Step-by-step explanation:
a ) Solution,
[tex] = \frac{7}{8} \div \frac{9}{10} \\ [/tex]
[tex] = \frac{7}{8} \times \frac{10}{9} \\ [/tex]
[tex] = \frac{70}{72} \\ [/tex]
Change into lowest term....
[tex] = \frac{35}{36} \\ [/tex]
A basket of oranges has 10 fruits, of which 4 are bad. Three balls are drawn at random.a)Calculate the probability of getting 3 bad balls.b)Calculate the probability of getting 1 bad fruit.c)Calculate the probability of getting at least one bad fruit.d)Calculate the probability of getting the most 2 bad fruits
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.0333 = 3.33%.
b) 0.5 = 50%.
c) 0.8333 = 83.33%.
d) 0.9667 = 96.67%.
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.The values of the parameters are:
N = 10, n = 3, k = 4.
Item a:
The probability is P(X = 3), 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 = 3) = h(3,10,3,4) = \frac{C_{4,3}C_{6,0}}{C_{10,3}} = 0.0333[/tex]
Item b:
The probability is P(X = 1), 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 = 1) = h(1,10,3,4) = \frac{C_{4,1}C_{6,2}}{C_{10,3}} = 0.5[/tex]
Item c:
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[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 = 0) = h(0,10,3,4) = \frac{C_{4,0}C_{6,3}}{C_{10,3}} = 0.1667[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1667 = 0.8333[/tex]
Item d:
The probability is:
[tex]P(X \leq 2) = 1 - P(X = 3)[/tex].
Considering item a:
[tex]P(X \leq 2) = 1 - P(X = 3) = 1 - 0.0333 = 0.9667[/tex]
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Let [tex]O[/tex] be the random variable for the number of bad oranges picked out. Then
[tex]P(O=o) = \dfrac{\dbinom6{3-o} \dbinom4o}{\dbinom{10}3}[/tex]
if [tex]o\in\{0,1,2,3\}[/tex] and zero otherwise, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
(a) Of the 6 good oranges, you pick 0. Of the 3 bad oranges, you pick 3. Of the 10 total oranges, you pick 3. So the probability of picking out all bad oranges is
[tex]P(O=3) = \dfrac{\dbinom60 \dbinom43}{\dbinom{10}3} = \boxed{\dfrac1{30}}[/tex]
(b) By similar reasoning, the probability of drawing exactly 1 bad orange is
[tex]P(O=1) = \dfrac{\dbinom62 \dbinom41}{\dbinom{10}3} = \boxed{\dfrac12}[/tex]
(c) "At least 1 bad orange" means you pick out 1, 2, or 3 bad oranges. These events are mutually exclusive, and we already know the probabilities of picking out exactly 1 or all 3 bad oranges. The remaining probability of drawing 2 bad oranges is
[tex]P(O=2) = \dfrac{\dbinom61 \dbinom42}{\dbinom{10}3} = \dfrac3{10}[/tex]
so the overall probability of drawing at least 1 bad orange is
[tex]P(O\ge1) = P(O=1)+P(O=2)+P(O=3) =\dfrac1{30} + \dfrac3{10} + \dfrac12 = \boxed{\dfrac56}[/tex]
(d) I assume you mean "at most 2 bad oranges," meaning you pick out 0, 1, or 2 bad oranges. Again, these events are mutually exclusive, and the probability of picking out no bad oranges is
[tex]P(O=0) = \dfrac{\dbinom63 \dbinom40}{\dbinom{10}3} = \dfrac16[/tex]
hence the probability of drawings at most 2 bad oranges is
[tex]P(O\le2) = P(O=0) + P(O=1) + P(O=2) = \dfrac16 + \dfrac12 + \dfrac3{10} = \boxed{\dfrac{29}{30}}[/tex]
Assume that the halting language [tex]H_T_M[/tex] is reducible to
some language B ([tex]H_T_M[/tex] [tex]$\leq$[/tex] [tex]_m[/tex] B). Is it possible that is decidable? Answer true/false and explain. Please help me this answer?
H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
How to Interpret Machine Language?A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.
Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.
Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .
S = “On input (M, B)
This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
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Solve log 5x = 3
A)
B)
C)
D)
Answer:
200
Step-by-step explanation:
log a is the same thing as: [tex]log_{10}{a}=b[/tex] which can be rewritten as [tex]10^b=a[/tex] and in general logarithms are in the form [tex]log_ba=c[/tex] which can be written as [tex]b^c=a[/tex]
Rewrite into exponential form
[tex]10^3=5x[/tex]
Simplify exponent
[tex]1000=5x[/tex]
Divide by 5
x=200
Answer:
200
Step-by-step explanation:
I don't know if there are answer choices but the answer is 200
Select all the correct answers.
For which values is this expression undefined?
x-1/(x^2-2x-3) + 5/(2x^2+2x)
The answer choice which represents values for which the expression is undefined is; x = -1.
What value of x renders the expression undefined?It follows from the task content that the expression in discuss is made up of 2 rational expressions and hence, the value of x which makes the expression undefined is -1 because, upon substitution, we have; (1/0) + (5/0); which yields undefined.
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Answer:
x= 3. x= 0, x= -1
Step-by-step explanation:
Correct on edmentum
Answer two questions about Equations A and B:
A. 2x - 1 = 5x
B. - 1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
A. Add/Subtract the same quantity to/from both sides
B. Add/Subtract a quantity to/from only one side
C. Rewrite one side (or both) by combining like terms
D. Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
1. Rewrite one side (or both) by combining like terms. Option C
2. Yes, the equations are equivalent. Option A
Reasons for the answers
1.
Equation A ; 2x -1 = 5x
Equation B ; -1 = 3x
To get equation B from equation A
2x - 1 = 5x
Collect like terms
-1 = 5x -2x
Subtract the like terms
-1 = 3x
Thus, rewrite one side (or both) by combining like terms. Option C
2. 2x - 1 = 5x ...... equation A
Solution ;
2x -5x = 1
-3x = 1
x = -1/3
-1 = 3x
Solution;
x = -1/3
Thus, the equations are equivalent. Option A
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What is x/7 >= -6? Please Answer!
Step-by-step explanation:
x/7 ≥ -6
we rewrite it as :
x/7 = -6
by cross multiplication
x = -42
In order words:
x ≥ -42
Hope this helps
Good luck ✅
Solve using the Quadratic Formula. 122+6−5=0
Step-by-step explanation:
You can't use quadratic formula in this
a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle
Answer:
r=21.01 cm
Step-by-step explanation:
2r = diameter
Circumference of a circle = pi 2r
difference = 90
pi2r - 2r =90
2r (pi-1) =90
90/(2(pi-1) = r = 21.01 cm
please help I will report if wrong... Brainlyest for the first right answer
Answer:
first three expressions are polynomials and last three are not.
Step-by-step explanation:
last three expression has negative powers of X and some powers of Xs are not integers.
don’t understand the question would be a pleasure if someone were to explain and answer the questions! thank you
What would be your weight on the Moon if your weight on Earth is 80 lbs?
6 times 80 lbs
one-sixth of 80. Four Times 80 lbs one-fourth of 80 lbs
For the system of inequalities below, which ordered pair is a solution?
3x-y<2
3y<9x-6
The solution to the given pair of inequalities is at any point on the line
System of inequalitiesInequalities are expressions that are not separated by an equal sign. Given the system of inequalities as shown:
3x-y<2
3y<9x-6
The solution of the system of inequality is the point of intersection of the lines. From the graphed line below, you can see that the point of intersection is at any point on the line since the lines are the same
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G.SRT.1 In the coordinate plane, quadrilateral ABCD has vertices A (1, 1), * 1 point B (5,1), C (5,9), and D (1, 9). Quadrilateral FGHJ is shown in the coordinate plane below. What are the scale factor and the center of dilation that map quadrilateral BCD onto quadrilateral FGHJ?
Based on the vertices of quadrilateral ABCD and Quadrilateral FGHJ, A. The scale factor is 1/2, and the center of dilation is point A.
What is the scale factor?First, note the vertices of Quadrilateral FGHJ:
F(1,1) G(3 ,1) J (1 , 5) H(3 , 5)
Find the lengths of the sides of both quadrilaterals:
FG = (3, 1) - (1, 1) AB = (5,1) - (1, 1)
= (2,0) = (4, 0)
FH = (3, 5) - (1, 1) AC = (5,9) - (1, 1)
= (2,4) = (4, 8)
AB is twice the size of FG.
AC is twice the size of FH
This shows that quadrilateral FGHJ is 1/2 the size of quadrilateral ABCD.
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
40 yds^3
Step-by-step explanation:
Which expression correctly represents “twice the sum of four and a number”?
Answer:
2 (4+x)
Step-by-step explanation:
4 + x is the sum of four and a number 'x' now multiply by 2
2 ( 4+ x)
Please help!!! If the first 4 terms of a geometric sequence are...
Answer:
c.) aₙ = 5 × 4ⁿ⁻¹
Explanation:
Geometric sequence: aₙ = a(r)ⁿ⁻¹
where 'a' resembles first term of a sequence, 'r' is the common difference.
Here sequence: 5, 20, 80, 320,...
First term (a) = 5
Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4
Hence putting into equation: aₙ = 5(4)ⁿ⁻¹
Find the outliers in the given data set below. 69, 16, 79, 80, 82
Answer:
16
Step-by-step explanation:
The outlier in the given dataset is "16".
Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,
To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).
Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.
An outlier is a value that significantly deviates from the rest of the dataset.
Let's examine the given dataset:
69, 16, 79, 80, 82
To identify outliers, we can consider any data points that are notably different from the others.
In this case, it seems that the value "16" is considerably lower than the other values.
Let's label it as a potential outlier.
Therefore, the outlier in the given dataset is "16".
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What is the value of the function when x = 1 in the
piecewise function
g(x) =
{
3x
-2x
when x>1
when x≤1
Answer:
-2
Step-by-step explanation:
3x isnt used because it stated when x>1.
so -2(1) is -2, because x =< 1 is true
Find the diffrence between 6/7 and 2/3 In lowest terms
Answer:
4/7
Step-by-step explanation: Multiply 2/3 x 6/7 Put your answer in lowest terms a. 4/7
Answer:
Difference: 4/21
Step-by-step explanation:
the difference between two quantities is the result of a subtraction
[tex]\frac{6}{7} -\frac{2}{3} =\frac{(6)(3)-(7)(2)}{(7)(3)} =\frac{18-14}{21} =\frac{4}{21}[/tex]
The fraction can no longer be reduced
Hope this helps
rewrite y= 16x-32 -3 to make it easy to graph using a translation describe the graph
We can rewrite the given expression to:
[tex]4*\sqrt{x - 2} - 3[/tex]
So the correct option is the third one.
How to rewrite the expression?
Here we have the expression:
[tex]\sqrt{16x - 32} - 3[/tex]
Taking the 16 as a common factor inside the square root:
[tex]\sqrt{16*(x - 2)} - 3[/tex]
and 16 = 4², then:
[tex]\sqrt{16*(x - 2)} - 3 = \sqrt{4^2*(x - 2)} - 3\\\\4* \sqrt{(x - 2)} - 3[/tex]
Now, if the parent function is:
[tex]y = 4*\sqrt{x}[/tex]
Our function is the parent function translated 2 units to the right and 3 units down. The correct option is the third one
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LCM of 4x²-100 and 4x + 20
LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)
What is Least Common Multiple?
Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.
We have to factorise 4x²-100 which is of the form A²-B²,
= (2x)² -(10)²
= (2x+10)(2x-10)
= 2×2(x+5)(x-5)
= 4(x+5)(x-5).
We have to factorise 4x + 20
= 4(x+5)
LCM of 4x²-100 and 4x + 20 = 4(x+5)(x-5).
Hence, LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)
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Sanjeet paid $32.85 for 1 file and 3 identical pens. Leon paid $83.50 for 2 files and 8 identical pens. Find the cost of one such pen
The cost of the file is $6.15 and the cost of the pen is $8.9
Solving word problems with systems of linear equations.The interpretation of the given word problem leads to a system of linear equations.
From the given information:
Let the file be denoted with f and the pen be denoted with pf + 3p = 32.85 --- (1)
2f + 8p = 83.5 --- (2)
From equation (1)
f = - 3p+32.85
Replace the value of f in the above equation into equation (2)
2(-3p + 32.85) + 8p = 83.5
2p + 65.7 = 83.5
2p = 83.5 -65.7
2p = 17.8
p = 17.8/2
p = 8.9
Replacing the value of p = 8.9 into f = - 3p+32.85
f = -3(8.9)+32.85
f = 6.15
Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.
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MATH: GRAPHS AND FUNCTIONS 3. HELP! 12 PTS (HARD)
Answer:
Step-by-step explanation:
+
Select the correct answer.
The parent function f(x)=√ is transformed to g(x)=2x-3). Which is the graph of g(x)?
The graph is in the attached image.
Identify the key features of the following graph. If the Domain is all real numbers, type in "All Real" into the Domain box.
The key features of the graph are:
Vertex (-2, -1)Axis of symmetry x = -2y-intercept (0, 3)MinimumDomain, -∞ < x < ∞Range y > = -1How to determine the key features?The graph has a minimum value at (-2, -1)
This represents the vertex
The x coordinate of the vertex is the axis of symmetry.
So, we have
x = -2
The graph crosses the y-axis at (0, 3)
This represents the y-intercept
The graph opens up.
This means that the vertex is minimum.
The domain is the set of all real number, because the graph extends in both directions on the x-axis without end
While the range is y >= -1, because it has a minimum at this point
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On a unit circle, the terminal point of 0 is (1, 0). What is tan ?
By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.
How to find determine a trigonometric function associated with an unit circle
In trigonometry, an unit circle is a circle with a radius of 1 and used to determine the values of trigonometric functions. There are two fundamental trigonometric functions: (i) sine, (ii) cosine, and the tangent is a derivate trigonometric function, which is defined below:
tan θ = y/x (1)
If we know that x = 1 and y = 0, then the tangent of the terminal point of angle is:
tan θ = 0/1
tan θ = 0
By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.
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Answer:
tan= 0
Step-by-step explanation:
^^^correct :)
Hi, need help please to get my HS diploma...did not graduate :(
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
The answer is A Find the point-slope form.
y+3= −7/5 ⋅ (x+2)
Step-by-step explanation:
What is the quotient of
6/7 and 3/14 ?
Answer:
4/1 or 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
[tex]\frac{\frac{6}{7} }{\frac{3}{14} } =\frac{(6)(14)}{(7)(3)} =\frac{84}{21} =4[/tex]
Hope this helps
Determine the composition of transformations that would map figure ABCD to figure A''B'C''D'
The composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
What is transformation?It should be noted that transformation simply means the manipulation of a shape or geometric figure.
In this case, the composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
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The principal represents an amount of money deposited in a savings account subject to
compound interest at the given rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Click the icon to view some finance formulas.
A. The amount of money in the account after 5 years is $
(Round to the nearest hundredth as needed.)
Principal
$11,000
Rate
5%
Compounded
annually
Time
5 years
Step-by-step explanation:
So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just [tex]A = P(1+r)^t[/tex]. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula [tex]A = 11000(1.05)^t[/tex]. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be [tex]11000(1.05)^t-11000[/tex]. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation [tex]11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10[/tex]