i
Step-by-step explanation:
i
Example 1.29 Initially, a box contains three white and five red balls. Balls
are drawn at random from the box. Whenever a red ball is drawn, it is placed
back into the box together with one extra red ball. Whenever a white ball is
drawn, it is placed back into the box together with two extra white balls. What
is the probability that the first three balls are drawn out of the box alternated
in colour?
Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:
[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].
0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
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Use the graphing calculator to graph the function f(x)=√x Which list contains three points that lie on the graph of
the function?
0(83) (42) (-11)
O (11 (42) (9. 3)
Answer:
The last option that starts with (1,-1)
HELP IM TIMED!!!!
X
-2
-1
0
1
2
3
f(x)
20
0
-6
-4
0
0
Which is an x-intercept of the continuous function in the
table?
O (-1,0)
O (0, -6)
O (-6,0)
O
(0, -1)
3/5x + 3 = 6 whats is x?
Answer:
X = 3/53/5x + 3 = 6
3/5x = 6 - 5
3/5x = 1
Multiplying both the sides with 5x3/5x (5x) = 1* 5x
3 = 5x
3/5 = X
It took for 4 butterflies to give birth to 4 larvae. how many larvae would 12 butterflies give birth to in 12 days
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae
Hence for 12 butterflies in 12 days:
number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
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Can you translate that into slope intercept form
Answer:
y = (5/3)x + 4
Step-by-step explanation:
The general equation for slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.
slope (m) = 5/3
y-intercept (b) = 4
y = mx + b
y = (5/3)x + 4
Cheryl mixes 350ml of cranberry juice with 2 litres of blueberry juice. Write the ratio of cranberry juice: blueberry juice in its simplest form. Find the ratio of 2/5 h to 250 S.
cranberry juice = 350 ml
blueberry juice = 2 liters = 2000 ml
Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40
The simplest ratio is 7 : 40 or 7/40
The difference of the product of 3 and 6 minus the quotant of 6 / 2
Answer:
Answer:
(3*6) - (6/2) = 15
Step-by-step explanation:
3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.
The answer of the equation is 15.
Susan makes purple paint by mixing red and blue paint in the ratio 2:3
She has 12ml of red and 15ml of blue
What is the maximum amount of purple she can make?
A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,
Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint
If Susan wants to use the complete blue paint then,
Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint
As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.
Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,
Total Paint = 10ml + 15ml = 25ml
Hence, the maximum amount of purple that Susan can make is 25 ml.
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anwer this question with full method please
Step-by-step explanation:
Let simplify the identity
[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]
[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]
Combine Like Fractions
[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]
Multiply by reciprocals.
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]
Pythagorean Identity
[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]
Double Angle Identity
[tex] \frac{ \cos(2x) }{1} [/tex]
[tex] \cos(2x) [/tex]
Now, we need to find cos 2x. Given that we have tan x.
Note that
[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]
So let find cos x and tan x.
We know that
[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We know that
[tex] \tan(x) = \frac{o}{a} [/tex]
[tex] \sin(x) = \frac{o}{h} [/tex]
[tex] \cos(x) = \frac{a}{h} [/tex]
So naturally,
[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]
So we need to find the hypotenuse,
remember Pythagorean theorem.
[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]
Here o is 1
h is root of 5.
So
[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]
[tex] {h}^{2} = 1 + 5[/tex]
[tex] {h}^{2} = 6[/tex]
[tex]h = \sqrt{6} [/tex]
Now, we know h, let plug in to find sin x and cos x.
[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]
[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]
Let's find these values squared
[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]
[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]
Finally, use the trig identity
[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]
So part I.= 2/3
ii. Use the definition of sine and cosine and Pythagorean theorem
Let sin x= o/h
Let cos x= a/h.
So
sin x squared is
[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]
[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]
By definition,
[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]
[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]
Remember that
[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]
So
[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]
[tex]1 = 1[/tex]
Cate solved an inequality to find c, the possible number of cats that a shelter can house. She found that c < 28. Which statement best describes a possible solution to Cate’s problem?
The shelter can house 15.6 cats because 15.6 < 28.
The shelter can house –8 cats because –8 < 28.
The shelter can house 17 cats because 17 < 28.
The shelter can house 28 cats because 28 < 28.
Answer:
The shelter can house 17 cats because
17 < 28.
Step-by-step explanation:
We cannot have fractions of cats, and we cannot have a negative number of cats. So the third statement is reasonable because c < 28.
9(x - 11) = 9 what is x
Answer:
x=12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
12-1 is 11 and than 9 times 1 is 9
Glass bottles are redeemed for 50 cents each. Plastic bottles are redeemed for 25 cents each and aluminum cans are .75 cents each. At the end of the event the collected a total of 35 glass bottles 50 plastic bottles and 22 aluminum cans. If there goal was $50 did they make enough money to save the condors
Answer:
no they did not make enough money
Step-by-step explanation:
Glass: 35 ×0.50 = 17.5
plastic: 50 × 0.25 = 12.5
aluminum: 22 × 0.75 = 16.5
17.5 + 12.5 + 16.5 = $46.5
Solve for x.
log x = 3
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 1000}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{log(x) = 3}[/tex]
Find: [tex]\textsf{The value of x}[/tex]
Solution: In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base. When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.
Get rid of log
[tex]10^{\textsf{log}_{10}\textsf{(x)}}} = 10^{\textsf{3}}[/tex][tex]x = 10^{\textsf{3}}[/tex][tex]x = 1000[/tex]Therefore, the final answer would be that x is equal to 1000.
The semiperimeter is used to find the area of equilateral triangles only.
O False
O True
Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).
What is the semiperimeter?Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.
However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.
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A couple plans to have 4 children. The gender of each child is equally likely. Design a simulation involving 55 trials that you can use to model the genders of the children. Write your answer as number
Answer:
4x55x2
Step-by-step explanation:
4 kids 55trys 50 50 odds
on a number line point D is at -6 and point E is at 8 point F lies between points D and E if DF:FE is 3:1 where does point F lie on the number line
The point F lies on 4.5 in the number line.
Number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.
Here in the give problem that,
Point D lies on -6 in number line
Point E lies on 8 in number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence the point F lies on 4.5 in the number line.
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Answer: 4.5
Step-by-step explanation:
(MARKING BRAINLIEST TO FIRST CORRECT ANSWER!) Which statement below is true?
A. All squares are rectangles because both are quadrilaterals, have 90 degree angles and the opposite sides are parallel.
B. All trapezoids are rectangles because the opposite sides are parallel.
C. All parallelograms are rhombus' because they have 4 congruent sides and the opposite sides are parallel.
D. All rectangles are trapezoids because all the sides are parallel.
Answer:
A. All squares are rectangles because both are quadrilaterals, have 90-degree angles and the opposite sides are parallel.
Step-by-step explanation:
This is the only true statement because all squares are rectangles just with equal sides, the angles will always be 90-degrees.
Hope this helps!
If not, I am sorry.
what is the value of each of these prefix expressions? * 3 3↑3 3 3 5
Answer:
big bodie built
Step-by-step explanation:
i used to be dusty
Based on the calculations, the value of the given prefix expression is equal to 2205.
What is preorder traversal?The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.
For the preorder traversal of this tree (T), we would start from the right most expression:
Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3
Prefix expression = * + 3 + 3 ↑ 3 6 3
Prefix expression = * + 3 + 3 3⁶ 3
Prefix expression = * + 3 3 729 3
Prefix expression = * + 3 732 3
Prefix expression = * 735 3 ⇒ 735 × 3
Value = 2205.
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Complete Question:
Given the following prefix expression:
* + 3 + 3 ↑ 3 + 3 3 3
What is the value of the prefix expression?
Given: Lines p and q are parallel and r is a transversal.
Prove: ∠2 ≅ ∠7
Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7.
A 2-column table with 4 rows. Column 1 is labeled statements with the entries p is parallel to q and r is a transversal, A, B, angle 2 is congruent to angle 7. Column 2 is labeled reasons with the entries given, vertical angles are congruent, correlated angle theorem, transitive property.
Which statements could complete the proof?
A:
B:
The statements that would complete the proof where ∠2 ≅ ∠7 by the transitive property are:
∠2 ≅ ∠3
∠3 ≅ ∠7
What is the Transitive Property?The transitive property states that if x = y, and y = z, then x = z.
From the image given below, we have:
∠2 ≅ ∠3 because they are vertical angles which must be congruent.
∠3 ≅ ∠7 because corresponding angles are congruent.
Applying the transitive property, we can state that: ∠2 ≅ ∠7.
Therefore, the statements that would complete the proof are:
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william used 15 cm of tape to wrap 3 presents, Find the length of tape to wrap for 1 present?
Find the length of segment AC if AB = 7.8 cm and BC = 25 mm. How many solutions are there in each case? Point B lies on line AC .
Answer:
103mm or 53mm
Step-by-step explanation:
--A------B------C--
AB=78mm BC=25mm AC=AB+BC=103mm
--A----C---B---
AB=78mm BC=25mm AC=AB-BC=53mm
-B---A---C-
is impossible because BA<BC but 78mm>25mm
Nitrogen and oxygen are the most abundant gases in Earth’s atmosphere. A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
Which statements describe writing 0.00000000003 in scientific notation?
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
The complete question is
Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.
A.The exponent is negative.
B. The exponent is positive.
C.The coefficient is 0.3.
D.The exponent represents the number of places the decimal moves.
E.The decimal moves to the right.
What is meaning of Scientific Notation ?Scientific Notation means writing a decimal number in the form of 10ˣ .
It is given that
A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.
= 3 × 10⁻¹¹
(scientific notation)
The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.
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Which term best describes the horizontal cross-sections of an oblique cone?
O A. Congruent discs
OB. Similar discs
OC. Similar polygons
O D. Congruent polygons
Answer:
B. Similar discs
Step-by-step explanation:
Definitions
Cone: A three-dimensional solid figure that has a circle at one end (the "base"), a point at the other end (the [tex]\sf a\:\!pex[/tex]), and a curved side.
Right Cone: A cone where the [tex]\sf a\:\!pex[/tex] is aligned on the center of the base.
Oblique Cone: A cone where the [tex]\sf a\:\!pex[/tex] is not centered over the base.
Horizontal Cross-section: The intersecting plane parallel to the base of the solid figure.
Congruent: The same shape and size.
Similar: When one shape can become the other after being resized, reflected, translated or rotated.
Disc: The region in a plane bounded by a circle.
Polygon: A two-dimensional closed shape with a minimum of 3 straight sides.
Therefore, the horizontal cross-sections of an oblique cone are similar discs.
Which of the following did you include in your response? Check all of the boxes that apply. the range, or spread, of the salaries whether most people make a very low salary and one or two people make a high salary the minimum salary, and whether that is an entry level or starting salary the maximum salary whether the maximum salary is a lot higher than the average and other salaries are a lot lower than the mean
Answer:
to be honest i don't know
Step-by-step explanation:
uh
Answer: its all
Step-by-step explanation:
it does not matter which one you pic, you just have to pick one.
what is the slope of the line that passes through the points (-9,0) and (-17 , 0 )
Answer:
[tex]\mathrm{Slope=== > 0}[/tex]
Step-by-step explanation:
Hi student, let me help you out!
.............................................................................................................
First, let's recall the slope formula: [tex]\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}[/tex], where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.
Plugin the values: [tex]\mathrm{\cfrac{0-0}{-17-(-9)}}[/tex].
Upon simplifying, we obtain [tex]\mathrm{\cfrac{0}{-17+9}}[/tex].
Upon simplifying this further, we obtain [tex]\mathrm{\cfrac{0}{-9}}[/tex].
0 divided by anything results in 0.
✨ ∴, the slope of this particular line is 0, and this line looks something like this: [tex]\rule{200}{1}[/tex].
See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.
Hope this helped you out! Ask in comments if even the slightest queries arise.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
0.39 recurring as a fraction please [ 3 and 9 are both recurring]
Answer:
[tex]\frac{13}{33}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.3939.... (1) ← multiply both sides by 100
100x = 39.3939... (2)
subtract (1) from (2) thus eliminating the repeating digits
99x = 39 ( divide both sides by 99 )
x = [tex]\frac{39}{99}[/tex] = [tex]\frac{13}{33}[/tex] ← in simplest form
Step-by-step explanation:
0.39 repeating as a fraction
= 13/33
Which expression is the simplest form of - (4x³ + x²) + 2 (x³ - 3x²)?
OA.-223-5x²
B. -6x³6x²
OC.-6x³2x²
OD. -2x³-7x²
SUBMIT
Answer:
-2x³ - 7x².
Step-by-step explanation:
- (4x³ + x²) + 2(x³ - 3x²)
= - 4x³ - x² + 2x³ - 6x² Simplifying like terms:
= -2x³ - 7x².
Which expression represents the product of negative three-fourths x and –8x? negative 35 over 4 x 6x negative 35 over 4 x squared 6x2
The expression that represents the product of negative three-fourths x and –8x is 6x^2
How to determine the equivalent expression?The statement is given as:
the product of negative three-fourths x and –8x
Rewrite properly as:
-3x/4 * -8x
Divide 4 and 8 by 4
-3x * -2x
Multiply -3 and -2
6x * x
Multiply x and x
6x^2
Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2
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Answer:
answer is 6x2 or D
Step-by-step explanation:
What is the missing reason in the proof? (Reason 9)
Answer:
transitive property
Step-by-step explanation:
Generally proofs flow naturally from one step to the next. Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.
From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]
For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]
What changed between line 8 and 9? The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.
So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?
Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].
The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).
Recall that the transitive property states:
[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
There are three parts,
1. the first part needs a=b
2. the second part needs b=c
3. the third part produces a=c
Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.
Statement 8 is like the second part, and statement 9 is like the third part.
Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:
Original transitive property: [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]
Updated transitive property: [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]
In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true. The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.
