Find the value of the given expression, and most importantly show the steps please.
Answers
Answer:
Step-by-step explanation:
[tex]16^\frac{1}{n}=2[/tex] (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])
[tex](2^4)^\frac{1}{n}=2[/tex]
[tex]2^\frac{4}{n}=2[/tex]
[tex]2^\frac{4}{n}=2^1[/tex]
∴[tex]\frac{4}{n} =1[/tex] (indices must be equal when bases are equal)
∴[tex]n=4[/tex]
Related Questions
Noah and his friends are going to an amusement park. the total cost of admission for eight students is $100, and all students share the cost equal. Noah bought $13 for his ticket. did he bring enough money to get to the park? bring your reasoning.
Answers
Answer: The correct answer is yes, he brought enough money to get into the park.
Step-by-step explanation:
Well, let's analyze the information provided:
Admission to the amusement park for 8 students is $ 100. If each student agreed to share of cost equally, it means that we must divide those 100, for each of those students.
Therefore it will remain 100/8 = 12.5
If each student must pay 12.5, and Noah brought $ 13, that means he will have enough money to enter the park, and he will even have $ 0.50 left over.
How to determine the area of all faces in mm2
Answers
The surface area of all faces of the cube is found as in 150,100 mm².
Explain about the cube?A solid shape having six square faces is called a cube. Because every square face has an identical side length, each face is the same size.
A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex. A cube has twelve equal-length edges and six faces. Its faces are square-shaped. The cube's angles in the plane were right angles. The cube's faces are connected by four other faces.Area of the cube:
Area = 6*side²
Area = 6*(5)²
Area = 150 cm²
We know:
1 cm = 10 mm
Then,
Area = 150 x 100 mm²
Area = 150,100 mm²
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The complete question is-
The cube has the side length of 5 cm. How to determine the area of all faces in mm2
1. You work at a department store that needs at least 4200 labor hours covered per week. It employs full-time staff 40 hours per week and part-time staff 25 hours per week. The cost to employ a full-time staff member is more because the company pays benefits such as health care and life insurance
Full-time
Part-time
Hours per Week Cost per Hour
40 hr
$25
25 hr
$18
The store manager also knows that to make the store run efficiently, the number of full-time employees must be at least 1.25 times the number of part-time employees. You have been asked to help the store manager determine the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost.
a. Clearly define the variables in this problem.
b. Clearly state the constraints (all inequalities) related to the feasible region.
c. State the objective function.
d. Use the graphical method to
solve: Graph the solution region, showing the intercepts used. Label axes, units, points, and lines. Find and label all corner points. The grid for the graph is on the next page.
Show all necessary work.
e. In a complete sentence, state the number of full-time employees and the number of part-time employees that should be used to minimize the weekly labor cost.
Answers
Using linear programming, the minimum weekly labor cost of $2,616 occurs when there are 84 full-time employees and 67.2 part-time employees (which can be rounded up to 68 part-time employees)
What are the variables in this problema. Let x be the number of full-time employees and y be the number of part-time employees.
b. The constraints are:
Full-time employees work 40 hours per week, so the total number of full-time labor hours used must be at least 40x.Part-time employees work 25 hours per week, so the total number of part-time labor hours used must be at least 25y.The total number of labor hours used must be at least 4200: 40x + 25y ≥ 4200The number of full-time employees must be at least 1.25 times the number of part-time employees: x ≥ 1.25yThe number of full-time and part-time employees must be non-negative: x ≥ 0 and y ≥ 0c. The objective function is to minimize the weekly labor cost, which is given by:
Cost = 25x + 18y
d. To graph the solution region, we can first graph the inequality 40x + 25y ≥ 4200 as a line:
Convert the inequality to an equation: 40x + 25y = 4200Solve for y: y = (4200 - 40x)/25 = (168 - 1.6x)Plot the y-intercept: (0, 168)Plot the x-intercept: (105, 0) (found by setting y = 0 and solving for x)Draw the line passing through the two intercepts.Next, we can graph the inequality x ≥ 1.25y as a line:
Convert the inequality to an equation: x = 1.25yPlot two points on the line: (0, 0) and (0, 0) (found by setting y = 0 and x = 0 respectively)Draw the line passing through the two points.The feasible region is the shaded region that satisfies all the constraints and is bounded by the two lines and the x and y axes:
To find the corner points, we can solve the system of equations for the lines that form the boundaries of the feasible region:
40x + 25y = 4200 and x = 0 (y-axis intercept) --> (0, 168)40x + 25y = 4200 and y = 0 (x-axis intercept) --> (105, 0)x = 1.25y and y = 0 (x-axis intercept) --> (0, 0)x = 1.25y and 40x + 25y = 4200 --> (84, 67.2)Now we can evaluate the objective function at each of the corner points:
(0, 0): Cost = 0(0, 168): Cost = 25(0) + 18(168) = 3024(105, 0): Cost = 25(105) + 18(0) = 2625(84, 67.2): Cost = 25(84) + 18(67.2) = 2616Therefore, the minimum weekly labor cost of $2,616 occurs when there are 84 full-time employees and 67.2 part-time employees (which can be rounded up to 68 part-time employees).
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5,10,15,20,25 is this an arithmetic or geometric sequence
Answers
Because of the common difference of 5, this series is math because it has a common difference of 5.
What in mathematics is an arithmetic sequence?An arithmetic series is one in which each term grows by adding or removing a certain number, k. In a geometric series, each term grows by dividing by or increasing by a certain constant k. For instance, a1 = 25 and a(n) Equals a(n-1) Plus 5.
This is a list of numbers.
Each term in an arithmetic series is created by adding a fixed difference to the term before it. The distance between successive words in this order is 5:
10 - 5 = 5
15 - 10 = 5
20 - 15 = 5
25 - 20 = 5
Therefore, this sequence has a common difference of 5, which means it is an arithmetic sequence.
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Create 5 examples of gains and losses using positive and negative numbers.
Answers
Answer:
Step-by-step explanation:
gain
loss
gain loss
gain
Answer:
Gains : +1,+10,+3
loss: -3,-5,-9,-100
Step-by-step explanation: I think this question is basically just asking about givings examples of positive and negative numbers
Please help me solve
Answers
Answer:
x = -1 (multiplicity 2)
Step-by-step explanation:
Given the cubic f(x) = x³ -x² -5x -3 has x=3 as a root, you want the other roots.
Quadratic factorYou can find the quadratic factor of the polynomial using synthetic division. That tells you ...
f(x) = (x -3)(x² +2x +1)
You recognize the quadratic factor as the perfect square trinomial ...
x² +2x +1 = (x +1)²
RootsThe remaining roots will be the values of x that make these factors zero:
x +1 = 0 ⇒ x = -1 . . . . . and the other is the same: multiplicity 2
The remaining roots are x=-1 and x=-1.
__
Additional comment
We find a graphing calculator to be a quick and easy way to find the real roots of higher-degree polynomials. They are shown in the second attachment.
Griffin read 27 books about animals and 6 books
about space. How many books did he read?
Answers
Answer:
33 27 plus 6 = 33
Step-by-step explanation:
A collectible action figure is worth $1100. The value of the action figure increases by 6% each year.
Which explicit and recursive formulas can be used to model the situation.
Drag and drop each formula to the corresponding box.
Answers
In response to the query, we can state that r: the annual rate of increase equation (6% in this case)
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
Explicit Formula:
[tex]a_n = a_0 \times (1 + r)^n[/tex]
Recursive Formula:
[tex]a_n = a_{n-1} \times (1 + r)[/tex]
where:
[tex]a_n[/tex]: the value of the action figure after n years
[tex]a_0[/tex]: the initial value of the action figure ($1100 in this case)
r: the annual rate of increase (6% in this case)
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V(0) is the initial value of the action figure, and the recursive formula calculates the value of the action figure after n years by adding 6% of the previous year's value to the previous year's value.
What is equation?
In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements.
Let V(n) be the value of the action figure after n years.
Explicit formula:
V(n) = 1100(1 + 0.06)^n
Recursive formula:
V(0) = 1100
V(n) = V(n-1) + 0.06V(n-1)
Therefore, V(0) is the initial value of the action figure, and the recursive formula calculates the value of the action figure after n years by adding 6% of the previous year's value to the previous year's value.
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Is {A, B, C} a subset of the set of letters of the alphabet?
Answers
The set {A, B, C} is a subset of the set of letters of the alphabet.
What are sub-sets:A subset is a set that contains only elements that are also in another set, called the superset. In other words, all of the elements in the subset are also contained in the superset.
For example, suppose we have a superset S = {1, 2, 3, 4, 5}. Then, the following sets are subsets of S:
{1, 2, 3}, {2, 4, 5}, {1}, and {} etc.
Here we have
{A, B, C} a subset
As we know, the set of the alphabet = { A, B, C, D,... Z }
which also includes the elements A, B, and C
Hence,
The set {A, B, C} is a subset of the set of letters of the alphabet.
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David has 6 pounds of dried fruit to make snack bags. He separates each pound of dried fruit into fourths and wants to use 1 fourth for each bag. How many snack bags can he make with all of the dried fruit?
Answers
Answer: 24
Step-by-step explanation: 6*4=24
i did 6*4 because there are 4 fourths in each pound
Find the slope of the line shown below?
Answers
How do you find slope?
Remember y=mx+b
b=y intercept
m=slope
For future reference: Formula to find slope
y2-y1/x2-x1
(One of the ways to find slope)
The slope-intercept form for this picture is y=2/3x-1
Hope this helps have a nice day
how many solutions are in 16 (3x − 6) = 18 (4x + 8).
Answers
Answer:
alot
Step-by-step explanation:
Answer:
One solution, x = -10
Step-by-step explanation:
16 (3x − 6) = 18 (4x + 8)
48x - 96 = 72x + 144
-24x = 240
x = - 10
What is the eighth term of 4000, 800, 160, 32
Answers
The eighth term of 4000, 800, 160, 32... will be 0.0512.
What is geometric progression?
A geometric progression is also known as the geometric sequence which is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
We are given, 4000, 800, 160, 32, ....
a is the first term = 4000
The terms are in reducing order of 1/5 at each stage.
So, 5th term = 32/5 = 6.4
6th term = 6.4/5 = 1.28
7th term = 1.28/5 = 0.256
And 8th term = 0.256/5 = 0.0512
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Calculate the concentration for the following pH: pH = 2.44
Answers
The concentration οf hydrοgen ions in a sοlution with pH 2.44 is [tex]2.754\times 10-12 M[/tex]
What is the pH value?
The pH value is a measure οf the acidity or basicity of a solution. It is defined as the negative lοgarithm (base 10) of the concentration of hydrogen ions (H+) in moles per liter (mol/L) of solutiοn. The pH scale ranges from 0 to 14, where a pH of 7 is considered neutral. Solutions with a pH less than 7 are acidic, while solutiοns with a pH greater than 7 are basic οr alkaline.
a) Given pH = 2.44
We knοw pH + pOH = 14,
pOH = 14 - 2.44 = 11.56
[tex][H+] = 10^{-pH} = 10^{-2.44} = 3.63\times 10 ^{-3} M[/tex]
[tex][OH-] = 10-pOH = 10-11.56 = 2.754\times 10-12 M[/tex]
b) Given ,pOH = 10.85
and it is knοwn that pH + pOH = 14, thus pH = 14 - 10.85= 3.15
[tex][H+] = 10^{-pH} = 10^{-3.15} = 7.07\times10^{-4 M}[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-10.85} = 1.41\times10^{-11} M[/tex]
c) Given pH = -0.65
and it is knοwn that pH + pOH = 14, thus pOH = 14 +0.65 = 14.65
[tex][H+] = 10^{-pH} = 10^{0.65} = 4.466 M[/tex]
[tex][OH-] = 10^{-pOH} = 10^{-14.65} = 2.23 \times10^{15} M[/tex]
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Complete question:
Calculate the [H+] and [OH-] concentrations for the fοllowing solutions with: (a) pH = 2.44 (b) pOH = 10.85 (c) pH = -0.65
Use the graph of the function to find the indicated values.
Answers
The value of the indicated function instances as required to be determined are as follows;
f (π) = -3.f (π/2) = 0.f ( -3π/2 ) = 0.What is the value of the indicated function instances?It follows from the task content that a graph is given and the indicated values are to be determined.
By observation of the graph; it follows that;
On this note, f (π) = -3.
f (π/2) = 0.
f ( -3π/2 ) = 0.
The values above are as obtained from the graph.
Ultimately, the value of the indicated function instances are as evaluated from the graph above.
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A trapezium is shown below.
Work out the sizes of angles x and y.
Give your answers in degrees (°).
145°
X
Y
62°
PLEASE DO IT FOR 20 points
Answers
Answer:
x=118
y= 35
Step-by-step explanation:
180-62= 118
180-145=35
The value of x from the trapezium is 118° and the value of y from the trapezium is 35°.
What is a trapezium?
A trapezium is a quadrilateral with two parallel sides. It has two non-parallel sides that are called the legs of the trapezium, and the other two sides are called the bases.
From the given trapezium 4 angles are x, y, 62° and 145°.
Here, x+62°=180° (Sum of allied angles is 180°)
x=180°-62°
x=118°
Now, y+145°=180°
y=180°-145°
y=35°
Therefore, the value of x from the trapezium is 118° and the value of y from the trapezium is 35°.
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These lists show the ages of attendees in a yoga class and a dance class.
Yoga: 18, 31, 17, 44, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Which statement about attendees in the two classes is true?
A. The median age of the attendees in the yoga class is greater than the median age of
the attendees in the dance class.
B. The median age of the attendees in the dance class is greater than the median age of
the attendees in the yoga class.
C. The median age of the attendees in the yoga class is the same as the median age of the
attendees in the dance class.
D. The median age of the attendees in the yoga class is 44 years and the median age of
the attendees in the dance class is 47.
Answers
The true statement is the median age of the attendees in the yoga class is greater than the median age of the attendees in the dance class. (option A).
What is the true statement?
Median is the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
Ages of Yoga students arranged in ascending order: 18, 17, 20, 31, 33, 36, 44
Median = 31
Ages of Dance students arranged in ascending order: 20, 23, 26, 30, 38, 42, 47
Median = 30
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please help, need help understanding step by step.
Answers
we will need at least 96 bags of sand to cover the base of the circular pool.
what is circle?
A circle is a two-dimensional geometric shape consisting of all the points that are equidistant from a given point, called the center.
The area of a circular pool with a diameter of 22 feet can be calculated using the formula:
A = πr^2
where A is the area of the circle, π is a constant (approximately equal to 3.14), and r is the radius of the circle (which is half the diameter).
In this case, the diameter is 22 feet, so the radius is:
r = d/2 = 22/2 = 11 feet
Now we can calculate the area of the circle:
A = πr^2 = 3.14 x 11^2 = 379.94 square feet (rounded to 2 decimal places)
To cover this area with sand, we need to know how many bags of sand are required. We are told that one bag of sand covers about 4 square feet, so we can calculate the number of bags of sand required as follows:
Number of bags = Area of pool / Area covered by one bag
Number of bags = 379.94 square feet / 4 square feet per bag
Number of bags ≈ 95 bags
Since we need to round up to a whole number of bags, we will need at least 96 bags of sand to cover the base of the circular pool.
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Fins the center of the radius circle.
(x-1)^2 + (y-5)^2=4
Answers
Answer:
the radius is 1
Step-by-step explanation:
2/7
of the 140 students in a contest gave their speeches. How many students gave their speeches?
Yesterday,
Write your answer in simplest form.
Answers
Answer:40
140/7=20
20x2=40
40 is the same as two-sevenths of 140
The final RSVP guest count is 60 people Which catering company will offer the best deal for your family? How much money will your family save by choosing that company
Answers
a) The family's best deal is with Smokey's BBG which charges $780 for 60 guests.
b) Choosing Smokey's BBG over Bennie's BBQ will save (difference) the family $40.
How is the difference or saving determined?The total cost for each company's catering services is worked out using their cost functions.
Smokey's BBG does not charge a fixed cost, unlike Bennie's BBG.
The difference between the total costs of the companies is obtained by subtraction.
The number of guests = 60
Smokey's BBQ Bennie's BBQ
Catering Fees $0 $100
Charge per person $13 $12
The total charge for 60 $780 ($13 x 60) $820 ($100 + $12 x 60)
Difference between the charges = $40 ($820 - $780)
However, using a system of equations we can determine the number of guests that makes the total cost the same for each company as 100.
Thus, comparing the total costs for the two companies shows the difference or cost savings to be gained by the family.
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Question Completion:Smokey's BBQ charges $13 per person while Bennie's BBG charges a $100 catering fee and $12 per person.
What is the value of X? HELP ME PLEASE:) THIS QUESTION IS HARD WHATS THE ANSWER
Answers
Answer:
96 because 60 plus 36 equals 96 and value means add but if your multiplying the answer would be 2160
Step-by-step explanation:
A researcher watches popular television shows and records every time someone interrupts a speaker. She wants to understand the frequency of interruption on television.
Answers
Answer:
the frequency of someone interru
Step-by-step explanation:
The correct answer is (d) noise. Unwanted sound that is regarded loud, unpleasant, or disruptive to hearing is called noise.
What is noise?Even if the label "unwanted" is arbitrary, some sounds are frequently regarded as noise. A sound pressure level, expressed in decibels, is used to measure or anticipate noise (dB).
here, we have,
The measurements and noise meter used depend on the application; different noise metrics can account for magnitude, frequency, and time in different ways.
and, we have,
Another illustration is workplace noise, where the effect of noise on hearing loss is of utmost importance.
To offer a degree of exposure that can be associated to the possibility of hearing loss in employees exposed to the sound during the course of exposure, both the intensity and duration of sound are combined.
Hence, The correct answer is (d) noise. Unwanted sound that is regarded loud, unpleasant, or disruptive to hearing is called noise.
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Complete question:
ivan is trying to understand the concern of an angry customer, but several employees keep interrupting the conversion. these interruptions are an example of
3.
1
A decorative wooden piece is made up of four rectangles as shown to the
right. The smallest rectangle measures 4 inches by 7 inches. If 2
inches are added to each dimension as the rectangles get larger, what is
the total area of the entire piece?
Answers
The total area of the rectangle with the provided figures will be equal to 280 inches.
How to obtain the area of the rectanglesNote that the area of a rectangle is length * width.
So, given this formula:
The area of the smallest rectangle will be: 4 * 7 = 28
The area of the next rectangle will be: (4 + 2) * (7 + 2)
= 6 * 9
= 54
The area of the next rectangle will be: (6 + 2) * (9 + 2)
= 8 * 11
= 88
The area of the fourth and largest rectangle will be: (8 + 2) * (11 + 2)
10 * 11
= 110
The total area of the angles will be: 28 + 54 + 88 + 110
= 280.
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Select all of the expressions that are equivalent to (9x+6)-¹(8x-4).
M. 2(x + 1)
R. 2x+6
R. 2x + 2
S. 2(x + 3)
T. 8x
Answers
The expression that is equivalent to 2(9x+6)/3-(8x-4)/2 is 8x, the correct option is T.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
The function=2(9x+6)/3-(8x-4)/2.
Now,
First, let's simplify the expression given:
2(9x+6)/3 - (8x-4)/2 = (18x + 12)/3 - (4x - 2) = 6x + 4 - 2x + 1 = 4x + 5
Now let's check which of the given expressions are equivalent to 4x + 5:
M. 2(x + 1) = 2x + 2 (not equivalent)
R. 2x+6 (not equivalent)
R. 2x + 2 (not equivalent)
S. 2(x + 3) = 2x + 6 (not equivalent)
T. 8x = 8x - 40 + 45 = 4x + 5 (equivalent)
Therefore, the answer of the given expression will be 8x.
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30 gallons= 114 liters
Answers
Answer: 113.56235 Liters
Step-by-step explanation:
10. You are painting a room that is 18 feet long, 14 feet wide and 8 feet high. If the paint costs $6.50 a gallon and each gallon covers 128 square feet, how much will it cost to paint the room?
Answers
The total cost to paint the room is, $102.375.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, A room that is 18 feet long, 14 feet wide, and 8 feet high.
Therefore, The surface area of the room is,
= 18×14×8 aq feet.
= 2016 sq feet.
Now, Paint costs $6.50 a gallon and each gallon covers 128 square feet.
Therefore, The number of gallons of paint required is,
= (2016/128) gallons.
= 15.75 gallons.
So, The total cost of painting is,
= $15.75×6.50.
= $102.375.
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if the dilation of K(-2,4) equals K'(1,-2), the scale factor used for the dilation is
Answers
Answer:
-1/2
Step-by-step explanation:
We know
The dilation of K(-2,4) equals K'(1,-2)
To get from -2 to 1, we time -1/2
To get from 4 to -2, we time -1/2
So, the scale factor used for the dilation is -1/2
PLEASE HELP IM SO LOST !!
Answers
The function has domain = {2, , 5, - 4, - 5} and rangle = {1, 4, 5, 3, - 6} and it is not a function.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
From the given coordinate plots the ordered pairs are,
(2, 1), (2, 4), (5, 5), (- 4, 3), and (- 5, - 6).
We know a relation is not a function when two distinct ordered pairs have the same x-coordinate.
In this case (2, 1) and (2, 4) have the same x-coordinate and hence it is not a function.
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Solve:
|3x|=9
x= 3
x= 1 and x=-2
x=3 and x=-3
x= 0 and x= 7
Answers
The required solutions of the equation |3x| = 9 are x = 3 and x = -3.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
We can solve the given equation by isolating the absolute value on one side and simplifying it.
|3x| = 9
| x | = 3
Now, we need to solve two separate equations for x:
When x is positive:
|x| = 3
=> x = 3 (since x is positive)
When x is negative:
|x| = 3
-x = 3 (since x is negative)
x = -3
Therefore, the solutions of the equation |3x| = 9 are x = 3 and x = -3.
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