Let B = {b1, b2} and C = {c1, c2} be bases for R2. Find the change-of-coordinates matrix from B to C and then from C to B.
b1= [1 1], b2=[1 2], c1=[2 3], c2=[3 4]

Answer:

"t3"   was replaced by   "t^3".  

1 more similar replacement(s).Step by step solution :

STEP 1:Equation at the end of step 1 (((9 • (t6)) - (2•7t3)) + 4t) - 1 = 0

STEP 2 :Equation at the end of step 2: ((32t6 - (2•7t3)) + 4t) - 1 = 0

STEP 3:Checking for a perfect cube  3.1    9t6-14t3+4t-1  is not a perfect cube 

Trying to factor by pulling out : 3.2      Factoring:  9t6-14t3+4t-1 

Thoughtfully split the expression at hand into groups, each group having two terms:

Group 1:  4t-1 

Group 2:  -14t3+9t6 

Pull out from each group separately:

Group 1:   (4t-1)

(1)Group 2:   (9t3-14) • (t3)

Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Polynomial Roots Calculator : 3.3  

  Find roots (zeroes) of :  F(t) = 9t6-14t3+4t-1

Polynomial Roots Calculator is a set of methods aimed at finding values of  t  for which   F(t)=0  Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  t  which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading CoefficientIn this case, the Leading Coefficient is  9  and the Trailing Constant is  -1.  The factor(s) are: of the Leading Coefficient :  1,3 ,9  of the Trailing Constant :  1  Let us test ....  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      18.00        -1     3      -0.33      -1.80        -1     9      -0.11      -1.43        1     1      1.00      -2.00        1     3      0.33      -0.17        1     9      0.11      -0.57   Polynomial Roots Calculator found no rational roots Equation at the end of step 3: 9t6 - 14t3 + 4t - 1 = 0

STEP 4:Equations of order 5 or higher: 4.1     Solve   9t6-14t3+4t-1 = 0In search of an interavl at which the above polynomial changes sign, from negative to positive or the other wayaround.Method of search: Calculate polynomial values for all integer points between t=-20 and t=+20 Found change of sign between t= -1.00 and t= 0.00 Approximating a root using the Bisection Method :We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).The function is   F(t) = 9t6 - 14t3 + 4t - 1At   t=   0.00   F(t)  is equal to  -1.00 At   t=   -1.00   F(t)  is equal to  18.00 Intuitively we feel, and justly so, that since  F(t) is negative on one side of the interval, andpositive on the other side then, somewhere inside this interval,  F(t)  is zero Procedure :(1) Find a point "Left" where F(Left) < 0(2) Find a point 'Right' where F(Right) > 0(3) Compute 'Middle' the middle point of the interval [Left,Right](4) Calculate Value = F(Middle)(5) If Value is close enough to zero goto Step (7)Else : If Value < 0 then : Left <- MiddleIf Value > 0 then : Right <- Middle(6) Loop back to Step (3)(7) Done!! The approximation found is MiddleFollow Middle movements to understand how it works :  Left Value(Left) Right Value(Right)

0.000000000 -1.000000000 -1.000000000 18.000000000

0.000000000 -1.000000000 -1.000000000 18.000000000

-0.500000000 -1.109375000 -1.000000000 18.000000000

-0.500000000 -1.109375000 -0.750000000 3.508056641

-0.500000000 -1.109375000 -0.625000000 0.454410553

-0.562500000 -0.473213613 -0.625000000 0.454410553

-0.593750000 -0.050185024 -0.625000000 0.454410553

-0.593750000 -0.050185024 -0.609375000 0.191316528

-0.593750000 -0.050185024 -0.601562500 0.067944440

-0.593750000 -0.050185024 -0.597656250 0.008233857

-0.595703125 -0.021135877 -0.597656250 0.008233857

-0.596679688 -0.006491229 -0.597656250 0.008233857

-0.596679688 -0.006491229 -0.597167969 0.000861241

-0.596923828 -0.002817510 -0.597167969 0.000861241

-0.597045898 -0.000978764 -0.597167969 0.000861241

-0.597106934 -0.000058919 -0.597167969 0.000861241

-0.597106934 -0.000058919 -0.597137451 0.000401122

-0.597106934 -0.000058919 -0.597122192 0.000171092

-0.597106934 -0.000058919 -0.597114563 0.000056084

-0.597110748 -0.000001418 -0.597114563 0.000056084

-0.597110748 -0.000001418 -0.597112656 0.000027333

-0.597110748 -0.000001418 -0.597111702 0.000012957

-0.597110748 -0.000001418 -0.597111225 0.000005770     Next Middle will get us close enough to zero:      F( -0.597110868 ) is   0.000000379       The desired approximation of the solution is:        t ≓ -0.597110868      
Note, ≓ is the approximation symbol One solution was found :       t ≓ -0.597110868              
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There is 1 solution to this equation.

An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equals sign (=), and expresses a relationship between the two expressions. Equations can be used to represent a variety of problems and can help solve real-world problems. For example, an equation can be used to calculate the amount of money someone will have after a certain period of time, or to calculate the distance between two points.

In order to answer this question, we must first solve the equation. 9t6-14+³ +4+- 1 = 0 can be written as 9t6 - 11 + 4 - 1 = 0. After simplifying, this equation becomes 9t6 - 7 = 0, which can be further simplified to t6 = 7. Taking the sixth root of both sides, we can determine that t = √7. Therefore, there is 1 solution to this equation.

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Answer:

A = 18

Step-by-step explanation:

A = √30^2-24^2

A = 18

The exact value of sin (A-B) in simplest form for positive acute angle A and B is found to be 221/1445.

We can use the trigonometric identity sin(A - B) = sinAcosB - cosAsinB to find the exact value of sin(A - B) for positive acute angles.

From the given information, we know that cosA = 4/5 and sinB = 8/17. Using identities, sin²A + cos²A = 1 and sin²B + cos²B = 1:

sinA = √(1 - cos²A)

= √(1 - (4/5)²)

= 3/5

cosB = √(1 - sin²B)

= √(1 - (8/17)²)

= 15/17

Now, we can substitute these values into the identity:

sin(A - B) = sinAcosB - cosAsinB

sin(A - B) = (3/5)(15/17) - (4/5)(8/17)

sin(A - B) = 9/17 - 32/85

sin(A - B) = (765 - 544)/1445

sin(A - B) = 221/1445

Therefore, the exact value of sin(A - B) in simplest form is 221/1445.

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Answer:

1099 inches

Step-by-step explanation:

We know that formula for volume of a cylinder is:

\(V=\pi r^2h\)

\(V=\pi 5^2*14\)

\(V=\pi 25*14\)

\(V=\pi 350\)

\(V=3.14*350\)

\(V=1099\)

Answer:

1099

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 9x + 8

y = 7.5x + 16

1.5x = 8

x = 5.3 hours

Answer:

5.3hrs or 5hrs 18mins

Step-by-step explanation:

First, we have to put the information given to us about the money they earn into an expression

Let x represent the number of hours Kini and Duke work and y represent the total amount of money they earn in a week.

y(kini) = 9x + 8

y(duke) = 7.5x + 16

Now we subtract the x values and the constant values

9x - 7.5x = 1.5x

16 - 8 = 8

Make these into an equation

1.5x = 8

Divide both sides by 1.5 so x(the number of hours the both work) can stand alone.

\(\frac{1.5x}{1.5} =\frac{8}{1.5}\)

x = 5.3hrs or 5hrs and 18 mins

Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

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Step-by-step explanation:

\( { \sqrt[3]{8} }^{ \frac{1}{4}x } = {2}^{ \frac{1}{4} x} = {8}^{ \frac{1}{3} \times \frac{1}{4}x } \\ = {8}^{ \frac{1}{12} x} \\ = { \sqrt[12]{8} }^{x} \)

Answer: 18%

Step-by-step explanation:

I gogled

Answer:

triangle D............

Triangle B

\(cos \: x= \frac{adj}{hyp} = \frac{5}{8} \)

If you need, always label your triangles!

The measure of the central angle m ∠JIK is 160°.

Given that the circle I, in which IJ is the radius of 9 units, the area of shaded sector = 36π, we need to find the m ∠JIK, the central angle.

Area of the sector = central angle / 360° × π × radius²

∴ 36π = m ∠JIK / 360° × π × 9²

m ∠JIK = 360° × 4 / 9

m ∠JIK = 160°

Hence, the measure of the central angle m ∠JIK is 160°.

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The expected profit of playing the game is -$1. You can therefore anticipate losing $1 on each ticket you purchase on average.

To calculate the expected profit of playing the game, we need to determine the probability of winning each prize and the corresponding payout for each prize.

First, let's calculate the probabilities for each prize:

Next, let's calculate the payouts for each prize:

Now, let's calculate the expected profit for playing the game:

Expected profit = (Probability of winning grand prize x Payout for grand prize) + (Probability of winning second prize x Payout for second prize) + (Probability of winning third prize x Payout for third prize) - Cost of ticket

Expected profit = (1/500 x $2,000) + (2/500 x $400) + (10/500 x $200) - $5

Simplifying the calculation, we get:

Expected profit = $4 - $5

Expected profit = -$1

The expected profit of playing the game is -$1. This means, on average, you would expect to lose $1 for each ticket you buy. In other words, the game is expected to have a negative return, and playing it is not financially beneficial in the long run.

Therefore, the expected profit of playing the game is -$1, or a loss of $1 on average for each ticket bought.

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The sample consists of three scores: 7, 8, and 9. The mean is 8, the median is 8, there is no mode, and the range is 2.

In statistics and probability, a sample refers to a subset of a population that is used to make inferences or draw conclusions about the entire population. In this case, the sample consists of the scores you obtained in 5 quizzes. The scores are as follows: 7, 8, and 9.
To analyze this sample, there are several key measures that can be calculated:
1. Mean: The mean, also known as the average, is calculated by summing up all the scores and dividing it by the number of scores. In this case, the mean can be calculated as (7 + 8 + 9) / 3 = 8.
2. Median: The median is the middle value when the scores are arranged in ascending order. In this case, since there are three scores, the median is the middle score, which is 8.
3. Mode: The mode is the score that appears most frequently in the sample. In this case, none of the scores repeat, so there is no mode.
4. Range: The range is the difference between the highest and lowest scores in the sample. In this case, the highest score is 9 and the lowest score is 7, so the range is 9 - 7 = 2.
5. Standard Deviation: The standard deviation is a measure of how spread out the scores are from the mean. It quantifies the amount of variation or dispersion in the sample. To calculate the standard deviation, you would need the full set of scores, not just the three provided.

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After 60 minutes, approximately 376.725 grams of the radioactive substance will remain.

To calculate how much radioactive substance will remain after 60 minutes, we need to use the decay rate of 1.9% per minute. First, we need to convert the decay rate to a decimal. 1.9% is equivalent to 0.019.

Next, we can use the formula for exponential decay: Remaining amount = Initial amount * (1 - decay rate) ^ time Plugging in the values, we have: Remaining amount = 1000 g * (1 - 0.019) ^ 60 Simplifying the equation: Remaining amount = 1000 g * (0.981) ^ 60.

Evaluating the equation: Remaining amount ≈ 376.725 g.

Therefore, after 60 minutes, approximately 376.725 grams of the radioactive substance will remain.

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Answer:

That's alot of words, kinda hard to understand

Answer:

see explanation

Step-by-step explanation:

(a)

given the arithmetic series 5 + a + 14 + b

the difference between consecutive terms is constant , that is

a₂ - a₂ = a₃ - a₂ ( substitute values )

a - 5 = 14 - a ( add a to both sides )

2a - 5 = 14 ( add 5 to both sides )

2a = 19 ( divide both sides by 2 )

a = 9.5

then

a₄ - a₃ = a₂ - a₁

b - 14 = a - 5 = 9.5 - 5 = 4.5 ( add 14 to both sides )

b = 18.5

(b)

the sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 5 and d = a₂ - a₁ = 14 - a = 14 - 9.5 = 4.5 , then

S₁₀ = \(\frac{10}{2}\) [ (2 × 5) + (9 × 4.5) ]

     = 5(10 + 40.5)

     = 5 ×  50.5

     = 252.5

(c)

\(S_{n}\) > 500 , that is

\(\frac{n}{2}\) (50.5) > 500 ( multiply both sides by 2 )

50.5n > 1000 ( divide both sides by 50.5 )

n > 19.80198... , that is

n = 20

Answer:

The end behavior of f(x)=2/3x-2 is: as x->+ infinity, f(x)->+ infinity

as x->- infinity, f(x)->- infinity

Step-by-step explanation:

When you are asked about the end behavior of a function, look to see where the function is traveling on the graph. For instance, this graph is linear, so you should look to see if the slope is positive or negative. This linear function is positive, so as x is reaching positive infinity the f(x) would also be reaching positive infinity. As x is reaching negative infinity, f(x) would also be reaching negative infinity. The end behavior of a function describes the trend of the graph on the left and right side of the x- axis. (As x approaches negative infinity and as x approaches positive infinity).  

Answer:

Step-by-step explanation:

Angle measures should be ordered in same way as the opposite sides.

Sides in the ascending order:

Their opposite angles in same order:

Correct choice is B

Answer:

Explanation: If something (a number or pattern) in a decimal is repeating, then you can put it in fraction form like this. the pattern is 8 .

Hope this helps!-xoxo

Answer:

\(\frac{8}{9}\)

Step-by-step explanation:

We have to create 2 fractions with the repeating number placed after the decimal point.

let x = 0.88.... → (1) ( multiply both sides by 10 )

10x = 8.88.... → (2)

Subtract (1) from (2), eliminating the repeating decimal

9x = 8 ( divide both sides by 9 )

x = \(\frac{8}{9}\)

Thus 0.888..... = \(\frac{8}{9}\)

Answer:

  shifted down 4 units

Step-by-step explanation:

You want to know the effect on the graph of changing y=2x+2 to y=2x-2.

The constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.

When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.

The effect on the graph is to move it down 4 units.

The function's formula for the ice sheet's thickness is S(t) = 0.2t + 1.02.

Mathematically, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

S(t) = mt + b

Where:

After a time of 7 weeks and a rate of decrease of 0.2, the y-intercept or initial amount of ice can be calculated as follows;

S(t) = mt + b

2.42 = 0.2(7) + b

2.42 = 1.4 + b

y-intercept, b = 2.42 - 1.4

y-intercept, b = 1.02.

Therefore, the required linear function is given by S(t) = 0.2t + 1.02.

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Complete Question:

A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.42 meters thick.

Let S(t), denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks).

Write the function's formula.

S(t) = ?

Answer:

⏬⬇⤵

Step-by-step explanation:

The Fundamental Theorem of Algebra states that the degree of a polynomial is the maximum number of roots the polynomial has. A third-degree equation has, at most, three roots.

So:

1. 3

2. 4

3. 3

4. 0

5. 1

6. 4

Answer:

The length of the ladder  = 6.5077 ft

Step-by-step explanation:

Given A ladder leans against the side of a house

Given the angle of elevation of the ladder is 68° when the bottom of the ladder is 16 ft from the side of the house

Let 'C' be the point of observation.

Given CA= 16 ft

 From right angle triangle

     x = 16 × cos 68°

    x = 16 × 0.4067

    x = 6.5077

  x = 6.5 ft

The length of the ladder = 6.5 ft

The statement that , "The set Span{u,v} is always visualized as a plane through the origin" is False because if vectors are scalar multiples of each other, then set Span{u,v} is a line through origin .

The set Span{u,v} is defined as the set of all linear combinations of vectors "u" and "v" . This set can be visualized as a plane in three-dimensional space if the vectors are not scalar multiples of each other.

The plane may not necessarily pass through the origin, unless one of the vectors is the zero vector .

If the vectors are scalar multiples of each other, then the set Span{u,v} is a line through the origin, and if one of the vectors is the zero vector, then the set Span{u,v} is a plane through the origin.

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The equation that represents the situation is y = 6x + 73. This equation can be used to determine the total number of tiles (y) for a given figure (x).

To calculate this equation, we first need to identify the two variables – the figure number (x) and the total number of tiles (y). Then, we can use the given information to set up the equation. We know that for figure 0, there are 73 tiles, so we can say y = 73. We also know that the pattern is growing by 6, so we can say y = 6x. Combining these two equations, we can say y = 6x + 73.

In order to calculate the total number of tiles for a certain figure, we can plug in the figure number into the equation. For example, if we wanted to calculate the total number of tiles for figure 5, we would plug in 5 for x. That would give us y = 6(5) + 73. Simplifying the equation, we would get y = 48 + 73, which equals 121. So, the total number of tiles for figure 5 is 121.

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Answer:

x=.3 or 3/10

Step-by-step explanation:

to solve for x, we need to separate it

so, we add 13 to the left side

40-11x=x

then add 11x to the right side so we have different coefficients on each side to solve for x

40=12x

then we divide 40/12 to get what x equals

we get

x= 0.3 or 3/10

hope this helped!

Answer:

x=10/3

Step-by-step explanation:

27 - 11x = x - 13

27+13=x+11x

40=12x

x=40/12

x=10/3

Final Answer: \(s = -\frac{3}{2}\)

Steps/Reasons/Explanation:

Question: Equations with variables on both sides: decimals and fractions, algebra 2. \(0.5s + 1 = 7 + 4.5s\).

Step 1: Subtract \(0.5\) from both sides.

\(1 = 7 + 4.5s - 0.5s\)

Step 2: Simplify \(7 + 4.5s - 0.5s\) to \(7 + 4s\).

\(1 = 7 + 4s\)

Step 3: Subtract \(7\) from both sides.

\(1 - 7 = 4s\)

Step 4: Simplify \(1 - 7\) to \(-6\).

\(-6 = 4s\)

Step 5: Divide both sides by \(4\).

\(-\frac{6}{4} = s\)

Step 6: Simplify \(\frac{6}{4}\) to \(\frac{3}{2}\).

\(-\frac{3}{2} = s\)

Step 7: Switch sides.

\(s = -\frac{3}{2}\)

~I hope I helped you :)~

TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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Answer:

6%.

Step-by-step explanation:

For arguments sake lets assume each fruit cost $1.

He spent $50 for the fruit.

His income from the 30 kg he sold was $35.

His income from  the remaining 20Kg  was $18.

Total income = $35 + $18 = $53

So his profit was  53 - 50 = $3.

= (3/50) * 100

= 6%

Answer:

I can't see it

Step-by-step explanation:

We need a bigger picture.