Which of the following expressions is equivalent to 4 to the negative 3rd power
?

Answer:

Subtraction, and then division.

Step-by-step explanation:

We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.

[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]

Hope this helps.

To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.

A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.

Given that 6x + 3 = 9.

First, we have to separate variable and constants. So, we have to subtract 3 from both sides.

6x + 3 - 3 = 9 - 3

i.e. 6x = 6

Now, to solve this equation, we use division.

x = 6/6 = 1

i.e. x = 1

Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.

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Answer:

The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.

Step-by-step explanation:

Average rate of change:

Division of the subtraction of the final value by the initial value, divided by the length of time.

The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997.

Initial value: 1.3 billion

Final value: 1.7 billion

1997 - 1993 = 4 years.

Thus:

[tex]A = \frac{1.7 - 1.3}{4} = \frac{0.4}{4} = 0.1[/tex]

The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.

Answer:

5.23%

Step-by-step explanation:

See Image below:)

cos 36 × cos 72 = 0.25

cos 36 × cos 72 =

0.309 x 0.809 = 0.249 = 0.25

Answer:

0.837

Step-by-step explanation:

3850*4.65%=179.025

150/179.025=0.837

0.837

Answer:

D. An exponential parent function

Step-by-step explanation:

The basic parent function of any exponential function is f(x) = bx, where b is the base. Using the x and y values from this table, you simply plot the coordinates to get the graphs. The parent graph of any exponential function crosses the y-axis at (0, 1), because anything raised to the 0 power is always 1.

The parent function that represents the graph is exponential.

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is a function as shown in the image. It is asked to identify the parent function of this graph.

The parent function will be quadratic if the plotted graph is a parabola.

The parent function will be linear if the plotted graph is a straight line.

The parent function will be an absolute function if it is V - shaped.

So, none of the options other than the exponential parent function represents the graph.

Therefore, the parent function that represents the graph is exponential.

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9514 1404 393

Answer:

  8%

Step-by-step explanation:

The fraction donated was $632/$7900.

As a percentage, that is ...

  632/7900 × 100% = 0.08 × 100% = 8%

The store donated 8% of sales to charity.

Answer:

A: 9:5  B: 5:14

Step-by-step explanation:

Answer:

The numbers of ways to permute letters of the word Illinois if the two Ls must be consecutive is 7.

The word ILLINOIS contains 7 letters.

To estimate the number of different permutations, consider the total number of letters factorial and divide by the frequency of each letter factorial. The little n's exist the frequencies of each various (different) letter.

We will use the formula for the number of permutations with imperceptible objects. Since the two L's must be consecutive, we consider them to be a single letter LL. Then the word ILLINOIS contains n = 7 letters: 3 I's, 1 LL, 1 N, 1 O, and 1S.

Hence the number of methods to permute letters of the word ILLINOIS if the two L's must be consecutive exists:

[tex]$\frac{7 !}{3 ! 1 ! 1 ! 1 ! 1 !}=7 \cdot 6 \cdot 5 \cdot 4=840 \text {. }$$[/tex]

The word ILLINOIS contains 7 letters.

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Answer:

A statement that shows current balance of an account and all transactions that occurred on that account since the last statement.

Transactions such as deposits, withdrawals, checks written, debt card uses...

There are other examples of bank statements for things like home loans, business loans, and investments.

Answer:c>2

Step-by-step explanation:

-6c (divide) (-6) > -12 (divide) (-6)

c>-12 (divide) (-6)

c>12 (divide) 6

c> 2

D

Because slope of section D is greater than the others and hence speed is highest.

Answer:

B for first one.

75 for second.

Hope this helps !

Step-by-step explanation:

Answer:

X = 7

Step-by-step explanation:

Answer:

first option is the correct answer.

Step-by-step explanation:

Answer:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Step-by-step explanation:

Given

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

[tex]c = 6[/tex]

The geometric series centered at c is of the form:

[tex]\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.[/tex]

Where:

[tex]a \to[/tex] first term

[tex]r - c \to[/tex] common ratio

We have to write

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

In the following form:

[tex]\frac{a}{1 - r}[/tex]

So, we have:

[tex]f(x)= \frac{9}{3x+ 2}[/tex]

Rewrite as:

[tex]f(x) = \frac{9}{3x - 18 + 18 +2}[/tex]

[tex]f(x) = \frac{9}{3x - 18 + 20}[/tex]

Factorize

[tex]f(x) = \frac{1}{\frac{1}{9}(3x + 2)}[/tex]

Open bracket

[tex]f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}[/tex]

Collect like terms

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}[/tex]

Take LCM

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}[/tex]

[tex]f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}[/tex]

By comparison with: [tex]\frac{a}{1 - r}[/tex]

[tex]a = 1[/tex]

[tex]r = -\frac{1}{3}x + \frac{7}{9}[/tex]

[tex]r = -\frac{1}{3}(x - \frac{7}{3})[/tex]

At c = 6, we have:

[tex]r = -\frac{1}{3}(x - \frac{7}{3}+6-6)[/tex]

Take LCM

[tex]r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)[/tex]

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n[/tex]

Substitute 1 for a

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n[/tex]

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n[/tex]

Substitute the expression for r

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n[/tex]

Expand

[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n][/tex]

Further expand:

[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................[/tex]

The power series converges when:

[tex]\frac{1}{3}|x - \frac{7}{3}| < 1[/tex]

Multiply both sides by 3

[tex]|x - \frac{7}{3}| <3[/tex]

Expand the absolute inequality

[tex]-3 < x - \frac{7}{3} <3[/tex]

Solve for x

[tex]\frac{7}{3} -3 < x <3+\frac{7}{3}[/tex]

Take LCM

[tex]\frac{7-9}{3} < x <\frac{9+7}{3}[/tex]

[tex]-\frac{2}{3} < x <\frac{16}{3}[/tex]

The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]

Answer:

Contribution margin = Revenue − Variable costs

Step-by-Step Explanation

For example, if the price of your product is $20 and the unit variable cost is $4, then the unit contribution margin is $16.

The first step in doing the calculation is to take a traditional income statement and recategorize all costs as fixed or variable. This is not as straightforward as it sounds, because it’s not always clear which costs fall into each category.

Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)  

C.(f-g)(x) = 4x^3 +5x²-7x-1

Step-by-step explanation:

Given information :

[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]

Find :

[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]

Open bracket and Simplify

[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]

Answer:

This is the whole process I guess

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : quality does not vary among shift

H1 : quality varies among shift

The expected values :

(Row * column) / grand total

Given the data:

Observed values :

_________________total

_______467 191 42 __700

_______445 171 34 __650

_______254 129 17 _ 400

Total __ 1166 491 93 _ 1750

Expected value count using the formula :.

Expected Values:

466.4 ____196.4 ______37.2

433.086 _182.371___ 34.5429

266.514_ 112.229____ 21.2571

The Chisquare statistic (χ²) :

χ² = (observed - Expected)²/ observed

χ² = 5.76045

The degree of freedom = (row - 1) * (column - 1)

Degree of freedom = (3-1)*(3-1) = 2*2 = 4

Pvalue = 0.2178

Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift

Answer:

Option D, 55.45 to 70.95

Step-by-step explanation:

Alpha = 1 – confidence interval  

Alpha = 1 – 0.98 = 0.02

Sample size = n = 8

t (alpha/2) ; (n-1) = t (0.02/2) ; (8-1) = t 0.01, 7 = 2.998

Mean = sum of all frequencies /total number of frequency = 505.6/8 = 63.2

s = 7.309

E = t (0.01;7) * s/sqrt n

Substituting the given values, we get –  

E = 2.998 * 7.309 /sqrt  (8)

E = 7.75  

98% confidence interval  

Mean – E  and Mean + E

63.2 – 7.75 and 63.2 + 7.75  

(55.45, 70.95)

Answer: 55.45 to 70.95

Step-by-step explanation:

Answer:

Step-by-step explanation:

I=∫e^2x dx

put 2x=t

2dx=dt

dx=dt/2

I=1/2∫e^t dt

=1/2 e^t+c

=1/2 e^{2x}+c

9514 1404 393

Answer:

  y = (1/3)√x

Step-by-step explanation:

Vertical scaling of a function is accomplished by multiplying the function by the scale factor. If you want to scale the square root function by a factor of 1/3, then the scaled function is ...

  y = (1/3)√x

Answer:

The desired distance is √5

Step-by-step explanation:

Recall that the distance from a point to a line is measured along a path perpendicular to the line.  Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2:  +1/2.

The line perpendicular to y = -2x + 5 and passing through (4, 2) is

y - 2 = (1/2)(x - 4), or

2y - 4 = x - 4, or 2y = x, or y = (1/2)x.

Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."  

Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2.  If x = 2, then y = (1/2)(2) = 1.

Finally, find the distance between (2, 1) and (4, 2):

Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5

The distance from (4, 2) to the line y = -2x + 5 is √5

Step-by-step explanation:

[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]

Step-by-step explanation:

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Answer:

[tex]2 \sqrt{35} [/tex]

Write z in polar form:

z = 1 + √3 i = 2 exp(i π/3)

Taking the square root gives two possible complex numbers,

√z = √2 exp(i (π/3 + 2kπ)/2)

with k = 0 and k = 1, so that

√z = √2 exp(i π/6) = √(3/2) + √(1/2) i

and

√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i

Answer:

sin(C) = opposite side / hypotenuse

= 15/17

Answer:

[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]

Step-by-step explanation:

[tex] \small \sf \: Sin ( C ) = \frac {Opposite \: side }{Hypotenuse} \\ [/tex]

Where we have given :-

substitute the values, we get

[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]