The probability of at least 30 left-handed individuals in a sample of 100
What is boinomial probability ?
Binomial probability refers to the probability of a particular number of "successes" occurring in a fixed number of independent trials. In other words, it calculates the probability of a specific outcome happening a certain number of times in a given set of trials.
The binomial probability formula is:
P(X=k) = (n choose k) *[tex]p^{k}[/tex] * [tex](1-p)^{(n-k)}[/tex]
where:
P(X=k) is the probability of getting k successes in n trials
n is the number of trials
k is the number of successes
p is the probability of success on a single trial
(n choose k) is the binomial coefficient, which represent
He probability of selecting at least 30 left-handed individuals out of a sample of 100 adults in the US can be calculated using the binomial probability formula with x counting the number who are left-handed.
However, we must be careful when applying the formula to this problem because the sample is selected without replacement. The binomial distribution assumes that each trial is independent of the others, which is not the case when sampling without replacement.
In cases where the sample size is much smaller than the population size, the effect of not replacing the selected individuals is negligible. However, when the sample size is a substantial portion of the population size, as in this case, the probability of selecting an individual who is left-handed changes after each selection. This means that the probabilities of each selection are not independent, and the binomial formula cannot be used.
Therefore, to accurately calculate the probability of at least 30 left-handed individuals in a sample of 100 adults selected in the US without replacement, we need to use a different probability distribution, such as the hypergeometric distribution.
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how much is 1000 mcg to mg
To convert mcg to mg, divide the mcg value by 1000. Therefore:
1000 mcg = 1000/1000 mg = 1 mg
So, 1000 mcg is equal to 1 mg.
complete both transformations below then enter the final coordinaties of the figure below A(-6,-3) b (-1,-4) c (-5,-1) 1. reflect across x-axis 2. <3,-2>
The coordinates of the figure are A''(-3, 1),B''(2,2), C''(-2, -1).
What is the transformation of a point?
The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).
The rule of a reflection across the x-axis is (x,y)→(x,-y).
After reflection across the x-axis,
A(-6,-3)→ A'(-6,3)
B(-1,-4)→B'(-1,4)
C(-5,-1)→C'(-5,1)
A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).
Thus the new coordinates are:
A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)
B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)
C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)
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An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)=0.45
p(medium-quality oil)=0.15
p(no oil)=0.40
a. What is the probability of finding oil (to 2 decimals)?
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.
a. The probability of finding oil is 0.45
b. The probability of finding high-quality oil is 0.25
c. P(medium quality oil) = 0.20
d. P(no oil) = 0.55
How to solve thisThe probabilty of finding oil
P(oil) = P(high quality oil) + P(medium quality oil)
= 0.25 + 0.20
= 0.45
b. P(soil high quality oil) = 0.20
P(medium qty) = 0.80
P(no oil) = 0.20
The probability of finding oil is good.
Given the probability of finding good soil, the oil company is more likely to find medium quality oil.
The new probability of finding oil is
P(High quality) + P(medium quality) =
0.15625 + 0.5
= 0.65625
Using the conditional probabilty formula
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Can someone tell me the domain and range for this function?
The domain is all real values and the range is y <= 3
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
The domian is the set of the input values
In this case, the graph has no restriction on its input
So, we have
Domain = all set of real values
For the range, we have
Maximum y value = 3
So, we have
Range: y <= 3
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NEED HELP ASAP:In the year 2000, a person bought a new car for $15000. For each consecutive year
after that, the value of the car depreciated by 11%. How much would the car be worth
in the year 2004, to the nearest hundred dollars?
The car would be worth $9400 in the year 2004.
How to determine the worth of the car?If the car depreciates by 11% each year, then its value at the end of each year will be 89% of its value at the beginning of the year (100% - 11% = 89%). Therefore, the value of the car after 1 year will be:
$15000 * 0.89 = $13350
The value of the car after 2 years will be:
$13350 * 0.89 = $11881.50
The value of the car after 3 years will be:
$11881.50 * 0.89 = $10576.77
The value of the car after 4 years (in the year 2004) will be:
$10576.77 * 0.89 = $9422.19
Therefore, the car would be worth $9400 in the year 2004.
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Given that sin30˚=1/2. Find the exact value of sin120˚
Recognizing that sin(30º) = 1/2, the exact value of sin(120º) is √3/2.
The exact value of sin(120˚) can be found by using the double angle formula for sine. The formula is:
sin(2θ) = 2sinθcosθ
Since we are given that sin(30˚) = 1/2, we can substitute 30˚ for θ in the formula to find sin(120˚):
sin(120˚) = 2sin30˚cos30˚
sin(120˚) = 2(1/2)(√3/2)
sin(120˚) = √3/2
Therefore, the exact value of sin(120˚) is √3/2.
Note that to solve this type of problem it is crucial to know different types of trigonometric identities.
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What are the basic parts of a circle?
The basic parts of a circle are the circumference, diameter, radius, and center. The circumference is the outer boundary of the circle, and it is the distance around the circle.
The diameter is a line segment that passes through the center of the circle and connects two points on the circumference. The radius is a line segment that connects the center of the circle to a point on the circumference.
The center is the point in the middle of the circle, and it is equidistant from all points on the circumference. These four basic parts are essential to understanding the properties of circles, such as their area, circumference, and relationships between different parts.
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What is the area of the parallelogram?
396 ft2
four hundred ten and five-eights ft2
792 ft2
eight hundred twenty-one and one-fourth ft2
please finish these 4 I need help pls
a 6-ounce bottle of medicine contains 36 doses. how many doses are in a 15-ounce bottle of the same medicine?
Answer:
Step-by-step explanation:
If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:
6 ounces / 36 doses = 15 ounces / x doses
Cross-multiplying, we get:
6 x = 36 * 15
6 x = 540
Dividing both sides by 6, we get:
x = 90
Therefore, a 15-ounce bottle of the same medicine contains 90 doses.
Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 39 feet long and makes a 40 degree angle with the ground. How high is the kite?
Answer:
100
Step-by-step explanation:
A new car is purchased for 21,100 dollars. The value of the car depreciates at a rate of 2% per year. Which equation represents the value of the car after 5 years?
the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
How to calculate the equation that represents the value of the car after 5 yearsGiven:
The cost price of the car, P = $21100,
The depreciation rate = 2%
Calculate the value of the car after 6 years by the following formula,
A = P (1- r / 100)ⁿ
Here A is the value of the car after 6 years.
Substitute the values,
A = 21100 × (1- 2 / 100)^5,
A = $19,105.08
Therefore, the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
how to write a quadratic function in standard form y = 4 (x-1)^2 + 5
Evaluate
7
1
/
6
−
3
5
/
8
.
Answer:
3.542
Step-by-step explanation:
7 1/6 - 3 5/8 = (85/24) = 3(13/24) ≅ 3.5416667.
7⅙ - 3⅝ = 8524 = 3 1324 ≅ 3.5416667 (simplified) = 3.542
Are the triangles similar?
Yes or no?
How do you know?
Answer:
no
Step-by-step explanation:
The graphs of function f ang g represent the height of an object being launched into the air as a function of time. Which object was in the air longer?
Function g lingered for a while.
What does the physics projectile equation mean?h = v 0 y 2 2 g . This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.
What is the projectile's maximum height formula?The projectile formula's maximum height from the graph is H = u 2 sin 2 2 g.
An item named g was launched from a higher location when x=0... g(0)> f(0).
A higher point was reached by the object of g.
When the object was launched, f's slope was greater than g's slope.
The launch velocity of object f was greater.
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A pole 8 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Maya measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
A: 111 ft long. (Student pressed "see solution" instead of submitting an answer) (As the op i can't upload it as an Answer, so i am leaving it here in my edited question).
108ft is the length of the of the guy wire
Similar trianglesTriangles are known to be similar if the ratio of the similar sides of the triangle are equal.
From the given diagram, we need to determine of the guy wire. Using the similarity theorem of a triangle;
8/2 = l/25+2
8/2 = l/27
2l = 8 * 27
l = 4 * 27
l = 108 ft
Hence the length of the of the guy wire, to the nearest foot is 108ft
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Philippe is 13 years old and his father is 4 times older. In how many years will the father's age be twice the age of his son?
13×4=52
Ok Multiplacation is a simple Math formula everyone can do so you have to do this:
13+13+13+13=52
Now do this:
13×4=52
Answer is 52
Anna and her brother were collecting seashells,. she collected s shells and her brother collected twice as much
So, in response to the above question, we can state that They gathered a total equation of s + 2s = 3s shells.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
In the case where Anna gathered s shells and her brother gathered twice as many, the brother gathered 2s shells.
They gathered a total of s + 2s = 3s shells.
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Select all the correct answers to this question: ¿Cuántos hermanos tienes?
1. No tienes hermanos.
2. Tengo un hermano y dos hermanas.
3. Tiene un hermano y una hermana.
4. Yo tengo tres hermanos.
Answer:
The correct answers to this question would be 2. Tengo un hermano y dos hermanas and 4. Yo tengo tres hermanos.
Identify the vertex, axis of symmetry and whether the vertex is a minimum or maximum for the given function.
f(x)=2(x+1)^2-6
The vertex is (-1, -6) and the axis of symmetry is -1. The function is minimum. The solution has been obtained by using equation of parabola.
What is a parabola?
Any point on a parabola is equally separated from both the focus, or predetermined point, and the fixed straight line (known as the directrix).
We are given f(x) = 2(x + 1)² - 6
We know that a parabola of equation a(x - h)² + k always has its vertex at (h, k) with axis of symmetry at x = h.
So, the vertex here is (-1, -6) and the axis of symmetry is x = -1.
It is a minimum function because there is a positive value before (x - h)².
Hence, the vertex is (-1, -6) and the axis of symmetry is -1 and the function is minimum.
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Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^x and the line x = ln 8 about the line x = ln 8. Please show me in two ways (disk/washer method and cylindrical shells method)
the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical
Disk/washer method:
[tex]V = π ∫[ln 8]^8 (e^x)^2 dx\\V = π ∫[ln 8]^8 e^2x dx\\V = π(e^2x/2)|[ln 8]^8\\V = π(e^16 - (e^2(ln 8))^8)/2\\V = (π(e^16 - 64)/2)[/tex]
Cylindrical shells method:
[tex]V = 2π ∫[ln 8]^8 x(e^x) dx\\V = 2π ∫[ln 8]^8 xe^x dx\\V = 2π(x(e^x/2) - (e^x/2)ln x)|[ln 8]^8\\V = 2π((ln 8)(e^8 - 8) - (e^8/2)ln 8)\\V = (2π(e^8 - 64ln 8 - 4e^8))/2\\V = (π(e^16 - 64 - 8e^8))/2[/tex]
The disk/washer method can be used to solve for the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the area of a ring, which can be formed by subtracting the area of a disk from the area of the washer. In this case, the area of the disk is π(e^2(ln 8))^8 and the area of the washer is π(e^16). The volume is then equal to the integral of the area of the ring, which is π(e^16 - (e^2(ln 8))^8).
The cylindrical shells method can also be used to find the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the of a cylindrical shell, which can be formed by subtracting the area of the inner cylinder from the area of the outer cylinder. In this case, the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical
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The graph of f(x)=x² was translated 4 units to the right and horizontally compressed by a factor of 5 to create the graph of function g. Write an equation in vertex form to represent function g.
The vertex form of the quadratic equation g is:
g(x) = 25*(x - 4)²
How to find the equation for function g?We start with the parent quadratic function:
f(x) = x²
We know that first we apply a translation of 4 units to the right, so we will get:
g(x) = f(x - 4)
And then we compress it horizontally by a factor of 5, then we can write:
g(x) =f( 5(x - 4))
Replacing the actual function we will get:
g(x) = ( 5*(x - 4))²
Distributing the exponent we will get:
g(x) = 5² *(x - 4)²
g(x) = 25*(x - 4)²
That is the quadratic equation in vertex form.
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Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he has 7 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 19 left over. How many chairs does Liam have?
Answer: i think the answer would be 75
Answer:
55 chairs.
Step-by-step explanation:
Note the way Liam arranges the chairs.
1) He arranges chairs in 8 rows of the same length, with 7 chairs left over.
8x + 7
2) He arranges chairs in 6 rows of the same length, with 19 chairs left over:
6x + 19
Set the two expressions equal to each other:
8x + 7 = 6x + 19
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 6x and 7 from both sides of the equation:
8x (-6x) + 7 (-7) = 6x (-6x) + 19 (-7)
8x - 6x = 19 - 7
2x = 12
Next, divide 2 from both sides of the equation:
(2x)/2 = (12)/2
x = 12/2
x = 6
Plug in 6 for x in both expressions. It should give the same answer:
8x + 7
8(6) + 7 = (8 * 6) + 7 = (48) + 7 = 55
6x + 19
6(6) + 19 = (6 * 6) + 19 = (36) + 19 = 55
~
Therefore, Liam has 55 chairs in all.
~
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what is 1 gallon in oz?
The value 1 gallon has 128 fluid ounces(oz)
"How many ounces in a gallon?" This is one of the most frequently asked questions regarding liquid measurements. One gallon equals 8 pints, 4 quarts, or 16 cups. There are 128 fluid ounces in a gallon, and this number depends on whether you use imperial or metric units of measure.
There are 128 US fluid ounces in a US gallon. If you're in the UK, you'll find a gallon at 160 UK fluid ounces. This is because the US fluid gallon is smaller than the British imperial gallon (3,785 liters compared to
,5
6 liters). When converting
Gallons to Fluid Ounces, remember that the US Fluid Ounce is larger than the British Imperial Ounce. A US fluid ounce is 29.5735 ml. For comparison, a UK (Imperial) fluid ounce is 28.
131 ml. So the US has a smaller gallon than the UK, but a slightly larger fluid ounce. It's enough to make your head explode. For these two conversions you need the following information:
1 gallon (US) = 128 ounces (US, Fluid)
1 gallon (UK) = 160 ounces (UK, Fluid)
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Please, Help me with this question
how many teaspoons is 10 ml
Using the formula, we can convert milliliters to teaspoons. 1 milliliter equals 0.202 teaspoons, thus 10ml equals 2.02 teaspoons.
The volume unit is milliliters. A teaspoon is also a volume measure, however it is a smaller unit that is commonly used at dinner settings.
One millilitre is equivalent to 0.202 US teaspoons using normal conversion rates.
As a result, we may define the link using the unit conversion idea.
One milliliter is equal to 0.202 teaspoons in the United States.
For example, 10 milliliters equals 2.02 teaspoons.
As a result, we'll need roughly 2 tablespoons to get 10 ml.
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A number decreased by 3 is at least 7
Answer:
Step-by-step explanation:
x-3 is greater than or less than 7
What is the equation of the normal line to the curve
y=sin(sinx)
at x=π ? A. y=x−π
B. y=−x−π
C. y=Ï€x
D. y=πx−1
E.y=− π1 x−1
The equation of the normal line to the curve is y = -x + π
To find the equation of the normal line to the curve y = sin(sinx) at x = π, we need to find the slope of the tangent line at x = π and then use that to determine the slope of the normal line. We can find the slope of the tangent line by taking the derivative of y with respect to x and evaluating it at x = π.
y = sin(sinx)
Taking the derivative with respect to x, we get:
dy/dx = cos(sinx) * cosx
At x = π, we have:
dy/dx = cos(sin(π)) * cos(π) = -1 * (-1) = 1
So the slope of the tangent line at x = π is 1. Since the normal line is perpendicular to the tangent line, its slope is the negative reciprocal of 1, which is -1.
Now we need to find the y-intercept of the normal line, which is the point where the line intersects the y-axis. To do this, we can plug in the values of x = π and y = sin(sinx) = sin(sin(π)) = 0 into the equation of the line:
y = mx + b
0 = -1 * π + b
b = π
So the equation of the normal line is:
y = -x + π
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Mathematics word problem. Please show working out, 25 points.
Answer:
188 cm rounded to the nearest whole number.
Step-by-step explanation:
1 rotation = 2[tex]\pi[/tex]r
2[tex]\pi[/tex](15) If the dimeter is 30, the radius is 15
2 rotations would be
2[2[tex]\pi[/tex](15)]
188.495559218
Answer:
188.5 cm
Step-by-step explanation:
Circumference of a circle = C = 2πr = πD
D = 30 cm
C = π(30 cm) = 94.25 cm
2 revs = 2C = 2(94.25) = 188.5 cm
