The exponential growth function to model represents as P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.
What is the exponential growth function?The exponential growth function is given by:-
y = A(1 +r)ⁿ
where r is the rate of growth and A is the initial amount and n is the time period.
Let t represent the number of years since 2000 and P represent the population.
The population of a city is increasing at a rate of 4% each year. In 2000, there were 236,000 people in the city.
Put A = 236,000 , r = 0.04 and t = 9, we get
P = 236,000 (1+ 0.04)⁹
P = 335,902
Hence, the exponential growth function to model represents P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.
Learn more about exponential growth and decay here:
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What is the radius of a hemisphere with a volume of 839 cm", to the nearest tenth of a centimeter?
Answer:
7.4 cm
Step-by-step explanation:
Volume of sphere
v = (4/3)πr³
Volume of hemisphere will be half that
v = (2/3)πr³
(2/3)πr³ = 839
multiply both sides by 3/2
πr³ = 1,258.5
Divide both sides by π
r³ = 400.5929917623
Take the cube root of both sides
r = 7.3717022001
Rounded
r = 7.4 cm
Select the correct answer.
The variable g varies directly as the cube root of h. If g=128 when h=8, which equation can be used to find other combinations of g and h?
[tex]g \sqrt[3]{h} = 256[/tex]
[tex]g = 64 \sqrt[3]{h} [/tex]
[tex]gh = 1024[/tex]
[tex]g = 16h[/tex]
the second equation is correct
Step-by-step explanation:
I got it right on the test
the ratio of two complementary angles is 8:17. find the measure of the smallest angle.
Answer:
28.8
Step-by-step explanation:
Multiply each by x
8x : 17x
Complementary angles add to 90
8x+17x = 90
25x = 90
Divide each side by 25
25x/25 = 90/25
x=3.6
The smallest angle is 8x
8*3.6 =28.8
Compute the future value of $1,000 compounded annually for:
A. 10 years at 5 percent.
B. 10 years at 10 percent.
C. 20 years at 5 percent.
D. Why is the interest earned in part (c) not twice the amount earned in part (a)?
Answer:
1628.89
2593.74
2653.30
Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.
Step-by-step explanation:
A: 1000*(1.05)¹⁰= 1628.89
B: 1000(1.1)¹⁰= 2593.74
C: 1000(1.05)²⁰= 2653.30
D: Because the interest forms an exponential function. This means that the amount of interest earned in each period is increasing and should therefore be more than double.
10
El tiempo aproximado en caminar de tu casa (C) a la de tu amigo (A) pasando por la tienda (T)
es de 14 minutos; Si caminas a la misma velocidad, ¿Cuántos minutos te tomará caminar
directamente a la casa (C) de tu amigo (A)? Redondea al entero más cercano.
500yd
A
700yd
Respuesta:
10.0 minutos
Explicación paso a paso:
Distancia total recorrida caminando de C a A pasando por T:
500 yardas + 700 yardas = 1200 yardas
Tiempo necesario para recorrer 200 yardas = 14 minutos
Caminando directamente de C a A:
La distancia se puede obtener usando una relación trigonométrica:
Hipotenusa = √ (opuesto² + adyacente²)
Hipotenusa = √500² + 700²
Hipoteno = 860.23252 yardas
Por eso ; Si
1200 yardas = 14 minutos
860.23252 yardas = x
Multiplicar en cruz:
1200x = 12043,255
x = 12043,255 / 1200
x = 10.036 minutos
El tiempo necesario para caminar directamente será: 10.0 minutos
Mark is hosting a "Who Dunnit?" party at his house. He plans on taping off a triangular section of his backyard to represent the crime scene. If the sides measure 23 feet, 15 feet, and 32 feet, how much tape will be needed? DO NOT ANSWER JUST TO STEAL MY POINTS!! AND NO CHICKEN NUGGETS!!!!
Answer:
70 feet
Step-by-step explanation:
as perimeter of triangle =
23+15+32= 70 feet
Answer:
Solution given:
side 1=23ft.
side 2=15ft
side 3=32ft
we have
perimeter=sum of all sides
=23+15+32=70ft
70ft tape will be needed.
What is a solution to the system? y = x^2 + 2x - 15 y – 4x = -12
9514 1404 393
Answer:
(x, y) = (-1, -16) or (3, 0)
Step-by-step explanation:
Perhaps you want to solve the system of equations ...
y = x^2 +2x -15y -4x = -12Substituting the first expression for y into the second equation gives ...
x^2 +2x -15 -4x = -12
x^2 -2x -3 = 0 . . . . . . . . add 12
(x -3)(x +1) = 0 . . . . . . . factor
Solutions are the values of x that make the factors zero: x = 3, x = -1.
The corresponding values of y are ...
y = -12 +4x
y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}
The solutions to the system are ...
(x, y) = (-1, -16) or (3, 0)
solve the system of equations by graphing
3x+y=7
x+2y=4
9514 1404 393
Answer:
(x, y) = (2, 1)
Step-by-step explanation:
The graph of these equations is attached. The solution is ...
(x, y) = (2, 1)
Tasta's bank account was. She deposited a check into her bank account and her new total is. How much was the check that Tasta deposited into her account?
Answer:
Step-by-step explanation:
New Total equals Previous Total plus the Check value
New Total minus Previous Total equals the Check value
Her new total is - Tasta's bank account was = Check value
The area of a parallelogram is 108 square inches. What is the length of the parallelogram if the height is 6 inches
Answer:
18
Step-by-step explanation:
Hope this help!!!
Have a nice day!!!
Is 0.01011011101111011111 rational or irrational?
Answer:
It is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful....Evaluate [315 + 6) + 2] : 7
23
O
0
03
05
Answer:
323 : 7
Step-by-step explanation:
[ ( 315 + 6 ) + 2 ] : 7
[ 321 + 2 ] : 7
323 : 7
Which expression is equivalent to Cube root of 343 x Superscript 9 Baseline y Superscript 12 Baseline z Superscript 6?
7x3y4z2
7x3y6z2
49x3y6z2
49x3y4z2
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Answer:
7x^3y^4z^2
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{343x^9y^12z^6}=\sqrt[3]{(7x^3y^4z^2)^3}=\boxed{7x^3y^4z^2}[/tex]
Answer:
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
Step-by-step explanation:
[tex] \small \sf \leadsto \: \sqrt[3]{343 \: x {}^{9} \: y{}^{12} \: z {}^{6} }[/tex]
[tex] \small \sf \leadsto \: \sqrt[3]{7x {}^{3}y {}^{6}z {}^{2} } [/tex]
[tex] \small \sf \leadsto \: 7x {}^{3}y {}^{6}z {}^{2} [/tex]
(125/64)-1/3 as a radical
-1/3 is square it should be and the top of 64 outside the bracket
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Answer:
∛(64/125) = 4/5
Step-by-step explanation:
Maybe you want to express ...
[tex]\displaystyle\left(\frac{125}{64}\right)^{-\frac{1}{3}}=\left(\frac{64}{125}\right)^{\frac{1}{3}}=\boxed{\sqrt[3]{\frac{64}{125}}}[/tex]
__
The denominator of the fractional exponent is the index of the radical. The other applicable rule of exponents here is a^-b = 1/a^b.
A parallelogram is shown below: A B A 2 foot D с 3 feet Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
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Answer:
Part A: 2 ft²
Part B: draw a diagonal (AC, for example); 1 ft²
Step-by-step explanation:
Part A:
The area of a parallelogram is given by the formula ...
A = bh
where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.
Using the numbers shown on the diagram, the area is ...
A = (3 ft)(2/3 ft) = 3·2/3 ft²
A = 2 ft² . . . . . area of the parallelogram
__
Part B:
Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.
The area of a triangle is given by the formula ...
A = 1/2bh
A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²
A = 1 ft² . . . . . . . . area of each triangle
_____
Additional comment
It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.
Keke's favorite book weighs 2lbs 14oz. How many total ounces does her book weigh? *
Answer:
i think it is 46
Step-by-step explanation:
Answer:
2.9lbs
Step-by-step explanation:
there are 14oz in a pound so 14/16 is 0.875. Rounded up to .9lbs.
The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?
Nathan is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1978 cans.
What is the mass, in kilograms, of these cans?
Answer:
33.5 kg
Step-by-step explanation:
Each 59 cans are about 1 kg.
He collected 1978 cans.
How many times 59 cans did he collect?
1978/59 = 33.5
He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg
PLS SOLVE!! e2 = d^2+f^2 -2df(cosE)
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Answer:
e = 25.7 m
Step-by-step explanation:
Put the given numbers in the given formula and do the arithmetic.
[tex]e^2=d^2+f^2-2df(\cos{E})\\\\e^2=11.9^2+18.5^2-2(11.9)(18.5)\cos{114^\circ}\approx 662.946\\\\e\approx\sqrt{662.946}\approx25.74774\\\\\boxed{e\approx25.7\text{ m}}[/tex]
Hello, here's the question :D
"Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n."
Answer:
(examples) n = 2
n = 3
n = 4
Step-by-step explanation:
to demonstrate, all you do is select a number to represent 'n' and plug it in.
so for example, n = 2:
2(2) + 3(2) = 5(2)
4 + 6 = 10, which is true.
Which expression can be used to determine the length of segment ZY?
On a coordinate plane, triangle X Y Z has points (3, 1), (3, 4), (negative 5, 1).
Answer:
The length of segment ZY is of [tex]\sqrt{73}[/tex] units.
Step-by-step explanation:
Distance between two points:
Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this question:
Point Z has coordinates (-5,1)
Pount Y has coordinates (3,4).
The length of segment ZY is the distance between points Z and Y. Thus
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D = \sqrt{(-5-3)^2+(1-4)^2}[/tex]
[tex]D = \sqrt{8^2+3^2}[/tex]
[tex]D = \sqrt{73}[/tex]
The length of segment ZY is of [tex]\sqrt{73}[/tex] units.
Find the missing length indicated. Hey can someone help me out?
Answer:
C) 6
by-step explanation:
y varies inversely as x. y=3 when x=10. Use the variation constant and inverse variation equation to find y when x=6.
Do not type y= in your answer.
Answer:
5
Step-by-step explanation:
Given :
Y α 1/x
Y = k/x
Where, k = constant of proportionality ;
y = 3 ; x = 10
3 = k / 10
k = 10 * 3
k = 30
Equation becomes :
Y = 30/x
Y =? ; when x = 6
Y = 30 / 6
Y = 5
y = 3 sine (one-third x)
Answer:
B on edge
Step-by-step explanation:
The 6 officers of the Student Council are going on a trip to an amusement park. Each student must pay an entrance fee plus $5 for meals. The total cost of the trip is $210. Solve the equation 6(e + 5) = 210 to find the cost e of the entrance fee for each
student.
Find the value of x.
A. 30
B. 60
C. 90
D. 120
Some one else didn’t add a picture
QUESTION:- Find the value of x.
A. 30
B. 60
C. 90
D. 120
ANSWER:-
ALL ANGLE SUMS HAVE SAME LOGIC OF STRAIGHT LINE ANGLES = 180°
[tex]y + x + y - x = 180[/tex]
[tex]2y = 180 \\ y = 90[/tex]
[tex]2x + y + x = 180[/tex]
[tex]3x + 90 = 180 \\ 3x = 90 \\ x = 30 \degree[/tex]
Answer:
30 degrees
Step-by-step explanation:
2x + y + x = 180
y + x + y - x = 180
3x + y = 180
2y = 180
y = 90
3x + 90 = 180
3x = 90
x = 30
5. The Jones family orders four pizzas to eat. Each pizza is sliced into four parts. How many pizza slices do they get in total?
Answer:
16 slices
Step-by-step explanation:
Given :
Number of pizzas ordered = 4
Number of slices per pizza = 4
If 4 pizzas are each sliced into 4 parts ; the we have :
Pizza 1 = 4 slices
Pizza 2 = 4 slices
Pizza 3 = 4 slices
Pizza 4 = 4 slices
Total slices = (4 +4 +4 +4) = 16 slices
What is the 8th term of the geometric sequence with a1=2 and r=-3.
Please asap last question
Answer:
-4374
Step-by-step explanation:
Given :
a1 = 2 ; r = - 3
The nth term of a geometric series :
A(n) = ar^(n-1)
The 8th term :
A(8) = 2(-3)^(8-1)
A(8) = 2(-3^7)
A(8) = 2(−2187)
A(8) = - 4374
A company's sales force makes 400 sales calls, with + 0.25 probability that a sale will be made on a call. What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.
Answer:
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.
This means that [tex]n = 400, p = 0.25[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]
What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?
Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.
X = 74.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -2.94[/tex]
[tex]Z = -2.94[/tex] has a p-value of 0.0016
X = 55.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -5.14[/tex]
[tex]Z = -5.14[/tex] has a p-value of 0
0.0016 - 0 = 0.0016
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Ayuda es para mañana plsss
Answer:
Divido es numero
Step-by-step explanation:
1. 1045.90
2. 579.60
3. 634.15
4. 1084.71
