Sorry I had to take down the answer, I might be wrong.
MODELING WITH MATHEMATICS The population P (in thousands) of Austin, Texas, during a recent decade can be approximated by y = 494.29 * (1.03) ^ f , where is the number of years since the beginning of the decade. a. Tell whether the model represents exponential growth or exponential decay b. Identify the annual percent increase or decrease in population . Estimate when the population was about 590,000 .
Show work
Answer:
a) growth
b) 3%
c) 6 years (since the beginning of the decade)
Step-by-step explanation:
Given:
The population P (in thousands) of Austin, Texas during a recent decade can be approximated by [tex]y=494.29(1.03)^t[/tex] when t is the number of years since the beginning of the decade.
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the y-intercept (or initial value)b is the base (or growth factor)x is the independent variabley is the dependent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
a) The model represents exponential growth as 1.03 > 1
b) The annual percent increase of the population is 3%
1.03 - 1 = 0.03
0.03 x 100 = 3%
c) To estimate when was population about 590,000 set y = 590 and solve for t:
[tex]\implies 590=494.29(1.03)^t[/tex]
[tex]\implies \dfrac{590}{494.29}=(1.03)^t[/tex]
Take natural logs of both sides:
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=\ln (1.03)^t[/tex]
[tex]\implies \ln\left(\dfrac{590}{494.29}\right)=t\ln (1.03)[/tex]
[tex]\implies t=\dfrac{\ln\left(\dfrac{590}{494.29}\right)}{\ln (1.03)}[/tex]
[tex]\implies t=5.988069001...[/tex]
Therefore the population was about 590,000 6 years since the beginning of the decade.
Don't Send links, don't Write random things and get the points for free.
Answer:
Option D, [tex]2010\ cm^3[/tex]
Step-by-step explanation:
Step 1: Determine the volume of a single cylinder
[tex]V=\pi r^2h[/tex]
[tex]V=\pi *(4\ cm)^2 * 10\ cm[/tex]
[tex]V = 3.14 * 16\ cm^2 * 10\ cm[/tex]
[tex]V = 502.4\ cm^3[/tex]
Step 2: Determine the total volume
[tex]502.4\ cm^3 * 4[/tex]
[tex]2,009.6\ cm^3[/tex]
Answer: Option D, [tex]2010\ cm^3[/tex]
Answer:
The last one :)
Step-by-step explanation:
I hoped this helped have a good day! <3
vertex (-3, -3), point (2,97) find equation of parabola in vertex form
Answer:
y = 4(x+3)^2 - 3
Step-by-step explanation:
Vertex form y = a(x+3)^2 -3 sub in 2,97 to calculate a
97 = a(2+3)^2 - 3
a = 4
Matt has a box that measures 23 feet long and 16 feet wide. The volume of the box is 4,416 cubic feet. What is the height of the box in yards?
Answer:
ok
Step-by-step explanation:
20 points and brainliest to the best correct answer, do and show work for numbers 13 and 15. Questions are in the photo, thank you.
Answer:
13. x=11; MN=65°; NP=115°; NQP=245°
15. x=9; AD=108°; BC=23°; DC=139°; DBC=221°
Step-by-step explanation:
13.The marked arcs are congruent, so we can equate the given expressions for their measures:
10x -45 = 6x -1
4x = 44 . . . . . . . . . add 45-6x
x = 11 . . . . . . . . . . divide by 4
The arc measures are found by using the value of x in the corresponding expression. Arcs around a circle total 360°.
arc MN = (10(11) -45)° = 65°
arc NP = 180° -65° = 115°
arc NQP = 360° -NP = 245°
__
15.The sum of arcs around a circle is 360°. We can use this fact to write an equation involving the given expressions. Clockwise from A, we have ...
90 +(2x +5) +(17x -14) +12x = 360
31x = 279 . . . . . . . subtract 81, collect terms
x = 9 . . . . . . . . . divide by 31
The arc measures are found by using the value of x in the corresponding expression.
arc AD = 12(9)° = 108°
arc BC = (2(9) +5)° = 23°
arc DC = (17(9) -14)° = 139°
arc DBC = 360° -DC = 221°
Six different names were put into a hat. A name is chosen 125 times and the name Grace is chosen 17 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Question content area bottom
The experimental probability of choosing the name Grace is __
(Type an integer or a simplified fraction.)
Answer:
Step-by-step explanation:
The experimental probability of choosing Grace is 13.6% (17/125*100)
The theoretical probability of choosing Grace is 16.67% (1/6)
Each probability would change because they depend on the data set so if the data set changes, that means the probability will also change depending on the amount it changes.
Solve the right triangle.
Round your answers to the nearest tenth.
Answer: A= 42 degrees
Step-by-step explanation:
A= 180-90-48=42 (degrees)
Answer:
A= 42 degrees
a = 27
c= 40.4
Step-by-step explanation:
48 - 90 = 42 (we know the remaining angle area is 90 because its a right triangle and a traingle is 180 degrees)
to find the answer of a we need to use tan(48) and when you convert that to radians you get 1.1106 ish tan is opposite over adjacent and we know the opposite is 30 but we dont know a so we put [tex]\frac{30}{a}[/tex] = 1.1106 and put a on both sides so you divide 30 by 1.1106 and dget 27.0124 and round to the nearest tenth to get 27
to find c you need to find the hypotanuse which is [tex]a^{2}[/tex]+[tex]b^{2} =c^{2}[/tex]
30 squared is 900 add that to 27 squared which is 729 and you get 1629
find the square root of 1629 to get 40.3608 and then round that to the nearest tentth to get 40.4
Does Anyone know #19?
[tex]\text{Endpoints of diameter,}~~ A(4,6)~ \text{and}~ B(-3,-1)\\\\\text{Diameter,}~AB = \sqrt{(4+3)^2+(6+1)^2}\\\\~~~~~~~~~~~~~~~~~~~=\sqrt{7^2+7^2}\\\\~~~~~~~~~~~~~~~~~~~=7\sqrt2\\\\\text{So , radius}~ = \dfrac{AB}2 = \dfrac{7\sqrt 2}2 =4.9~\text{units.}\\\\\text{Hence the answer is B.}[/tex]
The number of hours, t, it takes a boat to travel 15 miles upstream is represented
by the given equation.
15
t=
r-c
Which equation represents the rate of the current, c, in terms of r, the rate of the
boat, and t?
A.
15 - rt
CE
15-16
BC=
rt - 15
c = - 7
C. C= -15+r+t
D. C = 15 -r-t
The equation of c is an illustration of subject of formula
The equation of c in terms of r and t is c = r - 15/t
How to determine the equation?The equation is given as:
t = 15/(r - c)
Cross multiply
t(r - c) = 15
Divide both sides by t
r - c = 15/t
Subtract r from both sides
-c = -r + 15/t
Multiply both sides by -1
c = r - 15/t
Take LCM
[tex]c = \frac{rt - 15}{t}[/tex]
Hence, the equation of c in terms of r and t is [tex]c = \frac{rt - 15}{t}[/tex]
Read more about subject of formula at:
https://brainly.com/question/10643782
Find the Surface Area.
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Surface areas and volumes.
Here we will find surface areas by adding individual parts.
Surface area ==> Small rectangle + big rectangle + base rectangle + 2* right angled triangles.
so we get as,
area of shape = 721.1 yards.
option D.) is correct.
(3x-4)^2=22 identify the solutions to the quadratic equation by taking the square root
[tex]~~~~(3x-4)^2 = 22\\\\\implies 3x-4 = \pm\sqrt{22}\\\\\implies 3x = 4 \pm\sqrt{22}\\\\\implies x = \dfrac{4\pm \sqrt{22}}3 \\\\\text{Hence,}~~ x = \dfrac{4+ \sqrt{22}}3~~ \text{and}~~ x = \dfrac{4-\sqrt{22}}3[/tex]
If a car travels 213 miles in 3 hours, how many miles will the car drive in 5 hours? pls help
Answer:
355 miles
Step-by-step explanation:
Figure out how far the car travelled in 1 hour - 3 hours can be divided by 3 for 1 hour, so do the same for the miles - 213 / 3 = 71 miles.
So we know the car travelled 71 miles in 1 hour.
Now just multiply the miles by 5 to figure out the answer - 71 * 5 = 355 miles
:)
Name the decimal illustrated by this model.
Answer:
1.97
Step-by-step explanation:
1 whole square is filled so that would equal 1
97 out of 100 squares in the second is filled so it would be = 0.97
combine them:
0.97+1=1.97
I think it’s b but I’m not sure
HELPPPPPPPPPpppp med
Step-by-step explanation:
Using the formula:
Sin☆=Perpendicular ÷ Hypotenus
Sin☆ = 35 ÷ 48
Sin☆ = 0.7291666667
☆ = Sin^-1 (0.7291666667)
☆ =46.8165782066
where ☆= Degree.
Hence final answer is 46.816
I hope this is right.....
Jason's summer job allowed him to save $1200
to use as spending money throughout the
upcoming school year. To make sure he has
enough money, Jason plans to spend the same
amount each month and not run out of money
until the end of the school year in 10 months.
120x + y = 1200
Answer:Slope=-240.000/2.000=-120.000
Step-by-step explanation:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
120*x+y-(1200)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve 120x+y-1200 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
What is the multiplication problem that means the same thing as the division problem 1/3 ÷ 7?
Answer:
1/21 * 7 = 1/3
Step-by-step explanation:
The numbers in 1/3 divided by 7 are labeled below:
1 = numerator3 = denominator7 = whole numberTo make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:
1
-------
3 x 7
=
1
-----
21
Thus, the answer to 1/3 divided by 7 in fraction form is:
1/21
To make the answer to 1/3 divided by 7 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
1/21 = 0.04761904761
1/21 * 7 = 0.3333333333.... ( 1/3 )
What is the slope of a line that is parallel to the line represented by the equation : y = 5x - 3?
Answer:
5
Step-by-step explanation:
This line equation is in y = mx + b form m will be the slope
m = 5 parallel line will have same slope = 5
Solve the system of equations using elimination: -5x - 8y = -8 and
6x +9y = 12. Please help and explain how to solve
here are two column vectors
Answer:
[tex] a = ( \frac{ - 6}{2} )[/tex]
Step-by-step explanation:
-2g=?
[tex] - 2( \frac{3 }{ - 1} ) \\ \\ ( \frac{ - 6}{2} )[/tex]
The base of a solid is a circle centered at the origin with a radius r, and every plane section perpendicular to a diameter is a square. What is the volume of the solid
The volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.
The equation of the circle can be given as,
[tex]x^2+y^2=r^2[/tex]
Here, (r) is the radius of the circle.
Rewrite this equation as,
[tex]y^2=r^2-x^2\\y=\sqrt{r^2-x^2}[/tex]
This will give you the half the length of the side. Thus, the length of the side of the square is,
[tex]s=2y=2\sqrt{r^2-x^2}[/tex]
The area of the square it square of its side. Thus, the area of the square is,
[tex]A(x)=s^2\\A(x)=(2\sqrt{r^2-x^2})^2\\A(x)=4(r^2-x^2})[/tex]
The volume of the solid can be got by integrating the area of the cross-section.
[tex]V=\int\limits {A(x)} \, dx[/tex]
Here, A(x), provides the area of the square at the point x. Thus,
[tex]V=\int\limits {A(x)} \, dx\\V=\int\limits_{-r}^r {4(r^2-x^2)} \, dx\\V=[ {4(r^2x-\dfrac{x^3}{3})}]^r_{-r}\\V= {4(r^2(r)-\dfrac{(r)^3}{3})}- {4(r^2(-r)-\dfrac{(-r)^3}{3})}\\V=4[r^3-\dfrac{r^3}{3}}+ {r^3-\dfrac{r^3}{3}]\\V=\dfrac{16r^3}{3}[/tex]
Thus, the volume of the solid whose base is a circle centered at the origin with a radius r is 16r³/3 cubed unit.
Learn more about the equation of circle here;
https://brainly.com/question/1506955
A farmer need to build a goat pen. The pen will be 5 meters wide and 16 meters long. The fencing material costs $8. 00 per meter. How much will it cost to buy enough fencing material to build the goat pen
Answer:
$336
Step-by-step explanation:
Find the perimeter, 5x2 + 16x2 = 10 + 32 = 42
Fencing material = $8 per 1 meter
42 meters, so 42 * 8 = $336
please help me!
What is the molarity of a solution composed of 5.85g of K dissolved in 0.125L of Water? Molar Mass for Ki= 166.1g/mol.
a. .282M
b. .182M
c. .0028M
d. 3.28M
Answer:butt no ayes
Step-by-step explanation:10 is a yes is no
What is the rate of change and y intercept
Answer:
5
Step-by-step explanation:
The sum of two numbers is equal to 272. When the numbers are divided, the quotient is 3 and the remainder is 52. Find the difference of the numbers.
Answer:
the difference of the numbers are 217 and 55.
Step-by-step explanation:
a+b=272
a/b=3…52
a=3b+52
4b+52=272
4b=220
b=55
a=272-55=217
In PQR, P = 90°, Q = 40° and PR =9cm. Find the length of QR .
Answer:
QR = 14.00 cm to the neatest hundredth.
Step-by-step explanation:
This is a right triangle with < P = 90.
So QR is the hypotenuse.
< Q is the angle opposite to the line PR.
sin Q = opposite/hypotenuse = PR/QR
sin 40 = 9/QR
QR = 9/sin40
= 14.002 cm.
Can someone please help me?
Answer:
24
Step-by-step explanation:
area = wl (6×4 = 24)
w width l length
If you were graphing y < -3x + 5, would you need a solid or broken line?
solid
broken
Answer:
broken
Step-by-step explanation:
when there isn’t an equals sign the line will always be broken
Peter weighs is 105 kg. His wants to lose 500 g per week. How many weeks will it take for him to have a mass of 90 kg
Answer:
30
Step-by-step explanation:
500 g = 1/2 kg => 2 weeks he loses 1 kg
105 - 90 = 15 kg
So he needs to take 30 weeks in total. ( 15 * 2)
Let weeks be x
So
105-0.5x=900.5x=105-900.5x=15x=15/0.5x=30weekswhich set of side lengths would form a right triangle