if a is an m × n matrix and b is in r m, the general least-squares problem is to find an x that makes ax as close as possible to b. true or false?

Answers

Answer 1

The statement that if a is an m × n matrix and b is in r m, the general least-squares problem is  is; TRUE

How to Interpret Least squares problem for augmented matrix?

The way that we compute a least-squares solution of Ax = b is;

Compute the matrix A T A as well as the vector A T b .Form the needed augmented matrix for the given matrix equation A T Ax = A T b , and then row reduce.This equation is always consistent, and as such any solution K x will be a least-squares solution.

By definition, the least squares problem is to find xˆ such that |Axˆ − b| ≤ |Ax − b| for all x in IRⁿ

This means that we are to find a vector x that makes Ax (which is in

the Col(A)) as close to b as possible.

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Related Questions

Answer the questions ⬇️

Answers

Answer:

page 1=45 points

page 2

1=30

2=10

3=56

page 3

$1000

Step-by-step explanation:

1000 the math adds up

During the 2008 - 2009 financial crisis, the GDP of the USA reduced from $14.72 trillion in 2008 to $14.42 trillion in 2009. What is the percentage change between these two years? around your answer to the nearest hundredth of a percent.

Answers

The percentage change in GDP is 2.04%

Percentage Change

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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2x + 3y = 13
4x - y =-2

Answers

Answer:

x = 1/2

y = 4

Step-by-step explanation:

Given equations:

2x + 3y = 13 ----------------------(1)

4x - y = -2  ------------------------(2)

Multiply Eq. (1) by 2

2(2x + 3y) = 13 × 2

4x + 6y = 26 -------------------(3)

Subtract Eq. (3) from Eq. (2)

4x - y - 4x - 6y = -2 - 26

-y - 6y = -28

-7y = -28

7y = 28

Divide 7 to both sides

y = 4

Put y = 4 in Eq. (2)

4x - 4 = -2

Add 4 to both sides

4x = -2 + 4

4x = 2

Divide 4 to both sides

x = 2/4

x = 1/2

[tex]\rule[225]{225}{2}[/tex]

what is 490 * 5 .
A. 98

B.
485

C.
5,560

D.
6,860

Answers

Answer:

None of the answers are right based on given context.

The product is 2,450.

Step-by-step explanation:

1) use the partial product method.

4 9 0

×    5

-------------------------------------

4 5 0 (5×90)

2 0 0 0 (5×400)

-----------------------------------------

2 4 5 0

2) Therefore 490 x 5 = 2,450.

2,450

none of the is right. this is a simple equation that can be put into a calculator which will give u the output of 2,450

Rewrite sin(x+5pi/4) in terms of sin(x) and cos(x)

Answers

sin(x+5pi/4) sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

What is trigonometry

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

Let find the common multiplier of sin

[tex](\frac{x + 5\pi }{4} )[/tex]sin (x), cos(x); cos (x) sin[tex](\frac{x + 5\pi }{4} )\\[/tex] sin (x)

Find the least common Multiplier of sin [tex](\frac{x + 5\pi }{4} )[/tex] sin (x) , cos (x)

Lowest common multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor sin [tex](\frac{x + 5\pi }{4 } )[/tex]sin ( x)

sin[tex]( \frac{x + 5\pi }{4} )[/tex]. sin(x)

Multiplier each factor with the highest power;

cos (x) .sin [tex](\frac{x + 5\pi }{4} )[/tex].sin (x)

Therefore, the trigonometry sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

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Help pls and thx 20 points

Answers

a) 7y and (2y²-9) are the length and width expressions where one dimension is the GCF.

b) When y= 2, the area of the rectangle is -14

What is meant by area?

The area amount expresses the size of a region on a planar or curved surface.

A two-dimensional figure's area is the amount of space it occupies. It is the number of unit squares that cover the surface of a closed figure in other words. Square units, which are frequently expressed as square inches, square feet, and so on, are the standard unit of area.

A rectangle is a two-dimensional figure, and if one of the dimensions is the GCF, as indicated in the job, then:

7y and (2y²-9) are the length and width expressions where one dimension is the GCF.

Furthermore, when y= 2, the area of the rectangle is;

14(2³) - 63(2) = 112-126

= -14

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Bilquis and her children went into a movie theater and she bought $60 worth of bags
of popcorn and pretzels. Each bag of popcorn costs $7.50 and each pretzel costs
$3.75. She bought 2 more bags of popcorn than pretzels. Graphically solve a system
of equations in order to determine the number of bags of popcorn, x, and the number
of pretzels, y, that Bilquis bought.

Answers

The number of bags of popcorn = 6

The number of pretzels  = 4

Let the number of bags of popcorn = x

the number of pretzels = y

From the question, we have

she bought $60 worth of bags of popcorn and pretzels.

Each bag of popcorn costs $7.50 and each pretzel costs $3.75.

7.50x+3.75y = 60................(i)

She bought 2 more bags of popcorn than pretzels.

x-y = 2................(ii)

Solving equation (i) and (ii), we get

x = 6

y = 4

The number of bags of popcorn = 6

The the number of pretzels  = 4

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Start Root 144 End Root=
A. 11
B. 12
C. 13
D. 14
pre algebra
fast would appreciate it

Answers

Answer:

the answer is 12

explanation 12x12= 144

Three artists Richard, Allan and Shelby are painting the rooms of a building which
are numbered from 10 – 150. Richard has to work in all the rooms. Allan has to work in rooms
where the room number is a multiple of 3. Shelby has to work in rooms where the room number
is a multiple of 5. In which rooms will they all work together?

Answers

The rooms which the three artists Richard, Allan and Shelby will work together are room 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 making a total of 10 rooms.

Which rooms will the three artist work together?

Richard works in all the roomsAllan works in rooms multiple of 3Shelby works in rooms multiple of 5

Find the multiples of 3 and 5

Multiples of 3 = 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150

The common multiples of 3 and 5 are; 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Each common multiple represent a room

= 10 rooms

Therefore, the rooms which the three artist will work together is 10 rooms

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What is the following sum?
5(³3√x)+9(³√x)
0 14 (√x)
14 (2√x²)
0 14 (3√x)
0
X

Answers

The solution for the given expression is 14∛x. The correct option is (C).

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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3x+2y=4 x=y+3
System of equations

Answers

Answer:

(2,-1)

Step-by-step explanation:

Given system of equations:

3x + 2y = 4x = y + 3

We are going to use the substitution method.

Step 1: Solve for x = y + 3 for x:
(Substitute y + 3 for x in 3x + 2y = 4)

3x+2y=4

3(y+3)+2y=4

5y + 9 = 4 ----> Simplify both sides of the equation

5y+9+−9=4+−9  -------> Add -9 to both sides

5y=−5

5y5 = -5/5  ------> Divide both sides by 5

y = −1

Step 1: Substitute -1 for y in x = y + 3:

x = y + 3

x = -1 + 3

x = 2 --------> (Simplify both sides of the equation)

Answer:

(2,-1)

(2,-1) hope this helps :\\\

At a company 75% of the employees were men . After six women joined the company the ratio of men to women was2:1. Work out how many men work at the company

Answers

The number of men and women that work at the company are;

Number of men = 36

Number of women = 18

How to solve ratio word problems?

Let the total number of employees in the company be x.

Now, we are told that 75% of the employees were men. Thus;

Number of men = 75% * x = 0.75x

Number of women = 0.25x

Now, we are told that after 6 women joined, the ratio of men to women became 2: 1.

Thus;

New total employees = x + 6

New total number of women = 0.25x + 6

Thus;

0.75x/(0.25x + 6) = 2/1

Cross multiply to get;

0.75x = 2(0.25x + 6)

0.75x = 0.5x + 12

0.75x - 0.5x = 12

0.25x = 12

x = 12/0.25

x = 48

Number of women = 0.25(48) + 6 = 18

Number of men = (48 + 6) - 18 = 36

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suppose h(t)=(3t+5)/t and k(t)=5/(t-3). Show that h(t) and k(t) are inverse functions using algebra.

Answers

We will see that the functions are inverses by proving that the composition is equal to the identity.

How to show that h(t) and k(t) are inverse functions?

Two functions are inverses if their composition is equal to the identity, this means that if h(t) and k(t) are inverses, then we can write:

h(k(t)) = t

and

k(h(t)) = t

Proving one of these will be enough.

Here the functions are:

h(t) = (3t + 5)/t

k(t) = 5/(t - 3)

Let's find h(k(t))

We will get:

h(k(t)) = (3*k(t) + 5)/k(t)

Now we can replace the function k(t) there.

h(k(t)) = (3*5/(t - 3) + 5)/(5/(t - 3))

Now we can simplify this using algebra.

h(k(t)) = ( 15/(t - 3) + 5)*(t - 3)/5

h(k(t)) = (15/(t - 3))*(t - 3)/5 + 5*(t - 3)/5

h(k(t)) = 3 + (t - 3) = t

h(k(t)) = t

So yes, the two functions are inverses.

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Mr. Evans is currently 4 times as old as his son, Dan. If Mr. Evans was 46 years old 2 years ago, how old is Dan now?

Answers

Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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36/(x-3)=4 thank uu :>

Answers

Answer:

12

Step-by-step explanation:

36 / (x - 3) = 4

multiply both sides by (x - 3):

(x - 3)(36 / (x - 3)) = 4(x - 3)

36 = 4(x - 3)

expand right side:

36 = 4x - 12

add 12 to both sides:

36 + 12 = 4x - 12 + 12

48 = 4x

divide both sides by 4:

48/4 = 4x/4

x = 12

5. If each month in Reno had the same
average rainfall as in August, what
would the total
amount of rainfall be
after 12 months?

Answers

Rainfall on August =x
Multiple 12 to x

Answer 12x

The selling price of an item is a
function of the cost of
making the item. is it a function or not?

Answers

Yes, the selling price of an item is a function of the cost of making the item.

A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.

Cost is often the expenditure incurred for producing a product or service that a firm sells. The selling price is the amount paid by the buyer to purchase a product or products.

The selling price of an item is a function of the cost of creating the item since the manufacturer must sell at a price higher than the cost of making the item in order to recoup his investment and make a profit.

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PLS QUICK How did the mountainous geography of Athens influence the economy?


The people of Athens mined gold for trade.

The people of Athens were unable to raise any crops.

The people of Athens focused on the military to protect their region.

The people of Athens relied on sea trade.

Answers

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

How did the terrain of  Athens influence the economy ?

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Which graph represents the function f(x) = |x − 1| − 3 ?

Answers

Answer:

See picture below.

Step-by-step explanation:

f(x) = |x|

This absolute value will have a v shape, the "v" point at (0,0)

Next,

f(x) = |x-1|

This (-1) moves the v shape one unit to the right, "a translation to the right by 1."

Finally,

f(x) = |x-1| - 3

This (-3) moves the v shape down 3 units. This is why the answer is the original

f(x) = |x|

except it's moved right by 1, and down by 3.

Step-by-step explanation:

The graph that represents is translated right by 1 units and 3 unit up to form. Hence, graph (a) is correct.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

The parent function of an absolute function is;

y = |x|

When a function is translated right by h units, the transformation rule by;

y = |x-h|

So:

|x-1|-3 means that it is translated right by 1 units

When a function is translated up k units, then the transformation rule is:

y = |x| + k

y = |x-1|-3

This means that it is translated right by 1 units and 3 unit up to form

Hence, graph (a) is correct

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What is this question √5 + √5

Answers

The simplification form of the expression √5 + √5 is 2√5 after adding like terms.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

√5 + √5

After adding like terms:

2√5

The question is:

Solve the expression:

√5 + √5

Thus, the simplification form of the expression √5 + √5 is 2√5 after adding like terms.

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what’s the solution for 7x - 10x + 2x = -5

Answers

Answer:

x = 5

Step-by-step explanation:

Finding the solution is getting the value for x that makes the math sentence true.

7x -10x +2x = -5

Combine like terms (all the x terms can add together)

-x = -5

Multiply (or divide) both sides by -1

x = 5

Juice A cost 0.10 more then per ounce than juice B. Ifa 12 ounce of juice A costs $564 what is the cost per ounce of juice B

Answers

bro I don’t know

1 ask your teacher

2 get sturdy

3

Express 602.16 dam in decimeters

Answers

The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

How can the  expression of 602.16 dam  be converted to decimeters?

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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Determine the distance between the points (−1, −4) and (−9, −8).

Answers

Answer:

The distance between these two points with coordinates (-1, -4) and (-9, -8) is 8.94 unites

asap pls

Simplify the expression and write the answer with
only positive exponent
(2p²)-³q4
(6q)-¹p-7​​

Answers

Answer:

8p^6q^4

6qp-7

Step-by-step explanation:

Please try to prove that the slope of the normal line of y=mx+bis -1/m

Answers

The slope of the normal line is proved to be -1/m using tangent

How to show that the slope of normal line is -1/m

Slope is similar to tangent and sometimes used interchangeably

assuming two lines of slope m and m', the angle between the two lines is x

tan x =  (m - m') / (1 + mm')

for a normal line x = 90

tan 90 =  (m - m') / (1 + mm')

tan 90 is ∞ = 1 / 0

1 / 0 =  (m - m') / (1 + mm')

cross multiplying

1 * (1 + mm') =  0 *  (m - m')

1 + mm' = 0

mm' = -1

m = -1/m'

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I NEED HELP ASAP WITH THIS

Answers

Answer: Jorge would have to run 3 [tex]\frac{3}{8}[/tex] miles to reach his 23 mile goal.

Step-by-step explanation:

When you add 5 [tex]\frac{3}{4}+ 7 \frac{3}{8}[/tex]=[tex]13\frac{1}{8}[/tex]

[tex]13\frac{1}{8}+6 \frac{1}{2}=19\frac{5}{8}[/tex]

Now you can subtract [tex]19 \frac{5}{8}[/tex] from 23, which would give you [tex]3\frac{3}{8}[/tex], being the total amount of miles left to run. You can add the terms without a calculator as well, by making the fractions have a common denominator.

Hope this helps!

answer again guys double points hi guys hurry please

Answers

The equation that represent the proportional relationship is t = 2 / 5 H.

How to represent proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

y = kx

for some constant k , called the constant of proportionality .

The equation that represent the proportional relationship can be represented as follows:

t = KH

using

t = 2

H = 5

Hence,

2 = 5k

k = 2 / 5

Therefore,

t = 2 / 5 H

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Differentiate the function with respect to x. Shot steps

Answers

[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex] is differentiation of   [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

By using chain rule we differentiated the function.

d/dx sin⁻¹x=1/√1-x²

[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex]

Hence,[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex] is differentiation of  [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

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Which of the following statements is true? Choose the correct statement below. 1 O A. The equation x3 - x2 - x - 1 = 0 is equivalent to the equation x2(x - 1)-(x - 1) = 0. B. The equation 2x3 - x2 + 4x - 2 = 0 has solutions x = or x= +2 1. C. The equation x3 – x2 - x + 1 = 0 is equivalent to the equation (x2 - 1)(x - 1)(x + 1) = 0. OD. The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0. 2

Answers

Option D. The statement that is true from the equations that we have here is D. The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

How to solve the equation

I will have to start for the equation D, because at close glance we can easily see that the powers would be equal

The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

We are to simplify x²(x - 1)-(x-1)

we would have to open the brackets from the above

 x² * x +  x² * (-1) - x - (-1) = 0

It would be important to pay attention at the signs

such that we would have

x³ -  x² - x + 1 = 0

Therefore the equation  x^3 - x^2 - x + 1 = 0 is equivalent or equal to  x³ -  x² - x + 1 = 0 because they have the same solution

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Other Questions
Examine the algebra tiles. which equation is being modeled? 4x 3 = 4x 5 ""3x (""3) = 4x 5 4x (""3) = 5x 4 ""3x 4 = 5x 4 of the two leadership behaviors, ________ leadership involves getting people to do ordinary things, while ________ leadership involves getting people to do exceptional things. What are the two sites on an enzyme?. A boat moves through the water with two forces acting on it. One is a 1,725-N forward push by the water on the propeller, and the other is a 1,000-N resistive force due to the water around the bow. (a) What is the acceleration of the 1,100-kg boat? m/s 2(b) If it starts from rest, how far will the boat move in 17.5 s? m(c) What will its velocity be at the end of that time? m/s A bike chain can support a tension of no more than 9800 N. The pedal connects to a crank 17 cm from the axle, and the gear pulling the chain has a 9.1 cm radius.When riding at a constant speed, with the crank and pedal horizontal, as in (Figure 1), what is the maximum force that can be applied to the pedal before the chain breaks?Express your answer with the appropriate units. A graduate student wants to examine the effect of print media versus televised media on individuals' position on several social issues. The superintendent of a local work release facility, a family friend, will allow the graduate student access to the prison population to help her quickly accrue subjects. The student's IRB should:______. liszt's method of modifying and expanding short motives and in the process expressing extramusical associations is known as Alya ha a 10. 2-gram bag of pretzel and a 21. 3-gram bag of nack mix. She put an equal amount of the combined pretzel and nack mix into each of the 3 large bowl. How much mix doe Alya put in each bowl? 150.0 mL of a solution containing Ba2+ ions is analyzed by adding 0.18 M Na2SO4 solution until no more precipitate forms. The mass of BaSO4 precipitate obtained is 11.20 g. Select all the options that correctly reflect the steps required to calculate the concentration of Ba2+ in the original solution.- The concentration of Ba2+ is equal to 0.18 M.- The original solution contained 0.0270 moles of Ba2+ ions.- The concentration of Ba2+ ions is equal to 0.320 M.- The molar mass of BaSO4 is 233.4 g/mol.- The original solution contained 4.80 x 10-2 moles of Ba2+.- The concentration of Ba2+ ions is equal to 0.320 M.- The molar mass of BaSO4 is 233.4 g/mol.- The original solution contained 4.80 x 10-2 moles of Ba2+. bradwardine then claims that an arithmetic increase in velocity corresponds with a geometric increase in the original ratio of force to resistance. Washing soda is used to make detergents and to remove minerals from water as part of a cleaning process. Write a chemical equation for what is occurring. What type of reaction is occurring? which of the following is/are caused by pseudomonas aeruginosa? to be marked correct, you'll need to select all true statements, as there may be more than one correct answer. the following payoff matrix is for two players, each with two strategies: what is player 2's dominant strategy in this game? always cooperate always cheat cooperate when player 1 cooperates and cheat when player 1 cheats player 2 does not have a dominant strategy. Sami is making necklaces for a craft show. each necklace is 33.4 centimeters long. if she has 233.8 centimeters of cord, how many necklaces can Sami make? Which of the following is not a valid exception to the exclusionary rule ?. will a continental polar air mass most likely be found north or south of a front east of the rocky mountains in the central united states during the current year, merchandise is sold for $18,300 cash and $295,700 on account. the cost of the goods sold is $188,000. what is the amount of the gross profit?. Consider w1 = ""3i and w2 = ""2. what is the result of subtracting w2 from w1? i ""i 2 "" 3i ""2 3i With regards to the Project Management Maturity Model, what level is the following characteristic: Working on projects is a struggle because it goes against the grain of established policies and procedures.Level 1 Where can a food worker wash her hands a utility sink or bathroom sink?.