Answer: The range is the best measure of variability for the given data set and its value is 500.
The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.
Step-by-step explanation:
From the data of the number of meters swam by students , range is the best measure of variability and equals 500
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the data set be represented as A
Now , the value of A is
A = { 600, 750, 800, 850, 900, 1100 }
The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.
And , range = 1100 - 600
R = 500
Hence , the range of the data set is R = 500
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The draft financial statements of Madras, a limited liability company, for the year ended 31
December 2022 is currently under review. The following points have been raised:
a. An ex-employee has started an action against the company for wrongful dismissal. The
company’s legal team have stated that the ex-employee is not likely to succeed. The following
estimates have been given by the lawyers relating to the case:
i. Legal costs (to be incurred whether the claim is successful or not) P50,000
ii. Settlement of claim if successful P150,000
Currently no provision has been made by the company in the financial statements.
b. The company has a policy of refunding the cost of any goods returned by dissatisfied
customers, even though it is under no legal obligation to do so. This policy of making refunds
is generally known. At the year end returns totalling P48,000 have been made.
c. A claim has been made against a company for injury suffered by a pedestrian in connection
with building work by the company. Legal advisers have confirmed that the company will
probably have to pay damages of P100,000 but that a counterclaim made against the building
subcontractors for P50,000 would probably be successful.
Required:
State with reasons what adjustments, if any, should be made by the company in the financial
statements.
Based on the given information, Madras Limited Liability Company (LLC) needs to make certain adjustments in their financial statements. Firstly, the company should make a provision for the legal costs of P50,000 related to the wrongful dismissal case. Even though the legal team is confident that the ex-employee will not be successful, the provision must be made as the costs are to be incurred regardless of the outcome. This will reflect the true financial position of the company and will ensure that the financial statements present a fair view of the company's affairs.
Secondly, the company needs to make a provision for the settlement of P150,000 if the ex-employee's case is successful. This provision needs to be made because there is a likelihood of an outflow of economic resources in the future, as a result of the company losing the case. This provision will reduce the company's profit and hence its tax liability.
Thirdly, the company needs to recognize the refunds of P48,000 made to dissatisfied customers as a liability. Even though Madras LLC is under no legal obligation to make refunds, their policy of making refunds is generally known. Hence, the company has a constructive obligation to make refunds and therefore, the refunds should be recognized as a liability in the financial statements.
Lastly, the company needs to make a provision for the damages payable to the pedestrian injured on their building site. The legal advisers have confirmed that the company will have to pay damages of P100,000. Hence, the company needs to make a provision for this amount as there is a likelihood of an outflow of economic resources in the future. However, as the company has a counterclaim against the building subcontractors for P50,000, this amount can be netted off against the provision. Therefore, Madras LLC needs to make a provision of P50,000 for the net amount of damages payable to the pedestrian.
In conclusion, Madras LLC needs to make the above-mentioned adjustments to their financial statements to ensure that the financial statements present a fair view of the company's affairs. These adjustments will also ensure that the company complies with the Generally Accepted Accounting Principles (GAAP) and will help stakeholders in making informed decisions based on the financial statements.
intelligence test scores refered to as intelligent quotient or IQ scores are based on characteristics such as verbal skills,abstruct reasoning power, numerical ability and spatial visualization.if plotted on a graph the distribution of IQ scores approximates a normal curve with a mean of about 100. an IQ scores above 115 is considered superior studies of "intellectually gifted" children have generally defined the lower limit of their IQ scores at 140: approximately 1% of the population have IQ scores above this limit.find the standard deviation of this distribution?
The standard deviation of the distribution is given as follows:
[tex]\sigma = 17.2[/tex]
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean of the distribution of IQ scores is given as follows:
[tex]\mu = 100[/tex]
X = 140 is the 99th percentile, as approximately 1% of the population have IQ scores above this limit, hence when X = 140, Z = 2.327, meaning that the standard deviation is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{140 - 100}{\sigma}[/tex]
[tex]2.327\sigma = 40[/tex]
[tex]\sigma = \frac{40}{2.327}[/tex]
[tex]\sigma = 17.2[/tex]
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\sin ^ { 2 } \frac { 3 \pi ^ { c } } { 4 } + 2 \tan ^ { 2 } \frac { 3 \pi ^ { c } } { 4 } - \sec ^ { 2 } \frac { 3 \pi ^ { c } } { 4 } - \cos ^ { 2 } \frac { 3 \pi ^ { c } } { 4 }
Step-by-step explanation:
The simplified expression is {3\tan^2\frac{3\pi^c}{4}}
What is the value of
Select one:
OA. -39
OB. -3
OC. 3
OD. 21
26² +46-9
6+4
when b= -3?
Use the given information to find the balance in the account earning compound interest after 6 years when the principal is $3500.
$r=1.26\%$r=1.26% , compounded monthly
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3500\\ r=rate\to 1.26\%\to \frac{1.26}{100}\dotfill &0.0126\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases}[/tex]
[tex]A = 3500\left(1+\frac{0.0126}{12}\right)^{12\cdot 6}\implies A=3500(1.00105)^{72} \implies A \approx 3774.71[/tex]
The triangular faces of the prism shown are equilateral triangles with a perimeter of 48 cm. Each of the other faces is a square. Find the surface area of the prism
Answer:
222.4 cm
Step-by-step explanation:
16cm x 13.9 cm =222.4 cm
hope this helped! :D
twelve cans of dog food cost $16.80. How much is one can?
Answer: 1.4
Step-by-step explanation: Just divide.
16.80 divided by 12, is 1.4(0). And if you multiply 1.4 by 12 you get 16.8(0)
advise zanele on whether or not to take a gap year.
questionnaire suggested for zanele.
1. what is your name?
2. why do you think that it is wise to take a gap year after school?
3. what are the benefits of taking a gap year ?
4. what are the reason for delaying a gap year than first pursuing a university degree?
5. what is the best way to spend a gap year?
after working through the suggested questions zanele realises that the questionnaire is not suitable. list two reasons why you think that the given questionnaire is not suitable.
If Zanele realized that the questionnaire is not suitable, it could be for various reasons, such as:
The questions may not be relevant to her specific situation or goals.
The questions may not provide enough information or options to help her make an informed decision.
What are the imports of the questions on the questionnaire?What is your name?
Name may not be needed to provide advice on taking a gap year.
Why do you think that it is wise to take a gap year after school?
Taking a gap year after school can provide students with a break from academic studies, help them gain life experience, and give them time to explore their interests before committing to a university degree.
What are the benefits of taking a gap year?
The benefits of taking a gap year include personal and academic growth, increased independence, cultural exposure, and the opportunity to gain valuable work or volunteer experience.
What are the reasons for delaying a gap year than first pursuing a university degree?
Some students choose to delay taking a gap year to pursue a university degree first so that they can stay on track with their academic and career goals. Others may want to save money or avoid interrupting their academic momentum.
What is the best way to spend a gap year?
The best way to spend a gap year depends on your interests and goals. Some popular gap year activities include traveling, volunteering, interning, working, learning a new language or skill, or pursuing a passion project.
If Zanele realized that the questionnaire is not suitable, it could be for various reasons, such as:
The questions may not be relevant to her specific situation or goals.
The questions may not provide enough information or options to help her make an informed decision.
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Answer:
Step-by-step explanation:
Need help with short problem 2
The transpose matrix of A is the one written below.
[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]
How to get the transpose matrix?Here we are given the matrix A, and we want to find the transpose matrix A^t.
To do so, just leave the elements in the diagonal as they are in the original matrix, and then do a "reflection" of the other elements along the diagonal line. So the elements with equal subindices stay where they are, and the others are reflected along them.
Then the new matrix will be:
[tex]\left[\begin{array}{ccc}3&2&0\\0&3&4\\0&0&3\end{array}\right][/tex]
That is the transpose matrix, where the diagonal is still "3, 3, 3" but the other elements changed.
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The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Answer:
a)10
Step-by-step explanation:
(xx)=(2×2)=4
2(4)=8
8+2=10
answer: a) 10
can someone help me
do the odds
please show work
Answer:
Step-by-step explanation:
To convert degrees to radians we use this formula
number of degrees x [tex]\frac{\pi}{180}[/tex]
1. [tex]-415 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{36} \pi[/tex]
3. [tex]570 * \frac{\pi}{180} =[/tex][tex]\frac{19}{6} \pi[/tex]
5. [tex]473 * \frac{\pi}{180} =[/tex][tex]\frac{473}{180} \pi[/tex]
7. [tex]-799 * \frac{\pi}{180} =[/tex][tex]\frac{-799}{180} \pi[/tex]
9. [tex]44 * \frac{\pi}{180} =[/tex][tex]\frac{11}{45} \pi[/tex]
11. [tex]270 * \frac{\pi}{180} =[/tex][tex]\frac{3}{2} \pi[/tex]
13. [tex]-712 * \frac{\pi}{180} =[/tex][tex]\frac{-178}{45}[/tex]
15. [tex]-332 * \frac{\pi}{180} =[/tex][tex]\frac{-83}{45} \pi[/tex]
17. [tex]-54 * \frac{\pi}{180} =[/tex][tex]\frac{-3}{10} \pi[/tex]
19. [tex]-875 * \frac{\pi}{180} =[/tex][tex]\frac{-175}{36} \pi[/tex]
21. [tex]763 * \frac{\pi}{180} =[/tex][tex]\frac{763}{180} \pi[/tex]
23. [tex]299 * \frac{\pi}{180} =[/tex][tex]\frac{299}{180} \pi[/tex]
25. [tex]-705 * \frac{\pi}{180} =[/tex][tex]\frac{-47}{12} \pi[/tex]
27.[tex]374 * \frac{\pi}{180} =[/tex][tex]\frac{187}{90} \pi[/tex]
29. [tex]-239 * \frac{\pi}{180} =[/tex][tex]\frac{-239}{180} \pi[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
Find a polynomial function with real coefficients
1, 3i
f(x) =
Pls help
A polynomial function with real coefficients and roots 1, 3i is f(x) = x^3 - x^2 + 9x - 9.
What is the polynomial functionIf a polynomial function has real coefficients, then complex roots must come in conjugate pairs. That is, if 3i is a root, then -3i must also be a root. Therefore, the polynomial with roots 1, 3i, and -3i is:
(x - 1)(x - 3i)(x + 3i)
Multiplying this out using the difference of squares, we get:
(x - 1)(x^2 - (3i)^2)
Simplifying the expression using (3i)^2 = -9, we get:
(x - 1)(x^2 + 9)
Expanding the expression using FOIL, we get:
x^3 + 9x - x^2 - 9
Simplifying this expression, we get:
f(x) = x^3 - x^2 + 9x - 9
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one number is less than 3 times another if their sum is increased by 5 the result is 25 find the number
Answer:
Let's use algebra to solve the problem.
Let x be the first number.
Let y be the second number.
From the problem, we can set up two equations:
"One number is less than 3 times another":
x = 3y - - - (Equation 1)
"Their sum is increased by 5 the result is 25":
x + y + 5 = 25
x + y = 20 - - - (Equation 2)
Now we have two equations with two unknowns. We can use substitution or elimination to solve for one of the variables.
Using substitution:
From equation 1, we know that x = 3y. We can substitute this into equation 2 to eliminate x:
3y + y = 20
4y = 20
y = 5
Now we can substitute this value of y back into equation 1 to find x:
x = 3y
x = 3(5)
x = 15
Therefore, the first number is 15 and the second number is 5.
A store sells bags of potato chips.
1/3 of the bags are barbecue-flavored chips.
3/5of the bags are cheese-flavored chips.
The rest of the bags are plain chips.
Which statement is true?
●
A More than of the bags are plain chips.
B There are no bags of plain chips.
C Exactly of the bags are plain chips.
D Less than of the bags are plain chips.
The statement less than 1/2 of the bags are plain chips is true, Option D is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's find the fraction of bags that are plain chips.
We know that the barbecue-flavored chips make up 1/3 of the bags, and Cheese-flavored chips make up 3/5 of the bags.
The fraction of bags that are plain chips is:
1 - 1/3 - 3/5
Lets convert the fractions with same denominator.
= 15/15 - 5/15 - 9/15
=15-5-9/15
= 1/15
1/15 is less than 1/2.
Therefore, less than 1/2 of the bags are plain chips, Option D is correct.
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A 17-foot pipe is cut into three sections. The longest section is two times as long as the shortest, and the middle-sized section is 5 feet longer than the shortest. Complete the diagram by
alving a and b as expressions involving x. Do not solve the problem.
The required 1-st section: 6 ft; 2-nd section: 6+9 = 15 ft; 3-rd section: 4*6 = 24 ft.
What are Sections?The 40 or 80 ft. (12-24 m) lengths of steel pipe sections, or joints, are trucked to the building site and strung out along the path in the locations where they are to be welded together.
According to question:The 45-foot conduit is divided into three pieces. The middle-sized section is 9 feet longer than the shortest segment, and the longest section is 4 times as long as the shortest. Finish the design.
x + (x+9) + 4x = 45, or
6x = 45-9
6x = 36,
x = 6.
Thus,1-st section: 6 ft; 2-nd section: 6+9 = 15 ft; 3-rd section: 4*6 = 24 ft.
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Complete Question:
A 45 foot pipe is cut into three sections. The longest section is 4 times as long as the shortest, and the middle-sized section is 9 feet longer than the shortest. Complete the diagram.
Creative Minds Bookstore decided to donate an overstock of
children’s books to some local elementary schools. They gave
two-fifths of the load to Sunshine Elementary. One-third of the
remaining books were donated to Lincoln Elementary. Two-thirds
of the books left were then given to Vineyard Middle School with
the last 16 books donated to the local library. How many books
were donated all together and how many books did each school
receive?
The answer will be as follows after answering the supplied question equation (8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School
What is equation?A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.
Let's tackle this problem with algebra.
Let's call the total number of books contributed "x".
According to the issue, Creative Minds Bookstore donated two-fifths of the books to Sunshine Elementary. Sunshine Elementary received (2/5)x books as a result.
That leaves (3/5)x books to be donated to other schools and libraries.
That leaves (7/15)x books available for donation to the library.
Given that the library acquired 16 books, we may conclude:
(7/15)x = 16
Calculating x:
x = (16)(15/7) = 34.29 (rounded to two decimal places) (rounded to two decimal places)
(2/5)x = (2/5)(34.29) 13.72 books at Sunshine Elementary
(1/5)x = (1/5)(34.29) 6.86 books at Lincoln Elementary
(8/15)x = (8/15)(34.29) 18.29 books Vineyard Middle School
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A punch recipe calls for 3/4 cup of grace juice. If Carlos wants to cut the recipe in half, how much grape juice should he use?
Answer:
thanks for the question
please mark me brainless
Simplify 14×5(13×2+13×5)
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.
From the given graph the function obtained is [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph g(x) given is a graph of function g(x) = √x.
The graph when drawn for g(x) = √x, starts from the origin (0,0).
In the graph it can be seen that the function is moved 3 units left and 1 units down.
For a function f(x) moving left with k units the formula is -
y = f(x + k)
For a function f(x) moving down with k units the formula is -
y = f(x) - k
Apply these formula to our basic function g(x) = √x.
So since the graph is moved 3 units left and 1 units down, the function will be -
[tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
Therefore, the function is obtained as [tex]g(x) = \sqrt{(x - 3)}+ 1[/tex].
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Complete the sentences about simplifying this expression once you given a value for b. 24 + b/b + 24 x 53.72
Answer:
Step-by-step explanation:
To simplify the expression 24 + b/b + 24 x 53.72, we first need to substitute the given value of b into the expression. For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72. Next, we can simplify the division by evaluating 5/5, which equals 1. Then, we can multiply 24 and 53.72 to get a product of 1288.28. Finally, we can add the simplified terms to get a final result of 1312.28. Therefore, the simplified expression, given that b is equal to 5, is 1312.28.
Find the sum of the first 33 terms of the following series, to the nearest integer. 13 , 22 , 31 , . . . 13,22,31,...
Answer:
5,181
Step-by-step explanation:
The arithmetic sequence has a common difference d = 9 which is the difference between successive terms
The sum of the first n terms of an arithmetic sequence is given by
[tex]S_n = \dfrac{n(a_1 + a_n)}{2}[/tex]
The nth term of an arithmetic sequence is given by
aₙ = a₁ + d(n - 1)
where a₁ = first term
In this particular sequence, a₁ = 13 and d = 9
Therefore
a₃₃ = 13 + 9(33-1)
= 13 + 9(32)
= 13 + 288
= 301
Therefore
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function
Exercise 1: 1) Suppose we have to select a manager, assistant manager, and night manager from a list of 11 people. How many ways can this be done
Find cos(β/2) and cot(β/2), if sin(β)= -(√(3)/2) and pi<β<(3pi/2)
Answer:
Step-by-step explanation:
We know that the sine of an angle is negative in the third and fourth quadrants. So, since β is in the third quadrant (pi < β < (3pi/2)), we know that sin(β) is negative.
Given sin(β) = -√(3)/2, we can use the half-angle formulas for sine to find sin(β/2):
sin(β/2) = ±√[(1 - cos(β))/2]
Since β is in the third quadrant, we know that cos(β) is negative. We can use the Pythagorean identity to find cos(β):
cos²(β) + sin²(β) = 1
cos²(β) = 1 - sin²(β)
cos(β) = -√(1 - sin²(β))
cos(β) = -√(1 - (3/4))
cos(β) = -√(1/4)
cos(β) = -1/2
Now we can substitute cos(β) into the half-angle formula for sine:
sin(β/2) = ±√[(1 - cos(β))/2]
sin(β/2) = ±√[(1 - (-1/2))/2]
sin(β/2) = ±√(3/4)
sin(β/2) = ±(√3/2)
Since β is in the third quadrant, we know that cos(β/2) is negative. So we can use the half-angle formula for cosine to find cos(β/2):
cos(β/2) = ±√[(1 + cos(β))/2]
cos(β/2) = ±√[(1 - 1/2)/2]
cos(β/2) = ±√(1/4)
cos(β/2) = ±(1/2)
Since β is in the third quadrant, we know that cot(β/2) is negative. We can use the half-angle formulas for cosine and tangent to find cot(β/2):
cos(β/2) = ±√[(1 + cos(β))/2]
cos(β/2) = ±√[(1 - 1/2)/2]
cos(β/2) = ±√(1/4)
cos(β/2) = ±(1/2)
cot(β/2) = cos(β/2) / sin(β/2)
cot(β/2) = (±1/2) / (±(√3/2))
cot(β/2) = ±(1/√3)
cot(β/2) = ±(√3/3)
Therefore, cos(β/2) is either -1/2 or 1/2, and cot(β/2) is either -√3/3 or √3/3, depending on the choice of sign for the square roots.
answer: cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,
Given sin()=-((3)/2, we can use the Pythagorean identity to calculate the value of cos():
cos(β) sqrt(1 - sin2()) sqrt(1 - sqrt(3)/2) = square (1 - 3/4) Equals square (1/4) = square 1/2
We know that is in the third quadrant, where cosine is negative, since pi (3pi/2). As a result, we have:
cos(β) = -1/2
Now we can calculate cos(/2) and cot(/2) using the half-angle formulas:
sqrt((1 + cos())/2) = cos(/2) = ±sqrt((1 - 1/2)/2) = ±sqrt(1/4) = ±1/2
We know that /2 is in the fourth quadrant, where tangent is negative, because is in the third quadrant. As a result, we have:
Tan(1/2) = -1/tan(1/2) = -1/sqrt((1 + cos())/1 - cos()) = -1/sqrt((1 - 1/2)/(1 + 1/2)) = -1/sqrt(1/3) = -sqrt (3)
The answers are therefore cos(/2) = 1/2 and cot(/2) = -sqrt (3). Nonetheless, we must establish the sign of cos(/2). We can exploit the fact that sine is negative in the third quadrant, where is located, to accomplish this. As a result, we have:
Sin(/2) is equal to sqrt((1 - cos())/2). = -sqrt((1 + 1/2)/2) = squared(3/4) = squared(3)/2
Given that cosine is positive and /2 is in the fourth quadrant, we have:
sqrt(1 - sin2(/2)) = cos(/2) 1/2 = sqrt(1 - 3/4) = sqrt(1/4)
Therefore, the solutions are cos(β/2) = 1/2 and cot(β/2) = -sqrt(3,
daniel has 40 coins that are either nickels or dimes. the total value of the coins is $2.85. how many of each coin does daniel have
Answer: 17 dimes or 23 nickels
Step-by-step explanation:
Let's use two variables to represent the number of nickels and dimes that Daniel has. Let: n be the number of nickels, and d be the number of dimes.
We can write two equations based on the information given in the problem:
n + d = 40 (because Daniel has a total of 40 coins)
0.05n + 0.1d = 2.85 (because the total value of the coins is $2.85)
To solve for n and d, we can use the first equation to express one variable in terms of the other, and substitute that expression into the second equation:n + d = 40
n = 40 - d0.05n + 0.1d = 2.85
0.05(40 - d) + 0.1d = 2.85
2 - 0.05d + 0.1d = 2.85
0.05d = 0.85
d = 17
So Daniel has 17 dimes. We can substitute this value back into the first equation to solve for n:n + d = 40
n + 17 = 40
n = 23
So Daniel has 23 nickels.
Therefore, Daniel has 23 nickels and 17 dimes.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))
Step-by-step explanation:
To find f1(x), we need to differentiate the given function f(x) with respect to x using the product rule and the chain rule. Here are the steps:
f(x) = (7 sin x + 3 cos x) tan-1 x
f1(x) = d/dx [(7 sin x + 3 cos x) tan-1 x]
= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)) (d/dx)x
= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))
Therefore, f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)).
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
A bank account pays interest at a rate of 5% compounded annually. How much is an initial investment of £230 worth after 4 years? Give your answer to the nearest penny.
So, after 4 years, a £230 investment will be worth roughly £283.52 at a 5% yearly income rate compounded annually.
An illustration of compound interest is given?Let's assume you spend $1,000 (your capital) and it makes 5% once a year in interest or profits (the compounding frequency). You would've had $1,050 at the end of the first year, which is your initial capital plus an additional $5, or $50. You would also have $1,102.50 in the following year.
We can use the compound interest algorithm to find a solution to this issue:
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
where A is the final amount, P is the initial investment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have:
P = £230 (the initial investment)
r = 5% = 0.05 (the annual interest rate as a decimal)
n = 1 (since the interest is increased yearly) (since the interest is compounded annually)
Given that we're searching for a number after four years, t = 4.
With these numbers entered into the algorithm, we obtain:
A = 230(1 + 0.05/1)⁴
A = 230(1.05)⁴
A = £283.52
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Problem 4.1
The table gives some sample data for two quantities, x and y, that are in a proportiona relationship. Complete the table.
Then the complete table is:
x y
14 21
64 96
26 39
What dοes the arithmetic wοrd prοpοrtiοnal mean?When the ratiοs οf the twο variables are equal, there is a prοpοrtiοnal relatiοnship. Anοther way tο view them is that they are twο variables, οne οf which is always a cοnstant value multiplied by the οther in a prοpοrtiοnate manner.
A prοpοrtiοnal relatiοnship between twο variables can be written as:
y = kx
Where k is the cοnstant οf prοpοrtiοnality.
If we lοοk at the table we can see the pair (14, 21), replacing that in the prοpοrtiοnal relatiοn we have:
21 = k*14
(21/14) = k
(3/2) = k
Then the equatiοn is:
y = (3/2)*x
Tο cοmplete the table, we need tο evaluate the οther values in the given equatiοn.
fοr x = 64 we have:
y = (3/2)*64 = 96
fοr y = 39 we have:
39 = (3/2)*x
x = (2/3)*39 = 26
Fοr x = 1 we have:
y = (3/2)*1 = 3/2
Then the complete table is:
x y
14 21
64 96
26 39
1 3/2
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Estimate the intercepts
of the graph of the
function.
-4
6
4
-2
y
y=-x²-x+2
4 x
2
The x-intercepts are about
and
and the y-intercept is about
■
The estimated intercepts are:
x-intercepts: (-1, 0) and (2, 0)
y-intercept: (0, 2).
We may take an approximation reading from the graph and use it to estimate the intercepts of the graph of the function y = -x2 - x + 2:
The graph's x-intercepts are the locations where it crosses the x-axis, indicating that y = 0. We can see from the graph that the x-intercepts are about at x = -1 and x = 2.
The graph's intersection with the y-axis, known as the y-intercept, indicates that x = 0. The graph indicates that the y-intercept is roughly at y = 2.
The estimated intercepts are as follows:
x-intercepts: (-1, 0) and (2, 0)
y-intercept: (0, 2)
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Some students performed an experiment in which they dropped a rubber ball from a height of 650 centimeters. They noticed that after each bounce, it reached 72% of its previous height. Which equation models the height, H, for n bounces?
a
Hn = 650(0.28)n − 1 where n = 1, 2, 3, …
b
Hn = 650(0.72)n − 1 where n = 1, 2, 3, …
c
Hn = 650(1.72)n − 1 where n = 1, 2, 3, …
d
Hn = 650(72)n − 1 where n = 1, 2, 3, …
The exponential function that models the height of the ball after n bounds is given as follows:
b) [tex]H(n) = 650(0.72)^{(n - 1)}[/tex], where n = 1, 2, 3, …
How to define an exponential function?The general format of an exponential function is given as follows:
y = ab^x.
In which the parameters are given as follows:
a is the initial value.b is the rate of change.Some students performed an experiment in which they dropped a rubber ball from a height of 650 centimeters, hence the parameter a is given as follows:
a = 650.
They noticed that after each bounce, it reached 72% of its previous height, hence the parameter b is given as follows:
b = 0.72.
Considering that the first bounce is the reference bounce, the equation is given as follows:
[tex]H(n) = 650(0.72)^{(n - 1)}[/tex]
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