2(4x-1)+3=7
i'm little confused on this

The given expression (axb)/(bt2) is a dimensionless quantity.

To find the dimensions of the expression (axb)/(bt2),

where f = ax + bt2 + c,

we will consider the units of each term in the equation.

Let's assume the unit of distance (x) to be meters (m) and the unit of time (t) to be seconds (s).

Therefore, the units of each term are as follows:

ax has units of (m) * (unit of a)bt2 has units of (s2) * (unit of b)c has units of (unit of c)

The final expression can be written as:

(axb)/(bt2) = a/m * b/ s2

The above expression is a dimensionless quantity.

This is because the dimensions of both the numerator and denominator cancel out each other.

Therefore, the dimensions of (axb)/(bt2) are dimensionless.

Note: A dimensionless quantity does not have any physical dimension or units.

It is also known as a pure number.

A physical quantity is expressed as the product of a numerical value and a physical unit. The unit of a physical quantity provides the scale or reference standard for measuring that quantity.

Dimensional analysis is a powerful tool for solving problems in physics.

It involves checking the consistency of units in an equation to ensure that it is physically meaningful. By using the correct units and dimensions, we can easily convert from one unit to another and avoid errors in calculations.

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Random variables X and Y have the joint PMFPX,Y(x,y) = c|x+y| x=-2,0,2; y=-1,0,1 the answers are: 1. the value of the constant c is 1/12, 2. P[Y=X] = P[X=0, Y=0] = 0, and 3.P[X<1] is equal to 1/2.

1. To find the value of the constant c, we need to ensure that the sum of the joint probabilities over all possible values equals 1.

The given joint probability mass function (PMF) P(X,Y) is:

P(X=-2, Y=-1) = c|-2+(-1)| = c|(-3)| = 3c

P(X=-2, Y=0) = c|-2+0| = c|(-2)| = 2c

P(X=-2, Y=1) = c|-2+1| = c|(-1)| = c

P(X=0, Y=-1) = c|0+(-1)| = c|(-1)| = c

P(X=0, Y=0) = c|0+0| = c|0| = 0

P(X=0, Y=1) = c|0+1| = c|1| = c

P(X=2, Y=-1) = c|2+(-1)| = c|1| = c

P(X=2, Y=0) = c|2+0| = c|2| = 2c

P(X=2, Y=1) = c|2+1| = c|3| = 3c

Summing up these probabilities, we get:

3c + 2c + c + c + 2c + 3c = 12c

For this sum to equal 1, we have:

12c = 1

c = 1/12

Therefore, the value of the constant c is 1/12.

2. To find P[Y|X], we need to calculate the conditional probability of Y given X. Since the PMF is given, we can directly read the values:

P[Y=-1|X=-2] = c|-2+(-1)| = c|(-3)| = 3c = 3/12 = 1/4

P[Y=0|X=-2] = c|-2+0| = c|(-2)| = 2c = 2/12 = 1/6

P[Y=1|X=-2] = c|-2+1| = c|(-1)| = c = 1/12

Similarly, for other values of X, we can calculate the conditional probabilities.

P[Y=X] refers to the probability that Y is equal to X. Looking at the given PMF, we can see that the only case where Y=X is when X=0, as no other values in the PMF have the same value for X and Y.

Therefore, P[Y=X] = P[X=0, Y=0] = 0.

3. Finally, to find P[X<1], we need to sum up the probabilities for all Y values where X<1:

P[X<1] = P[X=-2, Y=-1] + P[X=-2, Y=0] + P[X=0, Y=-1] + P[X=0, Y=0]

      = 3/12 + 2/12 + 1/12 + 0 = 6/12 = 1/2.

Therefore, P[X<1] is equal to 1/2.

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The lower limit is 1269 A.D., and the upper limit is 1291 A.D.

(a) The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution;194, 1,278, 1,292, 1,313, 1,268, 1,316, 1,275, 1,317, 1,275.Let x be the sample mean and s be the sample standard deviation. Using the calculator, we get:x = 1280.1111 (rounded to four decimal places)s = 18.7342 (rounded to four decimal places)Therefore, the sample mean year x is 1280.1111 A.D., and the sample standard deviation s is 18.7342 A.D.

(b) 90% Confidence Interval The formula for the confidence interval for the mean of a normal distribution with known standard deviation is: CI = x ± Zα/2 (σ/√n)where CI is the confidence interval, x is the sample mean, Zα/2 is the critical value from the standard normal distribution for a given level of confidence (α), σ is the known population standard deviation, and n is the sample size. Since the sample size is small and the population standard deviation is unknown, we use the t-distribution instead of the standard normal distribution. The formula becomes: CI = x ± tα/2 (s/√n)where tα/2 is the critical value from the t-distribution for a given level of confidence (α) and n - 1 degrees of freedom. Using a t-table with 8 degrees of freedom and a level of significance of 0.1 (because we want a 90% confidence interval), we get:t0.05 = 1.85955t0.05 = -1.85955, The sample mean is x = 1280.1111 A.D., the sample standard deviation is s = 18.7342 A.D., and the sample size is n = 9.So, the confidence interval is:

CI = 1280.1111 ± 1.85955 (18.7342/√9)CI = 1280.1111 ± 11.06677CI = (1269, 1291)

Hence, the lower limit is 1269 A.D., and the upper limit is 1291 A.D.

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Answer:

A.

Step-by-step explanation:

A. because an input cannot have two outputs. However, two different inputs can have the same output.

Answer: 38845

Step-by-step explanation:

Answer:

38,845

Step-by-step explanation:

Both of the given inequalities (∣u⋅v∣⩽∣u∣∣v∣ and ∣u+v∣⩽∣u∣+∣v∣) have been proved using the Cauchy-Schwarz inequality and the triangle inequality, respectively.

To prove the inequalities, let's consider vectors u and v in a vector space.

Proof: ∣u⋅v∣⩽∣u∣∣v∣

We start by using the Cauchy-Schwarz inequality:

∣u⋅v∣ ⩽ ∣u∣∣v∣

This inequality is a direct consequence of the Cauchy-Schwarz inequality, which states that for any vectors u and v in a vector space:

∣u⋅v∣ ⩽ ∣u∣∣v∣

Therefore, the first inequality is proven.

Proof: ∣u+v∣⩽∣u∣+∣v∣

To prove this inequality, we can use the triangle inequality:

∣u+v∣ ⩽ ∣u∣ + ∣v∣

The triangle inequality states that for any vectors u and v in a vector space:

∣u+v∣ ⩽ ∣u∣ + ∣v∣

Hence, the second inequality is proven.

Both of the given inequalities (∣u⋅v∣⩽∣u∣∣v∣ and ∣u+v∣⩽∣u∣+∣v∣) have been shown to be true using the Cauchy-Schwarz inequality and the triangle inequality, respectively.

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer:

Step-by-step explanation:

Given the speed of an object to be 4metres/month, we are to express the speed in inches/hour.

First we will need to convert 4meters to inches

From the conversion factors given,

1 foot (ft) = 0.305 meters (m)

x ft = 4metres

cross multiply

x * 0.305 = 4*1

x = 4/0.305

x = 13.115ft

4 metres = 13.115ft

Then we will convert 13.115ft to inches

From the conversion factors,

1 foot (ft) = 12 inches (in)

13.115ft = y

cross multiply

y = 13.115*12

y = 157.377 inches

Hence 4 metres = 157.77inches.

For 1 month to hour

First we need to convert month to days and from the conversion factor

1 month = 30 days

Next is to convert 30days to hours

Since 1 day = 24hours

30days = z

z = 30* 24

z = 720hours

Hence 1 month = 720hours

On converting 4metres/month to inches/hour

4metres/month = 157.77inches/720hours

4metres/month = 0.219inches/hour

Hence the speed of the object in inches per hour to the nearest hundredth is 0.22inches/hour

Step-by-step explanation:

please review the attachment

No, 1 1 2 3 5 8 is not an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant to the previous term.

Thus, the difference between successive terms is the same. In the given sequence, the difference between terms 1 and 2 is 0, between terms 2 and 3 is 1, between terms 3 and 5 is 2, and between terms 5 and 8 is 3. Therefore, the difference between successive terms is not the same and hence, 1 1 2 3 5 8 is not an arithmetic sequence.

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Answer:

3rd

Step-by-step explanation:

corner A + corner B + corner C = 180 degrees (in triangle)

so the correct answer is:

x + 68 + 72 = 180

Answer:

X>3

Step-by-step explanation:

X+9<4X

x-x+9<4x-x

9<3x

3<x

Answer:

Rs. 1250

Step-by-step explanation:

\(x\) is the cost of the video-game without VAT.

VAT is 162.5 at the rate of 13%.

13% of \(x\) is the VAT.

\(13/100 \times x = 162.5\)

\(0.13 \times x =162.5\)

\(x=162.5 \div 0.13\)

\(x=1250\)

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by  the three friends =  5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

An expressiοn is a way οf writing a statement with mοre than twο variables οr numbers with οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Example: 2 + 3x + 4y = 7 is an expressiοn.

It is given that,

number οf cans cοllected by Jessa = 5xy + 17

number οf cans cοllected by Tyree = x²

number οf cans cοllected by Ben = 4x² - 8  

Part(a)

tοtal number οf cans cοllected by three friends = cans cοllected by Jessa + Tyree + Ben

= 5xy + 17 + x² + 4x² - 8

= 5x² + 5xy - 9

Part(b)

the gοal οf fοοd cans cοllected = 8x² − 4xy + 8

Sο, the number οf fοοd cans still left tο cοllect = gοal - (number οf cans cοllected)

= (8x² − 4xy + 8) - (5x² + 5xy - 9)

= 8x² - 5x² - 4xy − 5xy + 8 + 9

= 3x² - 9xy + 17

Therefοre,

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by the three friends = 5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

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The system of equations that represents this situation will be a + c = 125 and 12a + 6c = 1140.

Therefore, the equation that can be used in solving the question will be:

a + c = 125

12a + 6c = 1140

The equation above will give the values needed.

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Answer: Choice C

y = 4x

Direct variation

=====================================================

Explanation:

We add 4x to both sides to isolate y. That leads to y = 4x

This is a direct variation equation because it's in the form y = kx, for some constant k.

Answer:

Exponente positivo

Potencias de 10

Escribe estos números en forma ordinaria:

           7'3·103;  4'724·108; 8'24·105

Notación científica. Orden de magnitud. Comparaciones

Expresa en notación científica las siguientes cantidades e indica su orden de magnitud.

235'74; 1985; 12 billones; 320 millones; 37.800.000.000; 220.000.

La desaparición de los dinosaurios ocurrió hace 65 millones de años, aproximadamente 108 años. Por ello hemos situado la D debajo de la potencia correspondiente:

El nacimiento del Universo (U) ocurrió hace 15 mil millones de años . Sitúa U en la casilla que le corresponde. Haz lo mismo con:

El califato cordobés de Abderramán (A): aproximadamente 800 años.

El control, del fuego (F): hace 600.000 años.

Aparición del hombre de Cromagnon (C): 30.000 años.

El nacimiento de la Tierra: (T): 4.5 mil millones de años.

El primer paso del hombre en la Luna (L): hace una veintena de años.

El primer paso del hombre en la Tierra (H): tres millones de años

La invención de la imprenta por Gutenberg (G): hace 550 años.

La nebulosa "Triangulum" está a 1'4·1022  metros de la Tierra. Escribe esta distancia en forma ordinaria.

Step-by-step explanation:

The number of 6-card hands  in which at least one card from each suit is equal to 8,184,220.

Total number of 6-card hands that can be formed from a deck of 60 cards is,

Using combination formula,

C(60, 6) = 50,063,860

Now, subtract the number of 6-card hands that do not contain at least one card from each suit.

There are 5 ways to choose the suit that will be missing from the hand.

Once this suit is chosen, there are 48 cards remaining in the other suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suit is,

C(48, 6) = 12,271,512

Overcounted the number of hands that are missing more than one suit.

There are C(5, 2) ways to choose 2 suits that will be missing from the hand.

Once these suits are chosen, there are 36 cards remaining in the other 3 suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suits is,

C(36, 6) = 1,947,792

We cannot have a 6-card hand that is missing more than 2 suits.

3 suits with no cards in the hand, which is not allowed.

Number of 6-card hands that have at least one card from each suit is,

C(60, 6) - 5×C(48, 6) + C(5, 2)×C(36, 6)

=50,063,860 - 5×  12,271,512 + 10 × 1,947,792

= 50,063,860 -61,357,560 + 19,477,920

= 8,184,220

Therefore, there are 8,184,220 of 6-card hands that have at least one card from each suit.

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Answer:

No, they cannot be becuase the points are too different- no same numerical values.

a.  The function for the total expenditures is F(x) = 4.11x² + 87.23x + 1386.52

b.  In 2017, total expenditures will be 3669.57 billion dollars.

a. Since the rate of increase of total expenditures is given as f(x) = 8.22x + 87.23, the function that gives the total expenditures x years after 2000 can be found by integrating the rate of increase:

F(x) = ∫ f(x) dx = 4.11x² + 87.23x + C

Since the total expenditures were $1590.5$ billion in 2002, we can use this information to find the constant $C$:

F(2) = 4.11(2)² + 87.23(2) + C = 1590.5

Solving for C, we get:

C = 1386.52

Therefore, the function that gives the total expenditures x years after 2000 is:

F(x) = 4.11x² + 87.23x + 1386.52 (in billions of dollars)

b. To find the total expenditures in 2017, we need to substitute x = 17 in the function F(x):

F(17) = 4.11(17)² + 87.23(17) + 1386.52≈ 3669.57

Therefore, the total expenditures in 2017 will be approximately 3669.57 billion dollars.

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A residual is the difference between "the measured and predicted values of the quantity of interest".

In regression analysis, a residual would be the difference between an observable and anticipated value.

The formula is;

Residual = Observed value – Predicted value

Some key features regarding the residuals are-

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The stretch of an exponential decay function is y = 2(1/6)^x

An exponential function is represented as

y = ab^x

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/6)^x

Hence, the exponential decay function is y = 2(1/6)^x

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The maximum population is -255.

To find the critical points of the function \(P(t) = -2t^5 + 5t^4 + 80t^3 + 1,\)we need to find the values of t where the derivative of the function is equal to zero.

i. Find the critical points:
To find the derivative of the function, we can differentiate each term separately:
\(P'(t) = -10t^4 + 20t^3 + 240t^2\)

Now, we set P'(t) equal to zero and solve for t:
\(-10t^4 + 20t^3 + 240t^2 = 0\\\)
Factoring out common terms, we get:
\(t^2(-10t^2 + 20t + 240) = 0\)

We have two factors:
\(t^2 = 0 -- > t = 0 (multiplicity 2)\)

\(-10t^2 + 20t + 240 = 0Dividing both sides by -10, we get:t^2 - 2t - 24 = 0\\\)
This quadratic equation can be factored as:
(t - 4)(t + 6) = 0

Setting each factor equal to zero:
t - 4 = 0   -->   t = 4
t + 6 = 0   -->   t = -6

Therefore, the critical points of the function are t = 0 (multiplicity 2), t = 4, and t = -6.

ii. In how many years will the population reach a maximum?
To determine when the population reaches a maximum, we need to analyze the behavior of the function at the critical points.

From the critical points we found, t = 0 (multiplicity 2), t = 4, and t = -6, we can see that t = 0 occurs twice, indicating a potential point of inflection rather than a maximum or minimum.

To determine the maximum point, we need to check the second derivative, which will help us identify whether the critical points are maximum or minimum points.

The second derivative of P(t) is obtained by differentiating P'(t):
\(P''(t) = -40t^3 + 60t^2 + 480t\\\)
Evaluating P''(t) at the critical points:
P''(0) = 0
P''(4) = 3520
P''(-6) = 2880

Since P''(4) > 0 and P''(-6) > 0, it means the function is concave up at t = 4 and t = -6. Therefore, the population reaches a maximum at t = 4.

iii. What is the maximum population?
To find the maximum population, we substitute the value of t = 4 into the original function P(t):
\(P(4) = -2(4)^5 + 5(4)^4 + 80(4)^3 + 1\)

Simplifying this expression, we get:
\(P(4) = -2(1024) + 5(256) + 80(64) + 1P(4) = -2048 + 1280 + 512 + 1P(4) = -2048 + 1793P(4) = -255\)

Therefore, the maximum population is -255.

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1/3 is the rate of change (slope) given the set of data points below

To find the rate of change (slope) given the set of data points, we can use the formula for slope:

slope = (change in y) / (change in x)

Using the given points:

Point 1: (10, 19)

Point 2: (4, 17)

Point 3: (-2, 15)

Point 4: (-8, 13)

We can calculate the slope between each pair of points:

Slope between Point 1 and Point 2:

slope = (17 - 19) / (4 - 10) = -2 / -6 = 1/3

Slope between Point 2 and Point 3:

slope = (15 - 17) / (-2 - 4) = -2 / -6 = 1/3

Slope between Point 3 and Point 4:

slope = (13 - 15) / (-8 - (-2)) = -2 / -6 = 1/3

The rate of change (slope) between these points is consistent and equal to 1/3.

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7

6 / 4 = 1.5 so that means 6 / 1.5 = 4

now that we have that, 10.5 / 1.5 = 7

Answer:

its 7.

Step-by-step explanation:

Answer:

acute = 30,right angle = 90,obtuse = 135,line = 180

D. 2322.50

Step-by-step explanation:

I hope it's right.

Answer:

y > -1/4x + 4

Step-by-step explanation:

First find the equation of the line itself, which is y = -1/4x + 4, then determine if graph shades above the line or below the line. If it shades above which is true in this case, it will be greater than. If it shades below which does not occur in this case, it will be less than. Because the line is dashed and not solid, it will just be greater than or less than.

Therefore y = -1/4x + 4 → y > -1/4x + 4 [Shades above the line, line is dashed].

The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is  \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

What is a polynomial?

⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.

Calculation;

We have been given two polynomial which we have to add   \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)

The sign after addition or subtraction will always be of the variable having more value.

\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)

On adding like terms with each other

⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)

⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)

Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).

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