Answer:
The correct answer is "0.7289".
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu = 15.5[/tex]
Standard deviation,
[tex]\sigma = 3.6[/tex]
As we know,
⇒ [tex]z = \frac{(x - \mu)}{\sigma}[/tex]
The probability will be:
⇒ [tex]P(11< x< 19) = P(\frac{11-15.5}{3.6} <z<\frac{19-15.5}{3.6})[/tex]
[tex]=P(z< 0.9722)-P(z< -1.25)[/tex]
By using the z table, we get
[tex]=0.8345-0.1056[/tex]
[tex]=0.7289[/tex]
Chang has 2 shirts: a white one and a black one. He also has 2 pairs of pants, one blue and one tan. What is the probability, if Chang gets dressed in the dark, that
he winds up wearing the white shirt and tan pants? Show your work.
Answer:
1/4
Step-by-step explanation:
White = w
Black = B
Blue = b1
Tan = t
Wb1
Wt
Bbi
Bt
The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.
Answer:
1/4
Step-by-step explanation:
it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.
Find the probability that the spinner will land on gray and then purple
Answer:
true the question is true and wait for others my could be wrong also
A wire 9 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each: For the equilateral triangle:
The length of wire used for the equilateral triangle is approximately 5.61 meters.
The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.
Here,
To minimize the total area of both figures, we need to find the optimal cut point for the wire.
Let's assume the length of the wire used for the equilateral triangle is x meters, and the remaining length of the wire used for the circle is (9 - x) meters.
For the equilateral triangle:
An equilateral triangle has all three sides equal in length.
Let's call each side of the triangle s meters. Since the total length of the wire is x meters, each side will be x/3 meters.
The formula to find the area of an equilateral triangle with side length s is:
Area = (√(3)/4) * s²
Substitute s = x/3 into the area formula:
Area = (√(3)/4) * (x/3)²
Area = (√(3)/4) * (x²/9)
Now, for the circle:
The circumference (perimeter) of a circle is given by the formula:
Circumference = 2 * π * r
Since the remaining length of wire is (9 - x) meters, the circumference of the circle will be 2π(9 - x) meters.
The formula to find the area of a circle with radius r is:
Area = π * r²
To find the area of the circle, we need to find the radius.
Since the circumference is equal to 2πr, we can set up the equation:
2πr = 2π(9 - x)
Now, solve for r:
r = (9 - x)
Now, substitute r = (9 - x) into the area formula for the circle:
Area = π * (9 - x)²
Now, we want to minimize the total area, which is the sum of the areas of the triangle and the circle:
Total Area = (√(3)/4) * (x²/9) + π * (9 - x)²
To find the optimal value of x that minimizes the total area, we can take the derivative of the total area with respect to x, set it to zero, and solve for x.
d(Total Area)/dx = 0
Now, find the critical points and determine which one yields the minimum area.
Taking the derivative and setting it to zero:
d(Total Area)/dx = (√(3)/4) * (2x/9) - 2π * (9 - x)
Setting it to zero:
(√(3)/4) * (2x/9) - 2π * (9 - x) = 0
Now, solve for x:
(√(3)/4) * (2x/9) = 2π * (9 - x)
x/9 = (8π - 2πx) / (√(3))
Now, isolate x:
x = 9 * (8π - 2πx) / (√(3))
x(√(3)) = 9 * (8π - 2πx)
x(√(3) + 2π) = 9 * 8π
x = (9 * 8π) / (√(3) + 2π)
Now, we can calculate the value of x:
x ≈ 5.61 meters
So, the length of wire used for the equilateral triangle is approximately 5.61 meters.
The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.
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I NEED HELP!! PLEASE
Answer:
Step-by-step explanation:
D is the answer. You shift the function to the left 5 units, hence the term |x+5|, and move it down 1, hence the term -1.
Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor, but 3 days later 68 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)
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 consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of tubes of each type is selected, and is computed. If equals or exceeds , the manufacturer would like to adopt type B for use. The observed difference is . a. What is the probability that exceeds by 3.0 or more if and are equal
Answer:
The answer is "0.7794".
Step-by-step explanation:
Please find the complete question in the attached file.
Given:
[tex]\to n_{1}=n_{2}=25\\\\[/tex]
Hypotheses:
[tex]\to H_{0}:\mu_{B}-\mu_{A}\geq 0\\\\\to H_{a}:\mu_{B}-\mu_{A}< 0\\\\[/tex]
Testing statistics:
[tex]\to z=\frac{(\bar{x}_{B}-\bar{x}_{A})-(\mu_{B}-\mu_{A})}{\sqrt{\frac{\sigma^{2}_{B}}{n_{1}}+\frac{\sigma^{2}_{A}}{n_{2}}}}=\frac{3.5-(0)}{\sqrt{\frac{16^{2}}{25}+\frac{16^{2}}{25}}}=0.77[/tex]
The test is done just so the p-value of a test is
[tex]\to p-value = P(z < 0.77) = 0.7794[/tex]
Because the p-value of the management is large, type B can take it.
Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1241 1210 1267 1314 1211 1299 1246 1280 1291
a. Determine if the data meets the initial conditions to construct a confidence interval.
b. Find the sample mean year x and sample standard deviation σ.
c. What is the maximal margin of error when finding a 90 % confidence interval for the mean of all tree-ring dates from this archaeological site?
Answer:
(1238.845 ;1285.376)
Step-by-step explanation:
Conditions for constructing a confidence interval :
Data must be random
Distribution should be normal and independent ;
Based on the conditions above ; data meets initial conditions ;
C. I = sample mean ± margin of error
Given the data :
1241 1210 1267 1314 1211 1299 1246 1280 1291
Mean, xbar = Σx / n = 11359 / 9 = 1262.11
The standard deviation, s = [√Σ(x - xbar)²/n - 1]
Using a calculator ; s = 37.525
The confidence interval :
C.I = xbar ± [Tcritical * s/√n]
Tcritical(0.10 ; df = n - 1 = 9 - 1 = 8)
Tcritical at 90% = 1.860
C. I = 1262.11 ± [1.860 * 37.525/√9]
C.I = 1262.11 ± 23.266
(1238.845 ;1285.376)
± 23.266
The margin of error :
[Tcritical * s/√n]
[1.860 * 37.525/√9]
C.I = ± 23.266
the adjacent sides of a parallelogram are (x + 3) and (x + 2). Find the perimeter of the parallelogram
9514 1404 393
Answer:
4x+10
Step-by-step explanation:
For parallelogram adjacent sides a and b, the perimeter is ...
P = 2(a +b)
For the given sides, the perimeter is ...
P = 2((x +3) +(x +2)) = 2(2x +5)
P = 4x +10 . . . perimeter of the parallelogram
hope anyone help me please
9514 1404 393
Answer:
a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22
b) 30
c) 6
d) yes; no
Step-by-step explanation:
a) The values are read from the graph.
__
b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest
__
c) -2 -(-8) = -2 +8 = 6 . . . positive difference
(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)
__
d) -2 + 5 < 5 . . . . true
-2 + 5 < -2 . . . . false
y
27
х
10
11
12
In order for the data in the table to represent a linear
, function with a rate of change of -8, what must be the
value of a?
a
11
O a = 2
O a = 3
O a = 19
a = 35
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The rate of change of a linear function is also known as the slope of the function.
To determine the slope of the function represented by the given table, we need to calculate the change in Y for a unit change in X.
Using the values given in the table, we can calculate the slope as follows:
Slope = (Change in Y) / (Change in X)
So,
(a - 27) / (11 - 10) = (11 - 27) / (12 - 10) = -8
Setting this equation equal to -8, we get:
= (a - 27) / 1
= -8
Simplifying the equation, we get:
a - 27 = -8
a = 19
Therefore,
The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.
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Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -x+3
Step-by-step explanation:
Slope intercept form => y = mx+b
To find 'm', the slope, pick 2 coordinates.
(0,3)
(2,1)
Use this equation to find the slope using these 2 coordinates: (y1 - y2)/(x1 - x2)
(3 - 1)/(0 - 2) = -1
m = slope = -1
'b' is the y-intersept, or the point when a line passes through the y-axis. That's (0,3).
b = y-intercept = 3
So the equation will be y = -1x + 3, or y = -x + 3
The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)
Answer:
30 clocks
Step-by-step explanation:
Set up an equation:
Variable x = number of clocks
1200 + 20x = 60x
Isolate variable x:
1200 = 60x - 20x
1200 = 40x
Divide both sides by 40:
30 = x
Check your work:
1200 + 20(30) = 60(30)
1200 + 600 = 1800
1800 = 1800
Correct!
what is the discrimination of the polynomial below ?
9x2-18x+9
HELP ASAP PLEASE! I tried inputting the numbers into the standard deviation equation but I did not get the right answer to find z. Can someone please help me? Thank you for your time!
Answer:
Z = -1.60
it is low ... it appears that for this problem 2 standard deviations below must be reached to be considered "unusual"
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help i will give
brainliest
Answer:
55
Step-by-step explanation:
55 appears 3 times, which is the most repetition in the data set
Answer:
55
Step-by-step explanation:
Mode = number that appears most often
The number 55 appears 3 times which is the most out of the other numbers
Hence mode = 55
Perimeter (numerical) cm
Answer:
101 cm
Step-by-step explanation:
Add all the side lengths up to get 101 cm.
Anthony read 46 pages of a book in 23 minutes.
To find the unit rate, use
.
Anthony read
pages per minute.
Answer:
2 pages per minute
Step-by-step explanation:
Take the number of pages and divide by the number of minutes
46 pages / 23 minutes
2 pages per minute
2 Pages per Minute
Solutions:46 ÷ 23 = 2
Final Answer:Anthony can read 2 pages per minute.
For -180°<θ<0 , which of the primary trigonometric functions may have positive values?
Answer:
cos theta = adj / hyp is positive (+/+)
Step-by-step explanation:
In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.
in this interval:
sin theta = opp / hyp is neg (-/+)
cos theta = adj / hyp is positive (+/+)
tan theta = opp / adj = (-/+) : negative
find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)
Answer:
Hello
Step-by-step explanation:
The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1
and the disk ? (inside of a circle) of center (0,0) and radius 2
[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]
which of the following values could NOT be a probability
Answer:
3/2, -1.1
Step-by-step explanation:
the probability cannot be greater than 1. probability is between 0 and 1
Create truth table to determine whether or not the following statements are logically equivalent
The statement is totally false.
[tex]\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q[/tex]
because (P and ¬P) is a contradiction.
Determine the domain and range of the graph
Answer:
5 ≤ x ≤ 10 5 ≤ y ≥ -1
Step-by-step explanation:
Cyril has six more than twice as many mangoes as Kubie and half as many mangoes as Maxine. If Kubie has six mangoes, then, in terms of x, how many mangoes do Cyril, Kubie, and Maxine have combined?
Answer:
(7x + 18) or 60 Mangoes
Step-by-step explanation:
Let the no. of mangoes Kubie possesses be x
So,
Cyril has mangoes = 2x + 6 ...(i)
So,
Maxine has = 2 * (2x + 6)
= 4x + 12
Given that,
Kubie has mangoes = 6
∵ The combined mangoes they have in terms of x,
= Cyril + Kubie + Maxine
= (2x + 6) + x + (4x + 12)
= 7x + 18
A.T.Q.
Cyril has = 2x + 6
∵ Cyril has mangoes = 2 * (6) + 6
= 18 mangoes
∵ Maxine has = 2 * Cyril's mangoes
= 2 * 18
= 36
Thus,
Total mangoes = Cyril + Kubie + Maxine
= 18 + 6 + 36
= 60 Mangoes
Please help with this question
9514 1404 393
Answer:
(d) -1/32
Step-by-step explanation:
It may be easier to rearrange the expression so it has positive exponents.
[tex]\dfrac{1}{2^{-2}x^{-3}y^5}=\dfrac{2^2x^3}{y^5}=\dfrac{4(2)^3}{(-4)^5}=-\dfrac{4\cdot8}{1024}=\boxed{-\dfrac{1}{32}}[/tex]
[(2021-Y)-5]*X-X=XX cho biết X,Y,XX là gì?
A chemist has three different acid solutions.
The first solution contains 25% acid, the second contains 35%acid, and the third contains 55% acid.
She created 120 liters of a 40% acid mixture, using all three solutions. The number of liters of 55% solution used is 3 times the number of liters of 35% solution used.
How many liters of each solution was used?
Let x, y, and z be the amounts (in liters, L) of the 25%, 35%, and 55% solutions that the chemist used.
She ended up with 120 L of solution, so
x + y + z = 120 … … … [1]
x L of 25% acid solution contains 0.25x L of acid. Similarly, y L of 35% solution contains 0.35y L of acid, and z L of 55% solution contains 0.55z L of acid. The concentration of the new solution is 40%, so that it contains 0.40 (120 L) = 48 L of acid, which means
0.25x + 0.35y + 0.55z = 48 … … … [2]
Lastly,
z = 3y … … … [3]
since the chemist used 3 times as much of the 55% solution as she did the 35% solution.
Substitute equation [3] into equations [1] and [2] to eliminate z :
x + y + 3y = 120
x + 4y = 120 … … … [4]
0.25x + 0.35y + 0.55 (3y) = 48
0.25x + 2y = 48 … … … [5]
Multiply through equation [5] by -2 and add that to [4] to eliminate y and solve for x :
(x + 4y) - 2 (0.25x + 2y) = 120 - 2 (48)
0.5x = 24
x = 48
Solve for y :
x + 4y = 120
4y = 72
y = 18
Solve for z :
z = 3y
z = 54
3.52 A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses. If the coin is unbalanced and a head has a 40% chance of occurring, find (a) the joint probability distribution of W and Z; (b) the marginal distribution of W; (c) the marginal distribution of Z
Answer:
a) The joint probability distribution
P(0,0) = 0.36, P(1,0) = 0.24, P(2,0) = 0, P(0,1) = 0, P(1,1) = 0.24, P(2,1)= 0.16
b) P( W = 0 ) = 0.36, P(W = 1 ) = 0.48, P(W = 2 ) = 0.16
c) P ( z = 0 ) = 0.6
P ( z = 1 ) = 0.4
Step-by-step explanation:
Number of head on first toss = Z
Total Number of heads on 2 tosses = W
% of head occurring = 40%
% of tail occurring = 60%
P ( head ) = 2/5 , P( tail ) = 3/5
a) Determine the joint probability distribution of W and Z
P( W =0 |Z = 0 ) = 0.6 P( W = 0 | Z = 1 ) = 0
P( W = 1 | Z = 0 ) = 0.4 P( W = 1 | Z = 1 ) = 0.6
P( W = 1 | Z = 0 ) = 0 P( W = 2 | Z = 1 ) = 0.4
The joint probability distribution
P(0,0) = 0.36, P(1,0) = 0.24, P(2,0) = 0, P(0,1) = 0, P(1,1) = 0.24, P(2,1)= 0.16
B) Marginal distribution of W
P( W = 0 ) = 0.36, P(W = 1 ) = 0.48, P(W = 2 ) = 0.16
C) Marginal distribution of Z ( pmf of Z )
P ( z = 0 ) = 0.6
P ( z = 1 ) = 0.4
Part(a): The required joint probability of W and Z is ,
[tex]P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16[/tex]
Part(b): The pmf (marginal distribution) of W is,
[tex]P(w=0)=0.36,P(w=1)=0.48,P(w=2)=0.16[/tex]
Part(c): The pmf (marginal distribution) of Z is,
[tex]P(z=0)=0.6,P(z=1)=0.4[/tex]
Part(a):
The joint distribution is,
[tex]P(w=0\z=0)=0.6,P(w=1|z=0)=0.4,P(w=2|z=0)=0[/tex]
Also,
[tex]P(w=0\z=1)=0,P(w=1|z=1)=0.6,P(w=2|z=1)=0.4[/tex]
Therefore,
[tex]P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16[/tex]
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A bus driver makes roughly $3280 every month. How much does he make in one week at this rate.
Answer:
I think around $36
Hope it helps!
Answer:
It depends...
Step-by-step explanation:
It depends how much weeks are in the month if there are three weeks and no extra days then you would have an answer of about 1093 (exact: 1093.33333333). just divide the number of weeks by the number of money.
An isosceles trapezoid has a consecutive-sides of length: 10,6,10 and 14. Find the measure of each angle if the trapezoid.
Answer:
Angle A = Angle D = 69° 30'
Angle B = Angle C = 110° 30'
Step-by-step explanation:
B ___ C
/ \
/ \
A ________ D
AB and CD are 10
BC is 6
AD is 14
If we divide the trapezoid, we can imagine a line.
B_ F_C
/ | \
/ | \
A ___E____ D
AE = ED = 7 (14/2)
BF = FC = 3
So now, we draw another line from B or C to AE or ED
B_ F_ C
/ | | \
/ | | \
A ___E_ G_ D
EG = GD = 3.5 (7/2)
There is a right triangle now, GCD
GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:
CD is H, and GD is A
cos D = A/H
cos D = 3.5/10 → 0.35
angle D = 69° 30'
By theory, we know that angle D and angle A, are the same so:
Angle D = Angle A = 69° 30'
Angle B = Angle C
We also make a cuadrilateral, which is EFCD.
Angle D is 69° 30', Angle E is 90°, Angle F is also 90°
Sum of angles in cuadrilateral is 360°
360° - 69° 30' - 90° - 90° = Angle C = Angle B
Angle C = Angle B = 110° 30'
Let's confirm the angles in the trapezoid:
69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°
A + B + C + D
Please help with this question
Answer:
im not too sure but try using a cartesuan plane and measure it precisely using a protractor then key in the measurements. Im not entirely sure its the correct method tho
