Answer:
69
Step-by-step explanation:
Since the values in the data set has been ranked already from smallest to largest, as shown in the question.
Then calculate the index,
To find the 36th percentile using the data set,
Multiply k (36/100) by n (25) to reach an index of 9.
Then since the index is whole number,
To calculate percentile according to the 'greater than' method, count the values in the data set from smallest to largest until you reach the number ranked 9th
Which is 69.
Since the value for the 36th percentile must be greater than the first nine values, the 10th ranked value would be the kth (36th) percentile. In this data set, that value is 69.
Alternatively, using the 'greater than or equal to' method, after getting the 9th rank,
Include the ninth-ranked value, (69) in this data set.
The kth (36th) percentile is then calculated by taking the average of that value in the data set (69) and the next ranked value (69). (59 + 69) / 2 = 69.
if f(x)=3x+7 what is f(2)
Answer:
13
Step-by-step explanation:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
g Suppose that twenty different hypothesis tests for whether jellybeans cause acne are conducted. In order that the probability of one or more type I error between these should be at most 0.05, at most what significance level should be used for each of them?
Answer:
The level of significance to be used is α = 0.0025
Step-by-step explanation:
Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test
We proceed as follows;
P(type 1 error) = α
From the question, n = number of hypotheses = 20
P( of one or more type one error) ≤ 0.05
1- P(no type one error) ≤ 0.05
Hence;
1- (1-α)^20 ≤ 0.05
(1-α)^20 ≥ 0.95
1- α ≥ 0.997438621223
α ≤ 0.00256
Thus α = 0.0025
The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population in 2010 was 12 million. a. Find an exponential model n(t)= no e^rt for the population t years after 2010. b. Estimate the fish population in the year 2015. c. After how many years will the fish population reach 14 million? d. Sketch a graph of the fish population.
Answer:
(a) n(t) = P(0)*e^(0.010939940t)
(b) 12,674,681 (nearest unit)
(c) 14 years (nearest year)
Step-by-step explanation:
rate = 1.1% / year = 1.011
(a)
P(0) = 12,000,000 = population in 2010
In compound interest format, after t years
P(t) = P(0)* (1.011)^t
Given format = P(0)* e^(rt)
therefore
e^(rt) = 1.011^t use law of exponents
(e^r)^t = 1.011^t
e^r = 1.011
r = log_e(1.011) = 0.010939940 (to 9 decimal places)
required formula is
n(t) = P(0)*e^(0.010939940t)
(b)
in 2015,
P(0)=12000000, n = 5 (years after 2010)
n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)
(c)
to reach 14 million, we equate
n(t) = 14,000,000
12,000,000 *e^(0.010939940*t) = 14,000,000
e^(0.010939940*t) = 14000000/12000000 = 7/6
take log on both sides
0.010939940*t = log(7/6)
t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.
See graph attached. Y-axis is in millions, x-axis is in years.
a) [tex]n(t) = 12e^{0.011t}[/tex]
b) The estimate for the population in 2015 is of 12.7 million.
c) The fish population will reach 14 million after 14 years.
d) The sketch is given at the end of this answer.
------------------------------------
Item a:
The exponential model is:
[tex]n(t) = n(0)e^{rt}[/tex]
In which:
n(0) is the population is 2010.r is the growth rate, as a decimal.Population of 12 million, thus [tex]n(0) = 12[/tex]Growth rate of 1.1%, thus [tex]r = 0.011[/tex].
Thus, the model is:
[tex]n(t) = 12e^{0.011t}[/tex]
Item b:
2015 is 2015 - 2010 = 5 years after 2010, thus this is n(5).
[tex]n(5) = 12e^{0.011(5)} = 12.7[/tex]
The estimate for the population in 2015 is of 12.7 million.
Item c:
This is t for which n(t) = 14, thus:
[tex]n(t) = 12e^{0.011t}[/tex]
[tex]14 = 12e^{0.011t}[/tex]
[tex]e^{0.011t} = \frac{14}{12}[/tex]
[tex]\ln{e^{0.011t}} = \ln{\frac{14}{12}}[/tex]
[tex]0.011t = \ln{\frac{14}{12}}[/tex]
[tex]t = \frac{\ln{\frac{14}{12}}}{0.011}[/tex]
[tex]t = 14[/tex]
The fish population will reach 14 million after 14 years.
Item d:
At the end of this answer, the sketch is given.
A similar problem is given at https://brainly.com/question/23416643
Can someone solve this for me
Answer:
[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]
Step-by-step explanation:
divide each term by 2y^3
Multiply through by the least common denominator.
Solve for w in terms of t
3w-8=t
Please explain steps
Answer:
[tex]w=\frac{t+8}{3}[/tex]
Step-by-step explanation:
[tex]3w - 8 = t[/tex]
Add 8 on both sides.
[tex]3w - 8 + 8 = t + 8[/tex]
[tex]3w = t + 8[/tex]
Divide both sides by 3.
[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]
[tex]w=\frac{t+8}{3}[/tex]
The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an equation:
3w - 8 = t
To solve for w in terms of t
Make the subject as w
In the equation:
3w - 8 = t
Add 8 on both sides:
3w - 8 + 8 = t + 8
3w = t + 8
Divide by 3 on both sides:
3w/3 = (t + 8)/3
w = (t + 8)/3
The equation represents a function of w in terms of t
As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
The length and width of a rectangle are measured as 27 cm and 50 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
7.7cm
Step-by-step explanation:
Area of a rectangle is expressed as
A = Length × Width
A = LW
Let dL and dW be the errors in the measurements.
If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.
The area of the rectangle with error will be expressed as A = LdW + WdL
Given L = 27cm and W = 50cm
A = 27(0.1)+50(0.1)
A = 2.7+5.0
A = 7.7cm
Hence, the maximum error in the calculated area of the rectangle is 7.7cm
Write the Verbal phrases as an equation or an inequality? Use "x" as the variable?
Step-by-step explanation:
8.x×8-12=50
8x-12=50
9.1/2x>or=100
10.2 whole number5/9-x=31
Solve equation :
A=Bt+c for t
Answer:
( A -c) /B =t
Step-by-step explanation:
A=Bt+c
Subtract c from each side
A-c=Bt+c-c
A -c = Bt
Divide each side by B
( A -c) /B = Bt/B
( A -c) /B =t
Answer:
Hey there!
A=Bt+c
A-c=Bt
t=(a-c)/B
Hope this helps :)
A six sided number cube is rolled twice. What is the probability that the first roll is an even number and the second roll is a number grater than 4?
Answer:
1/6
Step-by-step explanation:
The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.
Multiply these two values
1/2*1/3= 1/6
What is the value of x
Answer:
x=7
Step-by-step explanation:
En una fábrica de refrescos se envasan 1100 litros en 400 envases, unos de 2 litros y otros de 3 litros. ¿Cuantos envases de 2 y 3 litros se utilizan?
Greetings from Brasil...
X = 2 liter container
Y = 3 liter container
the total of containers are:
X + Y = 400
the capacity of the containers is
2X + 3Y = 1100
Assembling the equation system
2X + 3Y = 1100
X + Y = 400 x(-2)
2X + 3Y = 1100
-2X -2Y = - 800
Y = 300X + Y = 400 so
X + 300 = 400
X = 400 - 300
X = 100----------------------------------------------------------
BR:
Observe que:
1 vasilha de 2L = 1 × 2 = 2L
2 vasilhas de 2L = 2 × 2 = 4L
3 vasilhas de 2L = 3 × 2 = 6L
X vasilhas de 2L = X × 2 = 2X litros
.....
1 vasilha de 3L = 1 × 3 = 2L
2 vasilhas de 3L = 2 × 3 = 4L
3 vasilhas de 3L = 3 × 3 = 6L
X vasilhas de 3L = X × 3 = 3X litros
Logo 2X + 3Y = 1100
Existem X e Y vasilhas que num total sao 400, logo
X + Y = 400
Find the slope and y-intercept of the equation. y= 2/3x + 1
A. 2/3; 1
B. 1; 2/3
C. 2/3; -1
Answer:
The answer is A.
Step-by-step explanation:
In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.
So for this question, m is 2/3 and b is 1.
Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs
of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3
contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb
drawn from it at random is found to be defective. Find the probability that the box
selected was Box 2.
Answer:
1/6
Step-by-step explanation:
As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.
The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2 divided by total number of defective bulbs.
P(defective in box 2)= N(defective in box 2)/N(defective total)
As we know there is only 1 defective lamp in box 2.
So N(defective in box 2)=1
Total number of defective bulbs is Box1- 2 defective bulbs, box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.
So N(defective total)=6
So P(defective in box 2)=1/6
Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $10$ steps, how many different points could Franklin end up at?
Answer: Franklin could end at 4 different points.
Step-by-step explanation:
Given: Franklin the fly starts at the point (0,0) in the coordinate plane.
At each point, Franklin takes a step to the right, left, up, or down.
i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]
If he moves 10 steps, then the number of different points Franklin could end up at = choices of directions
= 4
Hence, Franklin could end at 4 different points.
a total of 309 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold
Answer: 103 adult tickets
Step-by-step explanation:
Adult tickets (a) = a
Student tickets (s) = 2a
Total = 309
a + 2a = 309
3a = 309
a = 103
Answer:
103Step-by-step explanation:
Total tickets sold = 309
Let the number of adult tickets sold be x
Let the number of student tickets sold be 2x
Adult tickets + student tickets = 309
[tex]x + 2x = 309[/tex]
Collect like terms
[tex] 3x = 309[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{309}{3} [/tex]
Calculate
[tex]x = 103[/tex]
Hence, 103 adult tickets were sold.
Hope this helps..
Good luck on your assignment...
How many solutions does the system have? You can use the interactive graph below to find the answer. 4x-2y=8 2x+y=2 4x−2y=8 2x+y=2 A.One solution B.two solutions. C.Many solutions
Answer:
one solution
Step-by-step explanation:
The given system of equations has one solution.
Hence option A is correct.
The given system is
4x-2y=8
2x+y=2
Since we know that,
For system
a₁x + b₁ y = c₁
a₂x + b₂y = c₂
If
a₁/a₂ = b₁/b₂ = c₁/c₂ then it has an infinite solution
a₁/a₂ ≠ b₁/b₂ then unique solution
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then no solution
Here we have
a₁ = 4, b₁ = -2 and c₁ = 8
a₂ = 2, b₂ = 1 and c₂ = 2
Now since
a₁/a₂ ≠ b₁/b₂ ⇒ 4/2 ≠ -2/1
⇒ 2 ≠ -2
Hence, the given system has a unique solution.
Learn more about system of equations at:
brainly.com/question/14323743
#SPJ2
Which equation satisfies all three pairs of a and b values listed in the table ?
A) a-3b=10
B) 3a+ b=10
C) 3a-b=10
D) a+ 3b=10
Answer:
The answer is option C.
3a - b = 10
Hope this helps you
Solve triangle ABC given:
(a) angle A = 40°, angle B = 60°, b = 8 cm.
(b) a = 4, b = 5, c = 6.
(c) angle B = 104°, a = 17 cm, c = 11 cm.
Answer:
(a) C = 80 a = 5.938cm c = 9.097cm
(b) unsure
(c) b= 22.147cm
A = 48.16 degrees
C = 22.82 degrees
Note angle sum higher than 180 due to rounding inaccuracies
Step-by-step explanation:
(a) <C == 180 - (40 + 60) == 80 (Interior angles on triangle have sum of 180 degrees)
side a = (8*sin(40))/sin(60) == 5.938cm by law of sines
side c = (8*sin(80))/sin(
60) == 9.097cm by law of sines
(b) unsure
(c) b^2 = 17^2 + 11^2 - 2(17)(11)cos(104) --> Law of cosines
b^2 = 289 + 121 - 2(187)cos(104)
b^2 = 400 - -90.479
b^2 = 490.479
b = 22.147 cm
sin(A)/17cm = sin(104)/22.147cm
A = arcsin((17/22.147)*sin(104))
A = 48.16 degrees
sin(C)/11cm = sin(104)/22.147cm
C = arcsin((11/22.147)*sin(104))
C = 28.82 degrees
please help me pleaseeeeeeee
Answer:
the first blank is 2, the second one is 1
Answer:
Yellow box #1=2
Yellow box #2=1
Step-by-step explanation:
#1) 8-6=2
#2)8-7=1
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n. A one-way analysis of variance showed that job satisfaction did not vary by marital status, F(2, 24) = 1.93, p > 0.05.
a. k = _____
b. N = _____
c. n = _____
Answer:
a. k = 3
b. N = 27
c. n = 9
Step-by-step explanation:
Given that,
Source : sS dF mS F
Between: k -1 sSB/k-1 mSB
within N-K sSw/N-K mSw
total N-1
Therefore F ( 2, 24 ) = F ( K - 1, N - K )
so K - 1 = 2
K = 2 + 1
K = 3
N - K = 24
N - 3 = 24
N = 24 + 3
N = 27
married, single and divorced are equal sizes
so n = N/3
n = 27 / 3
n = 9
a. k = 3
b. N = 27
c. n = 9
Maria has $46 to buy fish for her aquarium. Each goldfish costs $6. How
many goldfish can she buy? Do not include units in your answer.
Answer:
7
Step-by-step explanation:
Take the amount of money and divide by the cost per fish
46/6 =7 with 4 dollars remaining
She can buy 7 goldfish
Answer:
7
Step-by-step explanation:
7 x 6 = 42
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)
z = x8y9, x = s cos(t), y = s sin(t)
∂z/∂s =
∂z/∂t =
Answer:
Step-by-step explanation:
Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;
∂z/∂s = ∂z/∂x*∂x/∂s + ∂z/∂y*∂y/∂s
Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)
∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)
On substitution;
∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)
∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)
∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t
∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t
∂z/∂s = 17s¹⁶cos⁸tsin⁹t
∂z/∂t = ∂z/∂x*∂x/∂t + ∂z/∂y*∂y/∂t
∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)
∂z/∂t = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))
∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))
∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t
∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)
Draw the straight line y = x + 2
Answer:
Graph is attached below
Step-by-step explanation:
You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.
The plotted straight line is as shown in below graph.
Given straight line equation is y = x + 2
To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.
After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.
Example, take x = 1 and x = 2 for straight line y = x + 2
Then we get:
For x = 1, y = 1 + 2 = 3
For x = 2, y = 2 + 2 = 4
The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.
Learn more here:
https://brainly.com/question/959487
Is the given triangle scalene, isosceles, or equilateral? The Vertices are T(1,1), V(4,0), S(3,5)
Answer: It is a scalene triangle.
Step-by-step explanation:
It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.
I bought a tv for 532.50 including the 6%sales tax. What was the original price of the tv without the sales tax?
Step-by-step explanation:
Hey, there !!!
According to your question,
total c.p = 532.50
tax rate =6%
let original price be x.
now,
total c.p = x + tax rate of x.
or, 532.50= x+ (6/100) × x
or, 532.50 = 106x/100
or, 53200 = 106x
or, x= 53200/106
Therefore, the original price was 501.88.
Hope it helps...
What is the solution to the quadratic equation x2 + x - 30 = 0?
Answer:
try 3x=30 or 10
Step-by-step explanation:
Which value is a solution to the inequality 9-y >12
I believe the value is negative 4. If not, well, try any negative below that, such as -5,6,7,8, etc.
Answer:
y is less than -3
Step-by-step explanation:
To do this you would just subtract 9 from both sides so you get -y is greater than 3. Since you cannot have y as a negative number you will divide -1 from both sides but when you do that you will have to flip the sign so you get y is less than -3.
Trey is choosing a 2-letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are
possible?
Answer:
10
Step-by-step ex1planation:
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x