Answer: x= -1
Step-by-step explanation:
9x-3(x-5)=6x+3
9x-3x+15=6x+3
9x+6x-3x= 3-15
15x-3x= -12
12x= -12
x= -1
A stack of four cards contains two red cards and two black cards. I select two cards, one at a time with replacement. Consider the events A = the first card selected is red. B = the second card selected is red. The events A and B are O not independent O mutually exclusive O mutually exclusive and not independent. O independent
P(A) and P(B) are independent events.
Option (D) is correct.
What are events in probability?
In probability, an event is a set of outcomes of an experiment. For example, if you flip a coin, the possible outcomes are "heads" or "tails", and the event "getting heads" is the set of all outcomes where the coin lands on heads. Events can be mutually exclusive, meaning that they cannot happen at the same time, or they can be non-exclusive, meaning that they can happen at the same time.
The events A and B are independent. This means that the probability of event B happening (the second card selected is red) is not affected by whether or not event A has already happened (the first card selected is red).
In other words, the probability of selecting a red card on the second draw is still 1/2, regardless of whether a red card or a black card was selected on the first draw. This is because the cards are being drawn with replacement, meaning that the first card selected is returned to the stack before the second card is drawn, so the second draw is not affected by the first draw.
To calculate the probability of both events A and B happening, we can use the formula P(A and B) = P(A) x P(B|A) where P(B|A) is the conditional probability of event B given that event A has already happened. Since we know that the probability of event A is 1/2, and the probability of event B is also 1/2, we can calculate P(A and B) as: P(A and B) = (1/2) x (1/2) = 1/4
Therefore, P(A) and P(B) are independent events.
Option (D) is correct.
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A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies. How many more bags of cookies could they make?
Write an inequality describing the situation and solve. Which inequality below is correct?
They may bake 20 additional bags of cookies. The problem is represented by the inequality x < 80.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies.
Since each cookie pack can hold 4 cookies
Thus, 100 cookies will require = 100/4 packs
100 cookies will required = 25 packs
Since They have already bagged 20 cookies.
Thus,
The total pack they used = 20/4
The total pack they used = 5
Inequality:
let "x" be the number of cookies they can make
80 > x
Therefore, 20 more bags of cookies they could make. the inequality that represents the situation is x< 80.
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cindy has $26 that she has to spend. She can buy a box of cookies for $3 each or a box of brownies for $2 each. Complete this table showing some possible combinations of the number of each type of treat she can buy.
The possible combinations of the number of each type of treat that Cindy can buy include:
6 box of cookies and 4 box of brownies8 box of cookies and 1 box of brownies4 box of cookies and 6 box of brownies.How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, 6 box of cookies and 4 box of brownies will be:
= 6($3) + 4($2)
= $26
8 box of cookies and 1 box of brownies also give $26.
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what is the probability of getting the same number on two six-sided dice
Answer:
1/36, or approximately 0.028
Step-by-step explanation:
The probability of getting the same number on two six-sided dice is 1/6, or approximately 0.17.
This is because there are six possible outcomes for each dice, and only one of those outcomes results in the same number on both dice (for example, both dice showing a 6).
So, out of the 36 possible outcomes when rolling two dice, only one of them results in the same number on both dice. Therefore, the probability of this happening is 1/36, or approximately 0.028.
when representing a function as a power series do you have to ratio test to find the radius of convergence if geometric test does nto work
No, you do not have to ratio test to find the radius of convergence if geometric test does into work,
when representing a function as a power series, it is not necessary to ratio test to find the radius of convergence if geometric test does into work. A geometric test does not always converge to the right value if it is used to find the radius of convergence of a function at a given point.
The radius of convergence is the distance between two points within a specified radius. If the geometry test fails, the convergence radius may not be found. To find the radius of convergence, use another test like a Venn diagram to see if there is a compatibility pattern.
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Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head.
0.87 x 310
The estimation of the numbers given as 0.87 × 310 will give 270.
Howw to calculate the estimation?You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation. A figure is discovered through estimation.
A value, amount, or size that rounds off to the nearest whole number is said to be approximating.
The estimation of the numbers given as 0.87 × 310 will give:
= 0.9 × 300
= 270.
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HELP ASAP!!!! NO LINKS OR SPAM
Malek owns a home, has a bi-weekly gross income of $3,115.00, and has total minimum monthly debt payments of $3,165.00. Choose the inequality that shows the amount Malek needs to reduce his monthly debt payments by to have a debt-to-income ratio of 35%. (2 points)
x ≤ $802.79
x ≥ $802.79
x ≤ $984.50
x ≥ $984.50
The inequality that shows the amount Malek needs to reduce his monthly debt payments by to have a debt-to-income ratio of 35% is x ≤ $984.50.
What is Debt to Income Ratio?Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.
Given that Malek has a biweekly gross income of $3115.00.
Monthly gross income of Malek = 2 × $3115.00 = $6230
Monthly debt payments is minimum of $3165.00
We need the debt to income ratio as 35%.
Let x be the monthly debt payment to get the ratio 35%.
x / 6230 = 0.35
x = 2180.5
$3165.00 - $2180.5 = 984.5
So the inequality is x ≤ $984.50
Hence the inequality showing the amount to be reduced to get the debt top income ratio as 35 % is x ≤ $984.50.
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Use the confidence level and sample data to find a confidence interval for estimating the population μ. Find the margin of error E and round your answer to the nearest tenth.
Test scores: n = 82, = 89.1, σ = 6.3; 99% confidence
The margin of error round to the nearest tenth will be 1.8.
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The margin of error is given as
[tex]\rm ME = z\times \sqrt{\dfrac{\sigma ^2}{n}}[/tex]
The z-value for the 99% confidence will be 2.576. Then the margin of error is calculated as,
ME = 2.576 × √[(6.3)² / 82]
ME = 2.576 × √0.4840
ME = 2.576 × 0.6957
ME = 1.8
The margin of error round to the nearest tenth will be 1.8.
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what is the slope through the line of (4, 7) and (6, 2)
The slope through the line of (4, 7) and (6, 2) can be found by using the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Substituting the values for (4, 7) and (6, 2) into the formula:
m = (2 - 7) / (6 - 4)
m = -5 / 2
m = -2.5
So, the slope of the line through (4, 7) and (6, 2) is -2.5.
Hello:
--> find the slope between the points (4, 7) and (6, 2)
Let's consider our point given:
--> (x1, y1): (4, 7)
--> (x2, y2): (6, 2)
Let's consider what formula we need:
[tex]\text{Slope}=\dfrac{y2-y1}{x2-x1}=\dfrac{2-7}{6-4}=\dfrac{-5}{2}=-\dfrac{5}{2}[/tex]
Thus our slope is -5/2
Answer: -5/2
Solve for the indicated variable using the given value of the other variable.
Solve for y when x=0 using the equation y=2x+5
Answer: y is equal to 5
Solve for y :
x=0
y=2(0)+5
y=0+5
y=5
Hope this helped =)
-YinAhara
Which of the following expense items should be included when determining whether a taxpayer who wishes to file as head of household paid more than half the cost of keeping up their home? Education. Medical expenses. Real estate taxes. Rental value of the home owned by the taxpayer.
The item would be the rental value of the home owned by the taxpayer. The correct option is D.
What is a taxpayer?A taxpayer is a person or organization that is required to pay taxes. Modern taxpayers may have an identification number, which is a reference number issued by the government to individuals or businesses. The term "taxpayer" generally refers to someone who pays taxes.
A recurring payment made by a tenant to a landlord in exchange for the use of land, a building, an apartment, an office, or other property. a payment made by a lessee to an owner in exchange for the use of machinery, equipment, etc.
A taxpayer who wishes to file as head of household paid more than half the cost of keeping up their home will be the rental value of the home owned by the taxpayer.
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Find the area of all shaded regions. Give your answer as a completely simplified exact value in terms of pi. (no approximations) WHO EVER ANSWERS FIRST GETS 100 BRAINLY POINTS
Answer:
18 π cm^2.Step-by-step explanation:
The area of the whole circle = π r^2 = 81π cm^2.Since there are 360 degrees in a circle the area of the shaded region = 80/360 * area of the circle.
This = 80/360 * 81 π
= 2/9 * 81 π
= 18 π
hope it helps<3Answer:
Area = 18π cm²
Step-by-step explanation:
The shaded region is a sector of a circle with radius 9 cm.
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]
From inspection of the give diagram:
θ = 80°r = 9 cmSubstitute the values into the formula for area of a sector:
[tex]\implies A=\left(\dfrac{80^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2[/tex]
[tex]\implies A=\dfrac{2}{9} \pi \cdot 81[/tex]
[tex]\implies A=\dfrac{162}{9} \pi[/tex]
[tex]\implies A=18 \pi\;\; \f cm^2[/tex]
Therefore, the area of the shaded region is 18π cm².
An indoor staircase has a 14 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 47 degrees and there are 13 feet of horizontal space total for each of the landings
combined, answer the following questions showing each step of your work:
a) What is the landing space per step (in inches, rounded to the nearest inch)?b) Find the vertical rise from the 1st floor to the 2nd floor (in feet, rounded to the nearest foot).
The landing space per step for the indoor staircase is solved to be
13 inchesThe vertical rise from first floor to second floor is 14 feet
How to find the landing spaceThe figure defined to be a right triangle and the dimensions are worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The right angle triangle comprises of
opposite = total vertical height
adjacent = total horizontal height = 13 feet
The total vertical height is calculated using tan, TOA
let the angle be x
tan x = opposite / adjacent
tan 47 = opposite / 13
opposite = (13 * tan 47) feet
opposite = 12 * (13 * tan 47) inch
opposite = 167.2895 inch
For a 14 inch vertical rise per step say number of step is y
14 y = total vertical height
14 y = 167.2895
y = 11.9493 steps ≈ 12 steps
The landing space for 12 steps is solved by
= horizontal space total in inch / number of steps
= 13 * 12 / 12
= 13 inches
vertical rise from the 1st floor to the 2nd floor
opposite = (13 * tan 47) feet
opposite = 13.94 feet
opposite = 14 feet (to the nearest foot)
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711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
Anything help’s please!!
The value of x is 6, which can be calculated using triangle proportionality theorem.
What is the Triangle proportionality theorem?A triangle's other two sides are divided in the same ratio if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.The Triangle Proportionality Theorem, often known as the Thales Theorem, was developed by the well-known Greek mathematician Thales.Triangle Proportionality Theorem asserted that the ratio of any two related sides is always the same for any two equiangular triangles.Thales provided the Triangle Proportionality Theorem based on this idea (BPT). Similar triangles have introduced this idea before. The corresponding angles of two triangles are equal if they are identical.From the figure, we have both triangles' corresponding sides proportionate to one another.
so, PR/ PR' = RQ/ RQ'
so, x/10 = 9/15
x = 6
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A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she’s been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study?
answer choices
O Use a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flip a coin to decide which pavement to use on which member of the pair.
O Subjectively divide the 40 roadways into 20 pairs (making the roadways within each pair as different as possible) and then, for each pair, flip a coin to decide which pavement to use on which member of the pair.
O Use a table of random digits to divide the 40 roadways into two groups of twenty, and then use the table of random digits a second time to decide which pavement to use on which group.
O Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement.
O Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin once to decide which pavement is put on the first half-mile of all the roadways.
The best way for the materials engineer to carry out the randomization for this study is by using a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flipping a coin to decide which pavement to use on which member of the pair.
This can be represented by the formula P(A|B) = P(A) * P(B|A), where P(A|B) is the probability of pavement type A being used on a given roadway, P(A) is the probability of pavement type A being used on any given roadway, and P(B|A) is the probability of a given roadway being used for pavement type A.
The probability of pavement type A being chosen for any given roadway is 1/2 (since there are two pavement types). The probability of a given roadway being used for pavement type A is also 1/2 (since there are two members of each pair). This means that the probability of pavement type A being chosen for a given roadway is equal to P(A|B) = 1/2 * 1/2 = 1/4.
By randomly assigning pavement types to each pair of roadways, the materials engineer is ensuring that her experiment is as fair and unbiased as possible. This will allow her to accurately compare the durability of the two different types of paving material.
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Which of the following is the dependent variable in an experiment? Select the correct answer below: O lurking variable O explanatory variable O response variable O treatment
The dependent variable is the factor that is affected by the changes in the independent variable and is measured to observe the effects.
The dependent variable is the factor that is affected by the changes in the independent variable and is measured to observe the effects. This is the variable that is expected to change in response to changes in the independent variable. The dependent variable is the factor that is affected by the changes in the independent variable and it is measured to observe the effects of the changes in the independent variable. For example, in an experiment about plant growth, the dependent variable would be the height of the plant and the independent variable would be the amount of water added to the soil. By changing the amount of water, the height of the plant can be observed and measured to determine the effect of the water on the growth of the plant.
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple?
The probability that the next fruit out of the bag will be an apple is 2 / 3.
How to find the probability ?We're trying to figure out the probability of picking an apple at random from a bag of fruits, assuming that the odds are equal for each item.
Keep in mind that the chance is equal to the product of the quantity of apples and the quantity of all the other fruits in the bag.
The fruits taken out already include 2 plums and a peach which means 3 fruit have been taken out, leaving a total of:
= ( 4 + 3 + 2) - 3
= 6 fruits
The probability of the next fruit being an apple is:
= ( 4 apples + 2 peaches ) / 6 fruit
= 4 / 6
= 2 / 3
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Use the formula for finding the volume of
a rectangular prism to find the volume of
a rectangular prism that measures 1/2 in x 2 2/3 in x 2/5 in.
Options are
The volume of a rectangular prism is 8/15 in³ option - A is correct.
How can you calculate the volume of a rectangular prism using a formula?Therefore, the area of the base of a rectangular prism is multiplied by the height to determine its volume. The formula for calculating a rectangular prism's volume is Volume (V) = height of the prism base area. It is measured in cubic units like cm³, m³, and in³.
The Rectangular Prism's Volume Formula
The volume of a prism can be calculated by dividing the base area by the height. Consequently, a prism's volume is equal to its base area times its height.
The equation for calculating a rectangular prism's volume is
V = l × w × h
V = 1/2 in × 8/3 in ×2/5 in
V = 8/15 in³.
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In preparation for catering a picnic event, a restaurant bought potatoes that weighed 5 pounds less than the ones bought for catering an office party. The potatoes for the office party weighed 16 pounds. How much did the potatos for the picnic event weigh?
Answer:
11 pounds
Step-by-step explanation:
16 lbs - 5 lbs = 11 pounds
what is the slope through the line of (-5, 7) and (1, 1)
Answer:
m = -1
Step-by-step explanation:
Slope = rise/run = [tex]\frac{-5-1}{7-1} = \frac{-6}{6} = -1[/tex]
the expression 5t+16 can be used to approximate the hieght,in inches of a tree t yesrs after it was planted. what is the hieght of the tree 7 years after it was planted?
Using the expression 5t + 16, the height of the tree after 7 years it was planted is: 51 inches.
How to Evaluate an Expression?To evaluate implies that we find the value of the expression by plugging in the value of the variable and simplify accordingly.
Given that t represents the number of years after a tree is planted, and the expression, 5t + 16 represents the approximate height of the tree, to find its height after 7 years, substitute t for 7 into the expression and evaluate:
5(7) + 16
35 + 16
= 51
Thus, the height of the tree after 7 years it was planted is: 51 inches.
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What is the relative minimum of the function?
Enter your answer in the box.
Answer: -5
Step-by-step explanation:
The minimum value is -5 at x = 1. Coordinate (1,-5)
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.
ft (smaller value)
ft (larger value)
The lower limit that she traveled in three seconds is 33.45 feet and the upper limit that she traveled in three seconds is 43.45 feet
The first three seconds of a race saw a runner's pace rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Distance x Time Speed
Similarly
The distance equals speed x time.
t equals 0.5 seconds
Then, the minimum distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The maximum distance travelled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
Hence, the lower limit that she traveled in three seconds is 33.45 feet and the upper limit that she traveled in three seconds is 43.45 feet
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Find the minimum value of the function z = 4x+3y subject to the following constraints.
x≤ 15
y≤ 13
3x+y≥ 16
2x+11y252
Note that the ALEKS graphing calculator can be used to make computations easier.
Z=
The minimum value for given linear equation 4x+3y will be 24.
What are linear equations?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
The minimum value for z=4x+3y will be at (6,0) i.e. 24
because this point follows the given linear inequalities too
as given in the graph provided in image.
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 solve the following equation for g:
m+n^2 = g5M
Answer:
To solve for g in the equation m + n^2 = g5M, we first need to isolate g on one side of the equation. We can do this by subtracting m and n^2 from both sides:
m + n^2 = g5M
m + n^2 - m - n^2 = g5M - m - n^2
0 = g5M - m - n^2
Now we can divide both sides by 5M:
0 = (g5M - m - n^2) / 5M
And we get the equation for g:
g = (m + n^2) / 5M
if i helped you, can you mark my answer as best?
A car travels 84km in 2 hours. How far does it travel in 3hours
Answer:slow
Step-by-step explanation:
its slow
Answer:
Assuming it stays the same speed, 126km.
Step-by-step explanation:
By doing 84/2, I know it takes the car one hour to go 42km. For three hours, we must do 42x3, which is 126.
The graph shows the cube root parent function.
-5
5-
-5
5
K
Which statement best describes the function?
OA. The function is positive when x < 0 and when x > 0.
B. The function is always positive.
C. The function is positive when x > 0.
OD. The function is positive when x<0
The correct option, C. The function is positive when x > 0, for the graph of cube root parent function.
Define the term cube root parent function?The opposite of such cubic function is the cube root function.
We are aware that its parent cubic function is ascending, one-one, and onto, and that its form is f(x) = x³. It results in a bijection as a result. As a result, its cube root inverse function, of the type f(x) = ∛x, also forms a bijection.The definition of the cube root for all numbers may be found in the introduction, as we have already seen (positive, real, and 0). As a result, there is no x for which any cube root function, f(x), is not defined. Therefore, the set among all real numbers is its domain (R).Similar to the square root function, the range of a cube root function is the set among all real numbers because it produces all values (positive, real, and 0). Consequently, a cube root function is f(x): R → R.Thus, using the domain and range we can see from the graph that, for the positive values of the function, the graph is increasing for positive values.
Therefore, The function is positive when x > 0.
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Show that the set S={(3,2),(−1,1),(4,0)} is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.)
Is it asking for (0,0)=c1(3,2)+c2(−1,1)+c3(4,0) with the matrix being (32−114000)?
c1 = (-4/5)c3, c2 = (8/5)c3, and c3 = 0. That what i found but in the example problem this is not even close to how the answer was.
The nontrivial linear combination of vectors whose sum is equal to zero vector for the given set of linearly independent vectors is given by :
u = 2v + (5/4)w .
As given in the question,
Given set of linearly independent vectors are:
S={(3,2),(−1,1),(4,0)}
Let us consider vectors u , v , and w represents the given set of linearly independent vectors which is given by :
u = ( 3, 2 )
v = ( -1 , 1 )
w = ( 4, 0 )
To get the nontrivial linear combination of vectors whose sum is equal to zero that is ( 0 ,0 ) is given by :
( 3, 2 ) - 2( -1 , 1 ) - (5 / 4)(4 ,0 ) = (0 , 0)
⇒ u -2v - ( 5 / 4 )w = 0
⇒ u = 2v + ( 5 / 4 )w
Therefore, the nontrivial linear combination of vectors whose sum is equal to zero is given by u = 2v + ( 5 / 4 )w.
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if two differnt people are randomly selected, without replacement, from the 884 subjects, find the probability that they are both women. Round to four decimal places.O 0.00003906O 3274O 2500O 3276
The probability of randomly selecting two women from 884 subjects is 1.
The probability of randomly selecting two women from 884 subjects can be calculated using the following formula: P(A and B) = P(A) x P(B). In this case, A is the event of randomly selecting a woman from 884 subjects and B is the event of randomly selecting a second woman from the remaining 883 subjects.
Therefore, P(A) = 884/884 = 1 and P(B) = 883/883 = 1. Thus, P(A and B) = 1 x 1 = 1. Then, the probability of randomly selecting two women from 884 subjects is 1. To round to four decimal places, the probability is 0.0000.
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