A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(A and B) expressed in simplest form?
A. 5/18
B. 4/9
C. 1/2
D. 5/9
The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.The total sample will have 9 numbers
S = { 1,2,3,4,5,6,7,8,9} = 9
Even Number = { 2,4,6,8} = 4
Odd Number = { 1,3,5,7,9} = 5
P ( A ) = ( 4 / 9 )
P ( B ) = ( 5 / 9 )
The probability will be calculated as:-
P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]
P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]
P( A:B ) = 4 / 9
Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).
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there are 3 red pens, 4 blue pens, 2 Blac pens, and 5 green pens in drawer, suppose you choose a pen at random
help :(:
Answer:
1. 3/14
2. 2/7
3. 1/7
4. 5/14
5. 11/14
6. 9/14
Step-by-step explanation:
first get the total number of pens
3 red pens + 4 blue pens + 2 black pens + 5 green pens =
14 total number of pens
1. What is the probability that the pen chosen red?
3 red pens out of a total of 14 pens = 3/14
2. What is the probability that the pen chosen is blue?
4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7
3. What is the probability that the pen chosen is black?
2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7
4. What is the probability that the pen chosen is green?
5 green pens out of a total of 14 pens = 5/14
5. What is the probability that the pen chosen is NOT red?
of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens
4 blue pens, 2 black pens and 5 green pens are NOT red
4 blue pens + 2 black pens + 5 green pens =
11 total number of pens that are NOT red
11 total number of pens that are NOT red out of a total of 14 pens = 11/14
6. What is the probability that the pen chosen is NOT green?
of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens
the 3 red pens, 4 blue pens, 2 black pens are NOT green
3 red pens + 4 blue pens + 2 black pens =
9 total number of pens that are NOT green
9 total number of pens that are NOT green out of a total of 14 pens = 9/14
gathmath.com
Given :-
Red pens = 3Blue pens = 4 Black pens = 2 Green pens = 5>> Total no. of outcomes = 3 + 4 + 2 + 5
>> Total no. of outcomes = 3 + 4 + 7
>> Total no. of outcomes = 10 + 4
>> Total no. of outcomes = 14
Solution 1 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are three red pens. Therefore,
P(E) = 3 / 14Solution 2 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are four blue pens. Therefore,
P(E) = 4 / 14Solution 3 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are two black pens. Therefore,
P(E) = 2 / 14Solution 4 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are five green pens. Therefore,
P(E) = 5 / 14Solution 5 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there 11 pens that are not red (Green + black + blue).
P (E) = 11 / 14Solution 6 :-
We know,
P (E) = No. of possible outcomes / Total number of outcomes.As there are 9 pens that are not green (Red + blue + black).
P (E) = 9 / 14One third of a number less than nine equal to seven
If g(x) is the inverse of f(x), what is the value of f(g(2))?
0-6
O-3
02
O 5
Answer:
2
Step-by-step explanation:
When a function and its inverse are composed, the output is equal the input.
Solve for X
picture below
Which is a valid prediction about the continuous
function f(x)?
Of(x) ≥ 0 over the interval [5, ∞).
Of(x) ≤0 over the interval [-1, %).
Of(x) > 0 over the interval (-∞, 1).
Of(x) < 0 over the interval (-∞. –1).
33333333333333333333333333333333333
Eric is 8 years 4 months old. his mother is 40 years 3 months old. how old was his mother when eric was born?
Answer:
Eric´s mom had:
31 years 11 months
Step-by-step explanation:
1 year = 12 months
40 years = 39 years + 12 months
40 years 3 months = 39 years + 12 monts + 3 monts = 39 years 15 months
Then:
40 years 3 months
- 8 years 4 months
it´s equivalent to:
39 years 15 months
- 8 years 4 months
= 31 years 11 monts
Which of the following is an example of a quadratic equation?
A. y = 216+6
B. x²-64 = 0
C. y = 4x+6
D. x+10 = 33
Answer: B
Step-by-step explanation:
A quadratic equation has degree 2.
What is the missing reason in the proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD
Answer: Since they have the some points in common we can just plot them and seeing ang. DBC would just be a straight line and angle ABC would be 90 degrees and half of that angle so they would be equal
explain please thanks :)
Answer:
24
Step-by-step explanation:
The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.
Okay, on to the problem:
We can do one digit at a time.
First digit:
There are 4 digits that we can choose from. (3, 4, 6, and 7)
Second digit:
No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.
Third digit:
Using the same logic, there are only 2 options left.
We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.
Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.
Write the equation of the line in slope intercept form Slope=-4 Point=(2,-4)
Answer:
y=2x-8
or
f(x)=2x-8
Step-by-step explanation:
To write in slope-intercept form using this information, first use the point slope formula.
y-y1=m(x-x1)
m is slope.
y+4=2(x-2)
Use distributive property on the right side.
y+4=2x-4
Now, subtract 4 from both sides.
y+4-4=2x-4-4
y=2x-8
Written using function notation:
f(x)=2x-8
Hope this helps!
If not, I am sorry.
Please help asap
What is the domain and range of T
Answer:
Domain = {-3, -2}Range = {-4, -3, 4}Step-by-step explanation:
The domain is the set of x-values, and the range is the set of y-values.
Which expression is equivalent to 7a³ (8a² + a)²-4a³?
Simplify.
[tex]7a³ (8a² + a)²-4a³ \\ \\ 7 {a}^{3}(8 { {a}^{2} + a)(8 {a}^{2} + a )} - 4 {a}^{3} \\ \\ 7 {a}^{3} ( {8a}^{2} (8 {a}^{2} + a ) + a(8 {a}^{2} + a ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 8{a}^{3} + 8 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 16 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 448 {a}^{7} + 112 {a}^{6} + 7 {a}^{5} - 4 {a}^{3} \\ \\ {a}^{3} (448 {a}^{4} + 112 {a}^{3} + 7 {a}^{2} - 4).[/tex]
Which expression is equivalent to
(Q^5)^2
The correct value that equates to this expression is q¹⁰
.
To solve this expression, just:
eliminate the parentheses and multiply the exponents among themselves;[tex] \boxed{ \large \sf (a {}^{n} ) {}^{m} \rightarrow a {}^{n \times m} } \\ \\ [/tex]Resolution[tex]{ = \large \sf (q {}^{5} ) {}^{2} } [/tex]
[tex]{ = \large \sf q {}^{5 \times 2} } [/tex]
[tex] \pink{ \boxed{ = \large \sf q {}^{10} } } \\ [/tex]
Therefore, the answer will be q¹⁰
Answer:
Q¹⁰
Step-by-step explanation:
Given that,
(Q⁵)^2Solution:
Well,there is a law of exponents,which states that:
(a^b)^c = a^bcSame case is here as well.
Just multiply both powers given.
(Q⁵)²5*2 = 10
Q¹⁰Hence, the expression equivalent to (Q⁵)² is (Q)¹⁰
If the inspection division of a county weights and measures department wants to estimate the mean amount of
If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.
Given 95% confidence level, standard deviation=0.05.
We know that margin of error is the range of values below and above the sample statistic in a confidence interval.
We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data near the mean are more frequent in occurence than data far from mean.
We know that margin of error for a confidence interval is given by:
Me=[tex]z/2* ST/\sqrt{N}[/tex]
α=1-0.95=0.05
α/2=0.025
z with α/2=1.96 (using normal distribution table)
Solving for n using formula of margin of error.
[tex]n=(z/2ST/Me)^{2}[/tex]
n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]
=96.4
By rounding off we will get 97.
Hence the sample size required will be 97.
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The given question is incomplete and the full question is as under:
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?
Which number has a repeating decimal form?
O A.
[tex] \sqrt{15} [/tex]
OB.
[tex] \frac{11}{25} [/tex]
O C.
[tex] \frac{3}{20} [/tex]
O D.
[tex] \frac{2}{6} [/tex]
Answer:
D. [tex] \frac{2}{6} [/tex]
Step-by-step explanation:
2÷ 6 = 0.33333
As you can see 3 is repeating.
Therefore [tex] \frac{2}{6} [/tex] as repeating decimal form.
Determine the inequality that can be used to model when the population of bacteria will be greater than or equal to 656,100. Then solve the inequality for t.
The inequality is 100*[tex]3^{t}[/tex]≤ 656100.
The correct option is (B).
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
From the table attached below:
a=300, r= 900/300 = 3
As, it is GP
Now,
f(t) = [tex]ar^{t-1}[/tex]
f(t) = [tex]300*3^{t-1}[/tex]
f(t) = 300/3 *[tex]3^{t}[/tex]
f(t) = 100*[tex]3^{t}[/tex]
Inequality is used to determine greater than or equal to 656100
100*[tex]3^{t}[/tex]≤ 656100
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Find the length of diagonal BC of ABCD to the nearest hundredth.
The length of BC as shown in the diagram is 6.32units
Calculating distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
Given the following coordinate points (3, 6) and (5, 0)
Substitute
BC = √(0-6)²+(5-3)²
BC = √(36+4)
BC = √40
BC = 6.32 units
Hence the length of BC as shown in the diagram is 6.32units
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Which form of controls are effective in eliminating, reducing, or minimizing hazards, which eventually help in reducing or even eliminating the need for ppe?.
The form of controls that are effective in eliminating, reducing, or minimizing hazards is called; Engineering controls
What are engineering controls?Engineering controls are defined as strategies that are designed to protect workers from hazardous conditions by placing a barrier between the worker and the hazard or by removing a hazardous substance through air ventilation.
Now, the reason why this is effective in eliminating, reducing, or minimizing hazards is because they are designed to remove the hazard at the source, before it comes in contact with the worker.
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Which table correctly identifies the sample space of spinning the spinner and then selecting a card?
The table that correctly identifies the sample of spinning the spinner and then selecting a card is Option A.
What is a sample?A sample is a random element that belongs to a population. Another way to state it is that, it is a set of all the outcomes that are possible from a given set of events.
What is the explanation for the above?Table A accurately depicts each potential result. Along the column on the left is where you'll see the card outcomes.
The spinner's output is shown along the top row. The intersection of the left and top results appears in each cell.
For instance, row 1, and column 3 include "red, purple" to show that you received a card with the color "purple" and the color "red" on the spinner.
The labels on each cell in table A are accurate. At least one cell in the other tables (B, C, and D) contains an incorrect label.Table B's middle cell in the top row reads "blue, green" when it should read "blue, purple."Table C's upper left corner reads "green, green" when it should be "green, purple."In the bottom middle cell of Table D, "blue, blue" appears where "blue, green" should. Since there isn't a blue card, it is impossible to say "blue, blue."We can rule out options B through D using the three things outlined above.Learn more about samples at;
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f(x) = 3x + 2
g(x) = x^2 + 1
find gf(x) in the form ax^2 + bx + c
please add an explanation because i’ve seen it being solved i just do not understand some steps
like, where does 12x come from
Answer:
g(f(x)) = 9x² + 12x + 5
Step-by-step explanation:
g(f(x))
= g(3x + 2) ← substitute x = 3x + 2 into g(x)
= (3x + 2)² + 1
to expand (3x + 2)² = (3x + 2)(3x + 2)
each term in the second factor is multiplied by each term in the first factor
3x(3x + 2) + 2(3x + 2) ← distribute both parenthesis
= 9x² + 6x + 6x + 4 ← collect like terms
= 9x² + 12x + 4
then
g(f(x)) = (3x + 2)² + 1 = 9x² + 12x + 4 + 1 = 9x² + 12x + 5
Describe all of the transformations occurring as the parent function f(x) = x^3 is transformed into g(x) = -0.5(3(x+4))^3 -8
Step-by-step explanation:
The translations of the typical functions are
[tex]y = a(bx + c) + d[/tex]
Where a is the vertical translation,
If a is greater than 1 or less than -1, we have a vertical stretch
If a is between -1 and 1 , we have a vertical compressions or shrink.
If a is negative, we have a negative reflection across the x axis.
If b is greater than 1 or less than -1, we have a horizontal compression or shrink
If b is between -1 and 1, we have a horizontal stretch
If b is negative, we have a reflection about the y axis,
If c is negative, we have a translation to the right c units
If c is positive, we have a translation to the left c units
If d is positive, we have a translation upward d units
If d is negative, we have a translation downward d units.
Here in this problem, our parent function is x^3.
So I would do the following transformations.
Reflect about the x axis Vertical Shrink by a factor of 1/2Horizontal Shrink by a factor of 3Shift to the left 4 unitsShift downward 8 units.PLEASE ANSWER ASAP!!!!!!!!
Consider △ABC, where a = 8, c = 11, and m∠C=33∘.
What are the measures of the missing angles and missing side?
Enter your answer by filling in the boxes. Enter all values rounded to the nearest tenth.
m
m
b=
The missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.
What is a Triangle ?Triangle is a polygon with three sides , three angles and three vertices.
Given is triangle ABC , with sides a = 8, c = 11, and m∠C=33 degree
The missing angle and side is given by Cosine rule of triangle
c² = a² + b² - 2ab cosC
11² = 8² + b² - 2* 8 * b * cos 33
57 = b² -13.42 b
b² -13.42b -57 = 0
b = 16.8
By sine rule
a / sin A = b/sin B = c/sinC
8 / sin A = 11 / sin 33
A = 23.33 degree
Similarly
B = 123.7 degree
Therefore the missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.
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In parallelogram WXYZ, with diagonal XZ, m∠WXZ = 81° and m∠WZX = 28°. What is the measure of ∠XYZ?
A.
62°
B.
90°
C.
71°
D.
109°
The measure of angle XYZ in the parallelogram is: 71°.
What are the Opposite Angles of a Parallelogram?In a parallelogram, the angles that are opposite each other are congruent.
Find m∠XWZ using the triangle sum theorem:
m∠XWZ = 180 - m∠WXZ - m∠WZX
m∠XWZ = 180 - 81 - 28
m∠XWZ = 71°
m∠XWZ = m∠XYZ [opposite angles are congruent]
m∠XYZ = 71°
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Answer:
71°
Step-by-step explanation:
I got it right on Edmentum
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3x-1=2(x+34) in inches=feet. inches
Answer:
-69
Step-by-step explanation:
inches:-69
-5 9/12 (-5 3/4 clearer) feet
Explanation in detail:
Write the equation down and distribute it.
3x - 1 = 2(x + 34)
3x - 1 = 2x + 68
Remove the variable on one side first (it makes solving the equation less complicated.)
3x - 1 = 2x + 68
-3x -3x
-1 = -x + 68
On all sides, subtract 68.
-1 = -x + 68
-68 -68
-69 = x
I'm guessing the answer in feet and inches is...
inches:-69
-5 9/12 (-5 3/4 simplified) feet
Which of the following is equivalent to the
complex number ;³¹?
Choose 1 answer:
A
B
C
D
1
i
-1
-i
Step-by-step explanation:
[tex] = {i}^{31} [/tex]
[tex] = {i}^{28} \times {i}^{3} [/tex]
[tex] = {( {i}^{4} )}^{7} \times ( {i}^{2} \times i)[/tex]
[tex] = ( {i}^{2} \times {i}^{2} ) {}^{7} \times {i}^{2} \times i[/tex]
[tex] = ( - 1 \times ( - 1)) {}^{7} \times ( - 1) \times i[/tex]
[tex] = {1}^{7} \times ( - i)[/tex]
[tex] = 1 \times ( - i)[/tex]
[tex] = - i[/tex]
The answer is D.
The probability distribution for a
random variable x is given in the table.
-10
-5
15
20
Probability
.20
15
.05
.15
Find the probability that x ≥ 5
Answer:
Step-by-step explanation:
Comment
There is only 1 number under probability that is greater than or equal to 5. That number is 15
There are 4 possible answers. Only 1 is successful.
Answer: P(y≥5) = 1/4 or 0.25
PLEASE HELP MULTIPLE CHOICE (photo of question attached) WILL GIVE BRAINLEIST!
The triangles on the grid below represent a translation.
To form the image, the pre-image moved
a. five units right and three units up.
b. two units right and three units up.
c. five units left and three units down.
d. two units left and three units down.
Answer:
A five units right and three units up
Step-by-step explanation:
take coordinate C for example and count how many spaces you need to go either right or left and then up and down for the two triangles to be in the same place
PLEASE HELP ME WITH THIS
Answer:
Vertex
Vertex are the end points of parabola where it opens up
locus are the group of points
latus rectum is the line parallel to it .
Drag each tile to the correct location. The labels can be used more than once.
Match each polynomial expression with its degree.
0, 1, 2
The degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.
What is the degree of a polynomial?
The degree of the polynomial is defined as the highest power of the variable of the given polynomial or it is the maximum power of the polynomial.
The degree of the given expressions are shown as follows:-
(x-9) → degree 1,
(-4x²-6x+9) → degree 2,
(x²-2x+9) → degree 2,
(-3) → degree 0,
(3x-2) → degree 1,
(6x+2) → degree 1
(5) → degree 0.
Therefore the degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.
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