The prοbabilities fοr all pοssible values οf the randοm variable x are:
P(x) = 0.1785 P(x) = 0.3911 P(x) = 0.3462 P(x) = 0.1124 P(x) = 0.0118.
Hοw likely is it that twο randοm variables will οccur?The jοint prοbability is the likelihοοd οf twο (οr mοre) events. The jοint prοbability distributiοn is the sum οf the jοint prοbabilities οf twο οr mοre randοm variables. Fοr instance, P is the fοrmal nοtatiοn fοr the cοmbined prοbability οf events A and B. (A and B)
We can use the fοllοwing fοrmula tο find the prοbabilities fοr all pοssible values οf the randοm variable, x, in a binοmial situatiοn where n = 4 and = 0.35:
P(x) = (n chοοse x)[tex]* \pi ^x * (1-\pi)^{(n-x)[/tex]
where "n select x" is the binοmial cοefficient, which equals n! / (x! * (n-x)!).
Then, fοr x = 0, 1, 2, 3, and 4, we can cοmpute P(x) as fοllοws:
P(x=0) = (4 chοοse 0) [tex]* 0.35^0 * 0.65^4 = 0.1785[/tex]
P(x=1) = (4 chοοse 1) [tex]* 0.35^1 * 0.65^3 = 0.3911[/tex]
P(x=2) = (4 chοοse 2) [tex]* 0.35^2 * 0.65^2 = 0.3462[/tex]
P(x=3) = (4 chοοse 3) [tex]* 0.35^3 * 0.65^1 = 0.1124[/tex]
P(x=4) = (4 chοοse 4) [tex]* 0.35^4 * 0.65^0 = 0.0118[/tex]
When we rοund these numbers tο fοur decimal places, we get:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
As a result, the prοbabilities fοr all pοssible values οf the randοm variable x are as fοllοws:
P(x=0) = 0.1785
P(x=1) = 0.3911
P(x=2) = 0.3462
P(x=3) = 0.1124
P(x=4) = 0.0118
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I need help please with my math homework very hard 20 pts.
Answer:
a,c,d
Step-by-step explanation:
A railway club provides free train rides on their large circular tracks. There are two tracks. The distance from Track 1 to the center is 30 m. The distance between Track 1 and Track 2 is 5 m. How much farther is the train ride on Track 2 than Track 1
If the distance between the tracks is 5m , then the train ride on track 2 is 15.7 m farther than track 1.
Let the distance traveled on Track 1 be = "d₁" and
Let the distance traveled on Track 2 be = "d₂",
We know that the distance from Track 1 to the center is 30 m,
So, the radius of Track 1 is 30 m.
Therefore, the distance traveled on Track 1 is the circumference of a circle with radius 30 m, which is:
⇒ d₁ = 2×π×r1 = 2×π×30 = 60π ,
The distance between the track1 and track2 is 5m ,
So, the radius of Track 2 is = 30 + 5 = 35 m,
So, the distance traveled on Track 2 beyond Track 1 is the difference between the circumference of the two circle with radius 35 m and the circumference of a circle with radius 30 m, which is:
⇒ 35π - 30π = 5π
The distance traveled on Track 2 beyond Track 1 plus the distance traveled on Track 1 gives the total distance traveled on Track 2:
⇒ d₂ = d₁ + 5π = 60π + 5π = 65π
So, the train ride on Track 2 is farther than Track 1 by:
⇒ d₂ - d₁ = 65π - 60π = 5π
⇒ 5π = 5×3.14 = 15.7m .
Therefore, the train ride on Track 2 is 15.7 meters farther than Track 1.
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Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO.
What is the measure of \angle K∠Kangle, K?
^\circ
∘
degrees
The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. This central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4, so the measure of angle K is 90 degrees.
The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. The central angle is the angle formed by two radii inside the circle. When a shape is inscribed in a circle, each of the angles of the shape has the same measure as the central angle of the circle. In this case, the quadrilateral has four sides, so the measure of the central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4. Therefore, the measure of angle K is 90 degrees. This is true for all inscribed shapes; the measure of each angle is equal to the measure of the central angle of the circle. This is because when a shape is inscribed in a circle, each of its angles touches two radii of the circle. Therefore, the measure of each angle is equal to the measure of the central angle of the circle.
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complete question
Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of angle K∠Kangle, K? ^circ ∘ degrees
a water sprinkler that sprays out 35 feet from the center operates long enough to cover a circular area of 1.4 gallons of water per square foot. how many total gallons of water were used?
The area is covered with 1.4 gallons of water per square foot, approximately 5388.9 gallons of water were used.
We use the formula for the area of a circle: A = πr².
The radius can be determined by dividing the diameter, which is 70 feet, by 2. Therefore, r = 35 feet.
To find the area of the circle, substitute the value of r into the formula for the area of a circle: A = πr².
A = πr²
A = π(35)²
A = 3.14 × 1225
A = 3842.5 square feet
We know that this area is covered with 1.4 gallons of water per square foot, so we can multiply the area of the circle by 1.4 to get the total gallons of water used:
Total gallons of water used = A * 1.4
1.4 × 3842.5 ⇒ 5,379.5 gallons.
Therefore, the total gallons of water used is 5,379.5 gallons.
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The vertices of a rectangle are plotted on the coordinate grid shown. A graph with the both the x and y-axes numbered starting from negative 8 with units of one up to 8. There are points plotted at negative 4, 4, at 5, 4, at negative 4, negative 4, and at 5, negative 4. What is the area of the rectangle shown? 32 square units 36 square units 64 square units 72 square units
The rectangle is formed by connecting the points (-4, 4), (5, 4), (-4, -4), and (5, -4).
The length of the rectangle is the distance between the points (-4, 4) and (5, 4), which is 5 - (-4) = 9 units.
The width of the rectangle is the distance between the points (-4, 4) and (-4, -4), which is 4 - (-4) = 8 units.
Therefore, the area of the rectangle is:
Area = Length x Width = 9 x 8 = 72 square units.
So, the area of the rectangle shown is 72 square units. Therefore, the answer is 72 square units.
For the function below, complete the following.
f(x) = x^3 - 2x^2 - 25x + 50
a. List all possible zeroes
b. Use synthetic division to test te possible rational zeroes and find an actual zero.
c. Use the quotient from part (b) to find the remaining zeros of the polynomial function
a. The possible zeros of the polynomial function are ±1, ±2, ±5, ±10, ±25, ±50
b. x = -1 is a zero of f(x)
c. The remaining zeros of the polynomial function is -1, (3 + i√103) / 2, (3 - i√103) / 2
What are all the possible zeros of the functionTo find all possible zeros of the polynomial function f(x), we can use the Rational Root Theorem, which states that if a polynomial function with integer coefficients has a rational zero of the form p/q, where p and q are integers and q ≠ 0, then p must be a factor of the constant term and q must be a factor of the leading coefficient.
The constant term of f(x) is 50, which has the factors ±1, ±2, ±5, ±10, ±25, ±50. The leading coefficient of f(x) is 1, which has the factors ±1. So the possible rational zeros of f(x) are:
±1, ±2, ±5, ±10, ±25, ±50
b. We can use synthetic division to test each of the possible rational zeros and find an actual zero. Let's start by testing x = 1:
| 1 -2 -25 50
1 | 1 -1 -26 24
|______________
1 -1 -26 24
The remainder is 24, which means that x = 1 is not a zero of f(x).
Let's try x = -1:
| 1 -2 -25 50
-1 | 1 -3 28 -78
|______________
1 -3 28 -78
The remainder is -78, which means that x = -1 is a zero of f(x).
c. We can use the quotient from part (b), which is x^2 - 3x + 28, to find the remaining zeros of the polynomial function f(x). To do this, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -3, and c = 28. Plugging in these values, we get:
x = (3 ± √(-103)) / 2
Since the discriminant is negative, there are no real solutions. However, there are two complex solutions:
x = (3 ± i√103) / 2
So the zeros of f(x) are:
x = -1, (3 + i√103) / 2, (3 - i√103) / 2
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A, B & C form the vertices of a triangle. ∠
CAB = 90°,
∠
ABC = 57° and AC = 9. 2. Calculate the length of AB rounded to 3 SF
As per the given triangle, the length of AB rounded to 3 significant figures is 10.7 units.
We are given a triangle ABC with a right angle at A, i.e., CAB = 90°. Let AC be the side opposite to the right angle, and let AB be the hypotenuse. We are also given that ABC = 57° and AC = 9.2.
Using the trigonometric function, we can relate the angles and sides of a right-angled triangle. In particular, we can use the sine function to relate the angle opposite to a side and the hypotenuse. Thus, we have:
sin(ABC) = AC/AB
Substituting the given values, we get:
sin(57°) = 9.2/AB
Now, we can solve for AB by multiplying both sides by AB and dividing by sin(57°):
AB = 9.2/sin(57°)
Using a calculator, we get:
AB ≈ 10.692
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The insured value of a car is ¢10,500. Mr. Cudjo paid 8% of the insured value as premium in the first year. For the subsequent years
The answer of the given question based on the interest rate the answer is the premium paid for each subsequent year would be ¢840
What is Premium rate?A premium rate is price per unit of insurance coverage for specific risk that an insurer charges its policyholders. It is typically expressed as percentage of total insured value of policy.
To calculate the premium paid for subsequent years, we need to know what the premium rate is for those years. The premium rate may change from year to year depending on various factors such as the age of the car, the driver's record, etc.
Assuming the premium rate remains constant at 8% of the insured value for all subsequent years, we can calculate the premium paid for each year as follows:
First year: 8% of ¢10,500 = ¢840
Second year: 8% of ¢10,500 = ¢840
Third year: 8% of ¢10,500 = ¢840
And so on...
So the premium paid for each subsequent year would be ¢840 if the premium rate remains constant at 8% of the insured value.
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Caden wants to buy a jacket for $48.10. If he puts $1.85 in his piggy bank each day, how many days will it take for Caden to have enough money for the jacket?
We have ,
Cost of jacket , (F) = $48.10
Saving per day, (A) = $1.85
We have to find the no. of days(n) of saving to have the sufficient amount for jacket.
We know ,
A × n = F
=> n = F/A
=> n = $48.10/$1.85
=> n = 26
It will take 26 days for Caden to have enough money for the jacket.
The expression for the nth term of a sequence is n(n + 7)
What is the 11th term of the sequence?
Answer:
Step-by-step explanation:
Write the formula for the nth term of the sequence as a function: f(n)=n(n+7).
So now our goal is to compute f(11). To do that, we substitute x=11 in our function, meaning that the 11th term of the sequence = 11*18, which equals 198.
Given the expression
Choose all the equivalent expressions as your answer.
We can see here that the equivalent expressions are:
B. [tex](\frac{st}{x} )^{3} (\frac{xt^{2} }{s} )[/tex]
C. [tex](\frac{st^{4} x}{x^{7}t^{-2} } ) (\frac{sx^{7} }{tx^{3} } )[/tex]
What is an expression?An expression is a combination of values, variables, operators, and function calls that are evaluated to produce a result. Expressions can be simple or complex, and they can be used in various parts of a program to perform calculations, comparisons, assignments, and other operations.
We see here that the selected expressions are actually equivalent to [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex].
Thus, [tex](\frac{st}{x} )^{3} (\frac{xt^{2} }{s} )[/tex] = [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex]
and [tex](\frac{st^{4} x}{x^{7}t^{-2} } ) (\frac{sx^{7} }{tx^{3} } )[/tex] = [tex]\frac{s^{2}t^{5} }{x^{2} }[/tex]
When the selected expressions are simplified and broken down they actually give us the given expression.
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4.02 Lesson Check Arithmetic Sequences (1)
The first four terms of the sequence a(n) = 3n + 2 when evaluated are 5, 8, 11 and 14
How to determine the value of the first four terms?A sequence can be arithmetic or geometric or neither
The definition of the function is given as
a(n) = 3n + 2
The above definitions imply that we simply add 2 to the previous term to get the current term
So, we have
a(1) = 3 * 1 + 2
a(1) = 5
Next. we have
a(2) = 3 * 2 + 2
a(2) = 8
Also, we have
a(3) = 3 * 3 + 2
a(3) = 11
Lastly, we have
a(4) = 3 * 4 + 2
Evaluate the equation
a(4) = 14
Hence, the first four terms are 5, 8, 11 and 14
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Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar
Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.
See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.
In ∆AOR, measure of angle R = 105°
In ∆EOD, measure of angle D = 35°
measure of angle DOE = 40°
Sum of interior angles of triangle = 180°
so, measure of angle E = 180° - 35° - 40°
= 105°
Now, in ∆AOR and ∆EOD,
Measure of angle R = measure of angle E = 105° ( since equal angles)
Measure of angle AOR = measure of angle EOD ( corresponding angles)
Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.
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Complete question:
See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.
Sharon is five years older than Robert. Five years ago, Sharon was twice as old as Robert was then. How old is Robert?
Robert is currently 10 years old. Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)
We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.
Let x = Robert's current age
Let y = Robert's age five years ago
Given that Sharon is five years older than Robert, we can set up the following equation:
x + 5 = Sharon's current age
Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:
y + 5 = 2(y)
Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:
y + 5 = 2(Sharon's current age - 5)
Solving this equation for y, we get y = (Sharon's current age - 5)/2.
Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:
y = (x + 5 - 5)/2
Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.
Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.
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To promote his new business, Claudio made 300300300 tamales to give to pedestrians. The expression above describes the number of tamales remaining after passing out samples to ppp pedestrians. If Claudio passed out samples to 160160160 pedestrians, how many tamales would remain?
As a result, 140140140 tamales would be left as Claudio began with 300300300 and distributed samples to 160160160 passersby.
what is expression ?An expression in mathematics is made up of different numbers, variables, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Expressions can be simple or complicated and can express a wide range of mathematical connections and concepts. Expressions can be evaluated to get a numerical result or to be simplified using mathematical principles and rules. For instance, the equation "2 + 3" can be evaluated to get the value "5", whereas the expression "2x + 3y - 4z" can be made easier by fusing comparable terms to produce a more straightforward expression, such as "2x - z + 3y."
given
The quantity of tamales left if Claudio began with 300300300 and distributed samples to 160160160 passersby would be:
300300300 - 160160160 = 140140140
As a result, 140140140 tamales would be left as Claudio began with 300300300 and distributed samples to 160160160 passersby.
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Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
The equatiοn we wοuld use tο find the distance between the twο pοints is d = √((x₂ - x₁)² + (y₂ - y₁)² ) = √((2 - (-4))² + (y₂ - y₁)² ) = √(6² + (y₂ - y₁)² ) = √36 + (y₂ - y₁)² )
Tο find the distance between twο pοints οn a number line οr in a cοοrdinate plane, we use the distance fοrmula. The distance fοrmula is given by:
d = √((x2 - x1)² + (y2 - y1)² )
where (x1, y1) and (x2, y2) are the cοοrdinates οf the twο pοints.
Nοne οf the οptiοns prοvided represents the distance fοrmula in its entirety. Hοwever, we can use οptiοn B as the first part οf the distance fοrmula, since it represents the absοlute value οf the difference between the x-cοοrdinates οf the twο pοints:
|2 - (-4)|
Simplifying this expressiοn gives:
|2 + 4|
|6|
Therefοre, the equatiοn we wοuld use tο find the distance between the twο pοints is:
d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
We still need tο determine the y-cοοrdinates οf the twο pοintstοο cοmplete the distance fοrmula.
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Create a function using a set of four ordered pairs. Find the inverse of the function. Make sure that the inverse is also a function
To create a function from these points, we need to find an equation that passes through all four points. There are several ways to do this, but one common method is to use linear regression to fit a line to the data.
Here's a mathematical approach to creating a function using four ordered pairs, finding its inverse, and ensuring that the inverse is also a function: Let's assume we have four ordered pairs: (a, b), (c, d), (e, f), and (g, h). We can use the formula for a line, y = mx + b, where m is the slope and b is the y-intercept, to create the function. To find m and b, we can use the following formulas: m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
b = (Σy - mΣx) / n where n is the number of points, Σ denotes the sum of the values, and x and y represent the coordinates of the points. Substituting the coordinates of the four points into these formulas, we can find the equation of the line that passes through them. Once we have the equation, we can define our function as f(x) = mx + b. To find the inverse of the function, we can solve for x in terms of y. Starting with the equation y = mx + b, we can isolate x on one side: y - b = mx
x = (y - b) / m
Now we have an expression for x in terms of y, which defines the inverse of the function. We can define the inverse function as g(y) = (y - b) / m. To ensure that the inverse is also a function, we need to check that for each y in the range of the function, there is only one corresponding x value. In other words, we need to check that the function is one-to-one.
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Factoring expressions completely 3cd^2+12cd+12c
Answer:
3c(d^2+4d+4)
Step-by-step explanation:
common factor is 3 and c
The image shows a cone that has a base with area 36π square centimeters. The cone has been dilated using the top vertex as a center. The area of the dilated cone's base is 729π square centimeters.
What was the scale factor of the dilation?
The scale factor of the dilation of the vertices of the cone when dilated is 4.5
What was the scale factor of the dilation?The area of a circle is proportional to the square of its radius. Since the base of the cone is a circle
The ratio of the areas of the base of the dilated cone to the original cone is equal to the square of the scale factor.
Let the scale factor be k. Then, we have:
(area of dilated cone's base) / (area of original cone's base) = k²
(729π) / (36π) = k²
k² = 20.25
Taking the positive square root of both sides we get:
k = 4.5
Therefore, the scale factor of the dilation is 4.5.
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If a pair of opposite angles of a parallelogram are (3x+10)⁰and (4x_10)⁰,find the internal angles
Answer: In a parallelogram, opposite angles are equal, so we can set up the following equation:
3x + 10 = 180 - (4x + 10)
Simplifying and solving for x, we get:
3x + 10 = 170 - 4x
7x = 160
x = 20
Now we can substitute x = 20 into the expressions for the angles to find their values:
3x + 10 = 70 degrees
4x + 10 = 90 degrees
Since opposite angles in a parallelogram are equal, the other two angles must also be equal to these values. Therefore, the internal angles of the parallelogram are:
70 degrees, 70 degrees, 110 degrees, 110 degrees
Step-by-step explanation:
k(x) = 2x2 - 3Vx, then k(9) is
Answer:
-27V + 4
Step-by-step explanation:
i think
Suppose you bought a house for $349,634 and the value has increased by 63%. What is the new value of the house in dollars? Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
If the value of the house has increased by 63%, it is still worth 100% of the $349,634 it was originally, but now we are adding 63% to that 100% to find the new value. Thus, 349634(1.63) = $569,903.42. The 1.63 is 163% as a decimal, just in case.
A mobile phone company offers a data-only plan for a monthly charge of $15, plus an additional $10 for each gigabyte of data used. Which of the following equations can be used to calculate the total monthly cost, c, in dollars based on the number of gigabytes, g, of data used?
C(g) = 10 + 15g
C'(g) = 80
The monthly charges of Company C for using 2 Gigabyte of data usage.
Step-by-step explanation:
The cell phone plan from Company C costs $10 per month, plus $15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data.
Now, the monthly cost in Company C for using g gigabyte of data will be
C(g) = 10 + 15g ........ (1)
Again, the monthly cost in Company D for using g gigabyte of data will be
C'(g) = 80 ......... (2)
Now, from equation (1), the statement C(2) = 10 + 15 × 2 = 40, means that monthly charges of Company C for using 2 Gigabyte of data usage. (Answer)
A number, n, is multiplied by -5/8 . The product is - 0.4. What is the value of n?
The value οf n is -0.64.
What is equation?
An equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns, accοrding tο the definitiοn οf an equatiοn in algebra. Fοr instance, the twο equatiοns 3x + 5 and 14 are cοmbined tο fοrm the equatiοn 3x + 5 = 14, which is denοted by the equal sign.
The prοduct is -0.4 in this case when the given statement, n, is multiplied by -5/8.
Putting expressiοn intο practise nοw
=> [tex]n\times\frac{-5}{8}=0.4[/tex]
=> n = 0.4 × 8/-5
=> n = -0.64
Hence the value of n is -0.64.
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I don’t know how can I do this please help meeeee
Answer:
x = 8
Step-by-step explanation:
You want to know the value of x in this similar triangle geometry.
Similar trianglesWhen a segment is drawn in a triangle parallel to the base, it divides the sides proportionally. Every segment on the left has the same ratio to the corresponding segment on the right:
x/6 = 4/3
This equation is solved in the usual way. Multiply by the inverse of the coefficient of x:
6(x/6) = 6(4/3)
x = 8
__
Additional comment
Every proportion can be written several ways. Another way to write this one is ...
x/4 = 6/3
x = 4(2) = 8 . . . . . multiply by 4
If you need to, you can prove the triangles are similar by considering corresponding angles. ∠A≅∠A, ∠APW≅∠AVZ, so the triangles are similar by the AA postulate. (Corresponding angles where a transversal crosses parallel lines are congruent.)
Perhaps not so obvious is the relationship between segments of the long side and segments of the short side. The similarity relation tells us ...
AV/AP = AZ/AW
(4+x)/x = (3+6)/6
4/x +1 = 3/6 +1 . . . . . do the division
4/x = 3/6 . . . . . . . . subtract 1
x/4 = 6/3 . . . . . . invert both sides . . . compare to above
4.
[2020/Canberra Sec]
The numbers 1450 and 2400, written as a product of its prime factors are
2x5²x29 and 25×3×52 respectively. Find
(a) the largest integer which is a factor of both 1450 and 2400,
Therefore, 150 is the largest integer that is a factor of both 1450 and 2400.
What is prime factorization?Prime factorization is the process of breaking down a positive integer into its prime factors, which are prime numbers that can divide the integer without a remainder. Every positive integer can be written as a product of prime numbers in a unique way, called its prime factorization. Prime factorization is important in many mathematical applications, such as finding the greatest common divisor and least common multiple of two or more integers, simplifying fractions, and solving problems related to divisibility, prime numbers, and modular arithmetic.
Here,
To find the largest integer that is a factor of both 1450 and 2400, we need to first express both numbers in terms of their common prime factors and then find the product of the common prime factors raised to their lowest exponent.
The prime factorization of 1450 is 2 × 5² × 29.
The prime factorization of 2400 is 2⁴ × 3 × 5².
To find the common factors of these two numbers, we need to look for the prime factors that appear in both factorizations. These common prime factors are 2, 5², and 3.
To find the largest integer that is a factor of both 1450 and 2400, we need to multiply these common prime factors raised to their lowest exponent:
2 × 5² × 3 = 150
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we want to distribute 12 identical cookies to 4 distinct children such that all cookies are distributed. how many ways are there to do this if each child may receive 0, 1, 2, 3 or 4 cookies? g
The number of ways by using the generating functions and Binomial theorem is
There are various methods to solve the given question. Here's one way to solve it. To distribute 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies, we can use generating functions.
Let's assume that the generating function for the number of ways of distributing the 12 identical cookies to the 4 distinct children is given by:
(1 + x + x₂ + x₃ + x₄)⁴
We need to find the coefficient of x12 in the above equation. Using the Binomial theorem, the above equation can be expanded as:
(1 + x + x₂ + x₃ + x₄)⁴ ⇒ (1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)
After multiplying the above equation, we need to find the coefficient of x₁₂. The answer to the given question is as follows:
The coefficient of x₁₂ ⇒ 715 ways
Therefore, there are 715 ways to distribute the 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies.
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A pediatrician randomly selected 50 six-month-old boys from her practice's database and recorded an average weight of 15.7 pounds with a standard deviation of 0.42 pounds. She also recorded an average length of 27.6 inches with a standard deviation of 0.28 inches. Find a 99% confidence interval for the average length (in inches) of all six-month-old boys.
27.25 in. to 27.95 in.
27.32 in. to 27.98 in.
27.50 in. to 27.70 in.
27.74 in. to 27.98 in.
The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E
This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:
ME = (Critical Value) x (Standard Deviation/√Sample Size)
For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E
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The amount of time it takes or a crew of people to finish a job varies inversely with the number of people on the crew. If it takes a crew of 3 people 8 hours to complete a job, how long will the same job take a crew of 5 people?
The job will take 5 hours time for a crew of 5 people.
Inverse variation means that as one value increases, the other decreases. In this example, as the number of people on the crew increases, the amount of time it takes to complete the job decreases. To solve this problem, we must first find the rate of change. We can do this by dividing 8 hours (the amount of time it took the crew of 3 people) by 3 people, which gives us a rate of 2.67 hours per person. Then, to find the time for the crew of 5 people, we can multiply the rate of change (2.67 hours per person) by the number of people on the crew (5). This gives us a total of 13.35 hours, which can be rounded to 5 hours time.
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I dont know how to do this
pls answer if u know with simple working
i dont know if u add 4 each time it didnt work for last questionn