Answers
For this case we must simplify the following expression:
[tex]\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}[/tex]
We rewrite:
[tex]64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3[/tex]
So:
[tex]\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}[/tex]
Answer:
Option B
Related Questions
Angle 0 lies in the second quadrant, and sin 0=3/5
Cos 0=
Answers
Answer:
-4/5
Step-by-step explanation:
Please use a symbol such as x or Ф to represent an angle; your 0 is too easily confused with zero.
If Angle Ф lies in the second quadrant, and sin Ф=3/5, find cos Ф.
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: sin Ф = opp / hyp = 3 / 5. Thus the opp side has length 3 and the hyp has length 5. By the Pythagorean Theorem,
the adj side has length √(5² - 3²), or √(25-9), or √16, or ±4. Because the angle is in the 2nd quadrant, choose adj = -4.
Then the cosine of this angle is cos Ф = adj / hyp = -4 / 5
Final answer:
To find cos 0, use the Pythagorean identity and evaluate.
Explanation:
To find cos 0, use the Pythagorean identity and evaluate. The given information states that angle 0 lies in the second quadrant and sin 0 = 3/5. We need to find cos 0. Since angle 0 is in the second quadrant, cosine is negative in that quadrant. We can use the Pythagorean identity to find cos 0 = √(1 - sin² 0), which becomes cos 0 = √(1 - (3/5)²). Evaluating this gives us cos 0 = √(1 - 9/25) = √(16/25) = 4/5.
Select the correct answer.
What is the vertex of the parabola given by y = -(x − 2)2 − 1?
A.
(2, 1)
B.
(2, -1)
C.
(-2, 1)
D.
(-1, 2)
Answers
Answer:
Vertex: 2,-1
Step-by-step explanation:
you just gotta graph it
Final answer:
The vertex of the parabola given by the equation y = -(x - 2)² - 1 is (2, -1).
Explanation:
To find the vertex of the parabola given by the equation y = -(x − 2)² − 1, you should recognize that the equation is already in the vertex form, which is y = a(x − h)² + k, where (h, k) is the vertex of the parabola. In this case, h equals 2, and k equals -1, therefore the vertex of the parabola is (2, -1).
In about one hundred words, explain the importance of symbolism to short stories. Use two examples from the short stories in this unit.PLZ HELP
Answers
Answer:
portance of symbolism in short stories
Symbolism helps create meaning and emotion in a story. Metaphors and allegory are literary elements that help writers create symbolism in their literary pieces. Colors, objects, seasons, people, situations and words are all types of symbolism that might be used in a literary work.
Step-by-step explanation:
can i have brainlyest
Answer:
The mother's ironing is the main symbol of the story because it reflects on her hopes for Emily. As the mother irons she discusses Emily's life. Through her narration, readers can understand that the mother wanted a smooth life for Emily. But struggles like poverty, unexpected illness, and other negative experiences prevented a normal life for Emily. The iron indicates that the mother wanted to fix Emily. Her sentiments also can be interpreted as regrets that the mother could not help Emily overcome life trials. The ironing can therefore be seen by the readers like the heaviness of a mother's duties towards a child. The continuous action of ironing shows the mother's efforts to address Emily's problems in doing daily tasks. The mother cannot help but reflect upon the reasons Emily developed into a special child. Most importantly, the iron represents that the mother still believes Emily can become a confident person. With the mother's support, Emily may have hope.
(solve) 12 1/2-(-4 1/2) =
Answers
Answer:
17
Step-by-step explanation:
12 1/2 -(-4 1/2) = 12 1/2 + 4 1/2
=25/2 + 9/2
= 34 /2
= 17
The value of the given expression is 17
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 12 1/2-(-4 1/2), we need to simplify it,
12 1/2 -(-4 1/2)
= 12 1/2 + 4 1/2
=25/2 + 9/2
= 34 /2
= 17
Hence, the value of the given expression is 17
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Calculator
158°
120°
126
.
What is the value of x?
Enter your answer in the box
Answers
Answer:
is their more to this ?
Step-by-step explanation:
because it could be like X+70=140 what x was there anything like that ?
Answer:
Here it is
Step-by-step explanation:
How do I solve absolute value equalities?
4| n+8 | = 56
Answers
Answer:
Step-by-step explanation:
I believe you do, 4 times each number in the absolute value symbol. 4 times n, 4 times positive 8. 4n+32=56
You minus 32 on both sides and you get 24. Then you take 24 and divide it by 4, and there is your answer 6.
You can check it by plugging 6 into the equation.
which describes money that is received from a sale of goods or services?
Answers
Answer:
revenue
Step-by-step explanation:
It is another name for funds or money received from a sale of goods or services.
Answer:
it is revenue
Step-by-step explanation:
find Sn for the given arithmetic series a1=-26 d=-9 n=24
Answers
Answer:
- 3108
Step-by-step explanation:
The sum to n terms of an arithmetic series is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2[tex]a_{1}[/tex] + (n - 1)d ]
Substitute the given values into the formula
[tex]S_{24}[/tex] = [tex]\frac{24}{2}[/tex] [ (2 × - 26) + (23 × - 9) ]
= 12 ( - 52 - 207 )
= 12 × - 259 = - 3108
Please help me with geometry.
Answers
Answer:
m<6 = 50
Step-by-step explanation: Just trust me
Answer:
50 degrees
Step-by-step explanation:
When two parallel lines are cut by a transversal, same side interior angles are supplementary.
In the figure, parallel lines AB and CD are cut by the tranversal shown forming 8 angles. Angles 3 and 6 are same side interior angles, so they are supplementary. That means that their measures have a sum of 180 degrees.
m<3 + m<6 = 180
130 + m<6 = 180
m<6 = 180 - 130
m<6 = 50
Equation to find r in terms for V and h
Answers
V = πr²h
We want r in terms of V and h, so
[tex]r^2=\frac{V}{h\pi}[/tex]
[tex]r=\sqrt{\frac{V}{h\pi}}[/tex]
AB and BC form a right angle at point B. if A= (-3, -1) and B = (4, 4), what is the equation of BC
Answers
Answer:
With fractions: [tex]y=-\frac{7}{5} x+\frac{48}{5}[/tex]
With decimals: [tex]y=-1.4x+9.6[/tex]
Step-by-step explanation:
First we are finding the slope of line AB using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
The first point is A= (-3, -1) and the second one is B = (4, 4), so [tex]x_1=-3[/tex], [tex]y_1=-1[/tex], [tex]x_2=4[/tex] and [tex]y_2=4[/tex].
Replacing values
[tex]m=\frac{4-(-1)}{4-(-3)}[/tex]
[tex]m=\frac{4+1}{4+3}[/tex]
[tex]m=\frac{5}{7}[/tex]
Now, since AB and BC form a right angle, BC is perpendicular to AB. The slope of a perpendicular line is the negative reciprocal of the other line; in other words, the slope of BC is the negative reciprocal of the slope of AB. To find the negative reciprocal of the slope of AB we just need to multiply its slope by -1 and invert the fraction:
[tex]m_{AB}=\frac{5}{7}[/tex]
[tex]m_{BC}=-\frac{7}{5}[/tex]
Finally, to complete the equation of BC, we are using the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the point
We know that [tex]m_{BC}=-\frac{7}{5}[/tex], so [tex]m=-\frac{7}{5}[/tex]. Since the line passes throughout point B = (4, 4), [tex]x_1=4[/tex] and [tex]y_1=4[/tex].
Replacing values
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=-\frac{7}{5} (x-4)[/tex]
[tex]y-4=-\frac{7}{5} x+\frac{28}{5}[/tex]
[tex]y=-\frac{7}{5} x+\frac{28}{5}+4[/tex]
[tex]y=-\frac{7}{5} x+\frac{48}{5}[/tex]
[tex]y=-1.4x+9.6[/tex]
Answer:
-7x − 5y = -48
Step-by-step explanation:
This was correct on plato :D
SUBSTITUTION
p=-4.8 q=3.2
r=3-2p+q^2
Answers
R = 3 - 2(-4.8) + 3.2^2
R = 3 + 9.6 + 10.24
R = 22.84
Answer:
r=16.84
Step-by-step explanation:
As we know that [tex]p=-4.8[/tex] and [tex]q=3.2[/tex] we can substitute these values in to the equation in order to find the value of r
[tex]r=-3-2p+q^2\\\\r=-3-2(-4.8)+(3.2)^2\\\\r=-3+9.6+10.24\\\\r=16.84[/tex]
Is the ratio 25 to 16 proportional to 5 to 4.
Answers
No because 5:4 time 4 you get 20:16 not 25:16 and if you manage 25 it will be 25:20 so not promotional
Answer:
no
Step-by-step explanation:
because if you divide 25 by 16 you get 1.5625 and if you divide 5 by 4 you 1.25, so they are not proportional. and another way to see if its proportional or not, is to divide the numerators by the same number as you did with the denominators. for example, 25/5 = 5 but 16/5 does not equal 4, so they aren't proportional.
if f(x)=x/2-3 and g(x)=3x^2+x-6, find (f+g)(x)
Answers
The answer is:
[tex]f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Why?We are working with function addition, to add or subtract two o more functions, we need to follow the following form:
[tex](f+g)=f(x)+g(x)[/tex]
To simplify the expression, we need to work with the like terms, like terms are the terms that share the same variable and the same coefficient, for example:
[tex]x+3x+x^{2}=x^{2} +4x[/tex]
We were able to add only the first two terms since the third term does not share the exponent with the other two.
We are given the functions:
[tex]f(x)=\frac{x}{2}-3\\\\g(x)=3x^{2}+x-6[/tex]
So, solving, we have:
[tex]f(x)+g(x)=(\frac{x}{2} -3)+(3x^{2} +x-6)\\\\f(x)+g(x)=3x^{2}+\frac{x}{2}+x-3-6\\\\f(x)+g(x)=3x^{2}+\frac{x+2x}{2}-9\\\\f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Hence, the answer is:
[tex]f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Have a nice day!
To find (f+g)(x), we need to add the two functions f(x) and g(x). Let's do this step by step:
Given functions:
f(x) = x/2 - 3
g(x) = 3x^2 + x - 6
(f+g)(x) means the sum of f(x) and g(x), so we add the two functions together:
(f+g)(x) = f(x) + g(x)
= (x/2 - 3) + (3x^2 + x - 6)
Now, we combine like terms:
(f+g)(x) = 3x^2 + x/2 + x - 3 - 6
There is a common term x/2 and x, which we can combine by finding a common denominator. The common denominator is 2, so we convert x to 2x/2:
(f+g)(x) = 3x^2 + 2x/2 + x/2 - 3 - 6
= 3x^2 + (2x + x)/2 - 3 - 6
= 3x^2 + 3x/2 - 3 - 6
Now we add or subtract the constants:
(f+g)(x) = 3x^2 + 3x/2 - 9
So, the function (f+g)(x) is equal to:
(f+g)(x) = 3x^2 + 3x/2 - 9
And that is the final expression for the sum of f(x) and g(x).
this is my last question gn guys
pls answer so i can sleep
Answers
Answer:
48 cm²
Step-by-step explanation:
Area
= (6 x 2) + (10 - 6) x 9
= 12 + 36
= 48 cm²
Determine if direct variation x-2y=0
Answers
Answer:
x-2y=0 is a direct variation
Step-by-step explanation:
Direct variation is of the form
y= kx
Can we get the equation in that form
x-2y =0
Add 2y to each side
x-2y+2y =0_2y
x=2y
Divide each side by 2
x/2 = 2y/2
1/2x =y
Flip the sides
y = 1/2x
This is of the form y= kx where k = 1/2
x-2y=0 is a direct variation
Compute the following 7!/3!
Answers
If we reduce the expression by cancelling common factors, your answer would be 840.
Which expression can be used to represent 8 more than the product of 15 and 12?
Answers
Answer:
25
Step-by-step explanation:
15x12=180
8x25=200
The expression is [tex]\(15 \times 12 + 8 = 188\)[/tex].
To represent "8 more than the product of 15 and 12", you would first calculate the the product of 15 and 12, and then add 8 to to the result.
1. Calculate the product of of 15 and 12:
[tex]\(15 \times 12 = 180\)[/tex]
2. Add 8 to to the result:
[tex]\(180 + 8 = 188\)[/tex]
So, the expression representing "8 more than the product of of 15 and 12" is [tex]\(15 \times 12 + 8\)[/tex], which simplifies to to [tex]\(188\)[/tex].
Find the measure of angle x
Answers
x = 90 - 28
x = 62°
The answer is choice B.
Answer:
The answer is B; 62 degrees
Step-by-step explanation:
A straight line has an angle measure of 180 degrees
So our equation to solve for x is: 180 - 90 - 28 = x
Therefore, x = 62
Combine the like terms to create an equivalent expression: −5r+8r+5
Answers
Answer:
3r+5
Step-by-step explanation:
Since -5r and 8r both have r in them, we can combine them and the expression looks like:
3r+5
Which is our answer.
Answer:
3r+5
Step-by-step explanation:
Math
2x + 3y = 105
x + 2y = 65
Answers
Solve for x in x + 2y = 65
x = 65 - 2y
Substitute x = 65 - 2y into 2x + 3y = 105
130 - y = 105
Solve for y in 130 - y = 105
y = 25
Substitute y = 25 into x = 65 - 2y
x = 15
Therefore;
x = 15
y = 25
An angle with 43 is called
Answers
Answer:
Acute
Step-by-step explanation:
Anything with a measure less than 90 degrees is acute
An acute angle. It's less then 90 degrees.
^^^Is that the answer you're looking for?
Find the number of solutions of -x^2 + 5x - 4 = 0.
Answers
Answer:
There are 2 solutions for the equation -x^2 + 5x - 4 = 0 i.e x=1 and x=4
Step-by-step explanation:
We can find the number of solutions of the given equation -x^2 + 5x - 4 = 0 by solving the equation using factors method to solve the quadratic equation.
[tex]-x^2 + 5x - 4 = 0\\Taking\,\, - sign\,\, common\\x^2 - 5x + 4 = 0\\making\,\, factors\,\, of\,\, 4x^2\\x^2 -4x -x +4 = 0\\x(x -4) -1 (x - 4) = 0\\(x-1)(x-4)=0\\x-1 = 0 \,\, and \,\, x-4 =0\\x = 1 \,\,and\,\, x = 4\\[/tex]
The values of x are:
x=1 and x=4
So, there are 2 solutions for the given equation -x^2 + 5x - 4 = 0
A bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles. Which of the following statements is not true? The theoretical probability of selecting a red marble from the bag is 27.5%. The odds of selecting a yellow marble from the bag are 13 to 27. The theoretical probability of selecting a blue or green marble from the bag is . The odds of selecting a red or blue marble are .
Answers
Answer: In total there are 40 marbles because 11+7+9+13=40
There are 7 Blue marbles, so
P(blue)=7/40
\
Disclaimer: The options were not given correctly so they are added here:
a. The theoretical probability of selecting a red marble from the bag is 27.5%.
b. The odds of selecting a yellow marble from the bag are 13 to 27.
c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.
d. The odds of selecting a red or blue marble are 9/11.
Among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.
What is the probability of an event?The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:
P(A) = n/S.
What are the odds of a given event?When a given event suppose A, has a Probability of occurring = P(A) and Probability of not happening = 1 - P(A).
When we calculate the odds in favor of event A, the value is given by the ratio, P(A):(1 - P(A)).
When we calculate the odds against the event A, the value is given by the ratio, (1 - P(A)):P(A).
How do we solve the given question?We are informed that a bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles.
Let the event of selecting a red marble from the bag be R.
Number of outcomes favoring R = 11 (number of red marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event R is P(R) = 11/40
1 - P(R) = 1 - 11/40 = 29/40
Let the event of selecting a blue marble from the bag be B.
Number of outcomes favoring B = 7 (number of blue marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event B is P(B) = 7/40
1 - P(B) = 1 - 7/40 = 33/40
Let the event of selecting a green marble from the bag be G.
Number of outcomes favoring G = 9 (number of green marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event G is P(G) = 9/40
1 - P(G) = 1 - 9/40 = 31/40
Let the event of selecting a yellow marble from the bag be Y.
Number of outcomes favoring Y = 13 (number of yellow marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event Y is P(Y) = 13/40
1 - P(y) = 1 - 13/40 = 27/40
Now, we analyze all the options, to check for the ones which are not true.
a. The theoretical probability of selecting a red marble from the bag is 27.5%.
The probability of selecting a red marble P(R) = 11/40 =11/40 * 100% = 27.5%, which is the same we are looking for.
∴ The statement is true.
b. The odds of selecting a yellow marble from the bag are 13 to 27.
The odds of selecting a yellow marble (odds in favor) = P(Y)/(1 - P(Y)) = 13/27 or 13 to 27, which is the value we are looking for.
∴ The statement is true.
c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.
The probability of selecting a blue or green marble from the bag = P(B) + P(G) = 7/40 + 9/40 = 16/40 = 2/5, which is not the value we are looking for.
∴ The statement is not true.
d. The odds of selecting a red or blue marble are 9/11.
The probability of selecting a red or blue marble from the bag
P(R+B) = P(R) + P(B) = 11/40 + 7/40 = 18/40 = 9/20.
1 - P(R+B) = 1 - 9/20 = 11/20
∴ Odds of selecting a red or blue marble (odds in favor)
= P(R+B)/(1 - P(R+B)) = (9/20)/(11/20) = 9/11, which is the value we are looking for.
∴ The statement is true.
So, among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.
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What is the wavelength for radio waves with frequency 3x10^9
Answers
The wavelength of radio waves with a frequency of 3x10^9 Hz can be calculated using the equation c = λf. By substituting the given values and solving for λ, we find that the wavelength is approximately 10 cm.
Explanation:To find the wavelength of radio waves with frequency 3x10^9, first, we need to understand that wave speed, wavelength, and frequency are interconnected. This relation can be written as c = λf, where 'c' is the speed of light, 'λ' is the wavelength and 'f' is the frequency. Given the speed of light, c, is approximately 3.00x10^8 m/s, and the frequency, f, is 3x10^9 Hz, we can substitute these values into the equation and solve for λ (wavelength). This will give us λ = c / f = 3.00x10^8 m/s / 3x10^9 Hz = 0.1 m or 10 cm.
Therefore, the wavelength of the radio waves with a frequency of 3x10^9 Hz is 10 cm.
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To find the wavelength of radio waves with a frequency of 3x10⁹ Hz, use the equation c = fλ, where c is the speed of light (3.00x10^8 m/s). The wavelength is calculated to be 0.1 meters.
Explanation:The question is asking us to calculate the wavelength of radio waves with a given frequency. The formula that connects the speed of light (c), frequency (f), and wavelength (λ) is c = fλ, where c is the speed of light in a vacuum, which is approximately 3.00 × 108 m/s.
To find the wavelength for radio waves with a frequency of 3 × 10⁹ Hz, we can rearrange the formula to λ = c/f. Thus:
λ = (3.00 × 10⁸ m/s) / (3 × 10⁹ Hz)
= 0.1 meters
The wavelength of radio waves with a frequency of 3 × 10⁹ Hz is 0.1 meters.
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A gallon of paint will cover approximately 350 square feet. The family room measures 15x18 feet and has a 8 foot ceilings.How many gallons of paint must be purchased in order to pint the walls
Answers
Answer:
2 gallons
Step-by-step explanation:
So first, we need to figure out the total area of the walls,
so 15 x 8 = 120 x 2 = 240
18 x 8 = 144 x 2 = 288
240 + 288 = 384
2 gallons are needed
Write the standard form of the line that contains a slope -3/8 and passes through the point (5, -4).
Answers
Answer:
y+3/8x=-17/8
Step-by-step explanation:
y=mx+b
y=-3/8x+b
-4=-3/8(5)+b
-4=-15/8+b
-32/8+15/8=b
-17/8=b
y=-3/8x-17/8
change to standard form where x and y are on one side of the equation
y+3/8x=-17/8
solve........3 (5p - 3) = 5 (p - 1)
Answers
Step 1: multiply the numbers in front of the parentheses with each term inside the parentheses
15p - 9 = 5p - 5
Step 2: get like terms on the same side
10p = 4
Step 3: divide both sides by 10
p = 4/10
Step 4: simplify
p = 2/5
The solution for p in the given expression is p = 2/5.
Given is an expression 3 (5p - 3) = 5 (p - 1), we need to solve for p,
To solve the given expression for p, let's break down the steps:
Distribute the multiplication on both sides of the equation:
15p - 9 = 5p - 5
Rearrange the equation by moving all terms involving p to one side and the constants to the other side:
15p - 5p = -5 + 9
Combine like terms on both sides:
10p = 4
Divide both sides by 10 to isolate p:
p = 4/10
Simplifying the fraction:
p = 2/5
Therefore, the solution for p in the given expression is p = 2/5.
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A bag contains 5 red marbles, 6 white marbles, and 5 blue marbles. Find P(red and blue).
Please show work so I can undersand.
Answers
The probability of getting blue and red marble is [tex]0.0976[/tex].
What is Probability?
The probability of any event is the ratio of number of favourable outcome and Total number of outcome.
It is given that a bag contains [tex]5[/tex] red marbles, [tex]6[/tex] white marbles and [tex]5[/tex] blue marbles.
We have to find the Probability [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex].
So,
[tex]\[\text{The total number of marbles in the bag}=5+6+5\][/tex]
[tex]= 16[/tex]
Probability of getting red marble [tex]\[\text{P}\left( \text{red} \right)\text{=}\frac{\text{no}\text{.of red marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{5}{16}\][/tex]
Probability of getting white marble [tex]\[\text{P}\left( \text{white} \right)\text{=}\frac{\text{no}\text{.of white marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{6}{16}\][/tex]
Probability of getting blue marble [tex]\[\text{P}\left( \text{blue} \right)\text{=}\frac{\text{no}\text{.of blue marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{5}{16}\][/tex]
Now, we find the probability for [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex],
[tex]\[\text{P}\left( \text{red and blue} \right)\] = $\text{P}\left( \text{red} \right)\text{ }\!\!\times\!\!\text{ P}\left( \text{white} \right)$[/tex]
[tex]$=\frac{5}{16}\cdot \frac{5}{16}$[/tex]
[tex]$=0.0976$[/tex]
Hence, the Probability of [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex] is [tex]0.0976[/tex].
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Final answer:
The probability of drawing a red marble and then a blue marble from a bag containing a mix of marbles is 5/48, calculated by multiplying the probabilities of each individual event occurring in sequence.
Explanation:
The question asks for the probability of drawing a red and then a blue marble from a bag containing 5 red, 6 white, and 5 blue marbles. We begin by calculating the probability of drawing a red marble, which is 5/16 (since there are 5 red marbles out of a total of 16). After drawing a red marble, we do not replace it, so there are now 15 marbles left. The probability of drawing a blue marble next is 5/15 or 1/3, since there are 5 blue marbles left.
To find the combined probability of two independent events, we multiply their individual probabilities. Therefore, the probability of drawing a red then a blue marble without replacement is 5/16 * 1/3, which simplifies to 5/48. So, P(red and blue) is 5/48.
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Answers
Answer:
The correct option is the fourth one.
Step-by-step explanation:
FIRST QUESTION:
To solve this problems we need to know the following things:
1. Given f(x) = k*g(x). We know that the graph of f(x) will be identical to the graph of g(x) but enlarged or compressed depending on the value of k.
2. Given f(x) = g(x) + k. We know that the graph of f(x) will be identical to the graph of g(x) but shift downwards if k<0 or shift upwards if k>0.
Having said this, we have that:
f(x) = 1/2 * log_2 (x) - 8
In this case, there are two transformations: The function is supressed by 1/2 and also shifted downwards by 8 units.
SECOND QUESTION
We need to find the portion of domain where f(x) = x^2 + a is one-to-one.
A function f is one-to-one if each x in the domain has exactly one image in the range. And, no y in the range is the image of more than one x in the domain.
So if we want a one-to-one function we need to restrict the domain starting from x=0. So it would be: [0, inf)
Now to find the inverse function, we need to solve the equation for "x"
y = x^2 + a
y - a = x^2
x = sqrt(y-a)
Then, the inverse function would be:
y = sqrt(x-a)
The correct option is the fourth one.