subtitute its value into equation (ii) to find the value of a:
3280 = a + 4b
3280 = a + 4(280)
3280 = a + 1120
a = 2160 ... (v)
After finding the value of a and b, we could rewrite the equation (i) by inserting the and b values.
P(x) = a + bx
P(x) = 2160 + 280x ... (vi)
Next, we will predict the moose population to be in 2006.
First, we should determine the value of x, the difference between the year 2006 to the base year 1990.
x = 2006 - 1990
x = 16 ... (vii)
We would subtitute the equation (vii) into equation (vi) to predict the moose population to be in 2006:
P(16) = 2160 + 280(16)
P(16) = 6640...(viii)
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K
Question 1, 6.8.1
Part 1 of 5
The size P of a certain insect population at time t (in days). obeys the function P(t) = 300e0.05t
(a) Determine the number of insects at t=0 days.
(b) What is the growth rate of the insect population?
(c) What is the population after 10 days?
(d) When will the insect population reach 420?
(e) When will the insect population double?
(a) What is the number of insects at t=0 days?
0 insects
HW Score: 0%, 0 of 4 points
O Points: 0 of 1
**
a) At t = 0days : 300insects
b) The growth rate is 5.12% each day.
c) Population after 10days: P(10) =494.61
d) The population to reach 420 is equals roughly 70.129 hours
e) The insect population double in t=6.020 days , which is 144.48 hours.
What is Population?
Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.
Given: t in days, P(t)=300e(0.05t).
(a) The total number of insects at time t=0 days is equal to
P(0)=300(1)
P(0) =300.
(b) The growth rate is calculated as the percentage increase over time, which is equal to-
P(t+1)/P(t)=300e(0.05(t+1))/300e(0.05t)
P(t+1)/P(t) =e^(0.05(1))
P(t+1)/P(t) =1.0512
Therefore, the growth rate is 5.12% each day.
(c) Population after 10 days.
P(10)=300e^(0.05*10)
P(10) =300(1.6487)
P(10) =494.61
(d) When P(t)=420, the population will reach 420,
or 300e0.05t=420,
take log
0.05t=log(1.4), or
t = 2.922 days,
for the population to reach 420.
equals roughly 70.129 hours
(e) When P(t)=2*300=600 the population will double.
300e^(0.05t)=600
=> e^(0.05t)=600/300=2
Take log
(log 0.05t=log(2)),
t=6.020 days , which is 144.48 hours.
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Factor -4 out of -8+20 expression
Answer: -3
Step-by-step explanation:
which expression is equivalent to (2x3 +3x+7) / (x2 + x +10)
The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
Let us solve the given algebraic expression by the long division method:
We are given the expression:
(2x^3 + 3x + 7) / (x^2 + x + 10)
We need to perform the division of the given algebraic expression:
x^2 + x + 10 ) 2x^3 + 3x + 7 ( 2x - 2
2x^3 + 2x^2 + 20x
- - -
-2x^2 - 17x + 7
-2x^2 - 2x - 20
+ + +
-15x + 27
So,
quotient = 2x - 2
remainder = -15x + 27
Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.
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Simplify -1 2/3 minus 9 2/5
Answer:
one ninths
Step-by-step explanation:
1/3-2/9 - fraction calculator. The result is 1/9 ≅ 0.1111111 = one ninth.
Marc deposits $1000 into a savings account. The account pays 4% simple Interest on an annual basis. Is he does not add or withdraw money from the account, how much interest will he earn after 9 montgs?
A. $10
B.$20
C$30
D.$40
Answer:
C
Step-by-step explanation:
1000*0.04 = 40
(9/12) * 40 = 30
Determine whether the following probability is empirical or classical.
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
A. Empirical
B. Classical
In this backgammon game, the probability used is Classical one.
Probability:
Probability refer the possible way of happening the particular event.
Given,
Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.
Here we need to identify whether the given probability is empirical or classical.
In order to find the type of probability, first we have to know the definition of each of them.
So, classical probability means the the statistical concept that measures the likelihood (probability) of something happening where as the empirical probability means the probability that is based on historical data.
Therefore, based on the definition, the given situation is purely based on the classical probability.
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Which of the following number sentences is true? A. 5+3 x 22 = 256 C. 5+3 x 22 = 32 B. 5+3 x 22 = 180 D. 5+3 x 2² = 17
The sentence which is true is 5+3×2²=17. The correct option is D.
Given the sentences is 5+3×22=256, 5+3×22=32, 5+3×22=180 and 5+3×2²=17.
We want to choose the sentence which is true.
An operator is a wildcard symbol used to indicate a mathematical operation that results in one or more mathematical objects leading to another similar object.
The first option is 5+3×22=256.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The first option 5+3×22≠256.
The second option is 5+3×22=32.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The second option 5+3×22≠32.
The third option is 5+3×22=180.
Solve the LHS, we get
5+3×22=5+66
5+3×22=71.
The third option 5+3×22≠180.
The fourth option is 5+3×2²=17.
Solve the LHS, we get
5+3×2²=5+3×4
5+3×2²=5+12
5+3×2²=17.
The fourth option 5+3×2²=17.
Hence, the sentence which is true from the given sentences is 5+3×2²=17.
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5 customers entered a store over the course of 3 minutes. At what rate were the customers entering the store in customers per minute?
Answer: Par affluence
Step-by-step explanation: Car chaque 3 min le nombre de client augmentera
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the estimated value of each expression with its position on the number line.
From the number line √90-√40 match with D, [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C, 2√27 -√48 match with E and [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
In the given question we have to match the each expession with its position on the number line.
The given first expression is √90-√40.
We firstly simplifying the expression.
√90-√40=√9×10-√4×10
√90-√40=3√10-2√10
Taking common [tex]\sqrt{10}[/tex] on both side
√90-√40=√10(3-2)
√90-√40=√10
√90-√40=3.16
From the number line √90-√40 match with D.
The given second expression is [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{5\times7}-\sqrt{6\times7}}{\sqrt{5}-\sqrt{6}}[/tex]
Taking common √7 on both side
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{7}(\sqrt{5}-\sqrt{6})}{\sqrt{5}-\sqrt{6}}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\sqrt{7}[/tex]
[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] = 2.65
From the number line [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C.
The given third expression is 2√27 -√48.
We firstly simplifying the expression.
We can write it as
2√27 -√48=2√3×9 -√16×3
2√27 -√48=2×3√3 -4√3
2√27 -√48=6√3 -4√3
Taking √3 common on both side, we get
2√27 -√48=√3(6 -4)
2√27 -√48=2√3
2√27 -√48=2×1.71
2√27 -√48=3.42
From the number line 2√27 -√48 match with E.
The given fourth expression is [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex].
We firstly simplifying the expression.
We can write it as
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{9\times6}-\sqrt{4\times6}}{\sqrt{2\times9}-\sqrt{2\times4}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{3\sqrt{6}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{2}}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{6}(3-2)}{\sqrt{2}(3-2)}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\sqrt\frac{6}{2}[/tex]
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] =√3
[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] = 1.71
From the number line [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.
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Answer: d,c,e,
ur welcomee!
Increase 52 by 14% pl
Answer: 59.28
Step-by-step explanation:
your welcome :)
Write a quadratic equation that goes through
the points (1,-3), (2,-5), and (-1,-11).
Answer:
1-3+2-5+-1-11
Step-by-step explanation:
I hope this helps :’)
8. Why can a² + 100 not be factored using difference of squares? please help!!!
Answer:
the sum of squares kasi yan
Explanation:
first find the squareroot of a² and 100
the squareroot of a²=a
because a×a=a²
the squareroot of 100=10
because 10×10=100
second factor
(a + 10)² or (a + 10)(a + 10)
Find the value of the linear correlation coefficient r. Round your answer to 3 decimal places if necessary.
(1 , 6) , (3 , 4) , (5 , 2)
The value of the linear correlation coefficient r is of:
m = -1.
What is a linear function?A linear equation is a special function that has the format of the equation given as follows:
y = mx + b.
The coefficients of the equation y = mx + b are given as follows:
m is the slope, representing the rate of change of y relative to x, which is also the correlation coefficient of the linear function.b is the y-intercept, representing the value of y when x = 0.In this problem, the points of the function are listed as follows:
(1 , 6) , (3 , 4) and (5 , 2)
From these three points, we can gather that when x increases by 2, y decays by 2, hence the slope of the linear function is given as follows:
m = -2/2 = -1.
Meaning that the linear correlation coefficient r of the linear function is of r = -1.
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The price of a new computer is $1,393 at your local store. This is 20% less than what it costs at the brownstone mall. How much should it cost at the brownstone mall? Round to the nearest dollar.
I need to know how to do these problems!
The height of the triangle pictured in the question is 2 units.
According to the question,
We have the following information:
Area of triangle = 8
Base of triangle = 8
We know that the following formula is used to find the area of triangle:
Area of triangle = 1/2*base*height
Area of triangle = 1/2*8*height
8 = 4*height
Dividing by 4 on both the sides:
Height = 8/4
Height of the triangle = 2 units
(Note that every physical quantity has some units of measurements. For example, the unit of measurement of area is square units.)
Hence, the height of the triangle pictured in the question is 2 units.
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if x- 37 equals to 93 find x
Answer:
x = 130
Step-by-step explanation:
x - 37 = 93 ( add 37 to both sides )
x = 130
Answer:
x=130
Step-by-step explanation:
x-37=93
x=93+37
x=130
x-37=93
-37-93= x (- / - =+ )
130=x
So, your answer is 130
what is the derivative of tan(cos(t)) with respect to t at t=pi/2
The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is tan(cos(t)). The derivation will be done as below,
[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]
Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
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-4 represents the sand that lies under 4 feet of water. 4
represents a branch 4 feet above the water.
What does zero represent in this situation?
A. The distance between the sand and the branch
B. The distance to the branch
C. The surface of the water
D. The
distance
to the sand
176795
720-2
569095
$196
in this situation Zero represents, The surface of the water
-4 represents the sand that lies under 4 feet of water.
4 represents a branch 4 feet above the water.
Upon analysis, it can be said that as we move downwards, the value increases in negative sign
As we move upwards, the value increases in positive sign
The surface of water becomes the origin, as it is zero.
Therefore, , in this situation Zero represents, The surface of the water
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what is logarithm 4096^x=8
Answer:
Step-by-step explanation:
(4096)ˣ = 8
log ₂ (4096)ˣ = log ₂ 8
x·log ₂ (4096) = log ₂ 8
x = log ₂ 8 / log ₂ (4096)
x = log ₂ 2³ / log ₂ 2¹²
x = 3 / 12
x = 1 / 4
A regular polygon has 20 sides. If one of its angles measures (5h − 12)°, what is the value of h?
The value of h in the given polygon is 34.8°
What is a regular polygon?A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon.
The sum of the interior angles of a regular polygon = (n - 2) x 180
where n = number of sides of the polygon
here n = 20
Sum of the interior angle = (20 - 2) x 180
Sum of the interior angle = 3240°
which also means that 20(5h - 12) = 3240
100h -240 = 3240
100h = 3240+240
100h = 3480
h = 3480/100
h = 34.8°
In conclusion, the value of h = 34.8°
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the question in the picture please help
The measures, using the binomial distribution, are given as follows:
a) Probability that exactly six arrive within two days: 0.735 = 73.5%.
b) Probability that exactly five arrive within two days: 0.232 = 23.2%.
c) Mean: 5.7 letters.
d) Variance: 0.285 letters².
e) Standard deviation: 0.534 letters.
What is the binomial distribution formula?The mass function, formula for the probability of x successes, is defined as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the mass function are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Hence, in the context of this problem, the values of these parameters are given as follows:
n = 6, p = 0.95.
The probability that all six arrive within two days is of:
P(X = 6) = 0.95^6 = 0.735 = 73.5%.
The probability that five arrive within two days is:
P(X = 5) = 6 x 0.95^5 x 0.05 = 0.232 = 23.2%.
The statistical measures are calculated as follows:
Mean: E(X) = np = 6 x 0.95 = 5.7 letters.Variance: V(X) = np(1 - p) = 6 x 0.95 x 0.05 = 0.285 letters².Standard deviation: S(X) = sqrt(V(X)) = sqrt(0.285) = 0.534 letters.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Fill in the missing statement/reason for the following proof:
The missing statement and the reason of LN bisects ∠MLO, LM≅LO are given and ∠OLN≅∠MLO is because of definition of angle bisector, LN≅LN is because it is common to both the angles ∠LNO AND ∠LNM, LO≅LM is because ΔLNO and ΔLNM both are congruent.
Given that:
LN bisects ∠MLO and LM≅LO
Prove that: ΔLMN ≅ ΔLON
In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.
Hence, using this we will prove that the triangles are congruent by ASA congruence rule.
In ΔLON and ΔLMN
Side ON ≅ Side MN
∠LNO ≅ ∠LNM ( ∵ common angle)
∠ONL ≅ ∠MNL (∵ Given as LN is the angle bisector of ∠MLO)
⇒ ΔLMN ≅ ΔLON ( By ASA congruence theorem).
Statement 1: LN bisects ∠MLO
Reason: Given.
Statement 2: LM≅LO
Reason: Given.
Statement 3: ∠OLN≅∠MLO
Reason: Definition of angle bisector.
Definition of angle bisector: An angle bisector is defined as a line segment that bisects one of the vertex angles of a triangle.
Statement 4: LN≅LN
Reason: Common to both the angles ∠LNO AND ∠LNM and also these angles are 90° because angle made by angle bisector is always 90°.
Statement 5: LO≅LM
Reason: ΔLNO and ΔLNM both are congruent.
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X = 1/3 Y = 3/5 Z = 2 1/4
Work out the value of X x Y x Z
Give your answer as a fraction in its simplest form.
The solved answer for the given fraction expression in will be 2.6833.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
Given X = 1/3
Y = 3/5
Z = 2 1/4 = 9/4
The value of X*Y*Z = (1/3*3/5*9/4)
= (20+36+105)/60
=161/60
=2.6833
Hence the solved answer for the given expression will be 2.6833.
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Find the unknown term in the geometric proportion 8 : 2 :: x : 6
Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.
[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]
[tex] \sf8 : 2 :: x : 6[/tex]
Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:
[tex]\boxed{\: x = \frac{8 \times6}{2} = \frac{48}{2} = 24 }[/tex]
Therefore, the resulting geometric proportion would be:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{8 : 24 :: 6}[/tex]
Find the y-intercept and x-intercept of the following linear equation.
x+4y=4
Enter the coordinates to plot points on the graph.
Answer:
y intercept: 1
X intercept: 4
Step-by-step explanation:
to find y intercept we set x to 0
0+4y=4
/4. /4
y=1
y intercept is 1
Now for x intercept we set y to 0
x+4(0)=4
x=4
X intercept is 4
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Write the polynomial in standard form, name it using the degree and number of terms, identify the constant and the leading coefficient:(3x-8)^2(2x+5)
Answer:
It is a binomial, so it is (ax+b)^2. In this case, a=3, b=-8, and there are 2 terms. The constant is 64 and the leading coefficient is 9.
Yearly budget 1200 you spend 350 what percentage is spent
Answer:
29.16% is spent
you have to divide 350 by 1200 then multiply by 100 then the answer will come
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 30 liters
of 60% acid solution?
Gabe needs ___ of the 40% solution.
He needs 10 litres of solution of 40% and 20 litres of 70% solution to make 30 litres of 60% acid solution.
According to the question,
We have the following information:
Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution.
Now, let's take x litres of 40% solution and y litres of 70% solution.
So, we have the following expressions:
x+y = 30
x = 30-y ....(1)
40x/100 + 70y/100 = 30*60/100
Dividing 100 on the numerator by 100 on denominator:
40x+70y = 1800
Dividing both sides by 10:
4x+7y = 180
Putting the value of x from equation 1:
4(30-y)+7y = 180
120-4y+7y = 180
120+3y = 180
Subtracting 120 from both the sides:
3y = 180-120
3y = 60
y = 60/3
y = 20
Now, putting this value of y in equation 1:
x = 30-y
x = 30-20
x = 10
Hence, he needs 10 litres of 40% solution and 20 litres of 70% solution to make 30 litres of 60% acid solution.
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The inequality x ≤ -2 would represent the values {-1, -2, -3}.
False
True
Answer:
False
Step-by-step explanation:
x ≤ - 2
the symbol ≤ ( less than or equal to ) means that x can equal - 2 and any values to the left of - 2 on the number line.
- 1 is to the right of - 2 and - 3 is to the left , so
the values represented are - 2, - 3