Which expressions are equivalent to
5^2/5^8

Answer: 1: 9x

Step-by-step explanation:

2: 3b

3: 3m

4: 5a

5: 7x

6: 3a+5b

7: 9x-4

8: m-6b

9: 13a+3b+6c

10: 1+9b

11: 7p

12: 2a+1b-10

The weight of meteorite A and B are 21 and 168 tons respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The weight of meteorite A is 8 times the weight of meteorite B. And the sum of their weights is 189 tons,

To find their weights we need to establish an equation, relating their weights,

Let weight of meteoroid B be x, then weight of meteoroid A will be 8x,

Establishing the equation,

8x+x = 189

9x = 189

x = 21

8x = 21x8 = 168

Hence, The weight of meteorite A and B are 21 and 168 tons respectively.

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Answer:

[tex]6^{\frac{1}{12}}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } =\frac{6^{\frac{1}{3} } }{6^\frac{1}{4} }[/tex]

[tex]= 6^{\frac{1}{3}[/tex] ÷ [tex]6^{\frac{1}{4}}[/tex]

= [tex]6^{\frac{1}{3}-\frac{1}{4}}[/tex]

=[tex]6^{\frac{4}{12}-\frac{3}{12}}[/tex]

[tex]= 6^\frac{1}{12}[/tex]

The volume of the cone is approximately 134 ft cube.

The cone would fit in 4 times in the red beach ball.

The diameter of the red beach ball is 8 inches, then the cone has the same radius and a height of 8 inches .

Therefore, to know the number of times the beach ball will fit into the cone, we have to find the volume of each solid shape.

Therefore,

volume of the beach ball(sphere) = 4πr³

where

r = 8  /2 = 4 inches

volume of the beach ball(sphere) = 4 × π × 4³

volume of the beach ball(sphere) = 256π ft³

Therefore,

volume of the cone = 1 / 3 πr²h

where

volume of the cone = 1 / 3 × π × 4²  × 8

volume of the cone = 128π / 3

volume of the cone = 42.7π

volume of the cone = 134.078

volume of the cone ≈ 134 ft³

Therefore,

volume of beach ball / volume of cone = 256π / 42.7π = 5.99531615925

Therefore, the cone will fit 4 times into the red beach ball.

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The value of Safeco stock given the required return growth rate and the dividend of the stock is $89.60.

The value of the stock can be determined using the constant growth dividend model. According to the model, the value of the stock is a function of the growth rate, dividend and the required return of the stock.

Value of the stock = [dividend x (1 + g)] / (r - g)

where

r = required return

g = growth rate

Value of the stock = [1.60 x (1.12) / (0.14 - 0.12)

Value of the stock = 1.792 / 0.02

Value of the stock = $89.60

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The original number is 57.

The two equations are x+y = 12 and (10y+x)−(10x+y) = 18.

Let the digit at the tens place be x and the digit at the unit place be y.

x+y = 12 .........(1)

Required Number = (10x+y).

Number obtained on reversing the digits = (10y+x).

According to the condition, we get

(10y+x)−(10x+y) = 18

→ 9y−9x = 18

→   y−x = 2     ..........(2)

Adding (1) and (2), we get

2y = 14

y =7

x = 12 - 7

x  = 5

Hence, the required number is 57.

The equations used to solve this is x+y = 12 and (10y+x)−(10x+y) = 18.

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Answer What is the midpoint of /AB? =b. point G

Step-by-step explanation:

AB is the abbreviation of “artium baccalaureus,” which is the Latin name for the Bachelor of Arts (BA) degree. It's a liberal arts degree, so it emphasizes the humanities, languages, and social sciences fields

Answer:

To solve the given system of equations, we can start by substituting the value of x in the second equation into the first equation. Since the second equation tells us that x = y - 2, we can substitute y - 2 for x in the first equation to get:

x = 17 - 4y

y - 2 = 17 - 4y

Then, we can combine like terms on the right-hand side to get:

x = 17 - 4y

-3y = 15

Finally, we can divide both sides by -3 to solve for y, and then substitute this value back into one of the original equations to solve for x:

x = 17 - 4y

y = -5

x = 17 - 4(-5) = 17 + 20 = 37

Therefore, the solution to the system of equations is x = 37 and y = -5.

Answer:

No.

Step-by-step explanation:

A function have only one output (y) for each x.  This is not true with this graph.  For example: the point (6,1) and ( 6,5) are both on the graph.  The input 6 has more than 1 output. It has the output of 1 and 5.  Since it has more than one output, it is not a function.

The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.

The given sequence is -  4, 5, 7, 11, 19, 35, 67, ...

the first term - [tex]t_1[/tex] is 4

Hence, we can write the sequence as follows-

4 + [tex]2^0[/tex] = 5

5+[tex](2)^1[/tex]=7

7+[tex](2)^2[/tex]=11

11+[tex](2)^3[/tex]=19

and so on.

Here, we are adding the previous term with the exponential form of 2.

thus, we can conclude that -

[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]

where,  x is a set of whole numbers, and n is a set of natural numbers.

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Answer:

9,510,223.49 galones!

Step-by-step explanation:

Primero, tienes que saber la cauntidad de los litros en un galon.

Hay 3.7854 litres en un galon

ahora, hacemos un ratio

1 galon = 3.7854 litres

? galones = 600,000 litres

Para encontrar la respuesta, divide 600,000 por 3.7854 para obtener la cauntidad de los galones

600,000 ÷ 3.7854 = 158,503.725 galones

158,503. 725 litres fluyen por segundo.

Hay 60 segundos en un minuto asi que, tenemos que multiplica nuestra respuesta por 60 para calcular nuestra respuesta final.

158,503. 725 × 60 = 9,510,223.49 galones!

The friend should change the multiplication of 9/4 to multiplication by the reciprocal of 9/4.

Option C is the correct answer.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

4(2/3) and 2(1/4)

Divide 4(2/3) by 2(1/4)

4(2/3) ÷ 2(1/4)

= 14/3 ÷ 9/4

Multiply the reciprocal of 9/4.

= 14/3 x 4/9

= 56/27

= 2(2/27)

Thus,

The value of the division of the fraction is 2(2/27).

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The correct statements are:

a) The independent variable is the number of people.

b) The initial value (initial fee) for the picnic is $40.

d) As the number of people increases, the total cost of the picnic increases.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:

m = (y - y')/x - x'

Now let's analyze the table:

The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:

(6, 52) and (9, 58).

Then the slope is:

a = (58 - 52)/9 -6 = 2

Then the line is something like:

y = 2*x + b

To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.

We will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b = 40

Then the linear equation is:

y = 2*x + 40

Now let's see which statements are correct.

a) The independent variable is the number of people.

True, the "x" represents the number of people.

b) The initial value (initial fee) for the picnic is $40.

True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.

c)The rate of change is $8.67 per person.

False, the rate of change is equal to the slope, in this case is $2 per person.

d) As the number of people increases, the total cost of the picnic increases.

True.

e)  If 4 people attended the picnic, the total cost would be $46.

To see if this is true or not, we just need to evaluate the function that we got in x = 4.

y = 2*4 + 40 = 48

So we can see that this is false.

Therefore, the correct statements are A, B, D

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A is negative semidefinite if and only if all the kth order principal minors of A are ≤ 0 if k is odd and ≥ 0 if k is even. The given statement is true.

What is a negative semidefinite matrix?

A Hermitian matrix with all of its eigenvalues being nonpositive is known as a negative semidefinite matrix. Using the Wolfram Language's NegativeSemidefiniteMatrixQ[m], a matrix may be checked to see if it is negative semidefinite.

The direction of space is inverted when the determinant is negative. If you give your fingers dimensions before transformation and they remain true after, it indicates that the orientation of space has not changed and the determinant is positive.

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The linear equation that representing the given model is 6x-3 = 15.

In the given question, we have to choose the equation represented by the model given below.

As we know that;

A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.

The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.

To write the equation that represented by the given model, we count the variable that are of the same type. Then we write them after counting.

As we can see that in the model have 6 triangles of x, 3 circles of -1 and 15 circles of 1. So the linear equation that representing the given model is 6x-3 = 15.

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The expression using the common factor is 1/12xy(x² + 5y)

From the question, we have the following parameters that can be used in our computation:

1/12 x^3 y + 5/12 xy^2

Rewrite properly

So, we have

1/12x³y + 5/12xy²

Factor out 1/12 from the expression

So, we have the following representation

1/12(x³y + 5xy²)

Factor out x from the expression

So, we have the following representation

1/12x(x²y + 5y²)

Factor out y from the expression

So, we have the following representation

1/12xy(x² + 5y)

Hence, the expression is (c) 1/12xy(x² + 5y)

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Answer:The expression using the common factor is 1/12xy(x² + 5y)

Step-by-step explanation:

Answer:

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

Given expression:

Distribute and simplify:

The option that represents the arithmetic series is;

Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k

An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.

The series is given as;

-12 + (-5) + 2 + 9 + 16

By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.

The series here is therefore an example of arithmetic sequence.

The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k

Where;

-12 is the first term

7 is the common difference

n is the number of terms

k = n - 1

When k = 0, we have;

-12 + 7·k

= -12 + 7 × 0

= -12

When k = 1, we have;

-12 + 7·k

= -12 + 7 × 1

= -5

When k = 2, we have;

-12 + 7·k

= -12 + 7 × 2

= 2

When k = 3, we have;

-12 + 7·k

= -12 + 7 × 3

= 9

When k = 4, we have;

-12 + 7·k

= -12 + 7 × 4

= 16

Therefore, we conclude that  using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C

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In standard form the equation of the line passing through the points,

(-3, -2) and (-1, 0). is

x - y = -1

Information given in the question include

points,  (-3, -2) and (-1, 0).

Standard form of linear equations is of the form Ax + By = C

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculating using the points  (-3, -2) and (-1, 0).

m = (0 - (-2)) / (-1 - (-3))

m = (2) / (2)

m = 1

if the line passes through point X(-1, 0)

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

y = x + 1

x - y = -1

the intercept C = 1

The equation of the line is x - y = -1

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Answer:

y = 2x + 6

Step-by-step explanation:

The equation is in point slope form or y = mc + b

where m is the slope and b is the y intercept

Since the graph is simply shifted up 3 units, the y intercept will change by increasing by 3, but the slope will not

Answer: 44ft^2

Step-by-step explanation:

plug it into the equation, h=11, b=8

so A=1/2(11)(8) = 44ft^2

1. The equation of the inverse variation is, y = 272/x.

2. When x = 12, y = 68/3

When y = 30, x = 136/15.

An inverse variation is defined by the equation, y = k/x, where k is the constant of proportionality between the relationship of y and x.

1. Given that y varies inversely with x, substitute y = 34 and x = 8 into y = k/x, and find the value of the constant of proportionality, k:

34 =  k/8

34 × 8 = k

k = 272

To write the equation, substitute k = 272 into y = k/x:

y = 272/x

2. When x = 12, we have:

y = 272/12

Simplify

y = 68/3

When y = 30, we have:

30 = 272/x

30x = 272

30x/30 = 272/30

x = 136/15

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Answer:

c.

Step-by-step explanation:

as this can take on any value (with as many digits after the decimal point as necessary) between certain interval limits.

all the others are usually either pure integers (and every real number in between them is not valid) or at most have finite fractions (like 1/2 or 1/4 points for scores, and between these no value is valid).

g give a derivation to show that the following argument is valid in tfl. be p ∨ q) → r, p → s, ¬s → ¬r

1. (p ∨ q) → r Premise

2. p → s Premise

3. ¬s → ¬r Premise

4. p Assumption

5. s Modus Ponens (2, 4)

6. ¬r Modus Ponens (3, 5)

7. ¬(p ∨ q) Assumption

8. ¬p Simplification (7)

9. ¬q Simplification (7)

10. r Addition (1, 9)

11. Contradiction (6, 10)

12. ¬¬(p ∨ q) Double Negation (7-11)

13. (p ∨ q) Simplify(12)

14. r Modus Ponens (1, 13)

15. p → r Hypothetical Syllogism (4-14)

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A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Given,

As stated, the polynomial's leading coefficient is equal to 1.

The function's zeroes are also listed as -2, 3, and 6.

For root 3: ( x - 3)

for root 6: (x - 6)

As a result, the polynomial function is

f = 1(x+2)(x-3)(x-6) (x-6)

f = (x+2)(x² - 6x - 3x + 18)

f = (x+2)(x² - 9x + 18)

f = x³ - 9x² + 18x + 2x² - 18x + 36

f = x³ - 7x² + 36

A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.

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Number of marbles were not chosen = 62 marbles

Number of marbles were in the bag before the game = 86 marbles

Number pf blue marbles were chosen = 24

Number of blue marbles = 40

Number of white marbles = 46 marbles

Total number of marbles = 40 + 46

= 86 marbles

Of the 40 blue marbles, 3/5 fraction were chosen

Number of blue marbles chosen = 40 × (3/5)

= 24 marbles

Part a

Number of bag's marbles were not chosen = 86 - 24

= 62 marbles

Part b

Number of marbles were in the bag before the game = 86 marbles

Part c

Number of blue marbles were chosen = 40 × (3/5)

= 24 marbles

Therefore, the 62 marbles were not chosen. There were 86 marbles before the game and number of blue marbles were chosen is 24 marbles

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The distance between the satellite and the tracking station is 1220 miles

To find the distance between the satellite and the tracking station we need to apply cosine law:

                    [tex]c^{2} =a^{2} +b^{2} -2ab cos(\beta )----------(1)[/tex]

where:

c=length of side c

a=length of side a

b=length of side b

β=angle opposite c

we need to find the angle of β

computing the angle  β gives

[tex]\beta =\frac{3min}{120min} *360[/tex]

β=9°

Now substitute the β value ,a=4000,b=5000,in cosine law, and we get

[tex]x^{2} =4000^{2} +5000^{2} -2(4000)(5000)cos 9[/tex]

[tex]=(16+15-39.51)*10^{6 }\\=1.49*10^{6}[/tex]

x=1.22x10^3

x=1220 miles distance from the satellite to the tracking station.

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The point estimate of the difference between the two population means is -1.05.

Here, we are given the data representing the scores of the golf players in the 1st and final rounds.

a. The significance level is: α = 0.10

we can construct the following hypothesis test-

Null hypothesis H₀ ⇒ μd = 0

This implies that there is no difference between the population mean of the first round and final round.

Alternative hypothesis: Ha ⇒ μd ≠ 0

This implies that there is a difference between the population mean of the 1st round and final round.

Now, the test statistic will be-

[tex]t = (d-mean_{d})\sqrt{n}/ s_{d\\}[/tex]

we can use excel to calculate the test statistic.

This will give us: 0.10 < P < 0.20

b. the main margin of error is 90% confidence level. This means that there is no significant difference, hence - 1.05.

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