Considering the given function, we have that:
a) 28.31 years.
b) 0.3382 years a decade.
c) 2.6184.
What is the function?The median age of the U.S. population in t decades after 1960 is:
f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.
1970 is one decade after 1960, hence the median was:
f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.
The rate of change was is the derivative when t = 1, hence:
f'(t) = -0.6528t² + 3.924t - 2.933
f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.
The second derivative is:
f''(t) = -1.3056t + 3.924
Hence:
f''(1) = -1.3056 x 1 + 3.924 = 2.6184.
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PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
3 write the factor of the following (1) 48 (2) 36 (3) 28 (4) 100 (5) 125
Answer:
FACTORING THE NUMBERS :-
well u didnt say to prime factors so i am writing all factors
1) 48 => 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 ( all are plus and minus )
2) 36 => 1, 2, 3, 4, 6, 9, 12, 18 and 36 ( all are plus and minus )
3) 28 => 1, 2, 4, 7, 14 and 28 ( all are plus and minus )
4) 100 => 1, 2, 4, 5, 10, 20, 25, 50, and 100 ( all are plus and minus )
5) 125 => 1, 5, 25, 125 ( all are plus and minus )
is it worth brainliest...
yes ofc
[tex]\sqrt{25}[/tex]
Answer:
5
Step-by-step explanation:
Calculate the square root of 25 and get 5.
a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?
Answer:
25 workers
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
,
pls help me asap !!!
Answer:
11
Step-by-step explanation:
Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist). Iso triangle has two side the same length - as well as two angles the same.
The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?
Ali's average speed was 40 miles per hour.
What is an average speed?
The total distance traveled is to be divided by the total time consumed brings us the average speed.
How to calculate the average speed of Ali?
The total distance between the college from Ali's house is 135 miles.
She drove 2/3rd of the total distance in 135 minutes.
She drove =135*2/3miles
=90miles.
Ali can drive 90miles in 135 mins.
Therefore, her average speed is: 90*60/135 miles per hour.
=40 miles per hour.
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190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
5x-22 3x +105 x minus 22 3 X + 10
-291x+10
:)))))) Have fun
A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with the mean 3, find the probability that the shop sells. . (a) At least 3 in a week. (b) At most 7 in a week. (c) More than 20 in a month (4 weeks).
Answer:
a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.
b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.
c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.
Step-by-step explanation:
For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].
Poisson variable with the mean 3
This means that [tex]\lambda= 3[/tex].
(a) At least 3 in a week.
This is [tex]P(X \geq 3)[/tex]. So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]
0.5768 = 57.68% probability that the shop sells at least 3 in a week.
(b) At most 7 in a week.
This is:
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]
[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]
[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]
Then
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]
0.988 = 98.8% probability that the shop sells at most 7 in a week.
(c) More than 20 in a month (4 weeks).
4 weeks, so:
[tex]\mu = \lambda = 4(3) = 12[/tex]
[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]
The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]
[tex]Z = 2.31[/tex]
[tex]Z = 2.31[/tex] has a p-value of 0.9896.
1 - 0.9896 = 0.0104
0.0104 = 1.04% probability that the shop sells more than 20 in a month.
The probability of the selling the video recorders for considered cases are:
P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.What are some of the properties of Poisson distribution?Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is square root (positive) of variance,
Thus,
Standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
For this case, let we have:
X = the number of weekly demand of video recorder for the considered shop.
Then, by the given data, we have:
X ~ Pois(λ=3)
Evaluating each event's probability:
Case 1: At least 3 in a week.
[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]
Case 2: At most 7 in a week.
[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]
Case 3: More than 20 in a month(4 weeks)
That means more than 5 in a week on average.
[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]
Thus, the probability of the selling the video recorders for considered cases are:
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Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7)
Answer:
[tex]\displaystyle x \approx -4.28[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 1 = ln(x + 7)[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^1 = e^{ln(x + 7)}[/tex]Simplify: [tex]\displaystyle x + 7 = e[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 7[/tex]Evaluate: [tex]\displaystyle x = -4.28172[/tex]e^1 = x+7
e - 7 = x
x = -4.28
The measure of angle tis 60 degrees.
What is the x-coordinate of the point where the
terminal side intersects the unit circle?
1
2
O
O
Isla Isla
2
DONE
Answer:
Step-by-step explanation:
Not a clear list of options and/or reference frame
Probably 0.5 if angle t is measured from the positive x axis.
Use absolute value to express the distance between -12 and -15 on the number line
A: |-12-(-15)|= -37
B: |-12-(-15)|= -3
C: |-12-(-15)|= 3
D: |-12-(-15)|= 27
I'm interval notation please
9514 1404 393
Answer:
(-2, 4]
Step-by-step explanation:
-21 ≤ -6x +3 < 15 . . . . given
-24 ≤ -6x < 12 . . . . . . subtract 3
4 ≥ x > -2 . . . . . . . . . . divide by -6
In interval notation, the solution is (-2, 4].
__
Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.
use quadratic formula to solve the following equation
9514 1404 393
Answer:
x = 2 or x = 9
Step-by-step explanation:
To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).
2(3) +4(3(x -3)) = (x +4)(x -3)
6 +12x -36 = x² +x -12
x² -11x +18 = 0
Using the quadratic formula to find the solutions, we have ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]
The solutions are x=2 and x=9.
A box with a square base and no top is to be made from a square piece of carboard by cutting 4 in. squares from each corner and folding up the sides. The box is to hold 1444 in3. How big a piece of cardboard is needed
Answer:
[tex]C=27inch\ by\ 27inch[/tex]
Step-by-step explanation:
Squares [tex]h=4inch[/tex]
Volume [tex]v=1444in^3[/tex]
Generally the equation for Volume of box is mathematically given by
[tex]V=l^2h[/tex]
[tex]1444=l^2*4[/tex]
[tex]l^2=361[/tex]
[tex]l=19in[/tex]
Since
Length of cardboard is
[tex]l_c=19+4+4[/tex]
[tex]l_c=27in[/tex]
Therefore
Dimensions of the piece of cardboard is
[tex]C=27inch\ by\ 27inch[/tex]
A school has 4 different after school activities planned in the fall Janet has time to participate in 2 of these activities. How many different pairs of after-school activities can Janet choose from the available activities?
Answer:
6
Step-by-step explanation:
Of 4 options, Janet has to choose 2. This is combinations as A and B is the same as B and A.
Combinations formula gives us 4!/ 2!2! , or 6.
Twice a number increased by the product of the number and fourteen results in forty eight
Answer:
Let x = the number. Then you have:
2x + 14x = 48 Collect like terms
16x = 48 Divide both sides by 16
x = 3
PLEASE MARK AS BRAINLIEST ANSWER
The number that satisfies the given statement is 3.
We are given that twice a number increased by the product of the number and 14 results in 48.
We will find the value of the number that we used in the given above statement.
Understand the meaning of the keywords used in the statement.Increased means addition.
Product means multiplication.
Results mean equal to sign.
Let's write the given statement in equation form.
Consider P = the number
Twice a number = 2P
Increased = +
Products of the number and 14 = P x 14
Results in 48 = equals 48.
Combining all the above we get,
2P + P x 14 = 48
2P + 14P = 48
16P = 48
P = 48 / 16
P = 3
Thus the number that satisfies the given statement is 3.
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Is this the correct answer?
Answer:
25.40
Step-by-step explanation:
tickets ( 2 at 10.95 each) = 2* 10.95 = 21.90
popcorn ( 1 at 7.50) = 7.50
Total cost before discount
21.90+7.50=29.40
subtract the discount
29.40-4.00 =25.40
Answer:
Yep! That's correct!
Step-by-step explanation:
We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.
(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}
21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}
$29.40 (without the credit) in toal
A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.
After doing the math, I can deduce that your answer is correct!
which of the following is the correct graph of the solution to the inequality -18 > 5x + 2 > -48?
Answer:
good luck
.............
Answer: the third one. filled circle for 4 ,5,6,7,8,9, open circle 10
Step-by-step explanation:
Which of the fractions below are less than 2/5? Select two.
Answer:
1/8 is less than
Step-by-step explanation:
i dont see any fractions below gona have to edit your answer
What is the value of n to the nearest whole number?
O 10
o 13
18
o
21
Answer:
n is 13
Step-by-step explanation:
[tex] {n}^{2} = {12}^{2} + {6}^{2} - (2 \times 12 \times 6) \cos(90 \degree) \\ {n}^{2} = 180 \\ n = 13.4[/tex]
Answer:
n is 13
Step-by-step explanation:
A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.36 and the standard deviation is2.97 . Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.
Answer:
2.665 < σ < 3.379
Step-by-step explanation:
Given :
s = 2.97
Sample size, n = 60
α = 80%
χ² Critical value (two - tailed), df = (60-1) = 59
χ² = 45.577 ; χ² = 73.279
The 80% confidence interval for the standard deviation :
s * √(n - 1) / χ² critical
2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577
2.665 < σ < 3.379
Emily, Yani and Joyce have a total of 3209 stickers. Yani has 2 times
as many stickers as Joyce. Emily has 279 more stickers than Yani. How
many more stickers does Emily have than Joyce?
Answer:
279+x
Step-by-step explanation:
Emily + Yani + Joyce=3209 stickers
if Yani has 2 times as many stickers as Joyce:this statement states that Joyce has x stickers and Yani has 2x stickers because x multiplied by 2"Emily has 279 more stickers than Yani":therefore the equation for Emily will be ;279+2xhow many stickers does Emily have than Joyce:
(279+2x)-(x)
279+2x-x
=279+x
5 Cece draws these two figures to prove there is more
than one parallelogram with a 40° angle between a
2-cm side and a 6-cm side. Is Cece correct? Explain.
2 cm
40
4.
2 cm
Answer:
chash greatly ta 45uerywryrsyrsyrs
the age of furaha is 1/2 of the age of her aunt if the sum of their ages is 54 years. find the age of her aunt
Answer:
I think it is twenty seven
Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3
Answer:
A
Step-by-step explanation:
f(-1)=7, f(0)=2, f(1)=-3
Please help me with this on the image
Answer:
a) Obtuse angle b) Reflex angle3 log2 (x+1) - 2 = 13
Answer:
Hello,
Answer 31
Step-by-step explanation:
[tex]3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\[/tex]
Use the point-slope formula to determine the equation of the line that has a slope of 1⁄2 and passes through point (0, 0).
Answer:
y-0 = 1/2(x-0)
y = 1/2(x)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-0 = 1/2(x-0)
y = 1/2(x)
Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)
Answer:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
Step-by-step explanation:
We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.
Let the angle between the two given sides be θ and let the third side be c.
Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.
First, convert the degrees into radians:
[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]
Hence, dθ/dt = π/90.
From the Law of Cosines:
[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]
Since a = 13 and b = 19:
[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]
Simplify:
[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]
Take the derivative of both sides with respect to t:
[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]
We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:
[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]
Solve for dc/dt:
[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]
Evaluate. Hence:
[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]
The third side is increasing at an approximate rate of about 0.444 meters per minute.
9514 1404 393
Answer:
0.444 m/min
Step-by-step explanation:
I find this kind of question to be answered easily by a graphing calculator.
The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...
c = √(a² +b² -2ab·cos(C))
Since C is a function of time, its value in degrees can be written ...
C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest
Using a=13, and b=19, the length of the third side is ...
c(t) = √(13² +19² -2·13·19·cos(60° +2t°))
Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...
0.443855627418 m/min ≈ 0.444 m/min
_____
Additional comment
At that time, the length of the third side is about 16.823 m.
__
c(t) reduces to √(530 -494cos(π/90·t +π/3))
Then the derivative is ...
[tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]
