answer with steps please
Answer:
Step-by-step explanation:
Answer: [tex]\frac{-70a^3-195^2-20a-78}{60}[/tex] or [tex]-\frac{7}{6} a^3-\frac{13}{4} a^2-\frac{1}{3} a-\frac{13}{10}[/tex]
When we say subtract this from that, the value or word after from is the one which is ahead of the equation. For example, subtract 9 from 10, then the expression will be 10-9 . [Answer is 1]
The expression that can be formed from the picture is and the solution is shown in the steps below.
[tex](\frac{a^3}{3} -\frac{3a^2}{4} -\frac{5}{2}) - (\frac{5a^2}{2} +\frac{3a^3}{2} +\frac{a}{3} -\frac{6}{5} )[/tex] [Formed the expression]
[tex]\frac{a^3}{3} -\frac{3a^2}{4} -\frac{5}{2} - \frac{5a^2}{2} -\frac{3a^3}{2} -\frac{a}{3} +\frac{6}{5}[/tex] [Removed the brackets]
[tex]\frac{a^3-a}{3} +\frac{6}{5} -\frac{3a^2}{4} +\frac{-5a^2-3a^3-5}{2}[/tex] [Brought common denominators together]
[tex]\frac{20(a^3-a)}{60} +\frac{6*12}{60} -\frac{15(3a^2)}{60} +\frac{30(-5a^2-3a^3-5)}{60}[/tex] [LCM of 3,5,4 and 2]
[tex]\frac{20a^3-20a+72-45a^2-150a^2-90a^3-150}{60}[/tex] [Multiplied the numerators]
[tex]\frac{-70a^3-195^2-20a-78}{60}[/tex] [simplified]
[tex]-\frac{7}{6} a^3-\frac{13}{4} a^2-\frac{1}{3} a-\frac{13}{10}[/tex] [More simplified]
I tried my best to show my steps and solve it. Thank you.
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Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study
a) If μ₁ is the average learning rate of the 6th graders without background noise level and μ₂ is the average learning rate of the 6th graders with the background noise level
The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.
The null hypothesis, H₀: μ₁ = μ₂
b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.
An alternative hypothesis, Hа: μ₁ ≠ μ₂
c) Assumptions that must be met about the data before she can correctly use an independent t-test
There must be a random selection of the 6th graders
That the two groups are normally similar in their learning abilities
The division of students into the two groups should be at random
d) She has to make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.
She can still get accurate results if she includes some bias in the selection to prove a particular result.
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The table and Circle Chart display proportions of the expenditure of a local government. Which statement describes how the Circle Chart misrepresents the data?
A. The sum of the percentages in the sections is not 100.
B. The size of each section does not correspond to the percent expenditure for each category given in the table.
C. One of the categories in the table is not represented in the circle chart.
D. The size of the section representing highways is greater than the size of the section representing education.
This exercise refers to the identification of statistics that is misleading or erroneous. In this case, a circle graph and a table are involved.
What is a circle graph?A circle graph is simply a pie chart. It is used to depict information in percentages. An example is attached.
Although charts and tables are very useful descriptive and or illustrative statistics, they can be misleading.
This can happen when:
The sum of the percentages in the sections is not 100;The size of each section does not correspond to the percent expenditure for each category given in the table; andOne of the categories in the table is not represented in the circle chart.This answer is general in nature due to the limited information provided.
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Answer:
C
Step-by-step explanation:
The fit line equation for the scatterplot is y = -2.61x+152.51, where x is variable 1 and y is variable 2. according to the equation, what is the expected value of y when x-value is 45?
The expected value of y when x-value is 45 is 35.06
Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. For example, y = 2x+3 and 2y = 4x + 9 are two-variable linear equations.
In the given question value of x is given and value of y is asked.
The given equation : y = -2.61x+152.51 Such questions can be solved by substituting the given value of variable in the equation which will help us find the unknown.
Substituting x = 45 in the given equation , we get
y = -2.61 x 45 + 152.51
y = -117.45 + 152.51
y = 35.06
Thus the expected value of y when x-value is 45 is 35.06
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Let g(x) = f(x+3) for some function f(x). Is g(x) a function? From the previous problem, let the domain of f(x) be [1, 4). What is the domain of g(x)?
The domain of g(x) is [4, 7)
How to determine the domain of g(x)?The function is given as:
g(x) = f(x + 3)
Since f(x) is a function, then g(x) is also a function
The domain of f(x) is given as:
[1, 4)
The equivalent of these values in g(x) are
x = 1 + 3 = 4
x = 4 + 3 = 7
Hence, the domain of g(x) is [4, 7)
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Writing Exercises
587. When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?
Answer:
Therefore, we can say that the exponent will be negative if the number is less than 1 and vice versa.
Step-by-step explanation:
We are asked to explain that when we convert a decimal number to scientific notation how will we know whether the exponent is negative.
If the given number is greater than 1 then the exponent is positive and if less than 1 the exponent is negative.
1. How could you figure out the coordinates of a reflection over the x-axis? What would the coordinates of that reflected point be?
2. Then also tell how you could determine the coordinates when (-8,2) is reflected over the y-axis, and tell the coordinates of that new point.
The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).
If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The reflection of a point over the x axis is given by the equation (x, y) ⇒ (x, -y).
If the point (-8,2) is reflected over the y-axis, the new point would be (8, 2)
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Pete drive 50 miles in 4 hours work out his average speed in miles per hour
Answer:
Pete's average speed is 12.5 miles per hour
Step-by-step explanation:
Miles per hour means how many miles were driven in 1 hour so :
50 miles in 4 hours = ? miles in 1 hour
4 ÷ x = 1
4/x = 1
x = 4
50÷4 = ?
50/4 = ?
? = 12.5
Pete's average speed is 12.5 miles per hour
Hope this helped and have a good day
In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz? m∠x m∠z < 90° m∠y > 90° ∠x and∠y are complementary m∠x m∠y < 90°
m∠X + m∠Y < 90° is true.
How to solve it?XYZ is a triangle.
We have to find the option that is true about △XYZ.
By angle sum property of a triangle,
The sum of all the interior angles of a triangle is always equal to 180°.
So, ∠X + ∠Y + ∠Z = 180°
Given, m∠Z > m∠X + m∠Y.
This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.
so, ∠X + ∠Y must be less than 90°.
Hence, we can say that ∠X + ∠Y < 90°
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Answer: Option 4 or D. m∠x + m∠y∠90°
Step-by-step explanation: Trust Me! It is correct on Edge!
Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?
A: D. m∠x + m∠y∠90°
An approximate solution to an equation is found using this iterative process.
(x₂)³-1
and x₁ = -1
4
Xn+1 =
4/34
a) (i) Work out the value of x₂
(ii) Work out the value of x3
b) Work out the solution to 6 decimal places.
Answer:
a) i) -0.5
ii) -0.28125
b) -0.254102 (6 d.p.)
Step-by-step explanation:
Given iteration formula:
[tex]x_{n+1}=\dfrac{\left(x_n\right)^3-1}{4} \quad \textsf{and} \quad x_1=-1[/tex]
Part (a)(i)
Substitute the value of x₁ into the formula and solve for x₂ :
[tex]\begin{aligned}\implies x_2 & =\dfrac{\left(x_1\right)^3-1}{4}\\\\& =\dfrac{\left(-1\right)^3-1}{4}\\\\ & = \dfrac{-1-1}{4}\\\\ & = \dfrac{-2}{4}\\\\ & = -0.5\end{aligned}[/tex]
Part (a)(ii)
Substitute the value of x₂ into the formula and solve for x₃ :
[tex]\begin{aligned}\implies x_3 & =\dfrac{\left(x_2\right)^3-1}{4}\\\\& =\dfrac{\left(-0.5\right)^3-1}{4}\\\\ & = \dfrac{-0.125-1}{4}\\\\ & = \dfrac{-1.125}{4}\\\\ & = -0.28125\end{aligned}[/tex]
Part (b)
To find the solution to 6 decimal places, keep substituting each new value into the iteration formula until the answers are the same when rounded to the required level of accuracy.
[tex]\implies x_4=-0.2555618286...[/tex]
[tex]\implies x_5=-0.2541728038...[/tex]
[tex]\implies x_6=-0.2541051331...[/tex]
[tex]\implies x_7=-0.2541018552...=-0.254102\:\: \sf (6 \:d.p.)[/tex]
[tex]\implies x_8=-0.2541016964...=-0.254102\:\: \sf (6 \:d.p.)[/tex]
[tex]\implies x_9=-0.2541016888...=-0.254102\:\: \sf (6 \:d.p.)[/tex]
Therefore, the solution is -0.254102 (6 d.p.).
[tex]x + 6 = 10 \\ x = 10 - 6[/tex]
simultaneous equations
Answer:
False.
These are not simultaneous equations.
Step-by-step explanation:
Simultaneous equations are equations involving two or more unknowns that are to have the same values in each equation. In the equations given there is only one unknown value.
HEEEELPPP MEEEEEEE FRRRRRR!!!!!!! 30POINTS!!!!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Circumference of a circle: }[/tex]
[tex]\bullet\ \large\boxed{\mathsf{2\pi r}}}\\\rightarrow\large\boxed{\textsf{Whereas, } \pi \large\textsf{ is your pi and it is approximately equal to 3.14}}\\\rightarrow\large\boxed{\textsf{ And \underline{r} is the radius of the circle.}}[/tex][tex]\huge\textbf{Area of a triangle:}[/tex]
[tex]\bullet\ \large\boxed{\mathsf{\dfrac{1}{2}bh}}\\\\\rightarrow\large\boxed{\textsf{Whereas, }\mathsf{\dfrac{1}{2}} \large\textsf{ is half your triangle, \underline{b} is your \underline{b}ase, and b is your \underline{h}eight}}[/tex]
[tex]\huge\textbf{Surface area of a rectangular prism: }[/tex]
[tex]\bullet \ \large\boxed{\textsf{2(wl + hl + hw)}}\\\rightarrow\large\boxed{\textsf{Whereas, l is your \underline{l}ength, h is your \underline{h}eight, and w is your \underline{w}idth.}}[/tex]
[tex]\huge\textbf{Volume of a rectangular prism:}[/tex]
[tex]\bullet\ \large\boxed{\textsf{whl = v}}\\\rightarrow\boxed{\large\textsf{Whereas, v is your \underline{v}olume, w is your \underline{w}idth, h is your \underline{h}eight, l is}}\\ \ \large\boxed{\textsf{your \underline{l}ength}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which statement about the function is true?
O The function is increasing for all real values of x
where
x<-4.
Answer:
A.) The function is increasing for all real values of x where x < -4
Step-by-step explanation:
On the interval x < -4, all of the x values are increasing. Before x = -4, the line assumes a positive slope because it is heading upwards. After this interval, the function is decreasing because the slope is heading downwards.
On the interval -6 < x < -2, all of the x values are positive because they lie above the x-axis. This does not necessarily mean that all of the values are increasing.
On the interval x < -6 and x > -2, all of the x values are negative because they lie below the x-axis.
how to find volume of a prism
Answer:
- HOW TO FIND VOLUME OF PRISM -
1st step - Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x 5 x side x apothem] x height of the prism.
2nd step - Find the area of the pentagonal base face. Let's say the length of a side is 6 cm and the length of the apothem is 7 cm.
3rd step - Find the height. Let's say the height of the shape is 10 cm.
4th step - Multiply the area of the pentagonal base face times the height. ...
and last step - State your answer in cubic units.
Step-by-step explanation:
:):):)
Explain why statistical acceptance sampling is not an effective method for monitoring process quality.
Acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.
a) Concerned with inspection of products
b) Concerned with decision making regarding products
c) One of the oldest aspects of quality assurance
The Acceptance sampling procedure is necessarily a lot sentencing procedure. It cannot be used to estimate the lot quality or lot conformity to the standard specifications.
The acceptance sampling is used when the test is destructive, or the cost of 100% inspection is quite high, or when we need a continuously monitoring program
The Acceptance sampling procedure is used for decision making of either acceptation or rejection of a lot. It can’t be used as a lot quality estimator
As Acceptance sampling is just a lot sentencing process, it can’t estimate the quality of products in the lot. But designed experiments ensure good quality of the process output before even production
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8 times the number is 200. What is 80 times the number?
Answer:
2,000
Step-by-step explanation:
⇒ 200/8 = 25
⇒ 25 * 80 = 2,000
Answer:
2000.
Step-by-step explanation:
8 * x = 200
x = 200/8
80x = 80 * 200/8
= 10 *200
= 2000.
please help me with this problem
Answer:
Answer is 544
Hope it helps you
A triangle is shown. One side has a length of 16, another side has a length of 20, and the length of the longest side is unknown.
Janice examines the given triangle and estimates that the longest side has a length of 25 units―if it is a right triangle. How does her estimate compare to the actual length?
It is exactly correct.
It is under by approximately 0.6 units.
It is over by approximately 0.6 units.
It is over by 13 units.
Janice estimate is under by approximately 0. 6 units. Option B
How to determine the estimateThe longest part is called the hypotenuse
The formula for finding the hypotenuse, we use the Pythagorean theorem
Hypotenuse = square root of both opposite square and adjacent square
We have that,
Hypotenuse = [tex]\sqrt{16^2 + 20^2}[/tex]
Hypotenuse = [tex]\sqrt{256+ 400}[/tex]
Hypotenuse = [tex]\sqrt{656}[/tex]
Find the square root
Hypotenuse = 25. 6
The length of the longest part = 25. 6
Janice estimated it to be 25
Comparing her estimate with the actual length = Actual length - estimate
⇒ 25. 6 - 25
⇒ 0. 6
Therefore, Janice estimate is under by approximately 0. 6 units. Option B
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Answer: B. It is under by approximately 0.6 units.
Step-by-step explanation: Just did it on edge 2023
Please help ill give whoever answers the best the brainliest answer :)))
Answer:
3rd graph from the top.
Step-by-step explanation:
It can't be the top one because the kids shoulder doesn't start at the ground.
It can't be the second or fourth because it shows him not waiting in line.
Therefore it must be the 3rd!
Answer: 3rd option
Step-by-step explanation:
Because the description says that it starts not at 0(from the kid's shoulder), the 1st and 4th options are out.
2nd option is incorrect because the kid had to stand in line so the shoulder height doesn't change(unless he was picking stuff up or something)
That leaves the 3rd option.
How is copying segment similar to copying an angle ?
Answer:
Copying a line segment or angle is an illustration of transformation. Both are similar, because they are both rigid transformation.
When an angle is copied to a new angle, the new angle and the old angle will have the same measure
Similarly;
When a line segment is copied to a new segment, the new line segment and the old line segment will have the same measure
This type of transformation is referred to as a rigid transformation.
Hence, copying a line segment is similar to copying an angle, because they are both rigid transformations
Step-by-step explanation:
Evaluate the function f(x) = − x² + 10x – 6 Find f( -5)
Answer:
f (-5) = -81
Step-by-step explanation:
f (-5) = - (-5)² + 10.(-5) - 6 = -81
30 points plus brainliest if answered right!
Answer:
The second choice.
Step-by-step explanation:
The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.
Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.
Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.
Therefore, we are left with the second option.
Answer:
AC = 5, BC = √17, AB = √32
Explanation:
Given points: A(-3, -2), B(1, 2), C(2, -2)
Use distance between two points formula:
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
AC length:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2} = \sqrt{25+ 0} = 5[/tex]
BC length:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]
AB length:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]
The numbering system we commonly use is called the decimal numbering system because it uses ____ symbols to represent all possible numbers.
The numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.
A way of writing numbers is known as a number system.
There are the following number systems:
Decimal number system: "Deci" meaning 10, implies that the number system consists of 10 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.Binary number system: "Bi" meaning 2, implies that the number system consists of 2digits or symbols, namely 0, and 1.Octal number system: "Oct" meaning 8, implies that the number system consists of 8 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, and 8.Hexa-Decimal number system: "Hexa-Deci" meaning 16, implies that the number system consists of 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.
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Line I is parallel to line M. If the measure of 6 is 75 degrees, what is the measure of 3?
(please look at photo attached)
In the given diagram, the measure of ∠3 will be 105°.
In the given diagram, ∠3 and ∠6 are consecutive interior angles.
How to form supplementary angles by transversal?If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
That is,
∠3 + ∠6 = 180°
From the given information,
∠6 = 75°
Then,
∠3 + 75° = 180°
∠3 = 180° - 75°
∠3 = 105°
Hence, the measure of ∠3 will be 105°.
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Can someone help me with question 3? it geometry, gotta need an answer fast
Answer:
Step-by-step explanation:
So for the 1st one you're going to use your protractor and line it up so that BC is at 0 degrees, that way you can look at the point A to determine the angle. Now that you have the angle you're going to take your protractor and draw one point which will be where the two lines meet, line this up in the middle and then draw a point at 0 degrees and a point at the angle you found. Now draw another point at half the angle (like in the previous answer I answered). Draw a line from the middle point and connect it to all these three points (4 in total but one of them is going connected to all of them, like the point B in the image you sent).
For the second question you're going to take the angle you found in the first answer and multiply it by 2. Now start off by drawing a middle point which will connect the two other lines. Line up your protractor so that point is at bottom but in the middle (Check my photo for clarification). Now go to the value that is twice the angle and draw a point there, and also draw a point at 0 degrees) and then connect the two points to the middle point.
For question 3 you don't really need the hint, all you need is to multiply the angle by 1.5 but I'll send another image explaining what it's trying to explain.
Find the circumference and the area of a circle with diameter 6 ft.
Answer:
Circumference = 18.84 ft
Area = 28.26 ft squared
Step-by-step explanation:
C(circumference) = 2 x [tex]\pi[/tex] x r(radius)
radius = 1/2 circumference
1. divide circumference by two to get the radius, which would be three ft.
2. multiply the radius by pie (3.14) and then multiply that by two and you have your circumference, which is 18.84 ft
area = [tex]\pi[/tex] x r(radius)^2
1. find the radius squared, which would be 9 because 3^2 = 3 x 3 which = 9
2. multiply 9 by pie (3.14) and you get the area which = 28.26
A gardener is planning to fill her garden with mulch. she plots it on a grid to plan how much she will need. the garden is in the shape of a rectangle with vertices at (3, 9) (5, 9) (3, 3) (5, 3). one bag of mulch covers 5ft^2 and costs $5.00. how much will it cost her to cover her garden?
The cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².
The cost of one bag of mulch is given as $5.00.
The area covered by one bag of mulch is 5 ft.².
Therefore, the cost to cover 1 ft.² of the garden with mulch is $(5/5) = $1.00.
To find the area of the rectangular plot representing the garden, we do the follows:
The distance formula between two points (x₁, y₁) and (x₂, y₂) is,
d = √((x₂ - x₁)² + (y₂ - y₁)²).
The length of the rectangular plot between points (3, 9) and (5, 9):
Length = √((5 - 3)² + (9 - 9)²) = √(2² + 0²) = √(4) = 2.
The width of the rectangular plot between the points (3, 3) and (3, 9):
Width = √((3 - 3)² + (9 - 3)²) = √(0² + 6²) = √(36) = 6.
Therefore, the area of the rectangular plot = Length*Width = 2*6 = 12 ft.².
Therefore, the cost to cover the rectangular plot with mulch, at the cost of $1.00 per 1 ft.² = $1*12 = $12.00.
Therefore, the cost to cover the garden with mulch will be $12.00, as the area of the rectangular garden is 12 ft.².
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Which properties are necessary to claim that the two prisms are congruent? Check all that apply.
Answer:
1. The volumes are equal.
2. The base areas are equal.
3. The prisms have the same height.
Step-by-step explanation:
I don't see no answered to check all that apply but here is the answers about properties and two prisms
Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing three green, three yellow, and four red marbles.
The marbles are different colors.
Answer:
[tex]\frac{11}{15} =0.733333333333[/tex]
Step-by-step explanation:
• Here The sample space S is the set of possible outcomes (ordered pairs of marbles) that we can draw at random (without replacement) from the bag.
Then
[tex]\text{cardS} =P^{2}_{10}=10\times 9=90[/tex]
……………………………………………
Drawing two marbles where the marbles are different colors
means
drawing (1green ,1 yellow) or (1green ,1 red) or (1yellow ,1 red)
Remark: the order intervene
=========================
•• Let E be the event “Drawing two marbles where the marbles are different colors”.
CardE = 2×3×3 + 2×3×4 + 2×3×4 = 66 (2 is for the order)
Conclusion:
[tex]p\left( E\right) =\frac{66}{90} =\frac{11}{15} =0.733333333333[/tex]
Method 2 :
[tex]p\left( E\right) =2\times \frac{3}{10} \times \frac{3}{9} +2\times \frac{3}{10} \times \frac{4}{9} +2\times \frac{3}{10} \times \frac{4}{9} =0.733333333333[/tex]
Answer:
[tex]\sf \dfrac{11}{15}[/tex]
Step-by-step explanation:
The bag of marbles contains:
3 green marbles3 yellow marbles4 red marbles⇒ Total marbles = 3 + 3 + 4 = 10
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
First draw
[tex]\implies \sf P(green)=\dfrac{3}{10}[/tex]
[tex]\implies \sf P(yellow)=\dfrac{3}{10}[/tex]
[tex]\implies \sf P(red)=\dfrac{4}{10}[/tex]
Second draw
As the first marble is not replaced there are now 9 marbles in the bag.
If the first marble was green, the probability of drawing a yellow is now 3/9 and the probability of drawing a red is now 4/9.
If the first marble was yellow, the probability of drawing a green is now 3/9 and the probability of drawing a red is now 4/9.
If the first marble was red, the probability of drawing a green is now 3/9 and the probability of drawing a yellow is now 3/9.
To find the individual probabilities of picking 2 different colors, multiply the probability of the first draw by the probability of the second draw:
[tex]\implies \sf P(green)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(green)\:and\:P(yellow)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]
[tex]\implies \sf P(yellow)\:and\:P(green)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]
[tex]\implies \sf P(yellow)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(red)\:and\:P(green)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(red)\:and\:P(yellow)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]
To find the probability of drawing two marbles at random and the marbles being different colors, add the individual probabilities listed above:
[tex]\begin{aligned}\implies \sf P(2\:different\:color\:marbles) &=\sf \dfrac{12}{90}+\dfrac{9}{90}+\dfrac{9}{90}+\dfrac{12}{90}+\dfrac{12}{90}+\dfrac{12}{90}\\\\ & = \sf \dfrac{66}{90}\\\\ & =\sf \dfrac{11}{15}\end{aligned}[/tex]
if z varies jointly with x and y when x=3, y=-1, and z=12, what is z when x=-5 and y=6
Step-by-step explanation:
z = 12 = k × 3 × -1
12 = k×-3
-4 = k
z = k× -5×6 = k×-30 = -4 × -30 = 120