Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.
Define the term Gaussian random variable?We consider the Gaussian form whenever we need to describe complex valued random variables for whom the distribution is unknown. The Central Limit Theorem (CLT), which deals with the sum of several random variables, is substantially fundamental for this tendency.As, per the given question.
Gaussian random variable n (200, 256)
Part a: Probability that signal will exceed 240 micro volts.
P(x > 240) = 1 - P(x ≤ 240)
P(x > 240) = 1 - P(240 - 200)/16
P(x > 240) = 1 - P(2.5)
See p value for z = 2.5
P(x > 240) = 0.00621
Thus, Probability that signal will exceed 240 micro volts is 0.00621.
Part b: larger than 210 micro volts.
P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)
P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 / 1 - P(210 - 200)/16
P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599
P(x ≥ 240) | x ≥ 210) = 0.02335
Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.
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What is the equation of the line that passes through the points (-7.
-5) and (2, 3)? Write your answer in slope-intercept form.
Show your work here
The equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
The first point = (-7, -5)
The second point = (2, 3)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (3- (-5) / (2 - (-7))
= (3 + 5) / (2 + 7)
= 8 / 9
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point = (2,3)
Substitute the values in the equation
y - 3 = (8/9)(x - 2)
y - 3 = (8/9)x - 16/9
y = (8/9)x - 16/9 + 3
y = (8/9)x - 11/9
Hence, the equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
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Write 10x - 5y = -30 in slopeintercept form.
y =
X +
Answer:
[tex]y=2x+6[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex].
Therefore, rearranging the given formula:
[tex]10x-5y=-30[/tex]
[tex]-5y=-10x-30[/tex]
[tex]\frac{-5y}{-5}=\frac{-10x}{-5}-\frac{30}{-5}[/tex]
[tex]y=2x-(-6)[/tex]
[tex]y=2x+6[/tex]
Answer: y=2x+6
Step-by-step explanation:
A slope-intercept form is y=mx+b
Hence,
[tex]10x-5y=-30\\\\10x-5y+5y=-30+5y\\\\10x=-30+5y\\\\10x+30=-30+5y+30\\\\10x+30=5y[/tex]
Divide both parts of the equation by 5:
2x+6=y
Thus, y=2x+6
Find the perimeter of a rectangle with a diagonal of 20 inches that make angle measure 30 and 60 using trigonometric function (sine, cosine, tangent)
The perimeter of the rectangle is 20 + 20√3 inches.
How to find the perimeter of a rectangle?The perimeter of a rectangle is sum of the whole side of the rectangle. The side bounded by the rectangle is the perimeter of the rectangle.
Therefore, the diagonal of the rectangle is given as 20 inches.
Using trigonometric ratios, let's find the sides of the rectangle.
sin 30 = opposite / hypotenuse
sin 30 = x / 20
x = 20 sin 30
x = 20 × 0.5
x = 10 inches
Therefore, using Pythagoras theorem,
20² - 10² = b²
b² = 400 - 100
b = √300
b = √100 × 3
b = 10√3
Hence,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(10 + 10√3)
perimeter of the rectangle = 20 + 20√3
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50 points!!! Are rational functions and hyperbolas the same? Please explain why or why not.
3. the probability distribution shown below represents the number of trips of five nights or more that american adults take per year. (that is, 6% do not take any trips lasting five nights or more, 70% take one trip lasting five nights or more, etc.). number of trips x probability 0 0.06 1 0.70 2 0.20 3 0.03 4 0.01 1.00 (a) is this an example of a discrete or continuous probability distribution? (b) what is the expected value (mean) number of trips taken? (c) what is the standard deviation of the number of trips taken? (d) what is probability that an american will take three or more trips? (e) what is probability that an american will take two or less trips? (f) what is probability that an american will take at least one trip?
The probability distribution is a) discrete, with b) a mean of 1.23, the standard deviation is c) 0.6458, d) the probability that an American will take 3 or more trips is 0.04, e) the probability that an American will take 2 or less trips is 0.96 and, f) the probability to take at least one trip is 0.94
It is given that the probability distribution of the no. of trips an American adult takes that lasts 5 nights or more
x probability
0 0.06
1 0.70
2 0.20
3 0.03
4 0.01
a)
Here we can see that all the values are isolated and there is no continuity between them. The distribution clearly has breaks between them.
Hence, we can say that the distribution is discrete.
b)
The expected value of any probability
E(X) = ∑xp(x)
where,
x is the random variable
p(x) is the probability of the corresponding random variable hence we get
E(X) = 0 × 0.06 + 1 × 0.70 + 2 × 0.20 + 3 × 0.03 + 4 × 0.01
= 0 + 0.7 + 0.4 + 0.09 + 0.04
= 1.23
Hence the expected value is 1.23
c)
The standard deviation is √σ²
Where σ² = variance of the distribution
σ² = E(X²) - {E(X)}²
{E(X)}² = 1.23²
= 1.5129
E(X²) = ∑x²p(x)
= 0 × 0.06 + 1 × 0.70 + 4 × 0.20 + 9 × 0.03 + 16 × 0.01
= 0.7 + 0.8 + 0.27 + 0.16
= 1.93
Therefore,
σ² = 1.93 - 1.5129
= 0.4171
Therefore
σ = 0.6458
d)
The probability to take 3 or more trips is
P(X≥3)
= P(X = 3) + P(X = 4)
= 0.03 + 0.01
= 0.04
e)
The probability of an American taking 2 or less trips is
1 - P(X≥3)
= 1 - 0.04
= 0.96
f)
The probability that an American will take at least one trip is
P(X≥1)
= 1 - P(X = 0)
= 1 - 0.06
= 0.94
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30 point reward if you help ! find the volume of each shape and then compare. do not reduce your fractions.
The volume of the cuboid is [tex]\frac{6}{125}[/tex] and The volume of the cube is [tex]\frac{8}{27}[/tex]
The comparison of both a cube and a cuboid have six faces,a cube has six faces which are all squares and on the other hand, the cuboid is but a cuboid has rectangular faces.
What is a Cube?
A cube is a symmetrical three-dimensional shape which has all six sides equal.
To find the volume of cube is addition of all seen sides or the given sides all squared.
i.e volume of a cube= [tex]a^{3}[/tex]
volume of the cube=([tex]\frac{2}{3}[/tex])^3
Volume= [tex]\frac{8}{27}[/tex] cubic inches
How to dertermine the volume of a cuboid
Whar is a Cuboid?
A Cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges which the volume can be measured by multiplying the length by the breadth by the height .
Volume of a cuboid = L×B×H
Volume of a cuboid=[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{5}[/tex]×[tex]\frac{3}{5}[/tex]
Volume of a cuboid=[tex]\frac{6}{125}[/tex] cubic inches.
To compare,
A cube has shapes of equal sides six faces and a cuboid faces are non-equal with six faces, 8 vertices and 12 edges.
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a cellular telephone tower that is 110 feet tall is placed on top of a mountain that is 1300 feet above sea level. what is the angle (in degrees) of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level? (round your answer to two decimal places.)
The angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level will be 87.36 degrees.
What is angle?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.
Here,
The cell phone tower's peak will be at a height of 1300 + 110 = 1410 feet above sea level.
Assuming that the user of a cell phone is 200 feet above sea level, the distance between them is 1410 feet- 200 feet, or 1210 feet.
The distance between them horizontally is 5 miles, or 5 * 5280, or 26400 feet.
The opposite cathetus is 26400 feet away and the neighboring cathetus is 1210 feet away.
the angle is 87.376 degrees, or tan(angle) = 26400 / 1210 = 21.82
A cell phone user 5 horizontal miles away and 200 feet above sea level will be depressed at an angle of 87.36 degrees from the top of the tower.
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Simplify the following expressions by adding the like terms: 3a² - 2a - 7 + 3a + 4 - 2a² + 9a x² + 6xy + 5y² - 6xy + 2y² 1 2
What are the coordinates of the vertices after a rotation 90 counterclockwise around the origin.
Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Step-by-step explanation: trust me
a scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. in 1990s, the average amount of time spent playing computer games was 10.2 hours per week. is the amount of time greater than that for this year? ten students were surveyed and asked how many hours they spent playing video games. the test statistics is equal to 0.45. what is the p-value?
Using the concepts of the hypothesis test, it is found that the p-value is of 0.0007 corresponding to ten students who were surveyed and asked how many hours they spent playing video games.
At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:
H[tex]_o[/tex] = μ=10.2
At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:
H₁=μ> 10.2
Ten students were surveyed, so there are 9 df. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.
Thus, using a t-distribution calculator, the p-value of the test is of 0.0007.
Hence, when the ten students were surveyed and asked how many hours they spent playing video games and the test statistics is equal to 0.45,then the p-value is 0.0007
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Consider the equation 2x^(2)+2y^(2)+2x-2y-7-0 Write the equation in the standard form of a circle? What is the center and the radius
jack paid $99 for 6 pizzas. How much did he pay per pizza?
Answer:
99/6=16.5 per pizza
have u good day
Answer:
16 and a half, ($16.50)
Step-by-step explanation:
99 / 6 = 16.5
-3(4x-7) please answer quickly!!
the table below lists probabilities for the corresponding number of girls in three live births. what is the random variable, what are its possible values, and are its values all numerical?
The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..
All possible values of random variable is numrical in nature.
We have a table to right lists probabilities for the corresponding number of girls in three live births.
from the table we cleary see that the random variable is x which represents the number of girls in three live births.
Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.
Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)
So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..
From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.
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On September 16th you bought 2,500 shares of the stock you have chosen to follow this year,
along with 1,100 shares of Home Depot, 3,500 shares of Ford, and 900 shares of JetBlue.
Create a stock ticker to represent these trades.
The stock markets utilize "Ticker Symbols," which are distinctive one- to five-letter codes, to uniquely identify companies.Because stock quotes used to be printed on a ticker tape machine that resembled the images below, it is known as a ticker symbol.
Create a stock ticker to represent these trades ?A tracking stock is unique equity offered and issued by a parent company that tracts the financial performance of a segment of the division.Tracking stocks usually trade in open markets separate from the parent company's stock.An example of tracking stock is:Walt Disney Company's subsidiary which it owns fully named: go.com. The company is also known as The Go Network. The stock symbol is GOT.Its P/E Ratio is 11.38XI chose this stock because its parent company has a very strong brand and great leadership.Price/Earnings Ratio is used for establishing the value of a company. It measures the current share price against it's earnings per share (EPS).To learn more about stock ticker refer
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In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
I NEEEDD HELP ASAPP PLEASE
Solve negative three minus one and two fifths.
three fifths
one and two fifths
negative four and two fifths
four and two fifths
Answer:
Step-by-step explanation:
1. Put Words into Math.
Negative three minus one and two fifths= -3- 1 2/5
2. Solve the math problem
-3-1 2/5= -4 2/5 or -22/5 in improper fraction
Answer: -4 2/5 or -22/5
1 3/4 divided by 3
Please helppp
Answer:
= 7/12
Step-by-step explanation:
1 3/4 = 1 + 3/4 = 4/4 + 3/4 = (4+3)/4 = 7/4
(7/4)÷3 = 7/(4*3) = 7/12
if sec2a is 3 find the value of sina.
By using trigonometry, it can be calculated that
The value of sina is [tex]\pm \frac{1}{\sqrt{3}}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin \theta, \ cos\theta, \ tan \theta, \ cot\theta, \ sec\theta, \ cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here, the trigonometric equation is
sec 2a = 3
cos 2a = [tex]\frac{1}{3}[/tex]
we know,
[tex]1 - cos 2a = 2 sin^2a\\\\1 - \frac{1}{3} = 2sin^2a\\\\2 sin^2a = \frac{2}{3}\\\\sin^2a = \frac{2}{3} \times \frac{1}{2}\\\\sin^2a = \frac{1}{3}\\\\ sina = \pm \frac{1}{\sqrt{3}}[/tex]
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Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
The equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
According to the question,
We have the following information:
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
Now, we have the following arithmetic progression with common difference, denoted by d:
22, 22.5, 23, 23.5, ...
Formula used to find the nth term:
an = a+(n-1)d where a is the first term
A) 22+(d-1)0.5 = 30
B) The plant still have to grow 8 cm because the difference between 30 and 22 is 8 cm.
C) Value of d:
22+(d-1)0.5 = 30
22+0.5d-0.5 = 30
21.5+0.5d = 30
0.5d = 30-21.5
0.5d = 8.5
d = 8.5/0.5
d = 17
Hence, the equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
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- Use the rules of measurement to subtract:
123.9 g - 56.041 g
Answer:
67.859 g
Step-by-step explanation:
123.9 g - 56.041 g
= 123.900 g - 56.041 g
= 67.859 g
Answer:
Step-by-step explanation:
67.859
Complete the statement to describe the expression (a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains terms
The statement about the given expression is described below.
What is expression?A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.
According to given data:Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2
It has factors two which consist of 3 termsEach factor has a multiplicity of 2terms in factor (a+b+c) are a, b, cTerms in factor (d+e+f) are d, e, fThus, given expression has two factors which consist 3 terms.
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Can anyone write the equation of the graph?
The equation of the absolute function graph given in the diagram is: y = |x - 3| + 5.
How to Find the Equation of the Graph of an Absolute Value Function?y = a|x – h| + k is the equation, in vertex form, that represents the absolute value function where:
The vertex of the graph of the absolute value function = (h, k) The graph opens up or opens down depends on the value of a.The vertex of the graph is (3, 5). This implies that:
(h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation in vertex form, y = a|x – h| + k:
y = a|x – h| + k
y = a|x - 3| + 5
To find the value of a, substitute a point on the graph, (5, 7), into the y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 - 5 = 2a [subtraction property]
2 = 2a
a = 1 [division property of equality]
Substitute a = 1 into the equation y = a|x - 3| + 5:
y = |x - 3| + 5
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A large company releases summary statistics about the annual salaries for its employees. Mean standard deviation minimum Q1 median Q3 maximum $63,429 $38,439 $18,000 $50,000 $58,000 $68,000 $350,000 Based on this information, are there any outliers in the data? Explain your reasoning
Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high. The standard deviation calculates how much the data vary from the mean value. It is helpful for contrasting data sets that might have the same mean but a different range.In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.
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Will give brainliest. Please it needs to be correct. Refer to the image
Answer: D
PLEASE GIVE BRAINLIEST THANK YOU!!!
Unit 4 congruent triangles
Answer: 9/3
Step-by-step explanation: the trriangles proportion is three and 9/3=3
Factorise the following:
27t squared y - 18ty squared
Answer:
9ty(3t - 2y)
Step-by-step explanation:
27t²y - 18ty² ← factor out 9ty from each term
= 9ty(3t - 2y)
An emperor penguin dive down into the ocean at a contant rate. From the urface, he dive 1,760 feet in 8 minute. The number −1,760 repreent the location of the penguin in relation to the urface. What number repreent the location of the penguin in relation to the urface 2 minute after beginning hi dive?
The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.
First, we will calculate the speed of the penguin. The speed is represented by the variable "s".
s = 1,760/8
s = 220 feet per minute
The location of the penguin after 2 minutes is calculated below.
d = 2×s
d = 2×220
d = 440
Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
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Mason, a hardwood flooring installer, needs to calculate the amount of hardwood flooring needed to cover a floor that’s 3 3/4 yards Wide and 5 1/2 yards Long. How many square yards of hardwood flooring are needed? (Area= Length x Width). A) 20 5/8 B)15 3/8 C)18 3/4 D)16 1/2
A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.
length = 5 1/2 yd, breadth = 3 3/4 yd.
Make fractions out of both measurements first.
3 3/4 = 3 + 3/4
= 12/4 + 3/4
= 15/4
5 1/2 = 5 + ½
= 10/2 + ½
= 11/2
Area = (15 * 11)/(4 * 2) yd2
Area = 165/8 yd2
They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.
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Show that
tan15°=2−√3
It is proved that tan15°=2−√3 by using the identity of tan(A-B)
What are the 3 trignometric identities?
The right-triangle theorem, also known as Pythagoras theorem, is the foundation for the three Pythagorean trigonometric identities.
[tex]sin^{2}a+cos^{2}a=1[/tex]
[tex]1+tan^{2}a=sec^{2}a[/tex]
[tex]cosec^{2}a=1+cot^{2}a[/tex]
The reciprocal trigonometric identities are:
Sin θ = 1/Cosec θ or Cosec θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
tan 15 = tan(45 - 30)
As tan(A - B) = (tanA - tanB)/(1 + tanAtanB)
tan15 = tan(45 - 30) = (tan45 - tan30)/(1 + tan30tan45)
= [tex]\frac{1 - \sqrt{3} }{1+\sqrt{3} }[/tex]
= [tex]\frac{1-\sqrt{3} }{1+\sqrt{3} }[/tex] × [tex]\frac{1 - \sqrt{3} }{1-\sqrt{3} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-\sqrt{3} ^{2} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-3}[/tex]
= [tex]\frac{(1-\sqrt{3} )^{2} }{-2}[/tex]
= [tex]\frac{1+3-2\sqrt{3} }{-2}[/tex]
= [tex]\frac{4-2\sqrt{3} }{-2}[/tex]
= 2-[tex]\sqrt{3}[/tex]
Hence it is proved that tan15°=2−√3
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