Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer:
the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Step-by-step explanation:
Given that :
the current population of insect A to be 1.3 million
the current population of insect B to be 2.1 million.
As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:
[tex]\mathtt{y = pe^{-rt}}[/tex]
where;
P represents the population of each species of insect in millions
t represents the elapsed time in years
r is the rate of decrease
So, we can have:
[tex]\mathtt{p_1 = 1.3 }[/tex] in million and [tex]\mathtt{p_2 = 2.1}[/tex] in million
Also for rate of decrease;
[tex]\mathtt{r_1 = 0.038}[/tex] and [tex]\mathtt{r_2 = 0.046}[/tex]
Therefore;
the exponential decay for Population of insect A can now be:
[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]
the exponential decay for Population of insect B can now be:
[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]
Hence, the system of equation that can be used to determine how long it will be before the populations of the two species are equal is :
[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]
Answer:
A!
Step-by-step explanation:
Plato
Microsoft Excel might be useful when establishing relationships involving vertex-edge graphs.
O True
False
Answer:
True
Step-by-step explanation:
Microsoft Excel is a great tool and has saved me on countless occasions in graphs and tables. I agree with the earlier answer by Hedland.
Ohm's law states That the current That the current (I) In amps equals the voltage (E) In volts divided by the resistance (R) in ohms. If you connected a two megohm resistor (2 x 10 6 ohms) Across a 2.4 kilovolt Voltage source parentheses 2.4Times 10 to the third power volts) What would be the current in amps
Answer:
1.2 milli ampsStep-by-step explanation:
From ohms law the expression for voltage is given as
[tex]V= IR[/tex]
Now given that
Voltage, V= [tex]2.4*10^3[/tex] volts
Resistance R= [tex]2*10^6[/tex] ohms
Applying ohms law the current can be calculated by making I the subject of formula
that is I= V/R
[tex]I= \frac{2.4*10^3}{2*10^6} \\\\I= \frac{2.4}{2} *10^(^3^-^6^)\\\\I=1.2*10^-^3[/tex]
The current in amps is 1.2 milli amps
What does the law of cosines reduce to when dealing with a right angle
Answer:
It is reduced to the equation of the Theorem of Pythagoras.
Step-by-step explanation:
Any triangle can be modelled by this formula under the Law of Cosine:
[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.
[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.
Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:
[tex]\cos B = 0[/tex]
And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:
[tex]b = \sqrt{a^{2}+c^{2}}[/tex]
If P = (3,4), Find: Rx=1 (P)
Answer:
-1, 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer is (-1,4)
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground? A 0.6° B 35.0° C 39.0° D 58.0°
Answer:
C 39.0
Step-by-step explanation:
To find the approximate angle, x, that the second tree makes with the ground, we can use the concept of similar triangles Therefore the correct option is B.
Let's calculate the height of the first tree using the given information. We can use the formula for the opposite side in a right triangle: opposite = adjacent * tan(angle). Therefore, the height of the first tree is approximately [tex]19 * tan(32°) = 19 * 0.6249 ≈ 11.873[/tex] feet. Now, we can set up a proportion between the two trees based on their heights. Let x be the angle the second tree makes with the ground.
We have the following proportion: (height of first tree)/(height of second tree) = (length of first tree)/(length of second tree). Substituting the known values, we have [tex]11.873/16 = 19/x[/tex]. Cross-multiplying gives us [tex]11.873x = 304,[/tex] and dividing both sides by 11.873 yields[tex]x ≈ 25.63°.[/tex] The approximate angle, x, that the second tree makes with the ground is closest to 35.0°.
Hence the correct option is B
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Area of a trapeziod with a top base length of 6 cm a bottom base length of 12 cm and a height of 5 cm
Answer:
A=45cm^2
Step-by-step explanation:
A= h/2(b1 + b2) for trapezoid
A=(5/2(6+12))cm^2
A=(2.5(18))cm^2
A=45cm^2
1/4(8x-4)=
need help please answer
Answer:
2x-1 is the answer (or if you're trying to multiply it, the answer is -8.)
Step-by-step explanation:
Events A and B are mutually exclusive. Find the missing probability.
P(A) = 1/4 P(B) = 13/20 P(A or B) = ?
4/5
1/2
9/10
3/8
Answer:
Option C.
Step-by-step explanation:
It is given that,
[tex]P(A)=\dfrac{1}{4}[/tex]
[tex]P(B)=\dfrac{13}{20}[/tex]
It is given that events A and B are mutually exclusive. It means they have no common elements.
[tex]P(A\cap B)=0[/tex]
We know that,
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
On substituting the values, we get
[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]
[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]
[tex]P(A\cup B)=\dfrac{18}{20}[/tex]
[tex]P(A\cup B)=\dfrac{9}{10}[/tex]
Therefore, the correct option is C.
The P (A or B) should be [tex]\frac{9}{10}[/tex]
Given that,
P(A) = 1 by 4 P(B) = 13 by 20Based on the above information, the calculation is as follows:
[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]
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ASAP PLEASE GIVE CORRECT ANSWER
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point $(-15, 8)$? Enter your answer
distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$
so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$
Answer:
Distance=17 units
Step-by-step explanation:
Coordinates of the origin: (0, 0)
Coordinates of the point in question: (-15, 8)
Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]
Consider the equation x2+4x+9=0 in standard form. Which equation shows the coefficients a, b, and c correctly substituted into the quadratic formula? Please show all steps to get to the answer, please!!
Answer:
x = -2+i√5 and -2i-√5Step-by-step explanation:
The general form of a quadratic equation is ax²+bx+c = 0
Given the quadratic equation x²+4x+9=0 in its standard form, on comparing with the general equation we can get the value of the constant a, b and c as shown;
ax² = x²
a = 1
bx = 4x
b = 4
c = 9
The quadratic formula is given as x = -b±√(b²-4ac)/2a
Substituting the constant;
x = -4±√(4²-4(1)(9))/2(1)
x = -4 ±√(16-36)/2
x = -4±√-20/2
x = -4±(√-1*√20)/2
Note that √-1 = i
x = -4±(i√4*5)/2
x = (-4±i2√5)/2
x = -4/2±i2√5/2
x = -2±i√5
The solution to the quadratic equation are -2+i√5 and -2i-√5
PLS SOMEONE HELP ME ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!
Answer:
C.
Step-by-step explanation:
When you replace x by x - h, the graph is shifted h units horizontally.
Here, x is replaced by x - 6.
x - h = x - 6
h = 6
6 is positive, so the shift is 6 units to the right.
Answer: C.
Use the least common denominator of 10 and 15 to solve 2/10+7/15 .
Answer: 2/3
Step-by-step explanation: As you can see, the denominators are different so we need to find a common denominator to add these 2 fractions.
We find the common denominator by finding
the common multiple for these 2 denominators.
Multiples of 10
1 x 10 = 10
2 x 10 = 20
3 x 10 = 30
Multiples of 15
1 x 15 = 15
2 x 15 = 30
As you can see, we have a common multiple of 30.
To get 30 in the denominator of 2/10, multiply top and bottom by 3.
To get 30 in the denominator of 7/15, multiply top and bottom by 2.
So we have 6/30 + 14/30 which is 20/30.
20/30 can be reduced to 2/3.
4x + 5 = x + 26 need help
Answer:
x = 7
Step-by-step explanation:
4x + 5 = x + 26
4x - x = 26 - 5
3x = 21
x = 21/3
x = 7
Check:
4*7 + 5 = 7 + 26
28 + 5 = 33
Please i need to know the meaning of this! : Thanks.
In the expression 2^3 the 2 is known as the
base
exponent
rational number
irrational number
Answer:
Hey there!
In this problem, 2 is known as the base.
Let me know if this helped :)
Answer:
The Base
Step-by-step explanation:
The base in a power is the number being raised to the exponent's power. It is the bigger number in the power.
2 is being raised to the third power. This means that 2 is the base of the power.
3 would be the exponent in the power.
Brainilest Appreciated.
Rose likes to water ski using her sister's boat. The boat takes 3 gallons of gas each hour to run. Gas costs $5 per gallon, how much money will she spend on gas to ski for 4 hours?
Answer:
$60
Step-by-step explanation:
Answer:
60$
Step-by-step explanation:
3 gallons per hr
multiply by 4
12gl per 4hrs
5 dl per gl
multiply by 12
60 dl per 12 gl
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
what seven divided by 4
Answer:
7 divided by 4 is 1 ¾ as a fraction, or 1.75 as a decimal.
Step-by-step explanation:
Pls mark as brainliest answer
The calculated division of the numbers seven divided by 4 is 1 3/4
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
seven divided by 4
When represented as an equation, we have
seven divided by 4 = 7/4
Divide 7 by 4
So, we have the following result
seven divided by 4 = 1 3/4
Using the above as a guide, we have the following:
the result is 1 3/4
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Solve x∕4 + y∕3 = 1 for x.
Answer:
x = [tex]\frac{12-4y}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{4}[/tex] + [tex]\frac{y}{3}[/tex] = 1
Multiply through by 12 to clear the fractions
3x + 4y = 12 ( subtract 4y from both sides )
3x = 12 - 4y ( divide both sides by 3 )
x = [tex]\frac{12-4y}{3}[/tex]
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
Could you help with maths please? All shown on the picture :)
Answer:
4 is tenths (a) and 5 is hundredths (b)
Step-by-step explanation:
Now, 0.45
0 indicates the ones place (it comes before the decimal)
0.45 can also be written as:
0.4+0.05
= 4/10+5/100
what can we conclude from this?
we can say that 4 is in the tenths whilst 5 is in the hundredths.
therefore, a is 4 and b is 5.
Hope this helps you! :)
what is the angle taken in anticlockwise direction between (1) North-east and south- west
Answer:
Step-by-step explanation:
North-east has a bearing of 45 degrees
South-west has a bearing of 225 degrees.
Taken anticlockwise,
angle = south-west - north-east
= (225-45)
= 180 degrees
answer
hope this helps....
Solving Inequalities and graphing them.
Answer:
I used to know this not anymore sry g
10 points to the person who answers this question.
Answer:
your answer is
2 X l+b
2 X 6x + 3x
8x + 10...
Q.An observer 1.7m tall is 20sqrt(3)m away from a tower.The angle of elevation from the eye of observer to the top of the tower is 30 Find the height of the tower
plz Answer me
Answer:
21.7 m
Step-by-step explanation:
The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.
tan θ = Opposite/ Adjacent
Opposite side = Height = unknown
Adjacent = 20sqrt(3) m
θ = Angle of Elevation = 30°
Hence, we have:
tan 30° = Opposite/ 20√3
Opposite = tan 30° × 20√3m
Opposite = 20m
Height of the tower = Height of the observer + Height (Opposite side)
Height = 20m
Height of the the observer as given in the question is = 1.7m
Height of the tower = 20m + 1.7m
= 21.7m
Therefore, the height of the tower = 21.7m
Find the value of x. Round to the nearest tenth.
15.9
12.4
12.8
16.3
Answer:
x = 15.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 28 = 14/x
x cos 28 = 14
x = 14 / cos 28
x=15.85598
Rounding to the nearest tenth
x = 15.9
If ∠A and ∠B are vertical angles, what is true about their measures?
Answer:
they are equal due to the vertical angles theorem
vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent
Answer:
They are equal
Step-by-step explanation:
I just had it on a exam and can I have brainliest Im trying to level up
What is the 6th row of Pascal's triangle?
Answer:
1, 6, 15, 20, 15, 6, 1
Describe how to solve an absolute value equation
*will give brainliest*
Answer:
Step 1: Isolate the absolute value expression.
Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.
Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically.
Step-by-step explanation:
Answer:
Rewrite the absolute value equation as two separate equations, one positive and the other negative
Solve each equation separately
After solving, substitute your answers back into original equation to verify that you solutions are valid
Write out the final solution or graph it as needed
Step-by-step explanation:
Simplify the following expression.
Answer:
3x+11y-3
Step-by-step explanation:
Hey! So here is what you do to solve the problem-
Combine like terms:
(x) 5x-2x=3x
(y) 3y+8y=11y
(#) 7-10 =-3
So....
3x+11y-3 is your answer!
Hope this helps!:)
I REALLY NEED HELP PLEASE HELP ME :(
Answer:
I may be wrong but I think 8 is your answer.
Step-by-step explanation:
(-1)^(3/7) x 128^(3/7)
-1 x 128^3/7
128^(3/7) = 8
= 8
