Answer:
[tex]t=7.85 years[/tex]
Step-by-step explanation:
We can write this rate as an ordinary differential equation.
[tex]\frac{dP}{dt}=aP[/tex]
Where a is proportional constant, P the population variable, and t the time.
[tex]\frac{dP}{P}=adt[/tex]
Integrating each side of the equation.
[tex]\int \frac{dP}{P}=\int adt[/tex]
[tex]ln(P)=at+c[/tex]
[tex]P=e^{at+c}[/tex]
[tex]P=e^{c}e^{at}=Ce^{at}[/tex]
To find C we need to use the initial condiction, it means evaluae P at t=0.
[tex]P_{0}=Ce^{0}=C[/tex]
[tex]P=P_{0}e^{at}[/tex]
Now, we use the sentence the population has doubled in 5 years.
[tex]2P_{0}=P_{0}e^{a5}[/tex]
We can find "a" in this condition.
[tex]2=e^{a5}[/tex]
[tex]ln(2)=a5[/tex]
[tex]a=\frac{ln(2)}{5}[/tex]
[tex]a=0.14[/tex]
Finally, let's find how long will it take to triple.
[tex]3P_{0}=P_{0}e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
[tex]t=\frac{ln(3)}{0.14}[/tex]
[tex]t=7.85 years[/tex]
I hope it helps you!
Please help me if u know
Does the graph in Exercise 33 have a Hamilton path? If
so, find such a path. If it does not, give an argument to
show why no such path exist
;
Answer:
there is a graph first step to but I cannot draw it on here but you already have your answer without Step 2
Step-by-step explanation:
a simple path in a graph G that passes through every vertex exactly once is called a path . the graph G has no past because any past containing all vertices must contain one of the edges (e, c) (d, f ) and (B, G) move than once .
Find the scale factor of PQRS to JKLM and the values of w, x, and y.
The scale factor of PQRS to JKLM is 4/5 and the values of w, x and y are 20, 12.5 and 20 respectively.
What is Scale Drawing?A scale drawing is a drawing made by enlarging or reducing the size of the original object.
The factor by which the drawing is enlarged or reduced is called the scale factor.
Given two quadrilaterals PQRS and JKLM.
Since the shape is similar, the angles are equal and thus are similar figures.
The corresponding sides of two similar figures are proportional.
Scale factor of PQRS to JKLM = QR / KL = 12 / 15 = 4/5
Using the proportional rule for similar figures,
KL / QR = LM /RS = MJ / SP = JK / PQ
15 / 12 = x / 10 = y / 16 = 25 / w
Scale factor = 15/12 = 5/4
Consider 15 / 12 = x / 10.
12x = 150
x = 12.5
Consider 15 / 12 = y / 16
12y = 15 × 16
y = 20
Consider 15 / 12 = 25 / w
15w = 12 × 25
w = 20
Hence the option d is the correct answer.
Learn more about Scale Factor here :
https://brainly.com/question/3819163
#SPJ3
QR is parallel to ST Rs is parallel TU QS is congruent to SU
prove QRS is congruent to STU
Answer:
hope my answer is helpful to you
plz mark me as brainlist and also follow me
As QR is parallel to ST Rs is parallel TU QS is congruent to SU the measure of their included angle is also same ∠QRS ≅ ∠STU.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, Line segment QR is parallel to line segment ST.
Line segment RS is parallel to line segment TU, And line segment QS is similar to line segment SU.
So, The included angle of two pairs of parallel lines will also be the same as
line segment QS is similar to line segment SU.
∴ ∠QRS is similar to ∠STU.
learn more about congruency here :
https://brainly.com/question/7888063
#SPJ5
A computer company can inspect 12 laptops in 8 hours. what's the ratio
Answer:
4:1
Step-by-step explanation:
hope this helps
Answer:
The ratio is 1 hour to 1.5 laptops
Step-by-step explanation:
If you divide the time by amount done, there you have the answer.
Hannah is a photographer who specializes in portraits. This morning, she soent four hours doing graduation portrait sessions. In the afternoon, she soent four hours doing family portaits sessions but she didnt do as many session as the graduation portraits. Tomorrow, she has the same number of graduation and family sessions to work. Which will she likely finish in less time?
Please Help :))
Find the value of x in each pair of similar figures
Answer:
21
Step-by-step explanation:
set up proportion and solve
18/12=x/14 (cross multiply)
252=12x
21=x
When Georgie buys three boxes of apples she has 40 pounds more than when she has one box of apples. How many pounds of apples will there be an eight boxes?
Answer:
160 pounds
Step-by-step explanation:
If she has 3 boxes and there's 40 more pounds than if she had one, that means each box is 20 pounds so multiply 20 by 8 and you get 160 pounds
Please help me with this question
Answer:
5 x 3/4 < 5
2 x 4/3 > 2
6 x 5/5 = 6
4/7 x 1/8 < 4/7
2/5 x 7/7 = 2/5
1/3 x 6/4 > 1/3
how many 3/2s are in 5
Answer:
15 fifths
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
3/2 is equal to 1.5 and 3 1.5s can fit in 5 equaling 4.5
Evaluate 4x^2-12x+5 at x=6. A. 67 B. 77 C. 105 D. 221
Please hurry, I am giving 50 points! I only have a limited time to answer it!!!
Answer: B. 77
Sub x =6 into the given expression
4x^2 - 12x + 5
= 4(6)^2 - 12(6) + 5
= 144 - 72 + 5
= 77
[tex]\\ \sf\longmapsto 4x^2-12x+5[/tex]
[tex]\\ \sf\longmapsto 4(6)^2-12(6)+5[/tex]
[tex]\\ \sf\longmapsto 4(36)-72+5[/tex]
[tex]\\ \sf\longmapsto 144-67[/tex]
[tex]\\ \sf\longmapsto 77[/tex]
Somebody pls help me with this
please help me im pretty stumped
Length of the major axis: 4 Length of the minor axis: 2 Foci are on the y-axis with center (0,0)
Answer:
x²/4 + y²/16 = 1
Step-by-step explanation:
Foci on the y axis: major axis parallel to y axis
x²/b² + y²/a² = 1
x²/4 + y²/16 = 1
The required equation of an ellipse is given by x²/4 + y²/16 = 1
Given that,
Length of the major axis: 4 Length of the minor axis: 2 Foci are on the y-axis with center (0,0), the equation of the ellipse is to be determined.0
Ellipse is defined as the cross-section of the cone when cutting it with a plane parallel to its base.
Here,
Standard equation of the ellipse with origin as the center,
x²/a² + y²/b² = 1
where a and b are the minor and major axis of the ellipse.
From the given, we have a = 2 and b = 4
So the equation of the ellipse,
x²/4 + y²/16 = 1
Thus, the required equation of an ellipse is given by x²/4 + y²/16 = 1.
Learn more about the conic section here:
https://brainly.com/question/22105866
#SPJ2
Isabelle is plotting a pentagon on a grid. So far, she has plotted and connected the three points shown on the grid below.
On a coordinate plane, lines connect points (negative 2, 4), (negative 3, 2), and (0, negative 2).
To complete the pentagon, she can choose only from the points below.
(2, 0), (–2, 0), (–2, 4), (2, 4)
How can Isabelle complete her pentagon?
Connect the point already at (0, –2) to a new point at (2, 0), and then connect
( 2, 0) to (–2, 4).
Connect the point already at (0, –2) to a new point at (–2, 0), and then connect ( –2, 0) to (–2, 4).
Connect the point already at (0, –2) to a new point at (–2, 0), connect ( –2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).
Connect the point already at (0, –2) to a new point at (2, 0), connect
(2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).
Answer:
D
Step-by-step explanation:
Connect the point already at (0, –2) to a new point at (2, 0), connect
(2, 0) to (2, 4), and then connect (2, 4) to (–2, 4).
Im pretty sure
Answer:
D
Step-by-step explanation:
which expression is equivalent to 15+8x+3+2x
Answer:
10x + 18
Step-by-step explanation:
First, we need to add like terms. Like terms are terms that are alike. For instance 8x and 2x are like terms. 15 and 3 are also like terms.
So, we have to add 8x plus 2x and 15 plus 3. That’s comes out to 10x plus 18.
Therefore, this expression is equivalent to 10x + 18.
HELP ASAP WILL GIVE BRAINLY
Exercises
Determine whether each solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces.
edges, and vertices.
Answer:
1 and 2 are not polyhedrons, as a circle has infinite sides
1. cone, 1 vertex
2. sphere, nothing
3. pentagonal prism?
wait but can't every face be a base???
anyway 7 faces, 10 vertices
4. triangular prism
5 faces, 6 vertices
Step-by-step explanation:
We have given the figure
We have to determine whether each solid is a polyhedron.
Then identify the solid.
If it is a polyhedron, name the bases, and faces.
edges, and vertices.
What is the vertex?
A vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.
1 and 2 are not polyhedrons, as a circle has infinite sides
1. cone, 1 vertex
2. sphere, nothing
3. pentagonal prism
anyway 7 faces, 10 vertices
4. triangular prism
5. faces, 6 vertices
To learn more about the polyhedron visit:
https://brainly.com/question/24324783
#SPJ2
On Friday and Saturday, there were a total of 200 cars in a parking lot. On Friday, there were 120
m the lot. What percent of the total number of cars were in the parking lot on Saturday?
Answer:
0.4
Step-by-step explanation:
Part C
Use an exponential expression to calculate the area covered by purple loosestrife 7 years from now.
Answer:500(1.2)^x
Plato :)
Answer:
3
Step-by-step explanation:
PLATO
what graph shows the solution to the system of linear inequalities? y>2/3x+3 y<_-1/3x+2
What is the length of side EF in the triangle? Please give a step by step explanation, I'm having lots of trouble finding the solution. Thank you!
[tex]{\underline{\underline{\bf{Given:}}}}[/tex]
A right-angled triangle DEFMeasure of angle F = 90°Measure of side DF = 13.6 mMeasure of side DE = 16.2 m[tex]{\underline{\underline{\bf{Need\:to\:find:}}}}[/tex]
The measure of side EF.[tex]{\underline{\underline{\bf{Formula\:to\:be\:used:}}}}[/tex]
Pythagorean Theorem:
[tex]\underline{\boxed{\sf{{Base}^{2}+{Perpendicular}^{2}={Hypotenuse}^{2}}}}[/tex]
[tex]{\underline{\underline{\bf{Solution:}}}}[/tex]
According to the given data, we know the measures of Perpendicular and Hypotenuse. Hence, the measure of the base (Side FE) can be found by substituting the given measures in Pythagorean Theorem.
[tex]\implies{\sf{{Base}^{2}+{Perpendicular}^{2}={Hypotenuse}^{2}}}[/tex]
[tex]\implies{\sf{{EF}^{2}+{DF}^{2}={DE}^{2}}}[/tex]
[tex]\implies{\sf{{EF}^{2}+{(13.6)}^{2}={(16.2)}^{2}}}[/tex]
[tex]\implies{\sf{ EF = \sqrt{ {(16.2)}^{2} - {(13.6)}^{2} } }}[/tex]
[tex]\implies{\sf{ EF = \sqrt{ 262.44 - 184.96 } }}[/tex]
[tex]\implies{\sf{ EF = \sqrt{77.48 } }}[/tex]
[tex]\implies{\sf{EF=\red{\underline{\underline{8.802\:m}}}}}[/tex]
[tex]{\underline{\underline{\bf{Required\:answer:}}}}[/tex]
The length of side EF is 8.802 m.___________________________________________2) LaChina spherical glass decorative balls that she is filling with blue liquid to match the color of
her room. If there is 4,000 cubic inches of liquid to be poured into 20 glass spheres, what is the
diameter of each sphere? Round to two decimal.
Answer:
8000
Step-by-step explanation:
Francis heard that a car stereo system was on sale for 30% off. If the original price was $62.40, what was the sale price of the stereo?
Answer:
89.14
Step-by-step explanation:
Which quotient is greater than 2?
50 ÷ 28
45 ÷ 23
38 ÷ 16
28 ÷ 15
which ones are equal to eachother & why. A,B,C or D?
Dan brought 36 vanilla cupcakes and 49 chocolate cupcakes to his school bake sale. Then his friend brought 5 more cupcakes. How many total cupcakes did the bake sale have to sell?
Answer:
90
Step-by-step explanation:
Answer:
90 cupcakes
Step-by-step explanation:
So, to solve this question all we have to do is add the number of cupcakes that Dan brought and the number of cupcakes that his friend bought.
So the expression would look like this:
36 + 49 + 5 = 90
So, in conclusion, the bake sale had 90 cupcakes to sell
plz mark me brainliest if correct :)
Find z if the standard normal curve area between – z and z is 0.4530.
Answer:
Step-by-step explanation:
Hi,
1) Find z if the standard normal curve area between -z and z is 0.4530.
Y1 = normalcdf(-x,x,0,1) - .4530 and x = .60226
a. ± 0.118
b. ± 0.398
c. ± 0.602 <==ANSWER
d. ± 0.752
2) If a random variable has the normal distribution with μ = 104.3 and σ = 5.7, find the probability that the value will be greater than 112.3
normalcdf(112.3, 500, 104.3, 5.7) = .08023
a. 0.08 <==ANSWER
b. 0.09
c. 0.10
d. 0.11
3) Determine a 90% confidence interval for μ if σ = 5, \bar{x} = 70, and n = 82. Answer interval rounded to two decimal places.
70 ± 1.645 (5/√82) or 69.09 to 70.91 <==ANSWER
I hope that helps!! :-)
f(x) = x - 5; translation 7 units right
Answer:
f(x-7) = x -12
Step-by-step explanation:
horizontal translation 7 units right: f(x-7)
f(x) = x - 5
f(x-7) = x-7 -5 = x -12
Factor using the trinomial
10.
X2 + 13x + 12
Answer:
Factoring the trinomial: [tex]x^2+13x+12[/tex] we get the factors [tex]\mathbf{(x+1)(x+12)}[/tex]
Step-by-step explanation:
We need to factor the trinomial: [tex]x^2+13x+12[/tex]
We can factor the trinomial by breaking the middle term i.e 13x
Such that adding or subtracting gets the both terms we get 13x and multiplying both terms we get 12x^2
We can break 13x as: 12x and x
Adding them we get 13x and multiplying them we get 12x^2
So,
[tex]x^2+13x+12\\=x^2+12x+x+12\\=x(x+12)+1(x+12)\\=(x+1)(x+12)[/tex]
So, Factoring the trinomial: [tex]x^2+13x+12[/tex] we get the factors [tex]\mathbf{(x+1)(x+12)}[/tex]
Find the value of x.
Given:
Figure of a triangle.
To find:
The values of x.
Solution:
In the figure, we have an angle bisector.
According to the angle bisector theorem, an angle bisector of a triangle always divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Using angle bisector theorem, we get
[tex]\dfrac{x}{7}=\dfrac{15}{14}[/tex]
Multiply both sides by 7.
[tex]x=\dfrac{15}{14}\times 7[/tex]
[tex]x=\dfrac{15}{2}[/tex]
[tex]x=7.5[/tex]
Therefore, the value of x is 7.5 units.