Answer:
The orders of magnitude are numbers of the form:
10^n
where n can be any integer number.
So we can write something like:
"A is n orders of magnitude above B
Now we have the quantities:
Amjed cards = 223
Latif cards = 8741
We want to find how many times more trading cards does Latif have than Amjed.
Then we need to look at the quotient between the number of cards of Latif and Amjed.
8741/223 = 39.2
Now we need to approximate this to the nearest 10^n number.
(..., 0.1, 1, 10, 100, 1000, ...)
The nearest one to 39.2 is 10.
So we can say that Latif's collection is 10.
and 10 = 10^1
then n = 1
Then we can say that Latif's collection is one order of magnitude above Amjed's collection.
Determine the slope of the line
Answer:1+1
Step-by-step explanation:
Given that SQ⎯⎯⎯⎯⎯ bisects ∠PSR and PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯, which of the following triangle congruence statements can be used to prove that ∠P≅∠R?
The figure shows two triangles P S Q and R S Q with a common side S Q.
The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.
How to prove Triangle Congruence?
From the figure as seen online, we can see that;
The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.
Thus, the 2 column proof to show that ∠P≅∠R is;
Statement 1; ∠SPQ≅∠SRQ
Reason 1; Given
Statement 2; SQ bisects ∠PSR
Reason 2; Given
Statement 3; ∠PSQ≅∠QSR
Reason 3; Definition of angle bisector
Statement 4; SQ ≅ SQ
Reason 4; Reflexive Property of Congruence
Statement 5; △PQS≅△RQS
Reason 5; Angle - Angle Side (AAS) Congruency Postulate
Statement 6; PS ≅ SR
Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)
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¿Cuál de los siguientes números NO es un decimal periódico?
A.
11
30
B.
11
400
C.
11
600
D.
111
90
El número decimal que no es un decimal periódico es dado por:
B. [tex]\frac{11}{400}[/tex].
¿Que es un número decimal periódico?Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.
La conversión de las fracciones para decimales són:
11/30 = 0.366666 -> Periódico.11/400 -> 0.0275 -> No es periódico.11/600 -> 0.018333333 -> Periódico, en razón de lá repetición de el 3.11/90 = 0.1222222 -> Periódico.Puede-se aprender más a cerca de números decimales periódicos en https://brainly.com/question/1192529
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=
Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.
Given right triangle RST, what is the value of sin(S)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Thirteen-twelfths
Answer:
Step-by-step explanation:
I would use the law of sins.
13/sin90 = 5/sin s
sin s = (5 sin 90)/13
sin s = .3846.
Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.
Answer:
22.6 = 113/5
Step-by-step explanation:
How many of the 960 dvd players were repaired in the first year
if you get the right answer you get a 20k gaming setup
(D) 200 DVD players were repaired in the first year.
What are DVD players?A DVD player is a device that plays DVDs that adhere to both the DVD-Video and DVD-Audio technical standards, which are incompatible. Some DVD players are also capable of playing audio CDs.Given:
The DVD player shipped 960 players last month
There is a record that out of every 24 players, the 5 would be repaired.
So we need to find the number of DVD players that were repaired in these 960 players.
So,
[tex]\frac{960*5}{24} \\=200[/tex]
Therefore, (D) 200 DVD players were repaired in the first year.
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The question you are looking for is here:
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?
A: 40
B: 120
C: 192
D: 200
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
x intercepts: (1,0), (-3,0)
the roots are 1 and -3
Step-by-step explanation:
Using the Quadratic Formula:
x=−b±sqrt(b2−4ac)/2a
Substitute:
x= -8±sqrt(8^2-4(4)(-12))/2(4)
x=-8±sqrt((64- -192))/8
x=-8±sqrt(256)/8
Solve two equations (±)
x=-8±16/8
x=8/8 and x=-24/8
x=1 and x=-3
Answer:
x = -3
x = 1
Step-by-step explanation:
Hello!
We can solve the quadratic by Factoring the Equation and using the Zero Product Property.
Factor[tex]y = 4x^2 + 8x - 12[/tex][tex]y = 4(x^2 + 2x - 3)[/tex]
We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.
[tex]y = 4(x^2 -x + 3x - 3)[/tex][tex]y = 4(x(x - 1) + 3(x - 1))[/tex][tex]y = 4(x + 3)(x - 1)[/tex]Solve for x
Set each factor to 0 and solve for x in both.
[tex]0 = 4(x + 3)(x - 1)[/tex][tex]0 = (x + 3), x = -3[/tex][tex]0 = (x - 1), x = 1[/tex]Therefore, the x-interecpts are -3 and 1.
question 12 please, i cannot find the central angle.
Answer:
Below.
Step-by-step explanation:
12. That is a semicircle
The central angle is 180 degrees.
I need help with these questions because I don't understand it.
Evaluating the given expressions and inequalities, we have;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b) = 4
[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex] 16) \: x \geq 11\frac{2}{3} [/tex]
17) k > 9
18) v > 9
20) m ≤ 16
Which method can be used to evaluate the expressions and inequalities?The given expressions are;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]
Where x = 4, and y = 6, we have;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]
Therefore;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b)
Where a = 3 and b = 2, we have;
(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4
Therefore;
(8•a - 5•b) - 2•(a + b) = 4[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]
Where a = 7, and p = 6, we have;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]
Therefore;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]
Where m = 5, and n = 6, we have;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]
Therefore;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]
Which gives;
[tex] \frac{7}{6} \times 10 \leq x [/tex]
[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]
[tex] x \geq 11\frac{2}{3} [/tex]
17) 20 < k + 11
Therefore;
k > 20 - 11 = 9
k > 918) 6•v > 54
v > 54 ÷ 6 = 9
Therefore;
v > 9[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]
Therefore;
2 × 8 = 16 ≥ m
Which gives;
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Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
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can someone help me with answer C? its the last one i need
Using the monthly payment formula, it is found that her down payment should be of $1,419.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are:
A = 250, r = 0.072, n = 72.
Hence:
r/12 = 0.072/12 = 0.006.
We solve for P to find the total amount of the monthly payments, hence:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]
0.0171452057P = 250
P = 250/0.0171452057
P = $14,581.
The total payment is of $16,000, hence her down payment should be of:
16000 - 14581 = $1,419.
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What is the perimeter of a regular heptagon with a side length of 8 units? 48 units 56 units 72 units 32 units
Answer:
The answer to your question is P=56
Step-by-step explanation:
P=7a=7·8=56
I hope this helps and have a good day!
Which of the following lists of ordered pairs is a function?
OA. (2, 4), (3, 9), (4, 16), (5,25)
OB. (2, 4), (-2, 4), (3,9), (-2,-4)
OC. (1, 1), (2, 3), (1, 5), (4,7)
OD. (0, 2), (4, 2), (0, -4), (4, -2)
Answer:
OA
Step-by-step explanation:
because it only got a y parameter for each x
Answer:
Option A. (2,4),(3,9),(4,16),(5,25)
Please help!! a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y=-30x^2+1325x-8569
The widgets should be sold for $22.08 for the company to make the maximum profit.
To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.
Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.
In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.
The function given is:
y = -30x² + 1325x - 8569.
Differentiating this with respect to x, we get:
y' = -60x + 1325.
To find the point of inflection, we equate this to zero, to get:
0 = -60x+ 1325,
or, x = 1325/60 = 22.0833
Now, we differentiate, y' = -60x + 1325, with respect to x, to get:
y'' = -60 < 0, thus we have a maximum at x = 22.0833.
Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.
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What are the domain and range ofWhat are the domain and range of ?
D: [3, ∞) and R: [0, ∞)
D: [4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (3, ∞) and R: (–∞, 0)
Answer:
Domain:[-4,∞)
Range:[0, ∞)
Thus, choice C is the exact answer
Can someone please help me on this?
Answer:
[tex]\frac{9\pi }{4}[/tex] inches
Step-by-step explanation:
I suppose they are asking you for the length of the red part.
18[tex]\pi \\[/tex] * [tex]\frac{45}{360}[/tex] = [tex]\frac{9\pi }{4}[/tex] inches
Answer:
L = 7.07 in
Step-by-step explanation:
L = arc lenght
[tex]L=\frac{\pi (45)(9)}{180} =2.25\pi =7.07in.[/tex]
Hope this helps
Olivia is making 15 bead bracelets for her friends what is the proportional relationship?
5 minutes per bracelet.
because 15/3 = 5 mins.
To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality =15/3= 5 minutes.
Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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Two pulses are moving along a string. one pulse is moving to the right and the second is moving to the left. both pulses reach point x at the same instant. an illustration of a triangular trough traveling right and the same size and shape crest traveling left both toward point x. they are equidistant from x. will there be an instance in which the wave interference is at the same level as point x? no, the interfering waves will always be above x. no, the interfering waves will always fall below x. yes, the overlap will occur during the slope of the waves. yes, the overlap will occur when the first wave hits point x.
The sum of the pulses allows us to find that the answer for the sum at a point x is
There is no interference pattern as the amplitude does not remain constant.Traveling waves can add up as they travel, leading to different results.in which the wave interference is at the same level as point x?If the waves travel in the same direction, their sum gives resulting waves that can be maximum or minimum depending on the phase between them, un stationary patterns.
If the directions are coincident directions, they add place to the interference processes, in this case, stationary patterns are formed on a screen.
If the waves travel in the opposite direction the sum of the two waves gives rise to a wave that maximum is the sum of the amplitudes of the two pulses
In the case of a pulse that corresponds to a single wavelength, the result is an instantaneous maximum, which after the pulse passes, returns to zero.
Consequently, there is no stationary pattern, so there is no interference between the two pulses.
In conclusion with the sum of the pulses, we can find that the answer is No interference pattern is produced as the amplitude does not remain constant.
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Can you construct an example of a discrete random variable which does not have a finite expectation?
Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
For the given question,
A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.
It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.
Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,
[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]
⇒ [tex]E(X)=\infty[/tex]
Consider the following example,
You throw a coin until it lands tails.
Let n be the number of heads
Then number of heads can be found by, 2ⁿ
Now, the expected value function is
[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]
⇒ [tex]E(X)=\infty[/tex]
Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.
Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
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Chanda is planning to visit universities over the summer to help decide where she wants to attend college. The first two universities on her proposed route are 6 inches apart on Claudias map. In real life, this distance is 30 miles. What scale does the map use? 1 in = _____ miles.
The map scale to use would be: 1 in. = 5 miles.
What is Map Scale?The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.
Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:
6/30 = 1/x
Solve for x
x = (30 × 1)/6
x = 5.
Therefore, the scale of the map is: 1 in = 5 miles.
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There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the first ticket, since 5 out of 26 letters are vogal, the probability is:
5/26.
For the second ticket, since there is no replacement, the probability is:
4/25.
The probability of both tickets is:
[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]
0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
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In your opinion, what are the pros and cons of each projection? What are the limitations? In which circumstances, environments, or occupations is one type of projection likely preferred over the other? Describe any special tools that might be needed to create the projection. Which projection is easiest for you to interpret visually? Why?
The projection discussed are the isometric and the orthographic projection.
How to illustrate the information?The isometric projection is how the object look to the eyes when seen from a distance. It should be noted that orthographic projection give the actual measurements of the object.
The isometric drawing is through 100% true measurement of the height, width, and the depth.
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Type the correct answer in each box. Use numerals instead of words.
Simplify the following polynomial expression.
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
-
x +
The simplification of the polynomial expression will give 3x² - 20x + 8.
How to illustrate the polynomial?The polynomial expression is given as:
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7
Then collect like terms
= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19
= 3x² - 20x + 8.
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Find the equation of the line through point (−1,4) and parallel to 5x+y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
The equation of the parallel line is y = -5x - 1
How to determine the line equation?The equation is given as:
5x + y = 4
Make y the subject
y = -5x + 4
The slope of the above equation is
m = -5
Parallel lines have equal slope.
This means that the slope of the new line is 5
The equation is then calculated as:
y = m(x - x1) + y1
So, we have:
y = -5(x + 1) + 4
Expand
y = -5x - 5 + 4
Evaluate
y = -5x - 1
Hence, the equation of the parallel line is y = -5x - 1
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Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Step-by-step explanation:
The answer is 8 2 / 5 because ...
[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]
Answer:
Here your ans and dont forget to say dhanwyad ok.
If sint=18 , and t is in quadrant i, find the exact value of sin(2t) , cos(2t) , and tan(2t) algebraically without solving for t
The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
According to the statement
we have given that the sint=1/8 then we have to find the exact value of
sin(2t) , cos(2t) , and tan(2t).
Here the value of Sint = 18
then sin2t becomes
sin2t = 2*1/8 then
sin2t = 1/4.
And
(Cos2t)^2 = 1 - (Sin2t)^2
(Cos2t)^2 = 1 - 1/16
(Cos2t)^2 = (16 - 1)/16
(Cos2t)^2 = 15/16
(Cos2t) = (15/16)^1/2
then
tan2t = sin2t/cos2t
tan2t = (1/4)/(15)^1/2 / 4
tan2t = 1/(15)^1/2
these are the values of given terms.
So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2 and tan2t is 1/(15)^1/2.
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The lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value (in hours) is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages
The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.
Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.
We have to apply t test in this because the value of n which is sample size is less than 30.
We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8
t value=2.306.
We know that
t=X bar-μ/s/[tex]\sqrt{n}[/tex]
s/[tex]\sqrt{n}[/tex]=1/[tex]\sqrt{3}[/tex]=0.57
Put all the values in the above formula to calculate required mean.
2.306=X bar-13/0.57
X bar=1.31442+13
=14.31442
after rounding off we get
X bar=14.31
Hence the lifetime of the batteries is 14.31 for which the percentage exceeds 5%.
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I WILL GIVE BRAINLIEST!!!!
2 step equation:
4x + 3 = 19
2 step equation w/ fractions:
(4/3)x + 5 = 17
Distributive Property:
4x(6 - 2) - 10 = 20
Decimals:
4.3x + 0.7 = 5
Real world equation:
Sharon's restaurant is bringing in money from customers, and she needs to know how much she needs to pay off the bill for the electricity to run the place. To turn the electricity on, she has to pay $25. For every hour that the electricity is on for, she has to pay $4. How many hours can she have the electricity on for if she makes $49 profit?
i really need some help solving these
The answers to the questions are:
1. x = 4
2. x = 1.5
3. x = 1.875
4. x = 1
2 step equation:1. 4x + 3 = 19
4x = 19 - 3
4x = 16
divide by 4
x = 4
2 step equation w/ fractions:(4/3)x + 5 = 17
= 1.33x + 5 = 7
Take like terms
1.33x = 7-5
1.33x = 2
divide through by 1.33x to get 2
x = 2/1.33
x = 1.5
3. Distributive Property:4x(6 - 2) - 10 = 20
Multiply and open the bracket
24x - 8x - 10 = 20
Take like terms
16x = 20+10
16x = 30
x = 30/16
= 1.875
4. Decimals:4.3x + 0.7 = 5
4.3x = 5 - 0.7
4.3x = 4.3
x = 1
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If we sample from a small finite population without replacement, the binomial distribution should not be used because
the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types,
we can use the hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are
of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and
n-x objects of type B under the hypergeometric distribution is given by the following formula. In a lottery game, a bettor
selects four numbers from 1 to 54 (without repetition), and a winning four-number combination is later randomly
selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A = 4, B = 50, n = 4, and
x=2.)
P(x)=
A!
B!
(A + B)!
(A-x)!x! (B-n+x)!(n-x)! (A+B-n)!n!
+
P(2)=
(Round to four decimal places as needed.)
Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the parameters are given as follows:
N =A + B = 54, k = 4, n = 4.
The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]
There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.
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A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to
participate in a probability experiment. Compute the probability that
a) a male is selected, then a female.
b) a female is selected, then a male.
c) two males are selected.
d) two females are selected.
e) no males are selected.
The probability that a male is selected, then a female is 0.26
The probability that a female is selected, then a male is 0.26
The probability that two males are selected is 0.18
The probability that two females are selected is 0.30.
The probability that no males are selected is 0.30.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26
The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26
The probability that two males are selected = (11/25) x (10/24) = 0.18
The probability that two females are selected = (14/25) x (13 / 24) = 0.30
The probability that no males are selected = (14/25) x (13 / 24) = 0.30
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Select all that apply.
Which functions have a range of {y ∈ all real numbers | -∞ < y < ∞}?
f(x) = -(x + 1)^2 - 4
f(x) = -4x + 11
f(x) = 2/3x - 8
f(x) = 2^x+3
f(x) = x^2 + 7x - 9
The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.
What are the domain and range of a function?The domain is the set of all the possible values of x that are taken as inputs for the function.The range is the set of all the values(output) that are obtained for the domain of x.So, domain = {input values(x)} and range = {output values(y)}Calculation:Step 1: Finding the range for the function f(x) = -(x + 1)² - 4
The given function is quadratic in the form of a(x - h)² + k,
So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0
For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4
∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}
Step 2: Finding the range for the function f(x) = -4x + 11
This is a linear function. So, the range is R.
∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}
Step 3: Finding the range for the function f(x) = 2/3x - 8
This is also a linear function. So, the range is R.
∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}
Step 4: Finding the range for the function f(x) = 2^x + 3
This is an exponential function. So, the range is y > k
Here k = 3.
∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}
Step 5: Finding the range for the function f(x) = x² + 7x - 9
This is a quadratic function.
we can write it as,
f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9
= (x + 7/2)² - 85/4
This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4
Since a > 0, the range of the function is y ≥ -85/4
∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}
Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}
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