Part A
2 white, 5 red, 7 total
P(1st white) = 2/7
P(1st white, 2nd white) = P(1st white)*P(2nd white)
P(1st white, 2nd white) = (2/7)*(4/9)
P(1st white, 2nd white) = 8/63
Let m = 8/63
---------------
P(1st red) = 5/7
P(1st red, 2nd red) = P(1st red)*P(2nd red)
P(1st red, 2nd red) = (5/7)*(7/9)
P(1st red, 2nd red) = 5/9
Let n = 5/9 = 35/63
---------------
m+n = P(both are same color)
m+n = 8/63+35/63
m+n = 43/63
Answer: 43/63========================================
Part B
m = P(first white then red)
m = (2/7)*(5/9)
m = 10/63
n = P(first red then white)
n = (5/7)*(2/9)
n = 10/63
r = P(second bead isn't same color as first)
r = m+n
r = 10/63+10/63
r = 20/63
Answer: 20/63========================================
Part C
m = P(1st white, 2nd white)
m = (2/7)*(4/9)
m = 8/63
n = P(1st red, 2nd white)
m = (5/7)*(2/9)
m = 10/63
m+n = P(2nd is white)
m+n = 8/63+10/63
m+n = 18/63
m+n = 2/7
Answer: 2/7========================================
Part D
If we withdraw 1 white bead, but we add it back in, then the probability of selecting white has not changed on the second selection.
The same can be said if we picked a red bead as well. This is because we simply replace the red bead with a copy of some other red bead.
Nick's statement is another way of saying replacement is happening.
Answer: Truethe rate of college enrollment immediately after high school completion was 67
The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.
The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.
In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.
Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.
The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .
The given question is incomplete , the complete question is
What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?
(a) Descriptive
(b) Inferential
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Help me please and thank you
Answer:
n(A) = {6,9}
n(B) = {3,9}
n(A intersection B) = {9}
nA union B) = {1,3,6,9}
hope to this helps
Consider y"-2y"+2y'=2x2+ e+ cos(3). (a) Find the complementary solution (solution of the associated homo geneous equation) yc- (b) Find the form of the particular solution yp that can be used in the method of undetermined coefficients. [Note: You DO NOT HAVE TO find the values of the coefficients]
The complementary solution of the associated homogeneous equation is $y_c = c_1 e^{x} + c_2 e^{-x}$. The form of the particular solution $y_p$ that can be used in the method of undetermined coefficients is $y_p = Ax^2 + Bx + C + e^x + \cos{3}$.
The characteristic equation of the associated homogeneous equation is $r^2 - 2r + 2 = (r - 1)^2 = 0$, which has two distinct roots $r = 1$ and $r = 1$. Therefore, the complementary solution is of the form $y_c = c_1 e^{x} + c_2 e^{-x}$.
The method of undetermined coefficient can be used to find a particular solution of the form $y_p = Ax^2 + Bx + C + e^x + \cos{3}$. The coefficients $A$, $B$, $C$ can be found by substituting this expression into the differential equation and solving for $A$, $B$, and $C$.
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The product of 5 and the difference between x and 2 is 18.
A. 3(x + 2) = 18
B. (x + 3) / 2 = 18
C. 3 + 5x = 18
D. 5(x - 2) = 18
The quotient of x plus 3 and 2 result in 18.
A. 3(x + 2) = 18
B. (x + 3) / 2 = 18
C. 3 + 5x = 18
D. 5(x - 2) = 18
Combine 3 and 5 times x to get 18.
A. 3(x + 2) = 18
B. (x + 3) / 2 = 18
C. 3 + 5x = 18
D. 5(x - 2) = 18
Answer:
1) D
2) A
3) C
I thinkkkkkk... tell me if it's correct;?)
describe transformation of \(y= \frac{x^{4} }{6x+6}\)
The transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.
The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.
Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).
To transform a graph of a function, one can translate, stretch, or reflect it.
Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)
Vertical Shift: To get the new graph, we add or subtract a constant from the function.
When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:
\(y = (x^4) / (6x+6) - 2\)
This means that the graph of the function is shifted 2 units downwards.
Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.
When f(x+c) is replaced with f(x), the graph is shifted c units to the left.
When f(x-c) is replaced with f(x), the graph is shifted c units to the right.
In this case, we can shift the graph by substituting x-2 for x in the function.
The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)
This means that the graph is shifted 2 units to the right.
Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.
In this case, if the function is multiplied by 2, we get the following function:
\(y = 2(x^4) / (6x+6)\)
This means that the graph is compressed by a factor of 2.
It can also be stretched by dividing the function by a constant.
Horizontal Stretch/Compression:
When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:
\(y = (x^4) / (3x+3)\)
This means that the graph is compressed by a factor of 2.
It can also be stretched by multiplying the variable by a constant.
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An inscribed angle is an angle whose vertex is a point on a circle and whose sides are two _____ of the circle
An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.
The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.
This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.
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Simplify (step by steps, thanks!)
The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).
To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.
Let's start with the first fraction's denominator:
x² + x - 6
We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:
x² + x - 6 = (x + 3)(x - 2)
Now let's factor the second fraction's denominator:
x² - 6x + 8
We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:
x² - 6x + 8 = (x - 2)(x - 4)
Now we can rewrite the original expression with a common denominator:
(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))
Next, we can simplify the numerator:
(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))
(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))
Finally, we can't simplify this expression any further. Therefore, the simplified expression is:
(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))
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On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded. Which linear inequality is represented by the graph?
Answer:
y<= 1/3x-4
Step-by-step explanation:
Its an inequality thats why
Which segment is opposite to∠E?
Answer:
UJ
Step-by-step explanation:
The side that is opposite angle E is UJ
Since this is a triangle, we use the corners that do not touch the angle, U and J and the segment is the one that connects them
Louise is mixing red and
blue paint colors to
produce a shade of violet.
The diagram represents the
shade of violet Louise
created by mixing red and
blue paint.
Red Paint (cups) =
6
Blue Paint (cups)=
12
Part B. There are ______
cups of blue paint used for
every 36 cups of violet that
is mixed.
HELPPPP HELFJELNFND
Answer:
I'm pretty sure it's multiplication so it should be 12 x 36 which is 432
Which expression is represented by the model?
+
-X
+
O X-3
O X+3
O -x-3
O-X+3
first answer gets best marks
Answer:
-x+3
Step-by-step explanation:
3 plus signs so 1+1+1= 3
A regular admission for a movie is k8 per ticket seniors only pay k6 per ticket if the revenue for a movie totaled k1440 for an audience of 190 how many seniors attended?
Answer:
Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f
Using Cavalieri's principle, which of the following can be shown to have the same volume as a triangular prism with base area pi r² and height h?
Hence, a cylinder with height h and base area \(\pi r^{2}\) may be proven to have the same volume as a triangular prism.
What is a cylinder?Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.
When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.
A cylinder's volume may be calculated using the formula V = \(r^{2}\)h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.
Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.
Let's consider the given triangular prism with base area \(\pi\)\(r^2\) and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:
\(A(y) = \pi r^2 + (2r)(y) / 2\)
Simplifying, we get:
\(A(y) = \pi r^2 + ry\)
Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:
\(A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh\)
By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:
\(\pi r^² + ry = \pi r^² + 2rh\)
\(ry = 2rh\)
\(y = 2r\)
So, we see that the areas are equal for all y between 0 and h, except at \(y = 2r.\) However, this is just a single point and has no effect on the volume,
Therefore, the cylinder with base area \(\pi\)\(r²\) and height h has the same volume as the triangular prism, with base area \(\pi\)r² and height h.
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Plot the image point P under the translation (x,y)→(x-4,y-6).
You have a $20 coupon from the manufacturer that is good for the purchase of a cell phone. Look at my picture for the rest of the question
item (a):
Since we're going to have a 10% discount, it means the final price of the phone should be 90% of the regular price. To calculate 90% of a quantity is the same as multiplying by 0.9. This means our function can be modeled as
\(f(x)=0.9x\)item (c):
We have the following two functions
\(\begin{gathered} f(x)=0.9x \\ g(x)=x-20 \end{gathered}\)To calculate the compositions
\(\begin{gathered} (f\circ g)(x) \\ (g\circ f)(x) \end{gathered}\)We just need to use one of the functions as the argument of the other.
\((f\circ g)(x)=f(g(x))=f(x-20)=0.9(x-20)=0.9x-18\)Doing the same for the other order
\((g\circ f)(x)=g(f(x))=g(0.9x)=0.9x-20\)am i right? i just need to make sure
Answer:
im pretty sure
Step-by-step explanation:
Answer:
I think it is
Step-by-step explanation:
Suppose that nâ¡0 and n â¡ 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equationdv/dx+(1-n)P(x)v(x) = (1 â n)Q(x).
The substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x) is shown below.
An equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x alone or constants, is called Bernoulli's equation.
The substitution using \(v = y^{1-n}\)
Differentiate both side with respect to 'x'
\(v^{'} = (1-n)y^{-n}y^{'}\)
\(\frac{dy}{dx} = \frac{1}{1-n} y^{n}v^{'}\)
we get, \(\frac{1}{1-n} y^{n}v^{'}\) + P(x)y = Q(x)yⁿ
= \(v^{'} + (1-n)P(x)y^{1-n} = (1-n)Q(x)\)
using \(v = y^{1-n}\)
The given equation is well expressed as:
\(v^{'} + (1-n)P(x)v = (1-n)Q(x)\)
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
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What is the solution to this equation?
log_7 (5 + 11x) = 2
Answer:
x = 4
Step-by-step explanation:
Using the rule of logarithms
\(log_{b}\) x = n , then x = \(b^{n}\)
Given
\(log_{7}\) (5 + 11x) = 2 , then
5 + 11x = 7² = 49 ( subtract 5 from both sides )
11x = 44 ( divide both sides by 11 )
x = 4
A bag contain 3 red candy and 5 green candy
jackl take one a t random and eat it
what i the probality of him getting 2 red one
The probability of Jack taking 2 red candies is 3/28.
What do you mean by a union in probability?
The letter "U" (union) stands for "or." Specifically, P(AB) represents the probability of that event A or event B occurring. The sample points that are present in both event A and event B must be counted in order to determine P(AUB).
The new probability set made up of all the elements from both sets is created when two sets are joined. When two sets intersect, a new set is created that includes every element from both sets.
Solution Explained:
Given in the question,
A bag contains 3 red and 5 green candies.
Total possibilities is 3 + 5 = 8
Jack takes a candy at random and eats it
A/Q there are 3 red candies out of 8, the probability is given by,
P(R) = 3/8
Now there are 2 red candies out of 7, so the probability is given by,
P(R') = 2/7
The probability of both events is given by,
P(2R) = P(R) × P (R') = 3/8 × 2/7 = 3/28
Therefore, the probability of Tim taking 2 red candies is P(2R) = 3/28
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What is the probability of spinning an A in %
Line bisects at point g. if ae = be, which equation must be true? a coordination plane has points a (left end) and b (right end) of the horizontal axis. four points c (top), e (middle), g (origin), and d bottom) descending on the vertical bidirectional axis. the points a g b and e complete a triangle. a. be = bg b. ae = 2(bg) c. ae = bg d. ag = bg e. none of these
The correct answer is option D.
ag=bg
What is the work of the bisector?
Bisector cuts something in 1/2 of. An attitude bisector is a line that cuts a given attitude in 1/2 of. The perpendicular bisector of a line phase is the road that cuts the given phase in 1/2 of and is at proper angles to it.It is for this reason that line CD is bisecting the facet AB in triangle ABE.
Bisecting a line phase method that diving a line phase into same parts. So, whilst CD bisects facet AB at factor G it method that:AG = BG.and AE = BG
Since the line bisects at point g therefore ag=bg
It is given that line CD is bisects the side AB in triangle ABE
and AE = BE .
Bisecting a line segment means that dividing a line segment into two equal parts. So, when CD bisects side AB at point G it means that:
AG = BG
Hence, the correct answer is option D.
ag=bg
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I need help please❤️❤️❤️❤️
Answer:
x = 5
Step-by-step explanation:
the supplementary angle of (19x-18) = 180 - (19x-18) = 198-19x
all interior angles of a triangle = 180 degrees
180 = (7x+1) + (10x-9) + (198-19x)
180 = 7x+10X-19x+1-9+198
180 = -2x+190
-2x = -10
x = 5
how to find z-score on ti-84 with mean and standard deviation
To find the z-score on a TI-84 calculator with the mean and standard deviation, use the "invNorm" function.
The z-score measures how many standard deviations a data point is away from the mean. On a TI-84 calculator, you can find the z-score using the "invNorm" function, which calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution.
To find the z-score, follow these steps:
1. Press the "2nd" button, followed by the "Vars" button to access the DISTR menu.
2. Scroll down or press "3" to select "invNorm(" and press "Enter".
3. Enter the desired area under the normal curve (probability), followed by a comma.
4. Enter the mean (μ) followed by another comma.
5. Enter the standard deviation (σ) and close the parentheses by pressing ")".
6. Press "Enter" to calculate the z-score.
The result displayed on the calculator will be the z-score corresponding to the given area, mean, and standard deviation. The z-score helps in understanding the relative position of a data point within a normal distribution by indicating the number of standard deviations it is above or below the mean.
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(2) If the price of an item is represented by p, a final price of 0.7p indicates a discount of what percent?
Answer:
30%
Step-by-step explanation:
First subtract: 1 - .70 = .30
Then move decimal over to the right 2 times and add percentage sign instead of the decimal: 30%
help meee pleaseeeeeee
Answer:
9
Step-by-step explanation:
we can use the pythagorean theorem so (15)²= (12)² + (x)²--> (15)²-(12)²=x²
take the square root of both sides ans x=9
note! this is a special type of triangle called a 3-4-5 special right triangle because all the sides when divided by a factor of 3 will simplify down to the sides 3-4-5 (only true when the hypotheneuse is the 5 because it's the longest side of a triangle)
In right triangle ABC, if AC = 5/13 and AB = 1, what is the length of BC?
Answer:
BC = \(\frac{12}{13}\)
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
BC² + AC² = AB²
BC² + (\(\frac{5}{13}\) )² = 1²
BC² + \(\frac{25}{169}\) = 1 ( subtract \(\frac{25}{169}\) from both sides )
BC² = \(\frac{169}{169}\) - \(\frac{25}{169}\) = \(\frac{144}{169}\) ( take square root of both sides )
BC = \(\sqrt{\frac{144}{169} }\) = \(\frac{12}{13}\)
A rectangle with area 88 has width 11. What is the numerical value of the perimeter?
Please help! Pls show all work! Thx!
=============================================
Work Shown:
A = area of rectangle = 88
W = width = 11
L = unknown length
A = L*W
88 = L*11
11L = 88
L = 88/11 ... divide both sides by 11
L = 8
The length is 8
----------
P = perimeter of rectangle
P = 2L+2W
P = 2(L+W)
P = 2(8+11)
P = 2(19)
P = 38
a landscaper is designing a rectangular garden. the length of the garden is to be 555 feet longer than the width. if the area of the garden will be 104104104 square feet, what will be the length, in feet, of the garden?
Area of rectangle is the product of Length and Width, so by using this the length of garden will be 13 feet.
What exactly is a rectangle?The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a type of quadrilateral. As a result, it is also referred to as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
suppose x = width of rectangular garden.
length of the garden is 5 feet longer than width.
now, x+5 = Length
Area of rectangle L X B = \(x X(x+5)\)
Garden's area is = 104 square feet
Then,
\(x X (x +5) = 104\\x^{2} + 5x - 104=0\\(x-8)(x+13)=0\\x=8,-13\)
Now, width ==8
Therefore, Length = x+5= 13
13feet is the length of the garden.
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pls help asap
Twenty-seven minus 3/2 of a number (x) is not more than 36. What is the number? A. x > 42 B. x ≥ -6 C. x < 3 D. x ≤ -6
Answer: B.) x ≥ -6
Step-by-step explanation:
Create the smallest cone possible with the tool, and record the values of the radius, height, and volume in terms of . Then scale the original CONE
by the given scale factors, and record the resulting volumes (in terms of 7), to verify that the formula V=V xk³ holds true for a cone.
The Created cone with the possible record of the the values of the radius, and height is given in the image attached.
How do yo create the volume of the smallest cone?A scale factor is known to be a number that is known to often multiplies (doubles or triples, etc.,“scales”) a given quantity.
Since the volume is not attached, it will be manually created here.
Note that the resulting volumes must be in terms of 7.
Hence:
Volume Formula: V=V x k³
When scale factor is 2, radius = 4, height = 8, then volume will be:
7π x 2³
= 56π
When scale factor is 3, radius = 6, height = 18, then volume will be:
7π x 3³
= 189π
When scale factor is 4, radius = 8, height = 24, then volume will be:
7π x 4³
= 448π
Hence the volume that will be fixed into the scale factor diagram will be:
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