Answer:
1) 5√5
= 5^1 * 5^(1/2)
= 5^(1 + 1/2)
= 5^(3/2)
Value of n = 3/2
2) Create equivalent expressions in the equation that all have equal bases, then solve for n.
n = 5/2
The required simplified value ox n in both expressions is given as 1) n = 3/2 and 2) n = 5/2.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
(1)
5√5 can be written in form 5ⁿ.
5√5= 5ⁿ
[tex](5)^{1 + 1/2} = 5^n\\n = 3/2[/tex]
Similarly,
(2)
2√8 = 2ⁿ
n = 5/2
Thus, the required simplified value ox n in both expressions is given as 1) n = 3/2 and 2) n = 5/2.
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a. Compute the similarity dimension of the fractal. Round to the nearest thousandth. The Cantor point set, defined by the following stages. b. Compute the similarity dimension of the fractal. Round to the nearest thousandth. The Sierpinski carpet, variation 1, defined by the following stages.
The similarity dimension of the Cantor point set is approximately 0.631, while the similarity dimension of the Sierpinski carpet, variation 1, is approximately 1.893.
Cantor point set: First Stage - The interval is divided into three equal parts.
Second Stage - The middle third of the first and third intervals are removed.
Third Stage - The middle third of the remaining intervals is removed.
This process is continued infinitely to create the Cantor set. The Cantor set is a fractal that is self-similar, meaning that each part of the fractal looks like the entire fractal.
To find the similarity dimension of the Cantor set, we will use the following formula:
log(2)/log(3) ≈ 0.631
log(8)/log(3) ≈ 1.893
The similarity dimension of the Cantor point set is approximately 0.631, while the similarity dimension of the Sierpinski carpet, variation 1, is approximately 1.893.
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Q1. (5+5 Marks) A. Base - ten positional numeral system or occasionally called Denary system is a set containing ten digits from zero to nine. We use this system in our real life to all calculations. Write a matrix that represents all digits in this system except zero. Does this matrix have an inverse? Check your answer by calculating its determinant first.
The matrix that represents all digits in the base-ten positional numeral system, except zero, is a 9x9 matrix where each element represents a digit from 1 to 9.
The matrix that represents all digits in the base-ten positional numeral system, except zero, can be represented as follows:
[1 2 3 ... 9]
To check if this matrix has an inverse, we calculate its determinant. Since the matrix is a 9x9 matrix with elements from 1 to 9, the determinant can be calculated using standard methods such as expansion by minors or row reduction. However, since the matrix is a simple sequential arrangement of numbers, we can observe that the determinant of this matrix is zero. This is because the determinant of a matrix with identical rows or columns is always zero.
Since the determinant of the matrix representing the digits from 1 to 9 in the base-ten system is zero, we can conclude that the matrix does not have an inverse. Inverse of a matrix exists only if the determinant is non-zero. In this case, since the determinant is zero, the matrix does not have an inverse.
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NEED ASAP
A company rents out 16 food booths and 29 game booths at the county fair. The fee for a food booth is $200 plus $4 per day. The fee for a game booth is $95 plus $7 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
The expression is...
Answer:
204x+102y=p
Step-by-step explanation:
204x+102y=p
204(16)+102(29)=$6,222
a hybrid car uses 1 gallon of gasoline to drive 54 miles. how many gallons of gas would be used to travel 162 miles
Answer:
3
Step-by-step explanation:
162/54 = 3
Find the slope on this graph?????
Answer:
use the y=mx + b method
rise over fun
Answer:
-4/3
Step-by-step explanation:
Like the other person said, rise up 4 and 3 to the left. Line is going from left to right so it's negative.
A grocery store owner sells tangerines in 2/5 kg bags. bought 4 kg of tangerines for a school party. How many bags did he buy?
Answer:
10 bags
Step-by-step explanation:
To have 4 kg, he would need 20/5 kg. Each bag is 2/5, so 2/5 times 10 is 20/5 or 4 kg
Could somebody gives me the answer for this, thanks.
(WILL GIVE BRAINLIEST AFTER I FIGURE OUT HOW TO DO IT)
Can anyone help please ?!?! I’ll mark brainlist
Answer:
1/ 12
Step-by-step explanation:
Answer:
well i think it is number 2 but i really dont know sorry
Step-by-step explanation:
The sum of Micah’s age and Aria’s age is 29. Aria is 5 years older than twice Micah’s age. Let x represent Micah’s age. The equation that can be used to find Micah’s age is
Answer:
B) x+(2x+5)=29
Step-by-step explanation:
Micah = x
Aria =2x+5
x+(2x+5)=29
Juan had 5/7 of a spool of yarn. He used 5/5 of his yarn for a project. What fraction of the spool was used for the project?
Answer:
2/5
Step-by-step explanation:
You see he had 7/5 wich equals 1 2/5 who used 2/5 so subtract 2 and you have 1 whole left.
The function f(x) = (x - 4)(x - 2) is shown below. What is true about the domain and range of the function?
Answer:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)
[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)
Step-by-step explanation:
Graphically speaking, quadratic functions are represented by parabolas. In this case, we have a parabola in factorized form. From Theory of Functions, we get that domains of function represents the set of values of [tex]x[/tex] so that exist an image, whose set is known as range is represented by values of [tex]f(x)[/tex].
[tex]x[/tex] is represented by horizontal axis in the figure, whereas [tex]f(x)[/tex] is represented by the vertical axis. By using this approach we get that domain and range of the function are, respectively:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)
[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)
How many words can be typed in 10.5 minutes?
Answer: Around 2,000 words.
What am I supposed to do? Is it subtract 180 from 56?
In which situation is the distance traveled proportional to time?
When speed is constant, distance traveled is directly proportional to the time. As the formula tells:
Speed = Distance / Time
So, if speed is constant, and you are increasing distance then time will increase, in order to keep the speed constant
what two positive real numbers whose product is 11 have the smallest possible sum?
The two positive real numbers with a product of 11 that have the smallest possible sum are √11 and √11. In decimal form, these numbers are approximately 3.3166 and 3.3166.
To determine two positive real numbers whose product is 11 and have the smallest possible sum, we can use the concept of the arithmetic mean-geometric mean inequality.
Let the two numbers be x and y.
We have the following conditions:
1. xy = 11 (product of the two numbers is 11)
2. x > 0, y > 0 (both numbers are positive)
According to the AM-GM inequality, the arithmetic mean of two numbers is always greater than or equal to the geometric mean of those numbers.
Using this inequality, we have:
(x + y)/2 ≥ √(xy)
Substituting the value of xy as 11, we get:
(x + y)/2 ≥ √11
To minimize the sum (x + y), we need to make it as close as possible to the right side of the inequality.
This occurs when equality holds, that is, when:
x = y = √11
So, the answer is approximately (3.3166, 3.3166).
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Round each mixed number to the nearest whole number. Then, estimate the sum.
14 11/12 + 3 1/6
Answer:
18
Step-by-step explanation:
14 11/12 rounds to 15, and 3 1/6 rounds to 3. 3 plus 15 is 18.
how do I graph a equation using y= ⅕+3?
Answer: The y intercept (3) goes 3 up in the y axis.
To find the slope (rise/run), we start from the point we found at the y intercept ( which is 3). So we rise 1 (from the 3), and run 5.
(always run to the right)
The file is a picture of your equation.
After placing an equation into his calculator Rob got the following table. He then determents the x=6 when f(x)=-4 Is he correct Explain
Answer:
no
Step-by-step explanation:
From the table
when f(x) = - 4, then x = 2
Five times a number subtracted from twelve is triple the number. Find the number
Answer:
1.5
Step-by-step explanation:
Let the unknown number be x.
12 - 5x = 3x
12 = 3x + 5x = 8x
. : x = 12/8 = 3/2 = 1.5
A school fundraiser is selling pumpkins. They charge an amount per pumpkin, plus a flat fee. If 2 pumpkins cost $12, and 5 pumpkins cost $27, how much would 10 pumpkins cost? *
$42
$52
$54
$60
Answer:
42
Step-by-step explanation:
What are the x-intercept and the y-intercept of the graph of 12x – 4y = 48?
Answer:
The x-intercept and the y-intercept of the graph of 12x-4y=48 is 6.
Step-by-step explanation:
I used trial and error. I substituted x and y with 6 to get the answer.
12(6)-4(6)=48
Need some help on one question for geometry!
Answer:
AB = 23
Step-by-step explanation:
AC = AB + BC
(7x + 6) = (6x - 1) + (4x - 5)
7x + 6 = 6x - 1 + 4x - 5
7x + 6 = 10x - 6
-3x+ 6 = -6
-3x = -12
x = 4
AB = 6x - 1
= 6(4) - 1
= 24 - 1
= 23
a. Analyze the number of dark triangles. Describe the pattern.
Select the correct answer.
Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have?
A.
, which has no solution
B.
, which has infinitely many solutions
C.
, which has one solution
D.
, which has one solution
E.
, which has no solution
Reset Next
Answer:
A
Step-by-step explanation:
lance bikes 18 miles in 3 hours. how many miles does lance bike in 1 hour?
Answer:
6 miles
Step-by-step explanation:
Set up a proportion, where x is the number of miles he bikes in 1 hour:
[tex]\frac{18}{3}[/tex] = [tex]\frac{x}{1}[/tex]
Cross multiply and solve for x:
3x = 18
x = 6
So, he bikes 6 miles in 1 hour
Answer:
6 miles
Step-by-step explanation:
:)
A ball will be drawn from the bag containing 20 balls numbered one through 20 if each ball is equally likely to be drawn what is the probability that the number on the bar will be drawn even or less than five
Answer:
3/5
Step-by-step explanation:
There are 20 balls, numbered 1 through 20.
Of these, 10 are even, 4 are less than five, and 2 are both even and less than 5.
So the probability is:
P(even or <5) = P(even) + P(<5) − P(even and <5)
P(even or <5) = 10/20 + 4/20 − 2/20
P(even or <5) = 12/20
P(even or <5) = 3/5
The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer at that time The computer is worth 8850 initially; and it is worth S306 after 2 years. How much will the computer be worth after 5 years? Choose answer: $0
$66
$69
The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer at that time The computer is worth 8850 initially, and it is worth S306 after 2 years. Then $66 will the computer be worth after 5 years.
To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases exponentially over time.
Let's denote the value of the computer at any time t as V(t). We know that the rate of decrease is proportional to the value at that time. This can be expressed as:
dV/dt = k × V(t)
where dV/dt represents the rate of change of V with respect to t, and k is the proportionality constant.
To find the value of k, we can use the initial condition. The computer is worth 8850 initially, so we have:
V(0) = 8850
After 2 years, the computer is worth $306, so we have:
V(2) = 306
Now we can solve for k. Integrating the differential equation, we get:
∫(1 / V(t)) dV = ∫k dt
ln(V(t)) = kt + C
Taking the exponential of both sides, we have:
V(t) = e^(kt+C)
Since V(0) = 8850, we can substitute these values into the equation to solve for C:
e^(k × 0 + C) = 8850
e^C = 8850
C = ln(8850)
Now we have the equation:
V(t) = e^(kt + ln(8850))
Using the value V(2) = 306, we can substitute these values into the equation:
306 = e^(2k + ln(8850))
Taking the natural logarithm of both sides, we get:
ln(306) = 2k + ln(8850)
Solving for k:
k = (ln(306) - ln(8850)) / 2
Now, to find the value of the computer after 5 years (V(5)), we substitute t = 5 into the equation:
V(5) = e^(5k + ln(8850))
Calculating the value using the previously found value of k:
V(5) = e^(5 × [(ln(306) - ln(8850)) / 2] + ln(8850))
After evaluating this expression, we find that the value of the computer after 5 years is approximately $66. Therefore, the correct answer from the provided options is $66.
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A soft-drink machine can be regulated so that it discharges an average of ? oz. per cup. If the ounces of fill areNormally distributed with a standard deviation of 0.4 oz., what value should ? be set at so that 98% of 6-oz. cups will not overflow?
A. 5.18
B. 6.00
C. 6.18
D. 6.60
E. 6.82
The value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.
Given data
A soft- drink machine can be regulated so that it discharges an normal of? oz. per mug. The ounces of filler are typically distributed with a standard divagation of0.4 oz.
What value should be set at so that 98 of 6- oz. mugs won't overflow?
Let μ be the mean ounces of filler per mug.
μ can be attained by using the formula
μ = 6 oz. = 6/8 = 0.75 mugs.
Now, given σ = 0.4 oz.
The Z- score for a 6- oz mug can be calculated as follows
z = ( x- μ)/ σ
Then, x = 6 oz = 6/8 = 0.75 mugs.
μ = 0.75 mugs
σ = 0.4 oz.
z = (0.75-0.75)/0.4 = 0
For 98 of 6- oz mugs to not overflow, we need to find the value of μ similar that P( z Since the Normal distribution is symmetric about the mean, we have
P( 0< z We can look up the value of
z_score for P( 0< z
standard normal distribution table or use the inverse function on a calculator similar as Excel.
Using a table, we get the value ofz_score = 2.33.
Now, z = ( x- μ)/ σ2.33 = (0.75- μ)/0.4
μ = 0.75-0.4 ×2.33
μ = 0.75-0.932
μ = -0.182 oz.6 oz in terms of ounces = 6 *0.125 = 0.75 oz.
oz per mug in terms of ounces = ? *0.125 oz.
Using the values from above
μ = -0.1820.75 = 0.568 oz. ≈0.57 oz.
= 0.57/0.125 = 4.56 or 5
So, the value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.
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A number p, when truncated to 1 decimal place, is equal to 14.3
Find the upper and lower bound of p.
Lower bound =
Upper bound=
Submit Answer
The lower bound of [tex]\(p\) is \(14.25\)[/tex] and the upper bound is [tex]\(14.35\).[/tex]
The given truncated number is [tex]\(14.3\)[/tex]. To find the upper and lower bounds of [tex]\(p\)[/tex], we need to consider the possible range of values that could round to [tex]\(14.3\)[/tex] when truncated to 1 decimal place.
Lower bound: To find the lower bound, we need to consider the greatest number that rounds down to [tex]\(14.3\)[/tex]. This is obtained by subtracting 0.05 from the given truncated number:
[tex]\(\text{{Lower bound}} = 14.3 - 0.05 = 14.25\)[/tex]
Upper bound: To find the upper bound, we need to consider the smallest number that rounds up to [tex]\(14.3\)[/tex]. This is obtained by adding 0.05 to the given truncated number:
[tex]\(\text{{Upper bound}} = 14.3 + 0.05 = 14.35\)[/tex]
Therefore, the lower bound of [tex]\(p\) is \(14.25\)[/tex] and the upper bound is [tex]\(14.35\).[/tex]
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Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2
The value of the given expression [[tex]87^3+ 13^3/87^2 -87 * 13 + 13^2[/tex]] by simplifying the numerator and denominator using suitable identities is 100.
We will first calculate the numerator:
As ([tex]a^3[/tex] + [tex]b^3[/tex]) = (a + b)([tex]a^2[/tex] - ab + [tex]b^2[/tex]) :
[tex]87^3[/tex] + [tex]13^3[/tex] = (87 + 13)([tex]87^2[/tex] - [tex]87 * 13[/tex] + [tex]13^2[/tex])
= 100([tex]87^2[/tex] - 87 * 13 + [tex]13^2[/tex])
Now, calculate the denominator:
[tex]87^2 - 87 * 13 + 13^2[/tex]
As,([tex]a^2 -2ab +b^2[/tex]) =[tex](a - b)^2[/tex]:
[tex]87^2 - 87 * 13 + 13^2 = (87 - 13)^2[/tex]
[tex]= 74^2[/tex]
So by solving the equation further:
[tex](87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)[/tex]
As we can see the numerator and denominator are the same expressions ([tex]87^2 - 87 * 13 + 13^2[/tex]). so, they cancel each other:
[tex](87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100[/tex]
So, the value of the given expression is 100.
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