write 2^((5)/(2)) in surd form

Given:

The parent function is

\(f(x)=6\left(\dfrac{1}{8}\right)^x\)

The translated function is

\(f(x)=6\left(\dfrac{1}{8}\right)^{x+3}-2\)

To find:

The correct statement from the given options.

Solution:

The translation is defined as

\(g(x)=f(x+a)+b\)

Where, a is horizontal shift and b is vertical shift.  

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

In the parent function we have x in the power but in the translated function we have (x+3). So, a=3>0, the graph shifts 3 units left.

In the translated function, we have b=-2<0, so the graph shifts 2 units down.

The graph of \(f(x)=6\left(\dfrac{1}{8}\right)^{x+3}-2\) is a horizontal shift to the left 3 units and a vertical shift down 2 units from the original function \(f(x)=6\left(\dfrac{1}{8}\right)^x\).

Therefore, the correct option is A.

Answer:

3

Step-by-step explanation:

Let's write the statement as an equation and solve for that number.

x+7=10

x=3

Step-by-step explanation:

\(\bold{x + 7 = 10}\)

\( \longmapsto \: x = 10 - 7\)

\( \longmapsto \: 10 - 7 = 3\)

\(\bold{Hope}\)\(\bold{It}\) \(\bold{Helps!}\)

\(\bold{Study}\)\(\bold{Well}\)~

The mean and the standard deviation of the sampling distribution of x are given as follows:

The mean and the standard deviation of the sampling distribution of x are obtained using the Central Limit Theorem.

The mean is the same as the population mean, hence it is given as follows:

$70,000.

The standard deviation is given by the population standard deviation divided by the square root of the sample size, hence:

20000/25 = $800.

(as 25 is the square root of 625).

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Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years,

What is an interest rate?

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here, we have

A = P e^(rt) ......(1)

P = Amount Invested = $7000

Interest Rate = 9%

A = Accumulated Amount Double the amount invested = 2P = $14000

t = time in years

from equation (1) , we get

14000 = 7000×e^(0.09)t

2 =  e^(0.09)t

㏑2 = 0.09t

0.6931 = 0.09t

t = 0.6931/0.09

t = 7.7 years

Hence, Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years.

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The pοlynοmial οf degree 3 with zerοs −5, 0, and 4 is f(x) = x³+ x² - 20x.

In mathematics, a pοlynοmial is a mathematical expressiοn cοnsisting οf variables and cοefficients, which are cοmbined using arithmetic οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents. Pοlynοmials can have οne οr mοre variables and can be οf variοus degrees, depending οn the highest expοnent in the expressiοn.

A pοlynοmial οf degree 3 has the fοrm:

f(x) = ax³ + bx² + cx + d

where a, b, c, and d are cοnstants.

If the zerοs οf the pοlynοmial are −5, 0, and 4, then the factοrs οf the pοlynοmial are:

(x + 5), x, and (x - 4)

Tο find the pοlynοmial, we can multiply these factοrs tοgether:

f(x) = (x + 5) * x * (x - 4)

Expanding this expressiοn gives:

f(x) = x³ - 4x² + 5x² - 20x

Cοmbining like terms gives:

f(x) = x³ + x² - 20x

Therefοre, the pοlynοmial οf degree 3 with zerοs −5, 0, and 4 is f(x) = x³+ x² - 20x.

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Computer Question:

Find a polynomial f(x) of degree 3 that has the following zeros: −5, 0, 4 Leave your answer in factored form.

The answer is 0.16 using exponential function.

As the name implies, exponents are used in the exponential function. An exponential function, on the other hand, has a constant as its base and a variable as its exponent but not vice versa (if a function has a variable as if the base is a constant and the exponent is a constant, the function is a power function instead of an exponential function).

An exponential function is a type of mathematical function that is commonly used in daily life. It is mostly used to calculate investments, model populations, and determine whether or not an exponential decline or exponential growth exists, among other things.

(4a)² = 16 × a²
(4a)² = 16 × (1/10)²
(4a)² = 16 × 1/100
(4a)² = 16/100
(4a)² = 0.16

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Answer:

Peter missed five questions.

Step-by-step explanation:

Since the test has twenty-five questions, and Peter got 80% correct...

80/100 = __/25 <--What number is the numerator?

Well, to get from 100 to 25, you have to divide by 4. 100/4 = 25.

Now, what is 80/4? If you do the math, you should get 20.

25 (Total Questions) - 20 (Questions Correctly Answered) = 5 (Questions Incorrectly Answered)

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

7.5 is the answer to this

The interest will he be paid in the first six years is $360.

Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest.

Formula: (P x R x T)/100

Given:

P= $3000

R= 2%

T = 6 years

Using Simple interest

= (P x R x T)/100

= ( 3000 x 2 x 6)/100

= 30 x 2 x 6

= $360

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Here, the degree of the numerator, 2, is equal to the degree of the denominator, 2, so r(x) has a nonzero horizontal asymptote

Asymptote is a line taken in relation to curve. The line is always far apart from the curve irrespective of distance. Taking the definition in sense of curve, then the curve tries to reach this line while moving towards infinity. Horizontal asymptote indicates the behaviour of function at graph edge.

The equation to be considered for formation of horizontal asymptote is y = mx + b, where u is y-axis, m is slope, x is axis and b is constant. If the two values, that are numerator and Denominator are equal, then y = b.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Therefore, the end behavior of the function f(x) is: f(x) → 0- as x → -∞ and f(x) → 1 as x → ∞.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

To determine the end behavior of the function f(x) = (-4x³+ 7x + 9)/(8x⁶ - 9x⁴ - 2x), we need to consider the limit of the function as x approaches positive or negative infinity.

As x approaches negative infinity, the highest power of x in the numerator is -4x³, which will dominate the function. The highest power of x in the denominator is 8x⁶, which will also dominate the function. Therefore, we can simplify the function to:

f(x) ≈ (-4x³)/(8x⁶) = -1/(2x³)

As x approaches negative infinity, the denominator of this simplified function will become very large (since x³ becomes very negative), causing the function to approach 0 from the negative side:

f(x) → 0- as x → -∞

As x approaches positive infinity, the highest power of x in the numerator and denominator are both 8x⁶. Therefore, we can simplify the function to:

f(x) ≈ (8x⁶)/(8x⁶) = 1

As x approaches positive infinity, the function will approach 1 from the positive side:

f(x) → 1 as x → ∞

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Complete question:

Consider the following rational function fff. f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}f(x)= 8x 6 −9x 4 −2x −4x 3 +7x+9 ​ f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 4, x, cubed, plus, 7, x, plus, 9, divided by, 8, x, start superscript, 6, end superscript, minus, 9, x, start superscript, 4, end superscript, minus, 2, x, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.

Answer:

Step-by-step explanation:

Choose the equation below that represents the line passing through the point (1, -- 4) with a slope of

we know that

the equation of the line in point slope form is equal to

y-y1=m(x-x1)

in this problem we have

m

(x1,y1)=(1,-4)

substitute

y+4=m(x-1)

therefore

If the slope is 2 -------> y+4=2(x-1)

If the slope is f -------> y+4=f(x-1)

I need the value of the slope in the question to complete the answer

Answer:

PDF for a continuous random variable is given. Use the PDF to find (a) and the CDF.

The limits of the given iterated integrals are:

a) (limit from 1 to -4)∫ (limit from -4 to -7/5x-13/5) ∫ f(x,y)dydx

b) (limit from -4 to 1)∫ (limit from -4 to -13-5y/7 ∫ f(x,y)dydx

Given the line passes (1,-4) and (-4,3)

by two point form of a line

y + 4 = 3+4/-4-1 (x-1)

y + 4 = -7/5 (x-1)

y = -7/5x - 13/5

x from -4 to 1

y from -4 to -7/5x - 13/5

a) ∫∫Rf(x,y)dA = limit(AtoB)∫(Limit from C to D)∫f(x,y)dydx

                      = (limit from 1 to -4)∫ (limit from -4 to -7/5x-13/5) ∫ f(x,y)dydx

where A = -4, B = 1, C=-4, D = -7/5x-13/5

b) y = -7/5x -13/5 ⇒ x = -13-5y/7

y from -4 to 3

x from -4 to -13-5y/7

∫∫ Rf(x,y)dA = (limit from F to E)∫ (limit from G to H)∫ f(x,y)dxdy

                   = (limit from -4 to 1)∫ (limit from -4 to -13-5y/7 ∫ f(x,y)dydx

where E = -4, F=3, G=-4,H=-13-5y/7

Hence the change of the order of the integration not change the integration value.

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Answer:

5216.844

Step-by-step explanation:

Let x be the fourth number.

We know that the sum of the four numbers is 20500:

2341.578 + 10690 + x + 2341.578 = 20500

Simplifying and solving for x:

x = 20500 - 2341.578 - 10690 - 2341.578

x = 5216.844

The form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

To evaluate the polynomial \(y = x^3 - 5x^2 + 6x + 0.55\)at x = 1.37 using 3-digit arithmetic with chopping, we substitute x = 1.37 into the expression:

\(y = (1.37)^3 - 5(1.37)^2 + 6(1.37) + 0.55\)

Calculating each term;

\((1.37)^3\)= 2.559

5\((1.37)^2\)= 9.415

6(1.37) = 8.22

Substituting these values into the expression for y,

y = 2.559 - 9.415 + 8.22 + 0.55

y = 1.914

Now, let's move on to part (b).

We will express y as y = ((x - 5)x + 6)x + 0.55,

Now using 3-digit arithmetic with chopping.

Then, we substitute x = 1.37 into the expression:

y = ((1.37 - 5) 1.37 + 6) 1.37 + 0.55

Calculating each term separately:

(1.37 - 5) = -3.63

-3.63 x 1.37 = -4.98

-4.98 + 6 = 1.02

1.02 x 1.37 = 1.3974

Finally, adding 0.55:

y = 1.3974 + 0.55

y = 1.9474

Now, let's compare the percent relative round-off errors in both cases.

In part (a), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was also 1.914. Therefore, the percent relative round-off error is:

(1.914 - 1.914) / 1.914 x 100 = 0%

In part (b), the exact value of y was 1.914, while the approximate value using 3-digit arithmetic with chopping was 1.9474.

Therefore, the percent relative round-off error is:

(1.9474 - 1.914) / 1.914 x 100 ≈ 1.741%

Therefore, in this comparison, we can conclude that the form of the polynomial given in part (a) is superior, as it has a lower percent relative round-off error compared to the form given in part (b).

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a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Step-by-step explanation:

3/5 or 60% of the prism's volume will be filled with sand.

The volume of each cube is e³ = 5³ = 125 cubic centimeters.

Since the rectangular prism is made up of two cubes, its volume is 2e³ = 2(125) = 250 cubic centimeters.

If Arusha fills the prism with 150 cubic centimeters of sand, the fraction of the prism's volume that will be filled with sand is:

150/250 = 3/5

Therefore, 3/5 or 60% of the prism's volume will be filled with sand.

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