Answer:
Approximately after 66.15 years, there will be 100 coyotes left
Step-by-step explanation:
We can use the formula [tex]F=P(1+r)^t[/tex] to solve this.
Where
F is the future amount (F=100 coyotes)
P is the initial amount (P=750 coyotes)
r is the rate of decrease per year (which is -3% per year or -0.03)
t is the time in years (which we need to find)
Putting all the information into the formula we solve.
Note: The logarithm formula we will use over here is [tex]ln(a^b)=bln(a)[/tex]
So, we have:
[tex]F=P(1+r)^t\\100=750(1-0.03)^t\\100=750(0.97)^t\\\frac{100}{750}=0.97^t\\\frac{2}{15}=0.97^t\\ln(\frac{2}{15})=ln(0.97^t)\\ln(\frac{2}{15})=tln(0.97)\\t=\frac{ln(\frac{2}{15})}{ln(0.97)}\\t=66.15[/tex]
Hence, after approximately 66.15 years, there will be 100 coyotes left.
Rounding, we will have 66 years
If the probability of an event is 2/7 what must be the probability of its complement?
Answer:
5/7
Step-by-step explanation:Let
x------->the probability of its complement
we know that
The Complement Rule states that the sum of the probabilities of an event and its complement must equal
so
in this problem
2/7 + x = 1
solve for x
Adds 1- 2/7 both sides
x= 1 - 2/7
x= 5/7
Answer:
5/7
Step-by-step explanation:
help fast, please
A. Expand the following and state the Law that is indicated.
1. log4(3x)
2. log3(27/x)
3. log4(x5)
ANSWER
1.
[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]
2.
[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]
3.
[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) [/tex]
EXPLANATION
1. The given logarithmic expression is
[tex] log_{4}(3x) [/tex]
Use the product rule:
[tex] log_{a}(mn) = log_{a}(m) + log_{a}(n) [/tex]
We apply this rule to obtain:
[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]
2. The given logarithmic expression is
[tex] log_{3}( \frac{27}{x} ) [/tex]
We apply the quotient rule:
[tex]log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n) [/tex]
This implies that;
[tex]log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x) [/tex]
We simplify to get;
[tex]log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x) [/tex]
Apply the power rule:
[tex] log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]
[tex]log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x) [/tex]
simplify;
[tex]log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x) [/tex]
[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]
3. The given logarithmic expression is;
[tex] log_{4}( {x}^{5} ) [/tex]
Apply the power rule of logarithms.
[tex]log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]
This implies that,
[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) .[/tex]
Jenny has two congruent kleenex boxes. The first box has a volume of 72 in2, a length of 3 inches and a width of 4 inches. What is the height of the second box?
Answer:
The height of the second box is [tex]6\ in[/tex]
Step-by-step explanation:
we know that
If the two boxes are congruent
then
The volume of the first box is equal to the volume of the second box
The length of the first box is equal to the length of the second box
The width of the first box is equal to the width of the second box
The height of the first box is equal to the height of the second box
so
Find the height of the first box
Remember that
The volume of the box is equal to
[tex]V=LWH[/tex]
substitute the values and solve for H
[tex]72=(3)(4)H[/tex]
[tex]H=72/(12)=6\ in[/tex]
One solution to the problem below is 7. What is the other solution?
Answer:
-7
Step-by-step explanation:
7 and -7 squared both equal 49
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 8. If there were 3585 yes votes, what was the total number of votes?
Answer: 9321 votes
Step-by-step explanation:
1- You can express the ratio as following:
[tex]5:8[/tex] or [tex]\frac{5}{8}[/tex]
2- Let's call the number of no votes "N"
3- Therefore, if there were 3585 yes votes, then you can write the following expression to calculate the number of no votes:
[tex]\frac{5}{8}=\frac{3585}{N}\\\\N=\frac{3585*8}{5}\\\\N=5736[/tex]
4- Then, the total number of votes is:
[tex]t=3585votes+5736votes=9321votes[/tex]
Answer:
9321
Step-by-step explanation:
We can simply make a ratio (fraction) to solve this. Let total number of NO votes be N. Shown below is the ratio:
[tex]\frac{YesVotes}{NoVotes}=\frac{5}{8}=\frac{3585}{N}[/tex]
Now we can cross multiply and solve for N:
[tex]\frac{5}{8}=\frac{3585}{N}\\5N=8*3585\\5N=28,680\\N=\frac{28680}{5}=5736[/tex]
Hence, number of NO votes is 5736.
To get TOTAL number of votes, we add number of yes votes (3585) to that of number of no votes (5736).
Total votes = 3585 + 5736 = 9321
A scale on a map shows that 2.5 centimeters represents 15 kilometers. What number of actual kilometers are represented by 17.5 centimeters on the map?
Answer:
105
Step-by-step explanation:
to get this you must first divide 17.5 by 2.5 to see how many times to multiply 15 by 2.5
sorry if it does not make scence
Which best describes a triangle with side lengths 4 inches, 5 inches, 6 inches ?
Answer:
An Acute triangle
Step-by-step explanation:
It is an acute triangle, because the following characterization holds:
If [tex]c^2<a^2+b^2[/tex], the triangle is acuteIf [tex]c^2=a^2+b^2[/tex], the triangle is rightIf [tex]c^2>a^2+b^2[/tex], the triangle is obtuseIn this case,
[tex]6^2=36<5^2+4^2=25+16=41[/tex]
What is the following sum?
(please show how you worked it out)
Answer:
[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]
Step-by-step explanation:
Let's start by breaking down each of the radicals:
[tex]\sqrt[3]{16x^3y}[/tex]
Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of [tex]x^3[/tex], and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:
[tex]\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}[/tex]
We can apply this same technique of "extracting cubes" to the second term:
[tex]\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}[/tex]
Replacing those two expressions in the parentheses leaves us with this monster:
[tex]2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})[/tex]
What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:
[tex]4, \sqrt[3]{2} , x[/tex]
We can factor those out to give us a final, simplified expression:
[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]
Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.
The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?
Answer:
The measure of the complement angle is [tex]18\°[/tex]
Step-by-step explanation:
Let
x-----> the angle
we know that
The complement of an angle is equal to [tex](90-x)\°[/tex]
The supplement of an angle is equal to [tex](180-x)\°[/tex]
we have
The complement of an angle is one-sixth the measure of the supplement of the angle
[tex](90-x)\°=(1/6)(180-x)\°[/tex]
solve for x
[tex](540-6x)\°=(180-x)\°[/tex]
[tex](6x-x)=(540-180)\°[/tex]
[tex](5x)=(360)\°[/tex]
[tex]x=72\°[/tex]
Find the measure of the complement angle
[tex](90-x)\°[/tex] ------> [tex](90-72)=18\°[/tex]
Answer:
18⁰
Step-by-step explanation:
Angle = x
Complement = 90 - x
Supplement = 180 - x
Given:
90 - x = 1/6 × (180 - x)
540 - 6x = 180 - x
5x = 360
x = 72
Complement = 90 - 72 = 18⁰
The cost of having a plumber spend h hr at your house if the plumber charges $30 for coming to the house and $x per hour for labor. The expression for the cost of the plumber coming to the house is how many dollars.
Answer:
[tex]C(h)=\$30+xh[/tex]
Step-by-step explanation:
Let
C-----> the cost of having a plumber spend h hours at your house
h----> the number of hours
x----> the cost per hour of labor
we know that
The linear equation that represent the cost C is equal to
[tex]C(h)=\$30+xh[/tex]
In this linear equation in the slope-intercept form (y=mx+b)
the slope is equal to [tex]m=x\frac{\$}{hour}[/tex]
the y-intercept b is equal to [tex]b=\$30[/tex] ---> charge for coming to the house
Answer:
C = 30 + x * h
Step-by-step explanation:
The total cost for the plumber is his initial fee plus the number of hours times the cost per hour
C = 30 + x * h
What is the area of this triangle?
Round to the nearest hundredth.
Answer: 2.94 ft²
Step-by-step explanation:
Observe the figure attached:
The line LM divide the triangle into two right triangles.
Find the heigh "h" as following:
[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(40\°)=\frac{h}{2.7}\\\\h=(2.7)(sin(40\°))\\h=1.73ft[/tex]
Apply the formula for calculte the area of a triangle:
[tex]A=\frac{Bh}{2}[/tex]
Where B (B=3.4 ft) is the base and h is the height (h=1.73ft)
Then:
[tex]A=\frac{(3.4ft)(1.73ft)}{2}=2.94ft^2[/tex]
Graph the relation and its inverse. Use open circles to graph the points of the inverse. x –3 4 6 9 y 5 6 –9 –10
Answer:
See attached picture.
Step-by-step explanation:
Graph the function as (x,y) points.
(-3,5)
(4,6)
(6,-9)
(9,-10)
These are graphed in black on the picture.
To graph the inverse, switch the points from (x,y) to (y,x).
(5,-3)
(6,4)
(-9,6)
(-10,9)
These are graphed in red on the picture.
A room has a floor area of 120 square feet and a height of 8 feet. What is the volume of the room?
Answer:
V = 960 ft^3
Step-by-step explanation:
The volume of a room can be found by
V = Area of base time height
V = 120 * 8
V = 960 ft^3
Write the algebraic expression for the phrase below. Use k for the variable. The product of a number and six.
Answer:
[tex]6k[/tex]
Step-by-step explanation:
Let
k-----> the variable
we know that
The phrase " The product of a number and six" is equal to multiply the variable k ( the number) by 6
so
[tex]6k[/tex]
Item 7 Solve for x. ? 4(5x?20)=?20 ? Enter your answer in the box.
Answer:
x=3
Step-by-step explanation:
Sally is a sales manager.She makes $73,000 a year.Sally has worked hard all year and receives a 6% raise.How much will sally make next year?
Answer:
$77,380
Step-by-step explanation:
If she gets a 6% raise next year she will make 106% of what she makes this year.
106% is 1.06 as a decimal. Multiply her salary by 1.06 to find out how much she will make next year...
$73,000(1.06) = $77,380
Answer:
77,380
Step-by-step explanation:
divide 73000 by 100% and you get 730, then you multiply it by 6 since you need a 6% raise. once you get this value, you simply add it to the 73000 and you get the answer
Write the slope-intercept form of the equation that passes through the point (3,6) and is parallel to the line y = 5x - 5
Answer:
the slope-intercept form:
y = 5x - 9
Step-by-step explanation:
y = 5x - 5, this line has slope = 5
parallel line, slope is the same so slope of the parallel = 5
equation
y - 6 = 5(x - 3)
y - 6 = 5x - 15
y = 5x - 9 <------the slope-intercept form
Answer: [tex]y=5x-9[/tex]
Step-by-step explanation:
The slope-intercept form of a equation of the line is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept-
If the lines are parallel then they have the same slope:
m=5
Find b substitutin the point and the slope into the equation and solving for b:
[tex]6=3*5+b\\b=-9[/tex]
Then the equation is:
[tex]y=5x-9[/tex]
How many square feet will we need for this hole that has 4 feet 12 feet 3 feet 2 feet 1 feet 2 feet
I think you're answer is five hundred seventy six
The two solids are similar and the ratio between the lengths of their edges is 2:7 what is the ratio of their surface areas?
Answer:
The ratio of their surface areas is [tex]\frac{4}{49}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
In this problem the scale factor is equal to the ratio [tex]\frac{2}{7}[/tex]
and
Remember that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
therefore
In this problem the ratio of their surface areas is [tex](\frac{2}{7})^{2}=\frac{4}{49}[/tex]
Final answer:
The ratio of the surface areas of two similar solids with a linear dimension ratio of 2:7 is 4:49.
Explanation:
The question deals with the concept of geometric similarity and the ratio of surface areas for similar solids. When two solids are similar, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions. Therefore, if the ratio between the lengths of their edges is 2:7, then the ratio of their surface areas would be the square of this ratio, which is (22):(72) or 4:49.
The width of the Ochoa community pool is 20 feet. The length is twice as long as it's width. What is the perimeter of the pool?
Answer:
120 feet
Step-by-step explanation:
1. find the length of the pool (2*20 = 40 feet)
2. add the sides 2L + 2W
2L = 2*40 = 80
2W = 2*20 = 40
80+40=120
What is measure of angle A?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
The measure of the angle A is [tex]53.13\°[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
The tangent of angle A is equal to the opposite side to the angle A divided by the adjacent side to angle A
so
[tex]tan(A)=\frac{BC}{AB}[/tex]
substitute
[tex]tan(A)=\frac{4}{3}[/tex]
[tex]<A=arctan(\frac{4}{3})=53.13\°[/tex]
The perimeter of a square is represented by the expression 4x−6. 4
Which expression also represents the perimeter?
1) 4(x−24)
2) 4(x−6)
3) 2(x−3)
4) 4(x−32)
probably the formula is 4×(x-1.6)
Answer:
4) 4(x−32)
Step-by-step explanation:
Jason has two bags with 6 tiles each.
Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing an even tile from the first bag and an even tile from the second bag?
Answer:
1/4.
Step-by-step explanation:
I am assuming that there are 3 even and 3 odd tiles in each bag.
Probability( drawing an even tile form one bag) = 3/6 = 1/2.
The probability of drawing an even from the first and an even from the second = 1/2 * 1/2 = 1/4 (answer).
The individual probabilities are multiplied because the 2 events are independent.
Answer:
9/36
Step-by-step explanation:
Suppose f is a continuous function defined on a closed interval a,
b. (a) what theorem guarantees the existence of an absolute max- imum value and an absolute minimum value for f ? (b) what steps would you take to find those maximum and minimum values?
Answer:
Step-by-step explanation:
(a) The Extreme Value Theorem.
(b) We would differentiate the function and equate this to zero. The zeroes of the function will give us the values of the maxima / minima and we can find find the absolute maxima/minima from the results. Note we might have multiple relative maxima/ minima but only one absolute maximum and one absolute minimum.
Final answer:
The Extreme Value Theorem guarantees that a continuous function on a closed interval has an absolute maximum and minimum. To find these, one calculates the derivative to find critical points, analyzes the derivative's sign around these points, and evaluates the function at the critical points and the interval's endpoints.
Explanation:
Extreme Value Theorem and Finding Maximum and Minimum Values
The theorem that guarantees the existence of both an absolute maximum and minimum value for a continuous function defined on a closed interval a, b is known as the Extreme Value Theorem. This theorem plays a crucial role in calculus and mathematical analysis and is fundamental in understanding the behavior of continuous functions on closed intervals.
To find these maximum and minimum values, one would typically follow these steps:
Calculate f'(x), the derivative of the function f(x), to find the critical points.
Analyze the sign of f'(x) around the critical points to determine if they are local minima, local maxima, or saddle points.
Evaluate the function f(x) at each critical point as well as the endpoints of the interval [a, b] to determine the absolute extrema.
Moreover, if a function satisfies the criteria of being continuous on [a, b] and differentiable on (a, b), then by a related theorem called the Mean Value Theorem, there exists at least one c in (a, b) where f'(c) = 0.
These methods form the standard procedure for finding the extremal values that a continuous function may possess on a closed interval.
Basil earned 631.40 in 7 years on an investment at a 5.5% simple interest rate. How much was basils investment
7 * 0.055 = 0.385
631.40 / 0.385 = $1,640
Marcus needs 108 inches of wood to make a frame how many feet of wood Does Marcus need for the frame
Answer: 9 feet.
Step-by-step explanation: The formula to convert inches to feet is to divide the amount in inches by 12. 108/12 = 9.
Need help with this
Answer:
[tex]\large\boxed{\tan x(\cot x-\cos x)=1-\sin x}[/tex]
Step-by-step explanation:
[tex]Use\\\\(\tan x)(\cot x)=1\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\text{distributive property:}\ a(b-c)=ab-ac\\======================\\\\\tan x(\cot x-\cos x)=(\tan x)(\cot x)-(\tan x)(\cos x)\\\\=1-\left(\dfrac{\sin x}{\cos x}\right)(\cos x)=1-\sin x[/tex]
Suppose the roots of a polynomial are −3, 4, 5, and −7. Which choice is a factor of the polynomial? A) (x + 5) B) (x − 3) C) (x − 4) D) (x − 7)
Answer:
C) (x - 4)
Step-by-step explanation:
A root makes a factor be zero. The root of 4 will make the factor x-4 be equal to zero.
Answer:
(x-4)
Step-by-step explanation:
the roots of a polynomial are −3, 4, 5, and −7.
When 'a' is a root of the polynomial then (x-a) is a factor
Lets write the factors for all the root given
[tex](x-(-3))(x-4)(x-5)(x-7)[/tex]
[tex](x+3)(x-4)(x-5)(x-7)[/tex]
Check with the options, which factor is in our polynomial
(x-4) is one of the factor
40 packs of baseball cards for discounted price of 64 he sells 30 packs of baseball cards to A friend at cost much should he charge
Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=5t−5 and y(t)=2t−k, and the position of particle B is given by x(t)=4t and y(t)=t2−2t−1.(a) If k=−6, do the particles ever collide?(b) Find k so that the two particles are certain to collide.k=(c) At the time the particle collide in (b), which is moving faster?A. particle AB. particle BC. neither particle (they are moving at the same speed)
Answer:
a. No the particles will never collide.
b. The second particle is moving faster.
Step-by-step explanation:
We can tell they never collide based on the fact that they will never have the same two points. We can tell this because there is only one time in which they will have the same x value. To find this amount of time, set the two x values equal to each other and solve for t.
5t - 5 = 4t
-5 = -t
5 = t
So we know the x value will only be the same at 5 seconds. Now we can input that value and see if the y values are the same.
2t + 6 = t^2 - 2t - 1
2(5) + 6 = 5^2 - 2(5) - 1
10 + 6 = 25 - 10 - 1
16 = 14 (FALSE)
Therefore they do not collide.
For the second part of the question, we know that the second one is moving faster based on the fact that there is a squared value in the y formula. This shows that it is moving at an exponential rate, which always changes faster than a linear rate.
Particle A and particle B never collide.
The value of k where the particles collide is k = -4
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two particles:
Particle A:
x(t) = 5t - 5
y(t) = 2t - k
Particle B:
x(t) = 4t
y(t) = t² - 2t - 1
We see that,
The x(t) of particle A and x(t) of particle B are the same only at t = 5.
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
Now,
y(t) = 2t - k = 2 x 5 - k = 10 - k
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
(a) If k = -6.
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 6 = 16
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
In order to collide both the x(t) of particles A and B must be the same.
Similarly, y(t) must be the same.
So,
Particle A and particle B never collide.
(b)
The value of k where the particles collide.
k = -4
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
(c)
The time at which the particles collide.
t = 5 and k = -4
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
Thus,
Particle A and particle B never collide.
The value of k where the particles collide is k = -4
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
Learn more about equations here:
https://brainly.com/question/17194269
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