Answer:
If 3 people can complete half a job in 20 days, then three people can complete a job in 40 days. Since 12 people is four times as many, instead of taking 40 days, it should take 10 days
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I NEED ANSWER ASAP please and thank you
Answer:
hexagon and pentagon structure. also known as a truncated icosahedron
Step-by-step explanation:
hope that gives you a good enough description.
Prove that (- 1 + i)^7 = -8(1 + i)
Convert [tex]-1+i[/tex] to polar form.
[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]
By de Moivre's theorem,
[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]
QED
3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared the insect endangered and transplanted the insect to protected area. The population P(t) (in thousands) of insects in t months after being transplanted is
a. [3 pts] Determine the number of months until the insect population reaches 40 thousand (round to 2 decimal places).
b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your answer.
c. [3 pts] Sketch a graph of the function using the window and. Be sure to indicated the scale on the graph, label the axes, at least 2 points on the graph, and any asymptotes.
The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.
Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).
(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get
P(t)=40
(50(1+0.05t))/(2+0.01t)=40
Cross multiply both sides, we get
50(1+0.05t)=40(2+0.01t)
Apply the distributive property a(b+c)=ab+ac, we get
50+2.5t=80+0.4t
Subtract 0.4t and 50 from both sides, we get
50+2.5t-0.4t-50=80+0.4t-0.4t-50
2.1t=30
Divide both sides with 2.1, we get
t=14.29 months
(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get
[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]
(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.
Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.
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In 2012, the population of a city was 6.38million. The exponential growth rate was 2.38% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9million?
d) Find the doubling time.
Question content area bottom
Part 1
a) The exponential growth function is P(t)
enter your response here, where t is in terms of the number of years since 2012 and P(t) is the population in millions.
The exponential growth function is P(t) = 6.38 million x (1.0238^t).
The population of the city in 2018 is 7.35 million.
The year the population would be 9 million is 14.46 years.
The doubling time is 29.12 years.
What is the exponential growth function?FV = P (1 + r)^n
FV = Future populationP = Present populationR = rate of growthN = number of years6.38 million x (1.0238^t)
Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million
Number of years when population would be 9 million : (In FV / PV) / r
(In 9 / 6.38) / 0.0238 = 14.46 years
Doubling time = In 2 / 0.0238 = 29.12 years
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just need b1 and b2
brainliest to whoever answers
50 points
Step-by-step explanation:
b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.
The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.
b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.
The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.
find x and y pls help
30 + 110 + 30 + 110 = 280
360-280 = 80
2y = 80
y = 40 degrees
If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.
30 + 40 = 70
The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.
In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180
Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.
Angles in triangle add to 180.
180 - 110 - 30 = 40.
Thus, x = 40 degrees
There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)
Hope this helps!
Which equation can be used to solve for b?
Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 30 degrees. The length of side B C is 5 centimeters, the length of B A is 10 centimeters, and the length of C A is b.
tan(30o) = StartFraction 5 Over b EndFraction
tan(30o) = StartFraction b Over 5 EndFraction
tan(30o) = StartFraction 10 Over b EndFraction
tan(30o) =
Answer:
[tex]tan(30) = \frac{5}{b} [/tex]
Step-by-step explanation:
Trigonometric Ratios.
To solve for b, we check the parameters that are given in the triangle.
If we're considering 30°, we can see that the opposite is given as 5cm and the adjacent is b.
Applying:
[tex]tan \alpha = \frac{oppsite}{adjacent} \\ \\ tan \: (30) = \frac{5}{b} [/tex]
Answer:
a
Step-by-step explanation:
just did the quiz!!!!
Please Help! Brainliest Avaliable! Literally Multiple Choice!
It's very simple. Subract 554.26 from 866.32
then, we got the difference is
312.06
thank you
Brainlist please.
Consider the equation x+4=−2x+19. Let f(x)=x+4and g(x)=−2x+19. The graph of each function is shown. Coordinate plane with the graphs of two lines. The horizontal x axis labeled from negative three to nine in increments of one. The vertical y axis labeled from negative two to nineteen. The line f of x passes through ordered pairs zero comma four and two comma six. The line g of x passes through the ordered pairs zero comma nineteen and one comma seventeen. At what point do the graphs intersect? Enter your answer in the box.
The point of intersection of both graphs will have the coordinate (5, 9).
What is the Point of Intersection of the Graph?
We are given the functions;
f(x) = x + 4
g(x) = -2x + 19
Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;
x + 4 = -2x + 19
x + 2x = 19 - 4
3x = 15
x = 15/3
x = 5
Thus;
f(x) = 5 + 4 = 9
g(x) = -2(5) + 19 = 9
Thus, the point of intersection of both graphs will have the coordinate (5, 9)
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each statement with its contrapositive.
Option 4,option 6, and option 2 is the respective contrapositive to the statements given. This can be obtained by understanding what contrapositive is and converting the statements.
What is contrapositive? Contrapositive: A statement which is obtained by interchanging both the hypothesis and conclusion of a given statement after contradicting them. For "if p then q" the contrapositive is "if not-q,then not-p "For example,Statement = If a figure is a square, then it is a quadrilateral.
Contrapositive = If a figure is not a quadrilateral, then it is not a square.
Here,
Statement 1: If two figures are congruent, then their corresponding sides are equal.Contrapositive: If the corresponding sides of two figures aren't equal, then the two figures aren't congruent. (Option 4)
Statement 2: If two numbers are even, then their product is even.Contrapositive: If the product of two numbers isn't even, then the two numbers aren't even. (Option 6)
Statement 3: If a figure is a pentagon, then the sum of its interior angles is 540°.Contrapositive: If the sum of the interior angles of a figure isn't 540°, then the figure isn't a pentagon. (Option 2)
Hence Option 4,option 6, and option 2 is the respective contrapositive to the statements given.
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solve for x by completing the square: x2 − 8x + 13 = 0. show all work
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
How to find the roots of a polynomial by completing the square
In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:
x² - 8 · x + 13 = 0
x² - 8 · x + 16 = 3
(x - 4)² = 3
x - 4 = ± √2
x = 4 ± √2
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
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I cant figure this one out pls help
The value of x from the given expression is -2
Slope of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the following parameters
m = 1
(x1, y1) = (0, 2)
(x2, y2) = (x, 0)
Substitute
1 = x-0/0-2
1 = x/-2
x = -2
Hence the value of x from the given expression is -2
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Assignment
Slide the green dot from 0 to plot the number at the correct
location.
Plot-1.
-6 -5 4 -3 -2 -1 0 1
2
3 4
5
+
6
Use the interactive number line to find each sum to
complete the table.
A
1
-1
-4
-6
B
2
-2
1
-3
A + B
3
R
S
T
From the number line, the values which completes the sum in the table are:
R = -3.S = -3.T = -9.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
How to find each sum?From the table of values (see attachment), the values on the number line are represented as follows:
a + b = a + b
R = -1 - 2
R = -3.
a + b = a + b
S = -4 + 1
S = -3.
a + b = a + b
T = -6 - 3
T = -9.
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A and B are independent events. P(A) = 0.60 and P(B) = 0.30.
What is P(A and B)?
A. 0
B. 0.18
C. 0.90
D. 0.018
Answer: 0.18
Step-by-step explanation:
The probability of the event P(A and B) is equal to 0.18.
The correct option is (C).
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability has been introduced in Arithmetic to forecast how likely occurrences are to happen.
As per the given data:
We are given the probability of two events:
P(A) = 0.60 and P(B) = 0.30
We are also given that A and B are independent events.
To find the probability of P(A and B):
The term and is equivalent to the term intersection.
P(A and B) = P(A∩B)
For any 2 independent events A and B the probability P(A∩B) is given by:
= P(A) × P(B)
By substituting the given values in the question
= 0.60 × 0.30
= 0.18
The probability of the event P(A and B) is equal to 0.18.
Hence, The probability of the event P(A and B) is equal to 0.18.
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Pls help me I'm stuck
The measure of the angle BAM is approximately 40.894°.
What is the angle withing a rectangle?
In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:
[tex]\tan \theta = \frac{BM}{AB}[/tex]
[tex]\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{3}}{2}[/tex]
θ ≈ 40.894°
The measure of the angle BAM is approximately 40.894°.
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The current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?
The answer is x=21 the explanation is on the picture above I hope I helped
If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.
What is speed?Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:
Speed=Distance/ Time.
How to calculate speed?We have been given that the speed of stream is 7miles per hour.
Let v be the speed of the boat, and t the time to travel
98=t*(7+v) (1)
49=t(v-7) (2)
(1)+(2) => 2tv=147
7t+(49+7t)=98
14t+49=98
14t=49
t=49/14
t=7/2
Put the value of t in equation 1 to get the value of v:
98=t(7+v)
98=7/2(7+v)
196/7=7+v
28=7+v
v=28-7
v=21
Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.
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find the value of x and y
Calculate the following ratios, correct to 3 decimal places. a. sin 58 = b. cos 26 = c. tan 63=.
Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962
Step-by-step explanation:
A bagel shop sells coffee in a container shaped like a rectangular prism. A graphic designer who works for the bagel shop drew the net below to create a design for the container.
1598 cm square is the area of the container.
According to the statement
we have given that the container is rectangular prism
And Length of rectangular prism is 34cm
Width of rectangular prism is 17 cm
Height of rectangular prism is 20 cm
we use the below written formula to find the surface area
Surface area formula A=(wl+hl+hw)
To find the surface area of the container.
Substitute the values of Length, width and height in the formula then
A=(wl+hl+hw)
A=((17)(34)+(20)(34)+(20)(17))
After solving the values
A=(578+680+340)
A= 1598
So, 1598 cm square is the area of the container.
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The following are the ages (years) of 5 people in a room:
14
,
16
,
16
,
13
,
A person enters the room.
The mean age of the 6 people is now 21.
What is the age of the person who entered the room?
Answer:
67 years old. (you only gave 4 people and missed out one person)
Step-by-step explanation:
take all the ages first and put the unknown (age of the person who entered the room) as x.
14, 16, 16, 13, x
all of these numbers added to together would be:
59 + x
Because the question is talking about the mean age, to find mean:
add all the values in the data (ages) and divide by the total number of values on the list. (in your case would be 6 people (following your question) but you gave only 5 people including the x).
then (59 + x) / 6 = 21
21 x 6 = 126
126 = 59 + x
x = 67
answer this please only the ones that are blank
Answer:
#3 5(2a+4)
#4 5(a+2+4)
#5 5a+5(2+4)
Step-by-step explanation:
I think so, I am probably wrong
Help Me Please with this Math Money Question It Wont Me Screenshot But
Question: CD's are 5 for $30.00.
What is the price of 3 CD's?
Answers:
A) $18.00
B) $15.00
C) $6.00
D) $3.00
Answer:
A
Step-by-step explanation:
$30.00 ÷ 5 = $6.00
$6.00 × 3 = $18.00
Question 1 (3 points)
Solve the following linear system:
y = -2x - 5
y = 2/3x + 3
as an ordered pair (x,y)
Answer:
Step-by-step explanation:
hello : y = -2x - 5
y = 2/3x + 3
means : -2x-5 = 2/3 x+3
-6x-15 = 2x +9
-8x=24 so : x = -3
put the value for : x in the first equation :y = -2(-3)-5 =1
the ordered pair (-3;1) is solution
Question is attached as an image
The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].
The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].
What are the general and particular solutions of the logistic equation?
In this question we are before a type of ordinary differential equation known as equation with separable variables, that is to say, that variables t and y can be separated at each side of the expression in order to find a solution:
dy / dt = 3 · y · (1 - y /14)
dy / [(- 3 / 14 ) · y · (y - 14)] = dt
Then, we simplify the expression by partial fractions and integrate the resulting expression:
- (1 / 14) ∫ dy / y + (1 / 14)∫ dy / (y - 14) = - (14 / 3)∫ dt
- (1 / 14) · ㏑ |y| + (1 / 14) · ㏑ |y - 14| = - (14 / 3) · t + C, where C is the integration constant.
㏑ |(y - 14) / y| = - (14 / 3) · t + C
[tex]1 - \frac{14}{y} = C\cdot e^{-\frac{14\cdot t}{3} }[/tex]
[tex]\frac{14}{y} = 1 - C \cdot e^{-\frac{14\cdot t}{3} }[/tex]
[tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex]
The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].
If y(0) = 10, then the particular solution of the differential equation is:
10 = 14 /(1 - C)
1 - C = 1.4
C = - 0.4
The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].
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14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.
(Hint: Let x = smaller piece...)
Answer:
The small piece is 6 yards and the large piece is 8 yards.
Step-by-step explanation:
Let x = small
Let y = large
x + y = 14 3y = 4x
3y = 4x Divide both sides of the equation by 3 to solve for y
y = [tex]\frac{4}{3}[/tex] x Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.
x + y = 14
x + [tex]\frac{4}{3}[/tex] x = 14 x and 1 x mean the same thing. Another name for 1 is [tex]\frac{3}{3}[/tex]
[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14
[tex]\frac{7}{3}[/tex]x = 14 Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x
([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6
x = 6
If x = 6, then y must be 8 because 6 + 8 = 14
Some boys and girls are waiting for school buses. 25 girls get on the first bus. The ratio of boys to girls at the stop is now 3:2. 15 boys get on the second bus. There are now the same number of boys and girls at the bus stop. How many students were originally at the bus stop?
Answer:
100
Step-by-step explanation:
Forming algebraic equations and solving:
Let the number of boys originally at the stop = 'x'
Let the number of girls originally at the stop = 'y'
25 girls get on the first bus.
⇒ The number of girls now at the stop = y -25
Ratio of boys to girls:
[tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)
15 boys get on the second bus.
Now, the number of boys at the stop = x - 15
Number of girls at the stop = y - 25
Ratio of boys to girls,
[tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]
x = y -25 + 15
x = y - 10
Plugin x = y - 10 in equation (I)
2*(y-10) = 3y -75
2y - 20 = 3y -75
-20 = 3y - 75 - 2y
-20 = y -75
-20 +75 = y
[tex]\sf \boxed{\bf y = 55}[/tex]
Plugin y = 55 in equation (I)
x = 55 -10
[tex]\sf \boxed{\bf x = 45}[/tex]
Number of students originally at the stop = x + y
= 55 + 45
= 100
Sets A,B , and C are subsets of the universal set U.
These sets are defined as follows.
U= {f,g,h,p.q.r.x.y.z}
A={f,h,p.q.r}
B={q,r,y,z}
C={g,h,p,q,y}
Find (B' U A) ∩ C.
Write your answer in roster form or as Ø.
[tex]B'=\{f,g,h,p,x\}\\B'\cup A=\{f,g,h,p,q,r,x\}\\(B'\cup A)\cap C=\{g,h,p,q\}[/tex]
Theodore invests $20,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1
year period?
Answer:
Answer:
$21200
Step-by-step explanation:
6% × 20000 = 1200.
20000 + 1200 = 21200
basically yout find 6% of 20000 then add it the original 20000
In the following activity, write an equation to represent each verbal statement, and use it to find the value of each unknown number. Then, put the solution values in order from smallest to largest. [Note: The smallest solution is "first", and the largest solution is "fifth".]
The solution values in order from smallest to largest are;
-13 - First-10 - Second-3.5 - Third-2 - Fourth-0.75 - FifthUnknown equationlet
the unknown number = x(x - 5)-2 = 14
-2x + 10 = 14
-2x = 14 - 10
-2x = 4
x = 4/-2
x = -2
4x - 5 = -8
4x = -8 + 5
4x = -3
x = -3/4
x = -0.75
(x + 3) / 5 = -2
x + 3 = -2(5)
x + 3 = -10
x = -10 - 3
x = -13
1/2x + 4 = -1
1/2x = -1 - 4
1/2x = -5
x = -5 ÷ 1/2
= -5×2/1
x = -10
x + 2 = 6/-4
-4(x + 2) = 6
-4x - 8 = 6
-4x = 6 + 8
-4x = 14
x = 14/-4
x = -3.5
Therefore, the smallest value is -13 and the largest value is -0.75.
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56m² = ____________ GCF =
68m² = ____________ GCF =
The greatest common factor of the expression is 4m⁴.
What is GCF?GCF simply means the greatest common factor.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Hence,
56m⁵
68m⁴
The greatest common factor of the expression is the largest positive expression that divides evenly into all numbers with zero .
Hence, the greatest common factor is 4m⁴
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