Answer:
Step-by-step explanation:
Total number of marbles = 5 + 2 + 3 = 10
Probability of choosing 1 green marble = 2/10
Probability of choosing 1 yellow marble = 3/10
Notice (and this is important) that the denominator didn't change. Why?
Because you replaced the first marble into the bag. That word replacement is critical in a problem of this nature. There is the term non replacement which means that the second draw would have a denominator of 9.
So what is the probability of P(green then yellow)?
P(green then yellow) = 3/10 * 2/10 = 6/100
Answer: P(green then yellow) = 3/50 because 6 / 100 reduces.
Solve : 4-3sec²A = 0
Answer:
[tex]\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]4 - 3 \sec ^ { 2 } \theta = 0[/tex]
Let's solve this.
Isolate sec²θ.
[tex]4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}[/tex]
Now, we now that, cos θ is the reciprocal of sec θ. Therefore,
[tex]\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}[/tex]
Bring the square root on both the sides of the equation to remove the square.
[tex]\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}[/tex]
If,
[tex]\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
Also if,
[tex]\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Which algebraic expression is equivalent to the expression below? 12(5 + 3x) + 18
A.
36x - 78
B.
3x + 78
C.
36x + 78
D.
36x + 42
Step-by-step explanation:
12(5 + 3x) + 18
60+36x+18
C)36x+78
2. 3x = 18 then the value of x is
Answer:
x=6
Step-by-step explanation:
(I don't know if you mean question 2 3x= 18 or 2 times 3x = 18)
2.3x = 18
3x = 18 / 2 = 9
x = 9/3 = 3
Or : x = 18/3 = 6
Joe ran 5/6 mile each day for 5 days. How far did joe run?
Simplify 5^3/5^7 leaving your anwser in index form help!!!!!!!!
Answer:
0.0016
Step-by-step explanation:
Hope this helps!
The graph below represents which system of inequalities?
Oy> 2x - 3
y>-X-3
Oy < 2x - 2
Y-3
Oys 2x - 2
Y EX
None of the above
Answer:
Third option
Step-by-step explanation:
The y-intercepts are -2 and 3 so first option is wrong
One is dashed line and other is solid so one needs to have equal and other one shouldn't, so second option is wrong as both are less than but not also equal
Third option the -2 intercept one is less than or equal to And the slope is positive while the 3 intercept one is greater with negative slope.
The given graph represents the system of inequalities in the third option y ≤ 2x - 2 and y > -x + 3.
It is clear from the graph that one of the inequality has a solid graph line while other has a dotted graph line.
So one of the inequality must be of the form ≤ or ≥ and the other one is of the form < or >.
The only inequalities of this form in the options are,
y ≤ 2x - 2
y > -x + 3
Consider y = 2x - 2.
The points through the line are (0, -2), (1, 0), (2, 2), ...
At origin, (0, 0), 0 ≤ -2 is false. So (0, 0) does not include in the solution region.
So the solution region of y ≤ 2x - 2 is on the part of the line of y = 2x - 2 where (0, 0) is not included.
Consider y = -x + 3
Line passes through (0, 3), (1, 2), (2, 1), (3, 0),....
At (0, 0), 0 > 3, which is false.
So the solution region of y > -x + 3 does not contain the part where (0, 0) is included.
So the resulting graph is correct for this system of inequalities.
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Jordan wants to put wire fence around each of his tomato plants. He has a partial roll of fencing which is 18 1/6 feet long. How many tomato plants will Jordan be able to put a fence around using this roll if each plant requires exactly 2 2/3 feet of fencing.
Answer:
6 tomato plants
Step-by-step explanation:
[tex]18\frac{1}{6}= \frac{18\times6+1}{6}=\frac{108+1}{6}= \frac{109}{6}[/tex]
[tex]2\frac{2}{3}= \frac{2\times3+2}{3}=\frac{6+2}{3}= \frac{8}{3}[/tex]
then the number of tomato plants that Jordan will be able to put a fence around using this roll :
[tex]\frac{\frac{109}{6}}{\frac{8}{3}}= \frac{109}{6}}\times\frac{3}{8} = \frac{109}{2}}\times\frac{1}{8}= \frac{109}{16} = 6.8125[/tex]
then he can put fence only around 6 plants.
What is the value of x in the matrix equation below?
Answer:
-3
Step-by-step explanation:
Help immediate!! Find the value of
x
xx in the triangle shown below.
x
=
x=x, equals
∘
∘
degrees
Find a radius of a circle the length of which is 24π cm.
Answer:
12
Step-by-step explanation:
Length of a circle = circumference = 2πr = 24π
Radius (r) = 24π/2π
= 12cm
Please help me pleasee
Answer:
x = y = 64° , z = 20°
Step-by-step explanation:
x = y = [tex]\frac{180-52}{2}[/tex] = 64 °
m∠ADC = 52° + x
m∠ADC = 52° + 64° = 116°
z = 180° - 116° - 44° = 20 °
A 45-foot tall tree is leaning towards a house, making an 86° angle with the ground. To stop the tree from leaning further, a cable is tied from the top of he tree and secured to a point on the ground 30 feet from the tree, opposite from the house. What angle does the cable make with the ground?
The angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]
(c is opposite side to angle A)
Consider the diagram attached below.
In the diagram given, we have:
AB = tree with length of 45 ft
AC = cable, with length of 'x' ft (assume)
BC = distance of the base of the cable from the base of the tree of measurement 30 ft.
AD = vertical height of the point A (the top of the tree and cable) from the ground of 'h ft' (assume),
Using the cosine rule for the triangle ABC, taking:
|AC| = x = length of the side opposite to the known angle
|AB| = 45 ft and BC = 30 ft are rest of the two sides,
Angle opposite to AC is of 86°
Thus, we get:
[tex]45^2 + 30^2 -2(30)(45)\cos(86^\circ) = x^2\\\\2925 - 188.34 \approx x^2\\\\x \approx \sqrt{2736.66} \approx 52.31 \: \rm ft[/tex]
(took positive root because of x being length, which is a non-negative quantity).
For triangle ABD, using the sine ratio from the perspective of angle A, we get:
[tex]\sin(m\angle A) = \dfrac{\text{side opposite to A}}{\text{length of hypotenuse}} \\\\\sin(86^\circ) = \dfrac{h}{45}\\\\h = \sin(86^\circ) \times 45 \approx 44.89 \: \rm ft[/tex]
Now, for the triangle ACD, using the sine ratio from the perspective of angle C (smaller than 90°), we get:
[tex]\sin(m\angle C) = \dfrac{\text{side opposite to C}}{\text{length of hypotenuse}} \\\\\sin(\theta^\circ) = \dfrac{h}{x} \approx \dfrac{44.89}{52.31} \approx 0.858\\\\\theta =\sin^{-1}(0.858) \approx 59.09, 120.90[/tex]
Taking the angle smaller than 90°, we get:
[tex]\theta \approx 59.09^\circ \approx 59^\circ[/tex]
Thus, the angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.
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Answer:
That wasn't the correct answer
Step-by-step explanation:
c^2=45^2+30^2 - 2(45)(30)*Cos(94
c^2=2925+188.3425
c^2=3113.3425
take the square root:
c is approx. 55.8
sin86/55.8=sinx/45
55.8sinx=45sin94
divide both sides by 55.8
sinx=0.8045
sin^-1(0.8045)=53.6
Answer is 53.6 or "L" on the scavenger hunt worksheet
Phone numbers consist of a three-digit area code followed by seven digits. if the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? how did you come up with your answer? a. 8 times 10 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 6,400,000,000 b. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000 c. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 = 128,000,000 d. 8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 times 10 = 12,800,000,000
The possible number of different phone numbers will be 128000000
What is probabilty?
The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
In this exercise we have to use the knowledge of probability to find the phone number, so:
1 280 000 000 different ways.
First we have to establish some information about this exercise such as:
The first slot cannot start with 0 or 1, which leaves us 2, 3, 4 ..., 9 to fill.This means we have 8 different arrangements for the first slot.The second slot have a 0 or 1 for the second digit, which leaves us with 2 different arrangements.There are no restrictions for the third slot, so we would have 10 different arrangements.Thus, now calculating the possibilities of occurrence, we have:
[tex]8\times 2\times 10=160[/tex]
[tex]8\times 10^6=8000000[/tex]
[tex]160\times 8000000=1280000000[/tex]
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What is the general equation of a sine function with an amplitude of 6, a period of startfraction pi over 4 endfraction, and a horizontal shift of startfraction pi over 2 endfraction?
Answer:
f(x) = 6·sin(8(x -π/2))
Step-by-step explanation:
A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...
f(x) = A·sin(2π/P(x -S))
__
The equation for A=6, P=π/4, and S=π/2 is then ...
f(x) = 6·sin(8(x -π/2))
_____
Additional comment
The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.
pls help
Is this triangle acute, right or obtuse?
Probably between obtuse angle or triangle because sometimes they trick you
But I'm not 100 percent sure
Answer:
It is right
Step-by-step explanation:
Right triangles will always form a corner like an L shape
A snack company can pack 12 granola bars in a box. How many boxes are needed for 600 granola bars?
A.5
B.720
C.50
D.7, 200
Answer:
The Answer is C. 50
Step-by-step explanation:
To pack 600 granola bars, 50 boxes are needed.
The correct option is C.
To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.
Number of boxes = Total granola bars / Granola bars per box
Number of boxes = 600 / 12
Number of boxes = 50
So, 50 boxes are needed to pack 600 granola bars.
The correct answer is option C: 50.
To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.
To learn more about the division;
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3/5x2/5x4/9 in simplest form
Answer:
8/75 is the answers for the question
Please help, right now!!!
Answer:
its B
Step-by-step explanation:
Answer:
the answer is B 1/50. I think
show work and do it fast
Answer:
9 x 2/8 = 9/4
Step-by-step explanation:
Answer:
Step-by-step explanation:
9 divided by 2/8 but make the 2/8 into a decimal and the turn back to a fraction if it ask if not then leave it how it is and if you have to round which you prolly wont have to but ask to make sure ight
Help me find the perimeter of the shape please!
Answer: 10m +27
Step-by-step explanation: Add all the sides together to calculate Perimeter.
2(2m +10)+2m+7+2m +2m
4m + 20 + 2m +7 +2m +2m
10m +27
Ariana is playing a game. For each of her turns, she rolls a number cube landed with the numbers 1 through 6. She also spins the spinner shown below. To win the game Ariana needs to roll a 3 and spin a 3 on her next turn. What is thr probability that Ariana will win the game on her next turn?
Answer:
1/18
Step-by-step explanation:
probability of getting a three= 1/6
probability of getting a three on a wheel=1/3
probability of winning= 1/6x1/3=1/18
The value of a car is $25,500. It loses 14% of its value every year.
What is the volume of the rectangular prism shown below?
A. 224 in³
B. 320 in³
C. 512 in³
D. 5,120 in³
Answer:
[tex]\boxed{\sf{5120\ in^3}}[/tex]Step-by-step explanation:
Solution:
Volume of the rectangular prism formula:
[tex]: \Longrightarrow \sf{V=l*w*h}[/tex]
Given:
Length: 32 inWidth: 10 inHeight: 16 inThen, you multiply.
[tex]\sf{32*10*16=\boxed{\sf{5120}}[/tex]
Therefore, the correct answer is "D. 5120 in³".Answer:
D
Step-by-step explanation:
B1 of a trapezoid in which Area = (48x+68) inch squared, Height = 8 in, B2 = (9x + 12) in.
what I have so far is
48x +68 = 8 (B1 + 9x +12)
what do I do from there????????????????? the question is asking to solve for Base 1/ B1
A=(1/2)(b1+b2)h =
=(48x+68)in² = (1/2)( b1+(9x+12))8
=b1= 3x+5
Which quadratic expression represents the product of these factors? (2x + 5)(7 − 4x)
A.
-8x2 + 6x − 35
B.
-8x2 − 6x + 35
C.
-8x2 − 34x + 35
D.
-8x2 + 34x − 35
Answer:
[tex] - 8x {}^{2} - 6x + 35 [/tex]
Step-by-step explanation:
(2x+5)(7-4x)
expanding
2x(7-4x)+5(8-4x)
removing brackets
2x×7+2x×-4x+5×7+5×-4x
14x-8x^2+35-20x
arranging properly
-8x^2-6x+35
Angle 1 and 2 are complementary. Angle 1 is 28 degrees. what is the measure of angle 2?
Answer:
Step-by-step explanation:
Remark
All triangles are made up of 3 angles totally 180 degrees.
In addition a right triangle has a measurement of 90 degrees.
The other two angles must add to 90 degrees as will. That is the definition of complementary. (2 angles add to 90 degrees).
Formula
x + 28 = 90
Solution
x + 28 = 90 Subtract 28 from both sides.
x+28 -28=90 - 28
x = 62
The measure of the second angle is 62
What is the range of possible sizes for side xxx?
Answer:
2.3<x<8.7
Step-by-step explanation:
Alex for school I need help whoever helps first will get brainlyist
Answer:
wheres the question ?
Step-by-step explanation:
GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
Answer:
Step-by-step explanation:
In rectangle, the diagonals are equal bisect each other.
⇒ OA = OB
⇒ΔAOB is an isosceles triangle.
In ΔAOB,
x + x + 120 = 180°
2x + 120 = 180
2x = 180 -120
2x = 60
x = 30°
In ΔABD
∠A + ∠ABD ∠BDA = 180
90 + 30 + ∠BDA = 180
∠BDA = 180 - 90 -30 = 60°
ΔABD is 30 - 60 - 90 triangle.
The ratio of sides of 30-60-90 triangle is x : x√3 : 2x
x →shortest leg which is opposite ot 30°
∵ x = AD = 20
x√3 → longest leg which is opposite to 60°
x√3 ( AB) = 20*1.732
AB = 34.64
Area of rectangle = length * width
= 34.64 *20
= 692.8
≈ 693 square units
please helppppppppppppppp!!!!!!!!!!!!!!!!!!!!!11