9.51 as a mixed number in a simplest form

Answer:

a = 2x, b = 3.

Step-by-step explanation:

8x^3+27 = (2x)^3 + 3^3

a = 2x and b = 3.

We can cube root 8x^3 getting 2x and cube root 27 getting 3.

Answer:

D

Step-by-step explanation:

it is only in the positive so i would say d because they all only have one y-value each and they are all positive though so i am saying D.

No, because two points with the same x-value have different y-values.

Step-by-step explanation:

thank me later

Answer:

neither

Step-by-step explanation:

Answer:

Step-by-step explanation:

every time x goes up 1,  y goes up 4  

x = 3  minus x = 2  is a delta (a change of 1)

x = 4  minus x = 3  is a delta (a change of 1)

x = 5  minus x = 4  is a delta (a change of 1)

       the delta x is ALWAYS 1 for this table you can always substract x's to find the delta     delta is symbolized by Δ      Δx  for the delta x

y = 7  minus y = 3  is a delta (a change of 4)

y = 11  minus y = 7  is a delta (a change of 4)

y = 15  minus y = 11  is a delta (a change of 4)

    the delta y is ALWAYS 4 for this table you can always substract y's to find the delta     delta is symbolized by Δ     Δy  for the delta y

the slope m = Δy / Δx      m = 4 / 1     m = 4

     y = mx + b             when x = 0    then  y = b   (called the y intercept)

so how do we find the y intercept?    

look at the pattern in the TABLE  Δx  and Δy

   when x = 1    y = (3 - 4)  = -1

             x = 0    y =( -1 - 4)   = -5

so       y = 4x - 5     is a line equation for the data in this table

                                I believe there are other forms for linear equations

                               I chose the y-intercept form

use the point slope equation

       (y - y1)  =  m(x - x1)            where (x1, y1)  are the coordinates of a point on  

                                                the line

       when you know the slope of the line and a point on the line

       as before

       m = (y2 - y1)  / (x2 - x1)          from the table

           = (7 - 3) / (3 - 2)                 still equals

           = 4/1  =  4        

        pick a point on the line    say x= 4 and y = 11    (4, 11)

       (y - y1)  =  m(x - x1)    

        y - 11   =   4(x - 4)              point slope form

         solving point slope form  for  y

        y  - 11  =   4x - 16               add 11 to both sides    

           y  =  4x - 5                    back to the y-intercept form

by dividing both sides by 1.5.

To solve the problem, we need to first determine the total amount of time Ricky spends in his classes. We know that each class is 1.5 hours long, so if he takes c classes, then he will spend a total of 1.5c hours on class time. In addition, we know that he spends 6.5 hours on homework. Therefore, the total amount of time Ricky spends on his classes and homework is:

Total time = Class time + Homework time

Total time = 1.5c + 6.5

We also know that Ricky has 23 hours per week to dedicate to his classes and homework. Therefore, we can set up the following equation:

Total time = 23

Substituting the expression for a total time from the first equation, we get:

1.5c + 6.5 = 23

Now we can solve for c:

1.5c = 23 - 6.5

1.5c = 16.5

c = 11

Therefore, Ricky takes 11 classes.

The equation that models the question is b) 23=6.5+1.5c. This equation correctly represents the total time Ricky spends on his classes and homework (23 hours), as well as the time he spends on homework (6.5 hours) and the time he spends in class (1.5c hours).

by dividing both sides by 1.5.

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Answer:

The answer is \(\frac{4}{13}\).

Step-by-step explanation:

Additive rule:

According to this rule, the probability that events A or B will occur is given by the formula,

\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Here,

We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.

Then,

\(\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}\)

Therefore, the probability that the card you select is a spade or queen is given by,

\(\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}\)

Therefore, the answer is \(\frac{4}{13}\).

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Answer:

The scale factor is 3

Step-by-step explanation:

The width of A is 1, the width of B is 3

the length of A is 3, the length of B is 9 so the scale factor from A to B is 3

Answer:

the scale factor is 3

Step-by-step explanation:

The scale factor is 3

The width of A is 1, the width of B is 3

the length of A is 3, the length of B is 9 so the scale factor from A to B is 3 so yeah the scale factor is 3 theres the answer

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

To find the perimeter (p) of a parallelogram, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.
Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in length. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by multiplying a by n/a, which is n.
So, the length of the other side is also n, and the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

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The correct statement is B. For all b, the equation Ax=b has a solution.

Since the columns of A are linearly independent, then the matrix A has full rank, and its column space is equal to the entire vector space in which it resides. This means that for any given vector b, we can find a linear combination of the columns of A that is equal to b, and therefore the equation Ax=b has a solution for all b.

Option A is incorrect, as there may be certain b vectors for which Ax=b has a solution.

Option C is incorrect, as the equation Ax=b may have a solution even when A has fewer columns than rows.

Option D is incorrect, as we can determine whether or not the equation Ax=b has a solution for all b by checking the rank of A.

Option E is incorrect, as the equation Ax=b may have a solution even when A has more columns than rows.

Option F is incorrect, as a square matrix may or may not have linearly independent columns, and therefore may or may not have a solution for all b.

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3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

Given that,

The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).

We have to find how many such difference triangle are possible.

We know that,

Perimeter of the triangle is 12cm.

p=12

a+b+c=12

a+b≥c

b+c≥a

So,

a+b+c≥2c

12≥2c

c≤6

So,

a≤6,b≤6,c≤6

We get,

a=6,b=3,c=3

a=5,b=4,c=3

a=4,b=4,c=4

Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

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Answer: $39.60

Step-by-step explanation:

Here is the correct question:

Christopher has breakfast at a cafe and the cost of his meal is $36.00 . because of the service he wants to leave a 10% tip.What is his total bill including tip?

His total bill will be the addition of the cost of his meal and the tip. This will be:

= $36.00 + (10% × $36.00)

= $36.00 + $3.6

= $39.60

His total bill including tip is $39.60

While there may be other integration techniques that can be used to evaluate some chain rule integrals directly, u-substitution is a powerful and versatile tool that is often used to simplify and evaluate these types of integrals.

The chain rule is a fundamental concept in calculus, and it applies to differentiation as well as integration. The chain rule integration technique involves recognizing the function inside the integral as the composition of two functions, and then using substitution to simplify the integral.

In some cases, it may be possible to use other integration techniques to evaluate chain rule integrals directly, without using substitution. However, in general, the use of substitution (or a related technique, such as integration by parts) is often necessary to evaluate chain rule integrals.

That being said, there are some special cases where the chain rule integrals can be evaluated more directly, such as when the integrand is a polynomial or a rational function, or when it has a simple algebraic form.

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The statement "The fewest magazine appearances could be 1" is true based on the given information.

If the median number of magazine appearances made by 7 models is 5, then there must be at least one model with 5 or fewer appearances and at least one model with 5 or more appearances.

If the range of number of magazine appearances made by those models is 5, then the difference between the lowest and highest number of appearances is 5. This means that the lowest number of appearances could be as low as 1 (if the highest number of appearances is 6) or even lower (if the highest number of appearances is greater than 6).

Therefore, the statement "The fewest magazine appearances could be 1" is true based on the given information.

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The nearest tenth, the central angle of the circle is approximately 85.7 degrees.

To find the central angle of the circle, we can use the formula for the area of a sector:

A = (θ/360) * π * r²,

where A is the area of the shaded region, θ is the central angle of the circle in degrees, π is approximately 3.14, and r is the radius of the circle.

Given that A is 90.6 cm² and r is 11 cm, we can substitute these values into the formula and solve for θ:

90.6 = (θ/360) * 3.14 * 11².

Simplifying the equation:

90.6 = (θ/360) * 3.14 * 121,

90.6 = (θ/360) * 380.34.

To solve for θ, we can divide both sides of the equation by (θ/360) * 380.34:

90.6 / 380.34 = θ/360.

θ/360 = 0.238,

θ = 0.238 * 360,

θ ≈ 85.7.

Rounding to the nearest tenth, the central angle of the circle is approximately 85.7 degrees.

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The method of Lagrange multipliers is applied to minimize the function f(x, y) = xy^2 on the unit circle x^2 + y^2 = 1.

To minimize the function f(x, y) = xy^2 subject to the constraint x^2 + y^2 = 1, we can use the method of Lagrange multipliers.

Let's introduce a Lagrange multiplier λ to incorporate the constraint into the objective function. Our augmented function becomes F(x, y, λ) = xy^2 + λ(x^2 + y^2 - 1).

Next, we take partial derivatives of F with respect to x, y, and λ, and set them equal to zero to find critical points.

∂F/∂x = y^2 + 2λx = 0,

∂F/∂y = 2xy + 2λy = 0,

∂F/∂λ = x^2 + y^2 - 1 = 0.

Solving these equations simultaneously, we obtain three possibilities:

x = 0, y = 0, λ = 0, which does not satisfy the constraint equation.

x = 1/√3, y = ±√(2/3), λ = -1/2√3, which gives us two critical points.

x = -1/√3, y = ±√(2/3), λ = 1/2√3, which gives us another two critical points.

Finally, we evaluate the function f(x, y) = xy^2 at the critical points to find the minimum and obtain the solution.

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543 cubic centimeters has 0.543 L approximate displacement

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is

V = π/4 x \(D^{2}\) x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already show the displacement. So, we can ignore above formula and the 4 cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter ( cc ) into liter ( L )

Displacement = cc / 1000 L

                       = 543 / 1000 L = 0.543 L

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There are 210 ways to write 5 of the letters of the word ALGORITHM in a row if the 2 two letters must be TH

Given data

the word ALGORITHM

the first two letters must be TH

ALGORITHM has 9 letters and order of writing the letters is important, so we use Permutation to solve this

The 2 letters TH are fixed and this reduces the number of letters in the word from 9 to 7. Also, the the first two being fixed reduces the letters arrangement to be 3.

This means that we have the arrangement as follows:

7P3

= 7! / ( 7 - 3 )!

= 7! / 4!

= 7 * 6 * 5 * 4! / 4!

= 7 * 6 * 5

= 210 ways

Hence there are 210 ways to write 5 of the letters of the word ALGORITHM in a row if the 2 two letters must be TH

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The correct statement regarding whether female and blue are independent events is given as follows:

D) Yes, P(Female ∩ Blue) = P(Female) ⋅ P(Blue)

Two events, A and B are independent, if, and only if, the probability of both events is equals to the multiplication of the probabilities of each event.

\(P(A \cap B) = P(A)P(B)\)

From the table, the probabilities are given as follows:

The multiplication of these probabilities is of:

0.7 x 0.7 = 0.49 = P(Female and Blue).

Hence the events are independent.

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Answer:

Step-by-step explanation:

34.546.567

Answer:

AB = (-1–3)/2 = -2

AC: (7+1)/6 = 4/3

BC: (7–3)/(6+2) = 1/2

Step-by-step explanation:

The measure of T in the quadrilateral can be found to be B. 100 degrees.

The two quadrilaterals given are trapeziums and they are similar. This means that they have the same angles meausures.

As this is a quadrilateral, the total measure of the interior degrees would be the value of 360 degrees.

The value of T is the only missing angles and so can be found to be:

T = 360 - 125 - 60 - 75

T = 360 - 260

T = 100 degrees

In conclusion, the measure of T is 100 degrees.

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The given series Σ((-1)^k) / (k^(3/2) + 3) for k=1 to ∞ is absolutely convergent.

To determine if the given series is absolutely convergent, conditionally convergent, or divergent:

The series is:

Σ((-1)^k) / (k^(3/2) + 3) for k=1 to ∞

Step 1: Test for absolute convergence
To check for absolute convergence, we consider the absolute value of the series' terms:

Σ|((-1)^k) / (k^(3/2) + 3)| for k=1 to ∞
This simplifies to:
Σ(1) / (k^(3/2) + 3) for k=1 to ∞

Step 2: Apply the Comparison Test
We can compare our series with a known convergent series, 1/k^(3/2), since k^(3/2) ≤ (k^(3/2) + 3) for all k.

Therefore, we have:

(1) / (k^(3/2)) ≥ (1) / (k^(3/2) + 3)

Since the series Σ(1) / (k^(3/2)) converges (it's a p-series with p = 3/2 > 1),

by the Comparison Test, our series Σ(1) / (k^(3/2) + 3) also converges.

This means the original series is absolutely convergent.

The given series Σ((-1)^k) / (k^(3/2) + 3) for k=1 to ∞ is absolutely convergent.

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Answer:

x = 8

Step-by-step explanation:

\(\frac{9x}{4y}=1\)

\(\frac{9x}{4*18} =1\)

9x = 72

x = 8

Step-by-step explanation:

ratio =4:1

total= 4+1 =5

1/5 × 52= 10.4 years

Answer:

Step-by-step explanation:

let age of Shyam=x

age of Ram=x+4

x+x+4=52

2x=52-4=48

2x=48

x=48/2=24

age of Shyam=24 years

age of Ram=24+4=28 years.

Answer:

Happened in 1986

Maybe 37 years ago?

The expected value of winnings is 0.

The expected value will be calculated by taking the sum of winning and loosing = E(x) = ΣxP(x), where X is the outcome and P is the probability of that outcome.

The probability of winning = X P(x)

The probability of winning = 1 × 0.5

The probability of winning = 0.5

The probability of loosing = -1 × 0.5 (-1 because it will be the loss)

The probability of loosing = -0.5

Calculating their sum = 0.5 + (-0.5)

Expected value = 0.5 - 0.5

Expected value = 0

Hence, the expected value is 0.

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Answer:

Sally started by graphing the point (2,0) is wrong

Step-by-step explanation:

We know

The equation is  y = - 3/4x + 2

M = -3/4

Y-intercept located at (0, 2)

Sally started by graphing the point (2,0)

This is wrong because (2,0) is the x-intercept, not the y-intercept!

So, she is wrong right at the beginning.

Answer:2x^2+23

Step-by-step explanation:

7x^2+3-5x^2+20    (distribute (-5) to x^2 and (-4))

2x^2+3+20              (combine like terms)

2x^2+23

The probability that both smoke alarms will sound an alarm in the presence of smoke is 0.64.

When two independent events occur, the probability of both events happening is calculated by multiplying their individual probabilities. In this case, the probability of one smoke alarm functioning properly and sounding an alarm in the presence of smoke is 0.8. Since the two smoke alarms operate independently, we can multiply the probability of one alarm functioning (0.8) by the probability of the other alarm functioning (also 0.8).

So, the probability of both smoke alarms sounding an alarm is 0.8 * 0.8 = 0.64. Therefore, there is a 64% chance that both alarms will function properly and sound an alarm in the presence of smoke.

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