Given the volume is 105 inches³ for an 8 pound bowling ball, find the radius of the bowling ball,
to the nearest hundredth of an inch.

By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:

Now, we proceed to simplify the function:

[tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex]

[tex]\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}[/tex]

[tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex]

By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].

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The complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.

The polynomial is given as:

12x^3 - 5x^2 + 6x + 9

The first term in the above equation is 12 i.e. 12x^3, while the last term is 9

To determine the possible rational roots, we divide the factors of the last term i.e. 12 by the factors of the first term i.e. 12

Hence, the complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.

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Answer:

D

Step-by-step explanation:

I took the test

Answer:

Vertex (2 , -25)

Axis of symmetry: x = 2

Step-by-step explanation:

 The vertex is the highest point if the parabola open downwards and the lowest point if the parabola opens upward.

 f(x) = (x - 2)² - 25

The given quadratic function  is in vertex form.

 f(x)  = a(x - h)² + k

Here,  (h , k) is the vertex of the parabola.

 h = 2  ; k = -25

[tex]\sf \boxed{\bf Vertex (2 , -25)}[/tex]

 The axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

Axis of symmetry: x = h

  [tex]\sf \boxed{\bf x = 2}[/tex]

A statement which could be true for g is that: A. g(-13) = 20.

A domain can be defined as the set of all real numbers for which a particular function is completely defined.

Since the domain of this function is given by -20 ≤ x ≤ 5, it simply means that the value of x must between -20 and 5. Also, with a range of -5 ≤ g(x) ≤ 45, the value of x must between -5 and 45.

By extrapolating the function, we can deduce that:

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Complete Question:

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

A. g(-13) = 20

B. g(-4) = -11

C. g(7) = -1

D.g(0) = 2

Answer is slope of 5

Step by step

You can graph the slope as seen on the attached picture. You go up 30, you go right +6. Slope is y/x, so 30/6, equals 5

You can also use the slope formula

(y2-y1) over (x2-x1)

Using points on the graph

(6,0) and (0,-30)

(-30-0 ) over (0-6)

-30 over -6

-30/-6

= 5

Answer:

Please see picture below.

Step-by-step explanation:

The possible coordinates for the vertex D of the parallelogram could be (-4, 3)

It is given that A(1, –1), B (–1, 3), and C (4, –1) are the three vertices of the parallelogram.

Let us assume that the vertices are in the order A, C, B, and D where the coordinates of D are (a, b).

In this scenario, if we join AB and CD, they will become the diagonals of the parallelogram ABCD.

According to the properties of a parallelogram, diagonals bisect each other.

Hence, mid-point of AB = mid-point of CD

Now, according to the mid-point theorem, if mid-point of AB is given as (x,y), then,

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

Here, for AC,

x₁ = 1, y₁ = -1

x₂ = -1, y₂ = 3

Then, x = ( 1 - 1)/2 and y = (-1 + 3)/2

(x, y) ≡ (0, 1)  ............. (1)

Since (x, y) is also the mid-point of CD, we also have,

x₁ = 4, y₁ = -1

x₂ = a, y₂ = b

Then, x = (4 + a)/2 and y = (-1 + b)/2

(x, y) ≡ ((4 + a)/2, (-1 + b)/2) ................... (2)

From (1) and (2),

(4+a)/2 = 0 and (-1+b)/2 = 1

4+a = 0 and (-1+b) = 2

a = -4 and b = 3

Hence, the fourth vertex D of the parallelogram can be possibly located at (-4, 3)

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Please see the graph below

Answer:

Step-by-step explanation:

Use the mean and the standard deviation obtained from the last discussion and test the claim that the mean age of all books in the library is greater than 2005.

This is the last discussion:

The science portion of my library has roughly 400 books.

They are arranged, on shelves, in order of their Library of Congress

code and, within equal codes, by alphabetical order of author.

Sections Q and QA have a total of 108 books.

The bulk of the library was established in the early 1990s.

I used a deck of cards, removing the jokers and face cards, keeping

only aces (1) and "non-paints" (2 to 10). Starting from the start of

the first shelf, I would turn a card (revealing its number N) and I

would go to the Nth book. This uses ordinal numbers (1 would means the

"first" book, not a gap of 1).

The cards were shuffled sufficiently to assume that the cards have a

random order.

I sampled only the LC subsections Q and QA (therefore, not a true

sample of the entire library, as this classification is not purely

random).

Thus, I picked 21 books (the expected number being 108/5.5 = 19.6 --> 20 books)

The sampled dates of publication were (presented as an ordered set):

1967, 1968, 1969, 1975, 1979, 1983, 1984,

1984, 1985, 1989, 1990, 1990, 1991, 1991,

1991, 1991, 1992, 1992, 1992, 1997, 1999

The median date is 1990

The mean date is 1985.67

Variance = 84.93 ( Sum of (date-mean)^2 )

SQRT of variance = 9.2 (sample standard deviation)

The "sigma-one" confidence interval (containing 68% of the books), if

the sample were NOT skewed, and if the distribution were "normal"

would contain dates from "mean - 9.2" to "mean + 9.2"

Sigma-2 (95%) would have mean - 2(9.2) to mean + 2(9.2)

Sigma-3(99.7%) from "1985.67 - 3(9.2)" to "1985.67 + 3(9.2)"

1958.07 to 2012.6

There, you see one reason why the distribution is skewed (it is

possible to have books older than 1958, but it is impossible to have

book newer than 2012), but it still represents a usable model for the

library. If it applies to the entire library of 400 books, you would

expect one book (0.3% of 400) to fall outside the 3-sigma interval.

Answer:

Gievn that l=3m,b=5m,h=4m

L.S.A=2(l+b)h

=2×(3.5)×4

=2×8×4

=64sq.m

Step-by-step explanation:

Answer:

The answer to your question is p = 10.50b

Step-by-step explanation:

Since you want to find p, you're looking for an equation that has

p = <something>

The last selection has this form

p = 10.50b

I hope this helps and have a good day!

The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

An equation is an expression that shows the relationship between two or more variables and numbers.

Pressure = density * acceleration due to gravity (g) * depth

g = 10 m/s², hence:

Pressure = 1025 * 10 * 23000 = 2.3575 * 10⁸ N/m²

The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²

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If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

An equation is an expression that shows the relationship between two or more variables and numbers.

There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:

4x + 15000 ≥ 100000

x ≥ 21250

If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.

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Step-by-step explanation:

We can determine whether the change represents exponential growth or exponential decay by making a table for a few values of x.

0 -> [tex]38(1.09)^0[/tex] = 38 * 1 = 38

1 -> [tex]38(1.09)^1[/tex]= 38 * 1.09 = 41.42

2 -> 38(1.09)² = 38 * 1.09 * 1.09 = 45.1478

We see that y increases as x increases, which makes this function represent exponential growth.

The percentage rate of increase is how much the value of y increases by each time x increases.

Since we are multiplying by 1.09 each time, we are taking 109% of the previous y value to get the current y value. Hence, the rate of increase is 9%.

Answer: H. Parallel lines may intersect.

Step-by-step explanation:

By definition, parallel lines never intersect.

If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

m represents the slope

By comparison, we have:

m = 490

This means that the slope is 490

Hence, the interpretation is

Slope; 490

The company earns $490 per computer sold

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

c represents the vertical intercept

By comparison, we have:

c = -10780

This means that the vertical intercept is -10780

Hence, the interpretation is

Vertical intercept; -10780

If the company sells 0 computers, they will not make a profit. They will lose $10780

The function is  given as:

P = 490n - 10780

A linear equation is represented as:

P = mn + c

Where

-c/m represents the horizontal intercept

By comparison, we have:

-c/m = 10780/490

-c/m = 22

This means that the horizontal intercept is 22

Hence, the interpretation is

Horizontal intercept; 22

If the company sells 22 computers, they will break even. They will earn  $0

We have:

P = 490n - 10780

This gives

P = 490* 46 - 10780

P = 11760

If the company sells 46 computers, they will earn $11760

We have:

P = 490n - 10780

This gives

15190 = 490n - 10780

490n = 15190+10780

490n = 25970

n = 53

The company will earn $15190, if they sell 53 computers

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Answer: -x² + 4x + 6

Given:

f(x) = 4x + 1

g(x) = x² - 5

Solve:

= (f - g)(x)

= f(x) - g(x)

= 4x + 1 - (x² - 5)

= 4x + 1 - x² + 5

= -x² + 4x + 6

Answer:

(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6

Step-by-step explanation:

Explanation can be given if needed in the comments (ㅅ´ ˘ `)

The equivalent expression of [tex]1 - \frac{1}{x} \div 2[/tex] is [tex]\frac{2x - 1}{2x}[/tex]

The expression is given as:

1 minus StartFraction 1 Over x EndFraction divided by 2

Rewrite properly as:

[tex]1 - \frac{1}{x} \div 2[/tex]

Express the division as product

[tex]1 - \frac{1}{x} \times \frac 12[/tex]

Evaluate the product

[tex]1 - \frac{1}{2x}[/tex]

Take the LCM

[tex]\frac{2x - 1}{2x}[/tex]

Hence, the equivalent expression of [tex]1 - \frac{1}{x} \div 2[/tex] is [tex]\frac{2x - 1}{2x}[/tex]

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12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.

Para que un número sea divisible por 6 debe cumplir dos condiciones.

En este caso tenemos 12,480, que sabemos que es par.

La suma de sus digitos da:

1 + 2 + 4 + 8 + 0 = 15

15 es multiplo de 3.

Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.

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The quantity of rainfall that fell in the second half of the month is; ¹/₆ of an inch.

We are given;

Rainfall during first half of the month = 1/2 inch

Total rainfall for the month = 2/3 inch

Now, to find the rainfall for the second half of the month, we just subtract the one for the first half from the one for the month to get;

Rainfall in second half of the month = ²/₃ - ¹/₂ = ¹/₆ inches

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The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(n) represent the total cost of shoe rentals for n games, hence:

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

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hi

I cannot figure the number  2.16 thousand has it does not mean anything to me.

But the only thing you need to do is to add  15 times 220

so = 3300

Answer:

5,460 people

Step-by-step explanation:

2,160 + 220x is the expression. Now, we plug in 15 for x.

2,160 + 220(15)

2,160 + 3,300 = 5,460

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The length of side PS according to the quadrilateral descriptions is; 21.

Since, it follows from the task content that the two quadrilaterals given are congruent, hence, the corresponding sides are congruent and are in proportion to each other.

On this note, we have;

x/35 = 15/25

x = (35×15)/25

x = 21.

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Answer:

x = 9

Step-by-step explanation:

4x + 7 = 43

4x = 36

x = 9

Part A

1) (5, -1)

2) (1, -3)

3) (-2, -2)

4) (-5, -4)

Part B

1) (-5, 1)

2) (-1, 3)

3) (2, 2)

4) (5, 4)

Using the Poisson distribution, there is a 0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

A bank gets an average of 12 customers per hour, hence the mean is [tex]\mu = 12[/tex].

The probability that there will be 4 or more customers at this bank in one hour is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} \approx 0[/tex]

[tex]P(X = 1) = \frac{e^{-12}12^{1}}{(1)!} \approx 0[/tex]

[tex]P(X = 2) = \frac{e^{-12}12^{2}}{(2)!} = 0.0004[/tex]

[tex]P(X = 3) = \frac{e^{-12}12^{3}}{(3)!} = 0.0018[/tex]

Then:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0.0004 + 0.0018 = 0.0022.

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0022 = 0.9978[/tex]

0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

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