Answer:
106 people.
Step-by-step explanation:
Logistic equation:
The logistic equation is given by:
[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]
In which
[tex]A = \frac{K - P_0}{P_0}[/tex]
K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.
Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.
This means that [tex]K = 191, P_0 = 38[/tex], so:
[tex]A = \frac{191 - 38}{38} = 4.03[/tex]
Then
[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]
3 days later 68 people have heard it.
This means that [tex]P(3) = 68[/tex]. We use this to find k.
[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]
[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]
[tex]68 + 274.04e^{-3k} = 191[/tex]
[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]
[tex]e^{-3k} = 0.4484[/tex]
[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]
[tex]-3k = \ln{0.4484}[/tex]
[tex]k = -\frac{\ln{0.4484}}{3}[/tex]
[tex]k = 0.2674[/tex]
Then
[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]
How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?
This is P(6). So
[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]
Rounding to the nearest whole number, 106 people.
A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
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I need the answer explained
Answer:
1.33
Step-by-step explanation:
62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.
what value of x is in the solution set of 8x-6>12+2x
Answer:
x>3
Step-by-step explanation:
8x - 2x > 12+ 6
-> 6x > 18
-> x > 3
[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]
➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Step-by-step explanation:
[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]
What is the remainder when () = 3 − 11 − 10 is divided by x+3
Answer:
-18/x+3
Step-by-step explanation:
Write the equation of the line that passes through the points (0, 4) and (- 4, - 5) . Put your answer in fully reduced slope intercept form , unless it is a vertical or horizontal line
Answer:
y=9/4x+4
Step-by-step explanation:
Start by finding the slope
m=(-5-4)/(-4-0)
m=-9/-4 = 9/4
next plug the slope and the point (-4,-5) into point slope formula
y-y1=m(x-x1)
y1=-5
x1= -4
m=9/4
y- -5 = 9/4(x - -4)
y+5=9/4(x+4)
Distribute 9/4 first
y+5=9/4x + 9
subtract 5 on both sides
y=9/4x+4
find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}
The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2
The given set is presented as follows;
E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}
The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x ≤ B, while there all y ∈ E has a x ∈ E such that t < x
Therefore;
The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]
The greatest lower bound, glb, b, also known as the infimum, is defined as follows;
b is the greatest lower bound if for all x ∈ E then x ≥ b
Given that b < t, then where x ∈ E, there exist a x < t
The glb of the given set is 0.2
Learn more about lub, supremum, glb, infimum, here;
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Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
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Given the following matrices, what 3 elements make up the first column of the product matrix DA?
We have to figure out what the product of DA is,
[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]
We know that,
[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]
So,
[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]
[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]
[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]
So the solution is,
[tex]a,b,c=\boxed{20,-4,32}[/tex]
Hope this helps :)
y
Which point on the x-axis lies on the line that passes
through point C and is parallel to line AB?
5 4
C
NU
1
O (1,0)
O (1, 1)
0 (0, 2)
O (20)
А
54
214
2 3
4 5
х
h
B
3
4
ch
I think it's (2,0).
Because u use the slope of line AB to go down from point C until one of the answers are met.
The point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).
Slope of Parallel LinesTwo lines on a coordinate plane are parallel to each other if they have the same slope.Slope = change in y/change in x.Slope of AB = -(3/6)
Slope of AB = -1/2
Slope of from point (2, 0) to point C(-2, 2):
Slope = (2 - 0)/(-2 - 2) = 2/-4
Slope = -1/2
Therefore, the point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).
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If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4
What are the solutions to the quadratic equation 4x2 − x − 3 = 0?
Answer:
D
Step-by-step explanation:
f(x)=-x(x-4)
f(x)=-x²+4x
-x²+4x=0
x(-x+4)=0
x=0, x=4
(2)
4x²-x-3=0
(4x²+3x)-(4x-3)=0
x(4x+3)-1(4x+3)=0
x=1, x=-3/4
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?
Step-by-step explanation:
28000 ÷ 100
=280
280 × 5
=1400
The least-squares regression equation
y = 8.5 + 69.5x can be used to predict the monthly cost for cell phone service with x phone lines. The list below shows the number of phone lines and the actual cost.
(1, $90)
(2, $150)
(3, $200)
(4, $295)
(5, $350)
Calculate the residuals for 2 and 5 phone lines, to the nearest cent.
The residual for 2 phone lines is $___
The residual for 5 phone lines is $___
Answer:
First one: 2.5
Second: -6
8.5+69.5(5) = 147.5
150 - 147.5 = 2.5
8.5 + 69.5(5) = 356
350 - 356 = -6
ED2021
The residual for 2 phone lines is $2.5.
The residual for 5 phone lines is -$6.
What is the residual in a least-square regression equation?
The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
How to solve the question?In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.
We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
Thus for 2 phone lines:-
Actual Cost = $150.
Predicted Cost, y = 8.5 + 69.5*2 = 147.5.
Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.
Thus, the residual for 2 phone lines is $2.5.
Thus for 5 phone lines:-
Actual Cost = $350.
Predicted Cost, y = 8.5 + 69.5*2 = 356.
Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.
Thus, the residual for 2 phone lines is -$6.
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I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
I need help on this problem
9514 1404 393
Answer:
see attached
Step-by-step explanation:
(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.
__
(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.
Nhà trường muốn đánh giá tỉ lệ chăm học của sinh viên (trong một tuần). Khảo sát 236 sinh viên thì thấy có 32 sinh viên chăm học. Hãy ước lượng khoảng đối xứng cho tỉ lệ sinh viên chăm học của trường với độ tin cậy 95%
Answer:
can't understand the language
What is the x-coordinate of the point of intersection for the two lines below?
-6 + 8y = -6
7x -10y = 9
Answer choices
1.) -6
2.) -3
3.) 3
4.) 7
Answer:
c.
Step-by-step explanation:
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
Help please!??!!?!?
9514 1404 393
Answer:
a) CP = SP/1.1
b) CP = $59.50
c) GST = $5.95
Step-by-step explanation:
a) Divide by the coefficient of CP.
SP = 1.1×CP
CP = SP/1.1
__
b) Use the formula with the given value.
CP = $65.45/1.1 = $59.50
__
c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.
GST = SP -CP = $65.45 -59.50 = $5.95
GST = CP×0.10 = $59.50 × 0.10 = $5.95
Help me please and thank you
Step-by-step explanation:
jlejej
are u using chrome os
If ‘BOXES’ is OBXSE, then BOARD is
9514 1404 393
Answer:
OBADR
Step-by-step explanation:
The first two letters are swapped, and the last two letters are swapped.
BOARD . . . becomes
OBADR
if a stone is dropped from a cliff that is 122.5m high then its height in meters after t seconds is h=122.5-4.9t^2. find its velocity after 2s
Answer:
Step-by-step explanation:
Let t = 2
h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
PLEASE HELP!!!
Evaluate each expression.
(252) =
Answer:
1/5
Step-by-step explanation:
4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?
Please help explanation if possible
Answer:
N=18
Step-by-step explanation:
Hope it will help you
If it does pls give me Brainlest
Have a nice day
Answer:
18
Step-by-step explanation:
use the concept of similarity and enlargement.
[tex] \frac{15}{n} = \frac{5}{6 } [/tex]
[tex]n = \frac{15 \times 6}{5} [/tex]
[tex]n = 18[/tex]
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
9514 1404 393
Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
what song goes whoooooo Iiiiii smoooooooooke
Answer:
Lol yu lateee das "who i smoke by yung ace"
Step-by-step explanation:
Answer:
woogle said woo hoo by rock a teens
Step-by-step explanation:
