Answer:
Yes they do.
And yes they do follow a normal distribution.
Percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have a data of final exam scores of 20 Introductory.
a) Range of 1 standard deviation:
(77.7 – 8.44, 77.7 + 8.44) [69.3, 86.1]
Range of 2 standard deviation:
(77.7 – 2(8.44), 77.7 + 2(8.44)) [60.8, 94.6]
Range of 3 standard deviation:
(77.7 – 3(8.44), 77.7 + 3(8.44)) [52.4, 103.0]
Number of data points lie within 1 standard deviation = 14
Percent of data points lie within 1 SD = (14/20)×100 = 70%
Number of data points lie within 2 SD = 19
Percent of data points lie within 1 SD = (19/20)×100 = 95%
Number of data points lie within 3 SD = 20
Percent of data points lie within 1 SD = (20/20)×100 = 100%
Because these percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed.
b)
Because the histogram in the graph is symmetric, and the normal probability plot reveals that the points are very close to a straight line, the data appears to follow a normal distribution.
Thus, percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.
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b7
__
b6
Multiply or divide as indicated.
For this case we have the following expression:
[tex]\frac {b ^ 7} {b ^ 6}[/tex]
By definition of division of powers of the same base, we have to place the same base and subtract the exponents, that is:
[tex]\frac {a ^ m} {a ^ n} = a ^ {n-m}[/tex]
So:
[tex]\frac {b ^ 7} {b ^ 6} = b ^ {7-6} = b ^ 1 = b[/tex]
Answer:
b
Answer: [tex]b[/tex]
Step-by-step explanation:
You need to remember a property called "Quotient of powers property". This property states the following:
[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]
You can observe that the bases of the expression [tex]\frac{b^7}{b^6}[/tex] are equal, then you can apply the property mentioned before.
Therefore, you can make the division indicated in the exercise.
Then you get this result:
[tex]\frac{b^7}{b^6}=b^{(7-6)}=b[/tex]
You are going to play two games. The probability you win the first game is 0.60. If you win the first game, the probability you will win the second game is 0.75. If lose the first game, the probability you win the second game is 0.55. What is the probability you win exactly one game? (Round your answer to two decimal places)
The probability that you win exactly one game is:
0.37
Step-by-step explanation:The probability you win the first game is 0.60. If you win the first game, the probability you will win the second game is 0.75. If lose the first game, the probability you win the second game is 0.55.The probability that you win exactly one game is:
Probability you win first but not second+Probability you win second but not first.
= 0.60×0.25+0.40×0.55
= 0.37
( since probability of losing second game when you win first is: 1-0.75=0.25
and probability that you lose first game is: 1-0.60=0.40 )
Final answer:
The probability of winning exactly one game, rounded to two decimal places, is 0.37.
Explanation:
Probability of winning the first game = 0.60
Probability of winning the second game if the first game is won = 0.75
Probability of winning the second game if the first game is lost = 0.55
To find the probability of winning exactly one game, we calculate the probability of winning the first game and losing the second game, plus the probability of losing the first game and winning the second game:
Probability of winning 1st and losing 2nd = (0.60 * 0.25) = 0.15Probability of losing 1st and winning 2nd = (0.40 * 0.55) = 0.22Total Probability of winning exactly one game: 0.15 + 0.22 = 0.37Find (f-g)(x) for the following functions.
Answer:
B
Step-by-step explanation:
(f-g)(x) just means f(x)-g(x)
so let's do that
make sure you distribute the minus in front of g to it's terms
-12x^3+19x^2-5-7x^2-15
-12x^3+12x^2-20
B.
Amy and Alex are making models for their science project. Both the models are in the shape of a square pyramid. The length of the sides of the base for both the models is 8 inches. Amy’s model is 5 inches tall and Alex’s model is 3 inches tall. Find the difference in volume of the two models.
Answer:
The difference in volume of the two models is [tex]\frac{128}{3}\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a square pyramid is equal to
[tex]V=\frac{1}{3}b^{2}h[/tex]
where
b is the length of the side of the square base
h is the height of the pyramid
step 1
Find the volume of Amy's model
we have
[tex]b=8\ in[/tex]
[tex]h=5\ in[/tex]
substitute
[tex]V=\frac{1}{3}(8)^{2}(5)[/tex]
[tex]V=\frac{320}{3}\ in^{3}[/tex]
step 2
Find the volume of Alex's model
we have
[tex]b=8\ in[/tex]
[tex]h=3\ in[/tex]
substitute
[tex]V=\frac{1}{3}(8)^{2}(3)[/tex]
[tex]V=\frac{192}{3}\ in^{3}[/tex]
step 3
Find the difference in volume of the two models
[tex]\frac{320}{3}\ in^{3}-\frac{192}{3}\ in^{3}=\frac{128}{3}\ in^{3}[/tex]
A number is thrift if it is a multiple of 2 or 3. How many thrift numbers are there between -15 and 15
(a) 18 (b) 9 (c) 19 (d) 15
Answer:
(a) 19.
Step-by-step explanation:
The even numbers in the given range are -14, -12, -10, -8, - 6 , -4 and -2. and 7 more of their positive values. Total 14.
The numbers divisible by 3 and not 2 are -9, -3, 3 and 9.
Also 0 is a multiple of any number
Thus, number of thrift numbers are 14 + 4 + 1 = 19 (answer).
Consider two algorithms that perform the same function, that run in n/4 and log2(n), respectively, where n ∈ N (i.e. natural numbers).(a) Plot these runtimes on the same graph with the values n ∈ [1, 50] (don’t forget labels). Provide the set of intervals over N, where n/4 is the strictly better algorithm to use (think greater than, not greater than or equal).
Answer:
[2, 15]
Step-by-step explanation:
The graph shows the n/4 algorithm to be better (smaller run time) for n in the range 2 to 15.
Stones are thrown horizontally, with the same initial velocity, from the tops of two different buildings, A and B. The stone from building A lands 4 times as far from the base of the building as does the stone from building B. What is the ratio of building A's height to building B's height?
In this Physics problem, we calculate the horizontal distance a stone travels when thrown horizontally from a cliff to determine the ratio of heights between two buildings.
Explanation:The horizontal distance the stone will travel can be calculated using the formula:
d = v*t
Where d is the distance, v is the initial velocity, and t is the time of flight. Using the information given, we can calculate the distance the stone from block A will travel, and then find the ratio of building A's height to building B's height.
Find the area of the polygon with vertices of A(0, 1), B(0, 5), C(4, 5), and D(6, 1)
Check the picture below.
The given vertices define a polygon consisting of a rectangle and a triangle. The areas of the shapes are calculated separately and added together to find the total area of the polygon, which is 20 square units.
Explanation:The given coordinates define two distinct shapes, a rectangle, and a triangle. Considering point A(0,1), B(0,5), C(4,5), and D(6,1), we can see that the rectangle is A, B, C and a point E(4,1) and the triangle is E, C, D. The area of any rectangle is calculated as
width multiplied by height
. In the case of our rectangle, the width is the distance between A and E - 4 units - and the height is from A to B, or 5-1 = 4 units. Thus, the
area of the rectangle
is 4 * 4 = 16 units
2
. The area of a triangle is calculated as 1/2 * base * height. For triangle ECD, the base is the distance from C to D, or 6-4=2 units, and the height (equal to EC) is 4 units. Thus the
area of the triangle
is 1/2 * 2 * 4 = 4 units
2
. The total
area of the polygon
is the area of the rectangle + the area of the triangle = 16 units
2
+ 4 units
2
= 20 units
2
.
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Find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 29.
Answer:
27, 29, 31
Step-by-step explanation:
We want to find a, b, c so that
a + c = b + 29
and
a = b - 2, c = b + 2
and
b is odd.
This results in
b - 2 + b + 2 = b + 29
with one solution:
b = 29.
[tex]2n-1,2n+1,2n+3[/tex] - 3 consecutive odd integers
[tex]2n-1+2n+3=2n+1+29\\2n=28\\n=14\\\\2n-1=27\\2n+1=29\\2n+3=31[/tex]
27,29,31
c. Using a standard deck of 52 cards, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event. True of False
Answer:
True
Step-by-step explanation:
If two events X and Y are mutually exclusive,
Then,
P(X∪Y) = P(X) + P(Y)
Let A represents the event of a diamond card and B represent the event of a heart card,
We know that,
In a deck of 52 cards there are 4 suit ( 13 Club cards, 13 heart cards, 13 diamond cards and 13 Spade cards )
That is, those cards which are heart can not be diamond card,
⇒ A ∩ B = ∅
⇒ P(A∩B) = 0
Since, P(A∪B) = P(A) + P(B) - P(A∩B)
⇒ P(A∪B) = P(A) + P(B)
By the above statement,
Events A and B are mutually exclusive,
Hence, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event is a true statement.
Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x->7)f(x) text(, where ) f(x)={(x**2-8 x+7 text(if ) x < 7,-x**2 + 8 x - 7 text(if ) x >= 7)
Answer:
[tex]\large\boxed{\lim\limits_{x\to7}f(x)=0}[/tex]
Step-by-step explanation:
[tex]f(x)=\left\{\begin{array}{ccc}x^2-8x+7&if&x<7\\-x^2+8x-7&if&x\geq7\end{array}\right\\\\\lim\limits_{x\to7}f(x)=?\\\\\lim\limits_{x\to7^-}(x^2-8x+7)=7^2-(8)(7)+7=49-56+7=0\\\\\lim\limits_{x\to7^+}(-x^2+8x-7)=-7^2+(8)(7)-7=-49+56-7=0\\\\\lim\limits_{x\to7^-}=\lim\limits_{x\to7^+}=0\Rightarrow\lim\limits_{x\to7}f(x)=0[/tex]
In this question, we need to find the limit of the piecewise function f(x) as x approaches 7. After substitution of x=7 in both conditions of the function, we find that the limit of function f(x) exists and equals 0.
Explanation:To find the limit of the function f(x) as x approaches 7, we need to look at both cases as defined by the function, because f(x) is a piecewise function.
1. For x < 7, we substitute x as 7 in the function x^2 - 8x + 7:
((7)^2 - 8*(7) + 7 = 0)
2. For x >= 7, we substitute x as 7 in the function -x^2 + 8x - 7:
(-(7)^2 + 8*(7) - 7 = 0)
In this case, for both conditional statements the results are the same, so the limit of the function exists and equals:
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which expression is equivalent to (125^2/125^4/3)
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{125^2}{125^{\frac{4}{3}}}\implies \cfrac{(5^3)^2}{(5^3)^{\frac{4}{3}}}\implies \cfrac{5^{3\cdot 2}}{5^{3\cdot \frac{4}{3}}}\implies \cfrac{5^6}{5^4}\\\\\\ 5^6\cdot 5^{-4}\implies 5^{6-4}\implies 5^2\implies 25[/tex]
Suppose r(t) = cos t i + sin t j + 3tk represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? When? (If the particle is never moving downward, enter DNE.) t = (b) When does the particle reach a point 15 units above the ground? t = (c) What is the velocity of the particle when it is 15 units above the ground? (Round each component to three decimal places.) v = (d) When it is 15 units above the ground, the particle leaves the helix and moves along the tangent line. Find parametric equations for this tangent line. (Round each component to three decimal places.)
The particle has position function
[tex]\vec r(t)=\cos t\,\vec\imath+\sin t\,\vec\jmath+3t\,\vec k[/tex]
Taking the derivative gives its velocity at time [tex]t[/tex]:
[tex]\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k[/tex]
a. The particle never moves downward because its velocity in the [tex]z[/tex] direction is always positive, meaning it is always moving away from the origin in the upward direction. DNE
b. The particle is situated 15 units above the ground when the [tex]z[/tex] component of its posiiton is equal to 15:
[tex]3t=15\implies\boxed{t=5}[/tex]
c. At this time, its velocity is
[tex]\vec v(5)=-\sin 5\,\vec\imath+\cos5\,\vec\jmath+3\,\vec k\approx\boxed{0.959\,\vec\imath+0.284\,\vec\jmath+3\,\vec k}[/tex]
d. The tangent to [tex]\vec r(t)[/tex] at [tex]t=5[/tex] points in the same direction as [tex]\vec v(5)[/tex], so that the parametric equation for this new path is
[tex]\vec r(5)+\vec v(5)t\approx\boxed{(0.284+0.959t)\,\vec\imath+(-0.959+0.284t)\,\vec\jmath+(15+3t)\,\vec k}[/tex]
where [tex]0\le t<\infty[/tex].
a. The following events are mutually exclusive: Living in California and watching American Idol. True or False b. The number of patients seen by an outpatient practice is an example of a discrete random variable. True or False
c.The law of large numbers states that as the number of times an event experiment is conducted increases, the likelihood of the actual probability of an event approaching the theoretical probability decreases. True or False
d. Measuring the time it takes for patients to enter the operating room is an example of a continuous random variable. True or False
Answer:
a) False. Because you can live in California AND watch American Idol at the same time
b) True. Because the number of patients is a whole number, like 1, 2 or 3. There is no 1.5 patient
c) False. The actual probability should become closer to the theoretical probablity
d) True
s f(-x)= x^2 -1 odd, even or neither
Answer:
f(x) = f(-x) = x^2 -1 is an even function
Step-by-step explanation:
When f(x) = f(-x), the function is symmetrical about the y-axis. That is the definition of an even function.
___
An odd function is symmetrical about the origin: f(x) = -f(-x).
If (x - 3)2 = 5, then
x=-315
Ox= 3+V5
Ox= 5+13
Answer:
x = 3 ±sqrt(5)
Step-by-step explanation:
(x - 3)^2 = 5
Take the square root of each side
Sqrt( (x - 3)^)2 =±sqrt( 5)
x-3 = ±sqrt(5)
Add 3 to each side
x-3+3 = 3 ±sqrt(5)
x = 3 ±sqrt(5)
please help :')
Typist Words Typed Minutes Typing
Ella 640 16
Harper 450 15
Owen 560 14
Shaquille 540 12
who typed quickest??
Ella
Harper
Owen
or
Shaquille
Answer:
owen
Step-by-step explanation:
Answer:
Shaquille
Step-by-step explanation:
To determine the unit rate for each, divide the number of words by the number of minutes typed.
Ella: 640÷16=40
Harper: 450÷15=30
Owen: 560÷14=40
Shaquille=540÷12=45
Since Shaquille's is the most, we can tell he typed fastest.
Hope this helps!
Upper A 4-ft-tall fence runs parallel to a wall of a house at a distance of 24 ft. (a) Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house and the horizontal ground have infinite extent. (a) Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house and b be the distance from the ground to the point the ladder touches the house. What is the objective function, in terms of x?
Answer:
(a) shortest ladder length ≈ 35.7 ft (rounded to tenth)
(b) L = (d/x +1)√(16+x²) . . . . where 16 is fence height squared
Step-by-step explanation:
It works well to solve the second part of the problem first, then put in the specific numbers.
We have not been asked anything about "b", so we can basically ignore it. Using the Pythagorean theorem, we find the length GH in the attached drawing to be ...
GH = √(4²+x²) = √(16+x²)
Then using similar triangles, we can find the ladder length L to be that which satisfies ...
L/(d+x) = GH/x
L = (d +x)/x·√(16 +x²)
The derivative with respect to x, L', is ...
L' = (d+x)/√(16+x²) +√(16+x²)/x - (d+x)√(16+x²)/x²
Simplifying gives ...
L' = (x³ -16d)/(x²√(16+x²))
Our objective is to minimize L by making L' zero. (Of course, only the numerator needs to be considered.)
___
(a) For d=24, we want ...
0 = x³ -24·16
x = 4·cuberoot(6) ≈ 7.268 . . . . . feet
Then L is
L = (24 +7.268)/7.268·√(16 +7.268²) ≈ 35.691 . . . feet
__
(b) The objective function is the length of the ladder, L. We want to minimize it.
L = (d/x +1)√(16+x²)
The objective function for the length of the ladder in terms of x is L = sqrt((x+b)^2 + d^2).
Explanation:To find the length of the shortest ladder that extends from the ground to the house without touching the fence, we can use the concepts of similar triangles. Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house, and b be the distance from the ground to the point the ladder touches the house. In terms of x, the objective function for the length of the ladder is:
L = sqrt((x+b)^2 + d^2)
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evaluate the function at the fiven values of the variables:
f(x)= 5x^2 + 5x *+ 3
a f (-3)
b f (-9)
Answer:
f(-3)=5x^2+5x*3
-f*3=5x^2+5*3x
-3f=5x^2+15x
f=-5x(x+3)/3
f(-9)=5x^2+5x*3
-f*9=5x^2+5*3x
-9f=5x^2+15x
f=-5x(x+3)/9
Step-by-step explanation:
hope it helps you?
Consider the integral 8 (x2+1) dx 0 (a) Estimate the area under the curve using a left-hand sum with n = 4. Is this sum an overestimate or an underestimate of the true value? overestimate underestimate (b) Estimate the area under the curve using a right-hand sum with n = 4. Is this sum an overestimate or an underestimate of the true value? overestimate underestimate
Answer:
(a) 120 square units, underestimate
(b) 248 square units, overestimate
Step-by-step explanation:
(a) left sum
The left sum is the sum of the areas of the rectangles whose width is the total interval width (8-0) divided by the number of divisions (n=4). The height of each rectangle is the function value at its left edge.
We can compute the sum by adding the function values and multiplying that total by the width of the rectangles:
left sum = (1 + 5 + 17 + 37)×2 = 60×2 = 120 . . . square units
The curve is increasing throughout the interval of interest, so the left sum underestimates the area under the curve.
__
(b) right sum
The rectangles whose area is the right sum are shown in the attachment, along with the table of function values. The right sum is computed the same way as the left sum, but using the function value on the right side of each subinterval.
right sum = (5 + 17 + 37 + 65)×2 = 124×2 = 248 . . . square units
The curve is increasing throughout the interval of interest, so the right sum overestimates the area under the curve.
_____
The actual area under the curve on the interval [0, 8] is 178 2/3, just slightly less than the average of the left- and right- sums.
The left-hand and right-hand sums are common methods to estimate the area under a curve. Using n=4, the left-hand sum tends to be an underestimate, while the right-hand sum is usually an overestimate of the actual area.
Explanation:The integral 8(x²+1)dx from 0 to a is the area under the curve defined by the function 8(x²+1). A common way to approximate this area is by using left-hand and right-hand sums.
(a) Left-Hand Sum: Using n=4, we divide the interval [0, a] into 4 equal subintervals. For each subinterval, we find the left endpoint and plug it into our function, then multiply by the length of the subinterval. Sum these values to get the left-hand sum. This sum is usually an underestimate of the true area as it leaves out the area under the curve that lies to the right of the left-hand rectangle in each subinterval.
(b) Right-Hand Sum: The process is similar to the left-hand sum, but we use the right endpoint of each subinterval. The right-hand sum tends to be an overestimate of the true area as it includes the area above the curve that lies to the right of the rectangle in each subinterval.
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Bob's golf score at his local course follows the normal distribution with a mean of 92.1 and a standard deviation of 3.8. What is the probability that the score on his next round of golf will be between 82 and 89?
Answer:
The probability is 0.20
Step-by-step explanation:
a) Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- Bob's golf score at his local course follows the normal distribution
- The mean is 92.1
- The standard deviation is 3.8
- The score on his next round of golf will be between 82 and 89
- Lets find the z-score for each case
# First case
∵ z = (x - μ)/σ
∵ x = 82
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{82-92.1}{3.8}=\frac{-10.1}{3.8}=-2.66[/tex]
# Second case
∵ z = (x - μ)/σ
∵ x = 89
∵ μ = 92.1
∵ σ = 3.8
∴ [tex]z=\frac{89-92.1}{3.8}=\frac{-3.1}{3.8}=-0.82[/tex]
- To find the probability that the score on his next round of golf will
be between 82 and 89 use the table of the normal distribution
∵ P(82 < X < 89) = P(-2.66 < z < -0.82)
∵ A z-score of -2.66 the value is 0.00391
∵ A z-score of -0.82 the value is 0.20611
∴ P(-2.66 < z < -0.82) = 0.20611 - 0.00391 = 0.2022
* The probability is 0.20
Normal distribution and z-scores are applied in this context. The z-scores for the given range are calculated, followed by finding the correlating probabilities from the z-table, resulting in the probability of Bob's next score falling within the range of 82-89.
Explanation:To answer this question, we will utilize the concept of z-scores in a normal distribution. A z-score basically explains how many standard deviations a data point (in this case, a golf score) is from the mean.
Firstly, we calculate the z-scores for the limits given. Here, 82 and 89. The formula we use is Z = (X - μ) / σ, where X is the golf score, μ is the mean, and σ is the standard deviation.
The calculated z-scores are then used as references, and we refer a z-table (also known as a standard normal table) to find the probabilities which correspond to these z-scores, and the result is a probability of Bob's next golf score being between 82 and 89.
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Help on 3 algebra questions please !!!***
19. Write the domain of the function in interval notation. f(x)=root 3√x-12
A. (– ∞, ∞)
B. (– ∞, 12)
C. (12, ∞)
D. (–12, ∞)
17. Convert the expression to radical notation. (18 y2)1/7
10. What's the definition of the number i?
A. i = (–1) 2
B. i = –1
C. i = √ –1
D. i = – √ 1
Answer:
19) The domain is (12 , ∞) ⇒ answer C
17) The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]
10) The definition of number i is √(-1) ⇒ answer C
Step-by-step explanation:
19)
* Lets explain the meaning of the domain of the function
- The domain of any function is the values of x which makes the
function defined
- Examples:
# In the fraction the denominator con not be zero, then if the function
is a rational fraction then the domain is all the values of x except
the values whose make the denominator = 0
# In the even roots we can not put negative numbers under the radical
because there is no even roots for the negative number belonges to
the real numbers, then the domain is all the values of x except the
values whose make the quantity under the radical negative
* Now lets solve the question
∵ f(x) = 3 √(x - 12)
- To find the domain let (x - 12) greater than zero because there is
no square root for negative value
∵ x - 12 > 0 ⇒ add 12 to both sides
∴ x ≥ 12
∴ The domain is all values of x greater than 12
* The domain is (12 , ∞)
17)
* Lets talk about the radical notation
- The radical notation for the fraction power is:
the denominator of the power will be the radical and the numerator
of the power will be the power of the base
- Ex: [tex]x^{\frac{a}{b}}=\sqrt[b]{x^{a}}[/tex]
* Lets solve the problem
∵ (18 y²)^(1/7)
- The power 1/7 will be the radical over (18 y²)
∴ [tex](18y^{2})^{\frac{1}{7}}=\sqrt[7]{18y^{2}}[/tex]
* The radical notation is [tex]\sqrt[7]{18y^{2} }[/tex]
10)
* Lets talk about the imaginary number
- Because there is no even root for negative number, the imaginary
numbers founded to solve this problem
- It is a complex number that can be written as a real number multiplied
by the imaginary unit i, which is defined by i = √(-1) or i² = -1
- Ex: √(-5) = √[-1 × 5] = i√5
* The definition of number i is √(-1)
20 points! need help asap! Please do not answer the question if you don't know the answer
(VIEW PICTURE BELOW)
Drag and drop each expression into the box to correctly classify it as having a positive or negative product.
Positive product:
[tex](\frac{-2}{5})(\frac{-2}{5})\\(\frac{2}{5})(\frac{2}{5})[/tex]
With multiplication if two negative numbers are being multiplied together the answer is positive. If two positive numbers are being multiplied the answer is also positive. Another way to think of it is, that if two numbers with the SAME sign are being multiplied then the product will always be positive
Negative product:
[tex](\frac{-2}{5})(\frac{2}{5})[/tex]
[tex](\frac{2}{5})(\frac{-2}{5})[/tex]
If a negative and positive number are being multiplied then the product is ALWAYS negative
Hope this helped!
~Just a girl in love with Shawn Mendes
The rectangular coordinates of a point are (5.00, y) and the polar coordinates of this point are ( r, 67.4°). What is the value of the polar coordinate r in this case?
Answer:
r ≈ 13.01
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
cos(67.4°) = 5.00/r . . . . . . filling in the given values
Solving for r gives ...
r = 5.00/cos(67.4°) ≈ 13.01
_____
Check your requirements for rounding. We rounded to 2 decimal places because the x-coordinate, 5.00, was expressed using 2 decimal places.
Furnace repair bills are normally distributed with a mean of 267 dollars and a standard deviation of 20 dollars. If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 267 dollars and 269 dollars.
Answer: 0.7881446
Step-by-step explanation:
Given : Mean : [tex]\mu = 267\text{ dollars} [/tex]
Standard deviation : [tex]\sigma =20 \text{ dollars}[/tex]
Sample size : [tex]n=64[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x= 267 dollars
[tex]z=\dfrac{267-267}{\dfrac{20}{\sqrt{64}}}=0[/tex]
For x= 269 dollars.
[tex]z=\dfrac{269-267}{\dfrac{20}{\sqrt{64}}}=0.80[/tex]
The P-value : [tex]P(0<z<0.8)=P(z<0.8)-P(z<0)[/tex]
[tex]= 0.7881446-0.5= 0.2881446\approx 0.7881446[/tex]
Hence, the probability that they have a mean cost between 267 dollars and 269 dollars.= 0.7881446
Answer:
There is a 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]
Problems of normally distributed samples 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.
In this problem, we have that:
[tex]\mu = 267, \sigma = 20, n = 64, s = \frac{20}{\sqrt{64}} = 2.5[/tex].
Find the probability that they have a mean cost between 267 dollars and 269 dollars.
This probability is the pvalue of Z when X = 269 subtracted by the pvalue of Z when X = 267. So:
X = 269
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{269 - 267}{2.5}[/tex]
[tex]Z = 0.8[/tex]
[tex]Z = 0.8[/tex] has a pvalue of 0.7881.
X = 267
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{267 - 267}{2.5}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.50.
So there is a 0.7881 - 0.50 = 0.2881 = 28.81% probability that they have a mean cost between 267 dollars and 269 dollars.
1) Omar has scored 85, 71, and 77 on the first three exams in his math class. If the standard 70,80,90 scale is used for grades of C, B, and A, and the exams are equally weighted, what is the minimum he can score on the final exam in order to:
a) get a C average on exams?
b) get a B average on exams?
c) get an A average on exams?
Answer:
a. 47
b. 87
c. 127
Step-by-step explanation:
Assume a total of 4 exams ( first 3 plus a final)
Let final score be X,
Hence, average score = (85 + 71 + 77 + x) / 4 = (233 + x) / 4
a) to get a C, the average score must be 70
70 = (233 + x) / 4
(233 + x) = 70 (4) = 280
x = 280 - 233 = 47 (Ans)
b) to get a B, the average score must be 80
80 = (233 + x) / 4
(233 + x) = 80 (4) = 320
x = 320 - 233 = 87 (Ans)
c) to get a A, the average score must be 90
90 = (233 + x) / 4
(233 + x) = 90 (4) = 360
x = 360 - 233 = 127 (Ans)
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.
(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive?
(b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips?
(c) What proportion of bags contains more than 1225 chocolate chips?
(d) What is the percentile rank of a bag that contains 1425 chocolate chips?
The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
Probability
The probability of an event can be computed by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
The probability exists a branch of mathematics that deals with calculating the likelihood of a given event's happening, which is defined as a number between 1 and 0. An event with a probability of 1 can be regarded as a certainty.Utilizing the TI-83, 83+, 84, 84+ Calculator to estimate these probabilities
Go to 2nd DISTR, and select item 2: normalcdf
The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation)
a) P(1100 <= X <= 1500)
= normalcdf(1100, 1500, 1252, 129)
= 0.8534
b) P(X < 1125)
= normalcdf(-1E99, 1125, 1252, 129)
= 0.1624
c) P(X > 1200)
= normalcdf(1200, 1E99, 1252, 129)
= 0.6566 = 65.66%
d) P(X < 1000)
= normalcdf(-1E99, 1000, 1252, 129)
= 0.0254 = approx. 3rd percentile
To learn more about Probability refer to:
https://brainly.com/question/13604758
#SPJ2
Factor the Higher degree polynomial
5y^4 + 11y^2 + 2
[tex]\bf 5y^4+11y^2+2\implies 5(y^2)^2+11y^2+2\implies (5y^2+1)(y^2+2)[/tex]
For this case we must factor the following polynomial:
[tex]5y ^ 4 + 11y ^ 2 + 2[/tex]
We rewrite [tex]y ^ 4[/tex]as [tex](y^ 2) ^ 2[/tex]:
[tex]5 (y ^ 2) ^ 2 + 11y ^ 2 + 2[/tex]
We make a change of variable:
[tex]u = y ^ 2[/tex]
We replace:
[tex]5u ^ + 11u + 2[/tex]
we rewrite the middle term as a sum of two terms whose product of 5 * 2 = 10 and the sum of 11.
So:
[tex]5u ^ 2 + (1 + 10) u + 2[/tex]
We apply distributive property:
[tex]5u ^ 2 + u + 10u + 2[/tex]
We factor the highest common denominator of each group.
[tex](5u ^ 2 + u) + (10u + 2)\\u (5u + 1) +2 (5u + 1)[/tex]
We factor again:
[tex](u + 2) (5u + 1)[/tex]
Returning the change:
[tex](y ^ 2 + 2) (5y ^ 2 + 1)[/tex]
ANswer:
[tex](y ^ 2 + 2) (5y ^ 2 + 1)[/tex]
Solve the Equation for y . 9x +5y = -2
Answer:
[tex]\large\boxed{y=\dfrac{-9x-2}{5}}[/tex]
Step-by-step explanation:
[tex]9x+5y=-2\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\5y=-9x-2\qquad\text{divide both sides by 5}\\\\y=\dfrac{-9x-2}{5}[/tex]
Biologists estimate that the number of animal species of a certain body length is inversely proportional to the square of the body length.1 Write a formula for the number of animal species, N, of a certain body length as a function of the length, L. Use k as the constant of proportionality.
Answer:
[tex]N(L)=\frac{k}{L^2}[/tex]
Step-by-step explanation:
Here, N represents the number of animal species and L represents a certain body length,
According to the question,
[tex]N\propto \frac{1}{L^2}[/tex]
[tex]\implies N=\frac{k}{L^2}[/tex]
Where, k is the constant of proportionality,
Since, with increasing the value of L the value of N is decreasing,
So, we can say that, N is dependent on L, or we can write N(L) in the place of N,
Hence, the required function formula is,
[tex]N(L)=\frac{k}{L^2}[/tex]
Certainly! When we say that the number of animal species \( N \) is inversely proportional to the square of the body length \( L \), what we mean mathematically is that as the body length increases, the number of species decreases at a rate that is the square of the increase in length. This can be represented by the following formula:
\[ N = \frac{k}{L^2} \]
Here \( N \) is the number of species, \( L \) is the body length, and \( k \) is the constant of proportionality. This constant \( k \) represents the number of species at the unit body length (when \( L = 1 \)). The constant of proportionality is determined by the specific biological context, based on empirical data or theoretical considerations.
In this formula, \( L^2 \) denotes the body length squared, and the fraction represents the inverse relationship.
In summary, to find the number of species \( N \) for a given body length \( L \), we use the inverse square relationship with the constant of proportionality \( k \).