What is the simplified base of the function f(x) = One-fourth (Root Index 3 StartRoot 108 EndRoot) Superscript x?

Answers

Answer 1

Answer:

The base is: [tex]3 \sqrt[3]{4}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{4}(\sqrt[3]{108})^x[/tex]

Required

The base

Expand 108

[tex]f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x[/tex]

Rewrite the exponent as:

[tex]f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x[/tex]

Expand

[tex]f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x[/tex]

[tex]f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x[/tex]

An exponential function has the following form:

[tex]f(x)=ab^x[/tex]

Where

[tex]b \to base[/tex]

By comparison:

[tex]b =3 \sqrt[3]{4}[/tex]

So, the base is: [tex]3 \sqrt[3]{4}[/tex]


Related Questions

What is the simplified base of the function f(x) = One-fourth (Root Index 3 StartRoot 108 EndRoot) Superscript x?

Answers

Answer:

The base is: [tex]3 \sqrt[3]{4}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{4}(\sqrt[3]{108})^x[/tex]

Required

The base

Expand 108

[tex]f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x[/tex]

Rewrite the exponent as:

[tex]f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x[/tex]

Expand

[tex]f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x[/tex]

[tex]f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x[/tex]

Rewrite as:

[tex]f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x[/tex]

An exponential function has the following form:

[tex]y=ab^x[/tex]

Where

[tex]b \to base[/tex]

By comparison:

[tex]b =3 \sqrt[3]{4}[/tex]

So, the base is: [tex]3 \sqrt[3]{4}[/tex]

Answer:

B

Step-by-step explanation:

good luck

Mike forgot the last three digits of his friend's telephone number. He only remembers that the digits are not the same. What is the probability he dials the correct telephone number on the first try

Answers

Answer:

1/720 = 0.0014 = 0.14% probability he dials the correct telephone number on the first try.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order of the digits is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Desired outcomes:

One correct number, so [tex]D = 1[/tex]

Total outcomes:

3 non-repeated digits, so permutations of 3 digits from a set of 10(all digits). So

[tex]T = P_{10,3} = \frac{10!}{7!} = 10*9*8 = 720[/tex]

What is the probability he dials the correct telephone number on the first try?

[tex]p = \frac{D}{T} = \frac{1}{720} = 0.0014[/tex]

1/720 = 0.0014 = 0.14% probability he dials the correct telephone number on the first try.

What number is exactly halfway between 5/9 and 7/9​

Answers

Answer:

11/18

Step-by-step explanation:

Directly between 5/9 and 6/9 would be 5.5/9 (or 5 and half ninths. However, you’re not supposed to mix regular fractions and decimal fractions.

So, the easiest way to get the proper answer would be to convert the fractions to eighteenths, which would give you a whole number numerator between the two given fractions.

So, 5/9 = 10/18 and 6/9 = 12/18. What number is directly exactly between 10 and 12? 11.

Find the volume of the prism.

Answers

Answer:

Its A.

Step-by-step explanation:

remember its rectangle 1 + rectange 2.Once i did that i have seen the total volume must be greater then answer B

so it must be a

Which of the following rational functions is graphed below?
A. F(x) =1/(x-4)^2
B. F(X) =1/(x + 4)^2
C. F(X) = 1/4x^2
D. F(x) = 4/x^2

Answers

Answer to your question is B. f(x)= 1/(x+4)^2

The equation of the rational function is f(x) = 1/(x + 4)^2

How to determine the graph?

From the figure, we have the following property:

Vertical asymptote at;

x = -4

Add 4 to both sides

x + 4 = 0

Square both sides

(x + 4)^2 = 0

The above means that the denominator of the equation of the graph is (x + 4)^2

So, we have:

f(x) = 1/(x + 4)^2

Hence, the equation of the rational function is f(x) = 1/(x + 4)^2

Read more about rational function at:

https://brainly.com/question/1851758

#SPJ6


Given a mean of 75 and a standard deviation of 7, how many students out of 500
would score higher than 89?

Answers

Answer:

230

Step-by-step explanation:

isiwjsjxjxjsiqisjnx

How many real equations does 8-4x=o have ?

Answers

Answer:1 real solution

Step-by-step explanation:

Ordinary least squares estimation is subject to heterogeneity bias if _____. 答案选项组 the regression model exhibits heteroskedasticty the unobserved effect is correlated with the observed explanatory variables the regression model includes a lagged dependent variable the explanatory variables do not change over time

Answers

Answer:

Unobserved effect.

Step-by-step explanation:

The unobserved effect of heterogeneity is correlated with the observed explanatory variables. Population heterogeneity is bias in unobserved pre treatment factors which affect the outcome even without treatment.

solve the inequality
2(4 x + 1)< 3 (2 x - 3)​

Answers

Answer:

    [tex]2 (4x + 1) < 3(2x - 3) \\8x + 2 < 6x -9 \\8x - 6x < -9 - 2\\2x < -11\\\\x< - \frac{11}{2}[/tex]

Answer:

x> - 11/2

Step-by-step explanation:

See image below:)

Select the TRUE statement for completely random design.
a.)The experimental units are assigned randomly to exactly one control group and one treatment group.
b.)The experimental units are assigned randomly to one or more control groups and exactly one treatment group.
c.)The experimental units are assigned randomly to one or more control groups and one or more treatment groups.
d.)The experimental units are assigned randomly to exactly one control group and one or more treatment groups.

Answers

Answer:

d.)The experimental units are assigned randomly to exactly one control group and one or more treatment groups

Step-by-step explanation:

Completely randomized design can be regarded as a type of experimental design in which the experimental units are assigned randomly for different treatments. This experimental design is utilized in cases whereby experimental units are seen to be “uniform" this implies that no uncontrolled factor in the experiment. completely randomized designs are engaged in studying effects of one primary factor by ignoring other nuisance variables it perform comparison of values of a response variable taking into account of the different levels of that primary factor. It should be noted that in completely random design, the experimental units are assigned randomly to exactly one control group and one or more treatment groups

If the graph of the following parabola is shifted one unit left and two units up,
what is the resulting equation in vertex form?
x² = 12y

Answers

Answer: (x+1)^2=12(y-2)

Step-by-step explanation:

Find the distance between the pair of points: (2,6) and (0,−3).

Answers

Answer:

d = √85

Step-by-step explanation:

d^2 = (X2 - X1)^2 + (Y2 - Y1)^2

= (2 - 0)^2 + (6 + 3)^2

= 4 + 81

d = √85

On a coordinate plane, triangle B C D has points (negative 4, 1), (negative 2, 1), (negative 4, 3). Triangle B prime C prime D prime has points (negative 1, negative 4), (negative 1, negative 2), (negative 3, negative 4). Triangle BCD is rotated counterclockwise to form triangle B’C’D’. What is the angle of rotation? 45° 90° 180° 360°

Answers

9514 1404 393

Answer:

  90° CCW

Step-by-step explanation:

The transformation from B to B' is ...

  B(-4, 1) ⇒ B'(-1, -4)

  (x, y) ⇒ (-y, x) . . . . . matches the transformation for 90° CCW

Answer:

90 degrees

Step-by-step explanation:

hat is equivalent to but different from 7/13

Answers

Answer and Step-by-step explanation:

The answer is [tex]\frac{14}{26}[/tex].

This fraction is a multiple of [tex]\frac{7}{13}[/tex].

#teamtrees #PAW (Plant And Water)

what units are used to calculate distance

Answers

Answer:

Step-by-step explanation:

Miles

simplify 5x+(2x-y)- 4y)​

Answers

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\huge\text{5x + (2x - y) - 4}[/tex]

[tex]\huge\text{= 5x + 2x - y - 4y}[/tex]

[tex]\huge\text{COMBINE the LIKE TERMS}[/tex]

[tex]\huge\text{(5x + 2x) + (-y - 4y)}[/tex]

[tex]\huge\text{5x + 2x = \boxed{\bf 7x}}[/tex]

[tex]\huge\text{-y - 4y = \boxed{\bf -5y}}[/tex]

[tex]\boxed{\huge\text{= \bf 7x - 5y}}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \text{\bf 7x - 5y}}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\longrightarrow{\blue{ 7x - 5y }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]5x + (2x - y) - 4y[/tex]

➼ [tex] \: 5x + 2x - y - 4y[/tex]

➼ [tex] \: 7x - 5y[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

what is the correct answer?

Answers

Answer:

5

Step-by-step explanation:

Answer:4.5

[um i cant relay see it but il do my best]

Pls help I need a good grade

Answers

Answer:

b

Step-by-step explanation:

glad I helped..............

Complete the function table. i really need help please

Answers

Answer:

Here ya go

Step-by-step explanation:

A metal square used in an electronic device must have a thickness of 0.02 inch, with an allowable error of 1 percent. What is the GREATEST allowable thickness of the metal square?
A. 0.0002 inches
B. 0.02 inches
C. 0.0202 inches
D. 0.03 inches

Answers

Answer:

A.0.0002 inch

Step-by-step explanation:

0.02 inch×1%=0.02 inch×1÷100

=0.0002 inch

If A metal square used in an electronic device must have a thickness of 0.02 inch, with an allowable error of 1 percent, the GREATEST allowable thickness of the metal square is 0.0202 inches. So, correct option is C.

The allowable error for the thickness of the metal square is given as 1 percent. To determine the greatest allowable thickness, we need to find 1 percent of the given thickness and subtract it from the given thickness.

Given thickness: 0.02 inches

1 percent of 0.02 inches = (1/100) * 0.02 inches = 0.0002 inches

Subtracting the 1 percent allowable error from the given thickness:

0.02 inches ± 0.0002 inches = 0.0198 inches or 0.0202 inches

Therefore, the greatest allowable thickness of the metal square is 0.0198 inches or 0.0202 inches.

Among the answer choices provided:

A. 0.0002 inches is the 1 percent allowable error, not the greatest allowable thickness.

B. 0.02 inches is the given thickness.

C. 0.0202 inches is the greatest allowable thickness.

D. 0.03 inches is greater than the greatest allowable thickness.

Hence, the correct answer is C. 0.0202 inches.

To learn more about error click on,

https://brainly.com/question/23971440

#SPJ2

Fig. 14.36 3 A concrete floor is 4 m long and 3 m wide. Calculate: a the area of the floor, b the cost of making the floor if concrete is N2 400 per m². What is the area, in m², of the floor of a hall that is 6 metres square? (6 metres square means 6 m by 6 m.)

Answers

Answer:

Step-by-step explanation:

Area of floor = length * width

                     = 4 * 3

                     = 12 sq.m

Cost of making the floor = 12 * 2400

                                         = N 28800

can anybody help me? I'll give brainlest​

Answers

9514 1404 393

Answer:

  65°, 35°, 90°, 115°, 80°

Step-by-step explanation:

There are 9 of the longer tick marks in 90°, so each of them represents 10°. The shorter tick marks are halfway between, so are on multiples of 5°. This lets us make a list of the angle value associated with each of the letters.

A: 0 or 180

B: 65 or 115

C: 90

D: 145 or 35

E: 180 or 0

__

Using this list, we can find the measure of each angle by finding the positive difference of the corresponding angle values associated with each of its rays.

arc AOB = 65 -0 = 65°

arc DOE = 35 -0 = 35°

arc AOC = 90 -0 = 90°

arc EOB = 115 -0 = 115°

arc DOB = 145 -65 = 80°

Which of the following questions are statistical? A. How many hours did you sleep last night. B. How many hours did the students in your class sleep last night. C. How many hours did your friend spend reading last night. D. How many hours did your teacher spend reading on Saturday.

Answers

B. How many hours did the students in your class sleep last night?

This is a statistical question because you get multiple answers. The other choices can just be answered with a definitive answer. Statistical question are those that have data with variabilty, meaning many different values

MARK ME BRAINLIEST TYSM!
Have a nice day
-SpaceMarsh

Classify the triangle by its angles and sides.
acute isosceles
acute scalene
equiangular equilateral
obtuse isosceles

Answers

I’ll pay you to do my 7 math assignments(no scams no bs) Hmu asap

Answer:

equiangular equilateral

all sides are equal  

please answer both questions thanks ​

Answers

67 on the first one and the second one is 34

Answer:

3. sin(43) = a/17

a = 17sin(43)

= 11.594

≈ 11.6

4. sin(35) = 6/b

b · sin(35) = 6

b = 6/sin(35)

= 10.46

Choose the answer that represents the product below as a exponential
expression.
(-4).(-4).(-4).(-4).(-4).(-4)
A. (-4)^6
B. (-4)^4
C. 6•(-4)
D. (-6)^-4

Answers

Answer:

(-4) ^6

Step-by-step explanation:

(-4)*(-4)*(-4)*(-4)*(-4)*(-4)

There are six (-4)'s multiplied together

(-4) is the base and 6 is the exponent

(-4) ^6

Abby went to the store to buy ice cream for her party. Each box costs $3. She has a coupon for 20% off her total. If Abby buys 3 boxes, what will she pay after using the coupon?

Answers

Answer: 7.2$

hope it helps :)

step-by-step explanation:

Cost of each box = 3$

Cost of 3 boxes without 20% coupon = 9$

With 20% off Coupon = 9 by 100 multiplied by 20

                                     (the zero's cut with each other leaving)

                                     = 9 by 10 multiplied by 2

                                     (9 multiplied by 2 = 18)

                                     = 18 by 10

                                     (18 divided by 10 = 1.8)

                                     = the 20% of 9$ is equal to 1.8

                                        when subtracted with the total cost leaves 7.2$

0.87 written as a fraction

Answers

Answer:

[tex] \frac{87}{100} [/tex]

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.

Hope it is helpful...

Answer:

87/100

Step-by-step explanation:

The proportion of all high school students who watch national news is p = 0.47. A random sample of 50 high school students is selected. Which of the following is the mean of the sampling distribution of p hat ? Mu Subscript p hat = p = 0.47 Mu Subscript p hat = n p = 50 (0.47) = 23.5 Mu Subscript p hat = 1 minus p = 1 minus 0.47 =0.53 Mu Subscript p hat = n (1 minus p) = 50 (1 minus 0.47) = 26.5

Answers

Approximately 60% of all part-time college students in the United States are female. (In other words, the population proportion of females among part-time college students is p = 0.6.) What would you expect to see in terms of the behavior of a sample proportion of females (p-hat) if random samples of size 100 were taken from the population of all part-time college

The mean of the sampling distribution of p hat is,

⇒  Mu Subscript p hat = n p = 50 (0.47) = 23.5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The proportion of all high school students who watch national news is p = 0.47.

And, A random sample of 50 high school students is selected.

Hence, By definition we get;

The mean of the sampling distribution of p hat is,

⇒  Mu Subscript p hat = n p

                                  = 50 (0.47)

                                   = 23.5

Thus, The mean of the sampling distribution of p hat is,

⇒  Mu Subscript p hat = n p = 50 (0.47) = 23.5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ3

all the angles of polygon of 30 sides are equal what is the measure of each angle​

Answers

Answer:

(30-2)*180 calculate and get ur answer

Other Questions
Write the following equation in slope y-intercept form and identity m and b.x + 2y 4 = 0 find the measure of the exter angle. NO LINKS PLEASEWhich choice BEST explains why each island in the Galapagos has unique kinds of iguanas?A. Iguanas prefer a marine environment.O B. Some iguanas are better swimmers than others.O C. The species arrived on the islands in different ways.OD. The species adapted to each island's unique habitat. Es el nombre que se le da a un cuerpo celeste dentro de su trayectoria The Canton Corporation shows the following income statement. The firm uses FIFO inventory accounting.CANTON CORPORATIONIncome Statement for 2013Sales $340,100 (17,900 units at $19.00)Cost of goods sold 205,850 (17,900 units at $11.50)Gross profit $134,250Selling and administrative expense 20,406Depreciation 10,500Operating profit $103,344Taxes (30%) 31,003Aftertax income $72,341a. Assume in 2014 the same 17,900-unit volume is maintained, but that the sales price increases by 10 percent. Because of FIFO inventory policy, old inventory will still be charged off at $11.50 per unit. Also assume selling and administrative expense will be 6 percent of sales and depreciation will be unchanged. The tax rate is 30 percent.a. Compute after-tax income for 2014. (Do not round intermediate calculations. Round your answer to the nearest whole number.)b. In part a, by what percent did after-tax income increase as a result of a 10 percent increase in the sales price? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)c. Now assume that in 2015 the volume remains constant at 17,900 units, but the sales price decreases by 15 percent from its year 2014 level. Also, because of FIFO inventory policy, cost of goods sold reflects the inflationary conditions of the prior year and is $12.00 per unit. Further, assume selling and administrative expense will be 6 percent of sales and depreciation will be unchanged. The tax rate is 30 percent. Compute the after-tax income. (Round the sales price per unit to 2 decimal places but do not round any other intermediate calculations. Round your final answer to the nearest whole dollar amount.) pa help po ako dito need ko po answer A stone of mass 0.2 kg falls with an acceleration of 10.0 m/s. How big is the force that causes this acceleration? South Africa's population grew by 17,5% in a period of 10years to reach a total of 52million in 2011.what is the double time for South africa? What was the most immediate geographic impact of the Klondike Gold Rush?A. A surge in populationB. The expansion of AlaskaC. An acquisition of new territoryD. The construction of railroads in "Loveliest of trees, the cherry now" by A.E. Housman, what word does housman emphasize in the poemA. TwentyB. cherryC. nowD. springs Which action best supports the idea that Boadicea is a warrior?The Roman leader asks for peace with the Britons.Boadicea evokes pity by choosing death.The Roman leader is downcast and does not want to fight.Boadicea tells the Roman leader that she will speak with her sword. Briefly explain ONE major similarity or difference between President Ronald Reagans policies in the 1980s and President Franklin Roosevelts policies in the 1930s. What happens to a person's center of gravity once they achieve a proper athletic stance? The center of gravity will What are chromosomes ? explain Una empresa, para comprar ropa de trabajo para su personal, tiene un presupuesto de $ 10.000. La empresa pide cotizaciones y recibe las siguientes propuestas: a) pagar $ 5.000 al contado y $ 5.000 en 90 das; b) pagar $ 3.000 al contado; $ 3.000 en 30 das y $ 4.000 en 90 das; c) pagar $ 2.000 al contado, $ 4.000 en 30 das y $ 4.000 en 84 das. Si la tasa de inters es del 24% anual, cul oferta le conviene aceptar Lee y contesta santiago quiere comer la mitad de un pastel y alba quiere un tercio del mismo pastel para repartirlo bien reducen las fracciones a comun denominador en cuantas partes iguales deben dividir el pastel? cuantas partes debe tomar cada uno? To determine the density of a rabbit population, one would need to know the number of rabbits and __________. View Available Hint(s) To determine the density of a rabbit population, one would need to know the number of rabbits and __________. their pattern of dispersion the size of the region in which they live the factors that limit population growth for that rabbit population the growth rate of the population the birth rate How do borders play a part in the conflict of Kashmir? Write an equation for a circle in standard form with a center at (-6, 5) and has a radius equal to 5. 2 Find the area of the sector if the radius is 8cm show your work below 2 2 Show your work below. You have responded to 0 of 7 questions. Question Details Write an equation for a circle in standard form with a center at (-6, 5) and has a radius equal to 5. Look! John (go) ________________ to the movies.