Answer:
a) 7
b)64
c)2
Step-by-step explanation:
look at images
Answer:
x = 2
Step-by-step explanation:
The topic here is "fractional exponents."
Review: 2^3 = 8 (this is the cube of 2), and so the inverse function is
8^(1/3) = 2 ("8 raised to the fractional exponent 1/3 is 2"
Question a) 49^(1/2) ("49 to the power 1/2") can be rewritten as
(7^2)^(1/2), which simplifies to 7^(2*1/2) = 7^1 = 7
Caution: this is exponentiation, not division. So 49^(1/2) does not equal 49/2.
Question b) ( )^(1/3) = 4
I would prefer to write this as x^(1/3) = 4 and set the goal of finding the value of the base, x.
Then x^(1/3) = 4 ("x raised to the power 1/3 is 4")
Let's elimiinate the fractional exponent on the left by cubing both sides of the equation:
{x^(1/3)}^3 = 4^3, or, after simplification,
x^1 = 64, or, in simplest form,
x = 64
Question c)
Notice that the base here is 1/100
and that the square root of 1 is 1 and that of 100 is 10.
Therefore, the given
{1/100} is equivalent to {1/10)^2
and so we have:
1 1
(------------)^(1/x) = ------- (we are to find x)
10^2 10
Note that 10 is the square root of 10^2, also the square root of 100.
So let's take the square root of 10^2. We get 10.
Therefore, try x = 2 and see whether the given equation is true:
1 1
{---------)^(1/2) = ------
100 10
The square root of 1 is just 1. The square root of 100 is 10.
Therefore the above equation becomes
1 1
----- = ----- and so x = 2 is correct.
10 10
Please answer using IRAC method for each question.
Please Identify all the issues.
Question 1
XYZ Pty Ltd (XYZ) called for tenders for supplies of seedlings for its’ iceberg lettuce farm with a closing date of 30 June. The following tenders were submitted: 1. Lettuce R Us Pty Ltd hand-delivered its tender on 29 June to the head office of XYZ. 2. We Grow Pty Ltd posted its tender on 29 June. This letter arrived at XYZ head office on 1 July. Lettuce R Us Pty Ltd’s tender was the lowest of the two, however, XYZ awarded the contract to We Grow Pty Ltd because of their outstanding reputation. XYZ posted a letter to We Grow Pty Ltd advising that its tender was successful. Unfortunately, this letter never reached We Grow Pty Ltd because it was accidentally destroyed by a disgruntled postal worker who had just been made redundant. Since We Grow Pty Ltd had not heard from XYZ, it instead entered into a contract with another grower and committed its full stock of seedlings to this contract. XYZ became aware of the full situation concerning We Grow Pty Ltd. It seeks advice concerning its contractual position in relation to both tenders.
Question 2
Joseph leased a shop in the Central Shopping Centre for the past three years. Joseph is very concerned about his health and he has been diagnosed as suffering from a disease that will result in him requiring constant care in the near future. The lease on the shop was about to expire and the manager of the shopping centre, Thomas, told him that he had ‘better decide quickly’ whether he wanted to renew his lease because there were two other potential tenants who would take his space ‘at a moment’s notice’. Despite being aware of Joseph’s illness and needs, Thomas would only offer Joseph a new five-year lease at a substantially higher rent. Joseph really wanted to retire to look after his health but felt like he could not afford to give up the income from the shop. He reluctantly signed the new lease. One year later Joseph received a large payout from a legal claim and could now afford to retire. Advise Joseph whether he is able to avoid the lease at common law.
Question 3
Michael is a director of Road Bikes Pty Ltd (RB) which has developed sophisticated engineering for manufacturing high quality handmade road bikes. RB has attracted attention from professional and amateur cyclists’ around the State of Queensland. Michael is involved in a serious cycling accident and is left no choice but to sell RB. George is a world champion cyclist and is immediately interested in purchasing the business. George prepares a contract for the purchase of RB and hands the contract to Michael. The contract includes a term that would prevent Michael from opening another road bike manufacturing business anywhere in Australia for the next 25 years. Michael and George sign the contract. Michael quickly recovers from his accident and wants to know whether there is any way he can set up a new bike manufacturing business under common law. Advise Michael.
The issues in this scenario include the validity of Lettuce R Us Pty Ltd's tender, the late delivery of We Grow Pty Ltd's tender, the awarding of the contract to We Grow Pty Ltd based on reputation, and the destruction of the acceptance letter by a postal worker.
The issues in this scenario include whether Joseph can avoid the lease due to Thomas' conduct, the impact of Joseph's illness on the lease negotiation, and the validity of the new lease agreement.
The issues in this scenario involve the inclusion of a non-compete clause in the contract between Michael and George, and whether Michael can set up a new bike manufacturing business under common law.
In Question 1, the issues revolve around the validity of Lettuce R Us Pty Ltd's tender and the late delivery of We Grow Pty Ltd's tender. Additionally, the awarding of the contract based on reputation and the destruction of the acceptance letter raise concerns about contract formation and communication of acceptance.
In Question 2, the issues include Thomas' conduct in pressuring Joseph to renew the lease, the impact of Joseph's illness on the lease negotiation, and the validity of the new lease agreement in light of these factors.
In Question 3, the issue centers around the inclusion of a non-compete clause in the contract and whether Michael can set up a new bike manufacturing business under common law despite the restriction.
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Juan invested $100 in a savings account the earns 5% annually. The value, A, of the investment can be calculated using the equation A=p(1+r) with and exponent of t, where p is the investment in dollars, r is the interest rate, and t is the time of years. What amount will be in the savings account in two years?
Answer:
$110.25
Step-by-step explanation:
Step one:
given
principal= $100
rate= 5%
time = 2 years
Required
The final amount
Step two:
The compound interest formula is
\(A=p(1+r)^t\)
substituting we have
\(A=100(1+0.05)^2\\\\A=100(1.05)^2\\\\A=100*1.1025\\\\A=110.25\\\\\)
The final amount is $110.25
-4(x + 7) + 2(2 + x) = -20
Answer:
x = -2
Step-by-step explanation:
Step 1: Distribute
-4(x + 7) + 2(2 + x) = -20 ----> -4x-28 + 4+2x=-20
Step 2: Combine Like Terms
-4x-28+4+2x=-20 ----> -2x-24=-20 ----> -2x=4
Step 3: Divide both sides by -2, solving for x.
-2x=4 ----> -2/-2x = 4/-2 ----> x = -2
Donald used 1 inch cubes to make the rectangle prism shown. The volume of the prism is_____ cubic inches WILL GET BRAINLIEST
Answer:
am going to answer but it might be wrong
Step-by-step explanation:
i believe you do 12 Tom 6 * 8 because it's linked times with Tom's height which gives 576
Answer:
1, 30, 3, 90 :)
Step-by-step explanation:
you find the colume of each cube, then you go off of that
Find an equation for the line that passes through the points (4, -3) and (-2, 5)
Step-by-step explanation:
* start by finding the gradient/ slope of the line using the two points*
after finding the gradient you can now use the formula/ equation of any straight line which is *y = m×x + c*
I need help with this please I’ve been stuck on this question for a week now
Answer:
32 degrees
Step-by-step explanation:
Answer:
55!
Step-by-step explanation:
y= 100-45!
exterior angle in equal to sum of interior angles 100° = y +45°
Resources management questions for each 10 marks
Q 1- Explain in brief about and characteristics of
resources.
Q2- Write note on classification of resources.
Q 3- Explain Management Process
Q4- Write
Resources are the means by which an organization achieves its objectives and they are very important in organizational activities. There are various types of resources, such as material resources, human resources, financial resources, technological resources, and information resources, each with its own characteristics. Material resources, for example, are tangible and physical, while human resources are intangible and non-physical. Some of the common characteristics of resources include the fact that they are limited, have alternative uses, and have cost implications.
Resources can be classified in several ways, but the most common classification is as follows: Natural resources (e.g. water, air), Human-made resources (e.g. buildings, machinery), Human resources (e.g. employees, managers), and Financial resources (e.g. money, credit). Natural resources are generally limited and their usage is regulated by laws and regulations. Human-made resources, on the other hand, are created by humans to facilitate their activities. Human resources refer to people who work in an organization and include employees, managers, and executives, while financial resources include money, credit, and other financial assets.
Management process refers to a set of activities that are used to achieve organizational goals and objectives. It is composed of four main functions: planning, organizing, leading, and controlling. Planning involves setting goals, objectives, and strategies to achieve them. Organizing involves allocating resources and developing a structure to achieve goals. Leading involves motivating employees and communicating with them to achieve goals. Controlling involves monitoring and evaluating performance against goals and objectives. In summary, resources are critical to the success of any organization, and they need to be managed effectively to achieve organizational goals and objectives. This involves classifying resources, understanding their characteristics, and applying the management process to ensure that they are used efficiently.
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Identify the number of terms in this polynomial.
5k^5+7k-2
Answer:
cuatro terminos
If a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, at what depth is the team making their measurements
When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.
It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:
P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.
In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for
d.P = 0.433d + 14.7
Substitute P = 159 and solve for
d.159 = 0.433d + 14.7
Subtract 14.7 from both sides.
144.3 = 0.433d
Divide both sides by 0.433 to isolate d.
d ≈ 333.06
Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.
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(2x + 12y = −17) (3x + 2y = 7) value of x and y
Answer:
x = (59/16)
y = (-65/32)
Step-by-step explanation:
2x + 12y = −17
3x + 2y = 7
--------------------------
(2x + 12y = −17) × 3
6x + 36y = -51
(3x + 2y = 7) × -2
-6x - 4y = -14
----------------------------------
6x + 36y = -51
-6x - 4y = -14
-----------------------
32y = -65
÷32 ÷32
--------------------------
y = (-65/32)
3x + 2y = 7
3x + 2(-65/32) = 7
3x - (65/16) = 7
+(65/16) +(65/16)
-------------------------------
3x = (177/16)
÷3 ÷3
---------------------------
x = (59/16)
I hope this helps!
Maria has $120. She plans to purchase a shirt for herself and gifts for 6 of her
friends. She plans to spend the same amount for each gift. Which of the
following inequalities best represents the maximum amount Maria can spend on
each gift? *
DONT say the answer is on some link that’s annoying.
How much lace edging is needed to go around a circular tablecloth with a diameter of 6 ft?
Answer:
A= 28.27 ft²
Step-by-step explanation:
if its trying to find area for a circle then we use the formula A=πr²
A=π(3)²
A= 28.27 ft²
Answer:
the answer is 18.85ft
Step-by-step explanation:
the question is asking you to find the circumfrance (the outside of the circle) so the formula you would use is:
C = 2πr
input the values you have into the formula
C= 2 x π x 3
(the radius is the distance between the very centre of the circle to the outside. it gives you the diameter which is the distance all the way across the circle so just half the diameter, which gives you a radius of 3)
put that into your calculator and youll get the answer
C= 18.8495559215
(i rounded the answer to two decimal places = 18.85ft)
A rectangle has a length of
381
and a width of 33 inches. Find the area of the rectangle. (2 points)
Raul opened a savings account with 4300. Each week, x, Raul pays the dog sitter 30 from his savings account. Write a function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.
Given:
Amount in the savings account = 4300
Each week, Raul pays the dog sitter 30 from his savings account.
To find:
The function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.
Solution:
Let x be the number of weeks.
Raul pays the dog sitter in 1 week = 30
Raul pays the dog sitter in x week = 30x
Remaining amount = Initial amount - Amount he pays the dog sitter
\(f(x)=4300-30x\)
Therefore, the required function is \(f(x)=4300-30x\).
Ms. Grant recorded the numbers of students in her homeroom class who
participated in spirit week.
The table shows the number of students who dressed up each day.
Day
Mon Tues. Wed. Thurs. Fri. Total
Number of students O
1
4
5
5
15
Find the mean and the median of the data set.
Determine which of these values is greater.
A. The median, 4, is greater than the mean, 3.
B. The mean, 4, is greater than the median, 3.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
The mean and the median of the data set is given as the median, 4, is greater than the mean, 3. The correct answer is option a.
To find the mean of the data set, we add up all of the numbers and divide by the total number of days. So, the mean is (1+4+5+5+1+5+5)/6 = 3.
To find the median, we first need to put the numbers in order from least to greatest: 1, 1, 4, 5, 5, 5. The median is the middle number, which in this case is 4.
Now we need to determine which value is greater. The options are:
A. The median, 4, is greater than the mean, 3.
B. The mean, 3, is greater than the median, 4.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
We can eliminate options B and D because they don't make sense. The mean cannot be less than 0, and the median cannot be less than the mean.
Option A is correct. The median, 4, is greater than the mean, 3. This makes sense because there are two 1's in the data set, which bring down the mean. However, the median is not affected by outliers like this, so it remains higher.
Option C is incorrect because the mean is not 4, it is 3.
In summary, the mean of the data set is 3 and the median is 4. The median is greater than the mean, which is represented by option A.
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Is it possible to form a triangle with side lengths 3, 4, and 5? if so, will it be scalene, isosceles, or equilateral?.
Answer:
yesscalenehope this helps :)
(25x^3 + 5x^2 -7x + 6) divided by (5x^2 -1) **the ^ is for exponents**
Answer:
5x + 1 + (5x^2-1)/5x^2-1)
Step-by-step explanation:
Which expressions are equivalent to 1/3 - 2/5
Answer:
1/3+(-2/5) and 1/3+2/5
Step-by-step explanation:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
(x+3)n/2n
The series converges for -1 < x < 1, and the sum for these values of x is S = 2/(1-x).
For x = -1, the sum of the series is
S = 2/(1-(-1))
= 2/2
= 1.
For x = 0, the sum of the series is
S = 2/(1-0)
= 2.
For x = 1, the sum of the series is
S = 2/(1-1)
= 2/0
= undefined.
The given series is a geometric series, which converges when the absolute value of the ratio of the terms is less than 1. This can be expressed as |x+3| < 2. Solving for x yields -1 < x < 1. For these values of x, the sum of the series can be evaluated using the formula for the sum of a geometric series, S = a/(1-r), where a is the first term and r is the ratio of successive terms. In this case, a = x+3, and r = (x+3)/2. Substituting these values into the formula yields S = (x+3)/(1-(x+3)/2), which simplifies to S = 2/(1-x).
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The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find
(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)
Answer:
(a)
\(3 \sqrt{5} \)
(b)
\( \frac{6}{ \sqrt{5} } \)
Step-by-step explanation:
A(-3,0)
B(0,6)
\(d = \sqrt{{( - 3 - 0)}^{2} + {(0 - 6)}^{2} } = \sqrt{9 + 36} = 3 \sqrt{5} \)
\(d = \frac{ax0 + by0 + c}{ \sqrt{ {a}^{2} + {b}^{2} } } \)
2x-y+6=0
a=2, b=-1, c=6
x0=0, y0=0
\(d = \frac{6}{ \sqrt{4 + 1} } = \frac{6}{ \sqrt{5} } \)
Solve using substitution.
y = –7x − 8
y = 2x + 10
What are the values of a, b, and c in the matrix addition below?
4
1
-5
-8
0
6
-4 1
1
1
-10
2
2
13
-4
5
-1
a
7
12
+
3
3
3
15-12
3
18 b
3
-8
-9
6
-3
11
-8 C
17
a=-5
b=-9
o
C=-12
a=-14
O b= 15
C=-12
a=-14
b=-9
\(a = - 14 \\ c = - 12 \\ b = - 9\)
The solution is, the values of a = -14, b= -9, c = -12.
What is Matrix?Rows and columns of numbers are arranged in a matrix. A rectangular matrix is a grouping of numbers into rows and columns. The matrix A, for instance, has two rows and three columns.
here, we have,
A matrix is a rectangular arrangement of a collection of numbers into a fixed number of rows and columns.
We have a matrix of order 4 x 4 where the number of rows are 4 and number of column are 4.
and, the resultant matrix is also of order 4 x 4 where the number of rows are 4 and number of column are 4.
we get,
the addition of the two given matrices is,
\(\left[\begin{array}{ccc}-4 &1&1\\-14&7&12\\18&-9&3\\-8&-12&17\end{array}\right]\)
Then, the values of a = -14, b= -9, c = -12.
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80 people were laying out on the beach. Clouds started forming, and it looked like it was going to rain. 42 people left. What is a reasonable estimate for the percentage of people that left the beach?
Select the best answer from the choices provided.
A. 10%
B. 25%
C. 50%
D. 75%
Answer:
C. 50%
Step-by-step explanation:
Since 40 is half of 80, and 50% means half, and 42 out of 80 is close to half, then 42 out of 80 is close to 50%.
Answer: C. 50%
Answer:
b25
Step-by-step explanation:
beacuse that is a rain and reasonable he percentage
Determine the domain of the function (f of g)(x) where f(x)=1/ x+3, g(x) =2/x.
Answer:
(-infinity, -2/3)u(-2/3,0)u(0, infinity)
Step-by-step explanation:
since it is asking for f(g(x)) we plug g into x which looks like:
f(2/x)
now we plug that into the f(x) equation for all of the x's because that is what replaced the x so:
1/(2/x)+3
we look at the denominator so we can pull the 2/x+3 out and set it equal to zero, therefore solving for x
this gives us -2/3
and we get the 0 from g(x) 's denominator
that should be correct and hope this helps!
Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).
The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:
The equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x or constants, this is called Bernoulli's equation.
Now, we have to substitution using
\(v = {y}^{1 - n} \)
Differentiating both side with respect to 'x'
\(v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'\)
we get,
\(= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)\)
Now, by using
\(v' = {y}^{1 - n} \)
The given equation is expressed as:
\(v + (1 - n)p(x)v = (1 - n)q(x)\)
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.
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Which expression is equivalent to startfraction 10 x superscript 6 baseline y superscript 12 baseline over negative 5 x superscript negative 2 baseline y superscript negative 6 baseline endfraction? assume x not-equals 0, y not-equals 0.
\(3/ 5x^6*y^6\) is the solution f the expression \((-9x^-1*y^-9) / (-15x^5*y^-3)\)
Given expression:
(-9x^-1*y^-9) / (-15x^5*y^-3)
As we know, any number with negative power can be written in inverse form with positive power.
\(x^-a = 1/x^a\)
Two number having same base their powers are added:
\(x^a + x^b = x^a+b\)
\(= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)\)
Hence the solution would be \(3 (5x^6 y^6)\).
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Answer:
b
Step-by-step explanation:
Which of the following functions in Python would you use when conducting an unpaired two-sample t-test with equal variances,
O suttest_ind(var A, var B, equal _var=False)
O st.ttest_ind(var A, var B, equal _var = Truc)
O st.ttest_rel(var A, var B. equal var=True)
O sLttest_rel(var A, var B, equal_var=False)
The correct function to use when conducting an unpaired two-sample t-test with equal variances in Python is st.ttest_ind(var A, var B, equal_var=True).
The ttest_ind function from the scipy.stats module is used for independent two-sample t-tests. By setting the equal_var parameter to True, it assumes that the variances of the two samples are equal. This assumption allows for the use of the pooled variance estimate in the calculation of the test statistic.
The other options provided are incorrect:
sLttest_rel(var A, var B, equal_var=False): This function (sLttest_rel) does not exist in the scipy.stats module. Additionally, the ttest_rel function is used for dependent (paired) two-sample t-tests, not unpaired tests.
st.ttest_rel(var A, var B, equal_var=True): This function is used for dependent (paired) two-sample t-tests, where the two samples are related or matched. It is not suitable for unpaired t-tests.
suttest_ind(var A, var B, equal_var=False): This function (suttest_ind) does not exist in the scipy.stats module. Additionally, the correct parameter name for the equal_var argument is equal_var, not equal _var.
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Please help meeeeeeeeeeeeeeee
Answer:
1) B
2) D
3) A
4) B
Step-by-step explanation:
We use a closed/filled in dot in math to represent an inequality where we have ≤ or ≥ and an open dot when its < or >. This is to represent that from the inequality we are also including the = component of the inequality.
After you know this, its pretty simple to work out which way the numbers go on the number line when its greater or less than depending on the question
HEEELPP ASAP
1. Which number or symbol is a coefficient in the follwing algebraic expression?
y + 3x - 2
a 2
b 3
c x
d y
2. What operation is used when evaluating an exponent? (when we change from exponent form to standard form)
a add
b subtract
c multiply
d divide
3. Convert the following word phrase to an algebraic expression:
A number increased by 8.
a x + 8
b x - 8
c y x 8
d y ÷ 8
Find solutions for your homework
mathstatistics and probabilitystatistics and probability questions and answerschristmas lights are often designed with a series circuit. this means that when one light burns out, the entire string of lights goes black. suppose the lights are designed so that the probability a bulb will last 2 years is 0.995. the success or failure of a bulb is independent of the success or failure of the other bulbs. a) what is the probability that
Question: Christmas Lights Are Often Designed With A Series Circuit. This Means That When One Light Burns Out, The Entire String Of Lights Goes Black. Suppose The Lights Are Designed So That The Probability A Bulb Will Last 2 Years Is 0.995. The Success Or Failure Of A Bulb Is Independent Of The Success Or Failure Of The Other Bulbs. A) What Is The Probability That
Christmas lights are often designed with a series circuit. This means that when one light burns out, the entire string of lights goes black. Suppose the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success or failure of the other bulbs.
A) What is the probability that in a string of 100 lights all 100 will last 2 years?
B) What is the probability at least one bulb will burn out in 2 years?
A) The probability that all 100 lights will last 2 years is 0.9048.
B) The probability that at least one bulb will burn out in 2 years is 0.0952.
What is the probability?A) To find the probability that all 100 lights will last 2 years, we assume that the success or failure of each bulb is independent.
The probability of a single bulb lasting 2 years is 0.995, so the probability of all 100 bulbs lasting 2 years is:
P(all 100 bulbs last 2 years) is (0.995)¹⁰⁰ ≈ 0.9048
B) The probability that at least one bulb will burn out in 2 years is determined using the complement rule.
P(at least one bulb burns out) = 1 - P(no bulbs burn out)
Since the probability of a single bulb lasting 2 years is 0.995, the probability of a single bulb burning out in 2 years is 1 - 0.995 = 0.005.
The probability of at least one bulb burning out in 2 years is:
P(at least one bulb burns out) = 1 - P(no bulbs burn out)
P(at least one bulb burns out) = 1 - 0.9048
P(at least one bulb burns out) ≈ 0.0952
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