Write a function rule P(m) to represent Evelyn’s profit per mask so that she can always find what her profits will be for any amount of masks (m) she sells.
Answers
By answering the presented question, we may conclude that Evelyn will equation need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, 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 either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
Initially, we must determine the entire cost of producing and transporting one mask:
Total cost per mask = $1.25 plus $2.15 for delivery = $3.40
Profit per mask is selling price minus total cost per mask, which equals $5 - $3.40 = $1.60.
As a result, Evelyn will profit $1.60 for each mask she sells. We may use the following calculation to calculate how many masks she needs to sell to recoup her $450 initial project costs:
Total beginning project expenditures / profit per mask = number of masks to sell
Total number of masks to be sold = $450 / $1.60 per mask = 281 masks
Evelyn will need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
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Related Questions
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, …
Answers
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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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
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! :]
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.
Answers
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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one number is less than 3 times another if their sum is increased by 5 the result is 25 find the number
Answers
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.
One large jar and two small jars together can hold 8 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 2 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 8 and row 2 is 2.
Use matrices to solve the equation and determine how many ounces of jam are in each type of jar. Show or explain all necessary steps.
Please help me solve it through matrices, not by equations. There's a certain way to solve this, I'm just confused on this specific way by using matrices.
Answers
There are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.
Describe Matrix?In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are commonly used to represent and manipulate linear transformations and systems of linear equations.
The elements of a matrix are typically denoted by lowercase letters with subscripts, such as aij or bij, where i and j refer to the row and column indices, respectively. For example, a 3x3 matrix might look like this:
| a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
This matrix has three rows and three columns, and the element in the first row and second column is denoted by a12.
Matrices can be added, subtracted, multiplied, and divided, and these operations follow specific rules that are defined in matrix algebra. For example, to add or subtract two matrices of the same size, we simply add or subtract the corresponding elements. To multiply two matrices, we multiply the rows of the first matrix by the columns of the second matrix and sum the products.
Let's represent the number of ounces of jam in the large jar as "L" and the number of ounces of jam in each small jar as "S". Then we can write the system of equations:
1L + 2S = 8
1L - 1S = 2
We can write this system in matrix form as:
[1 2; 1 -1][L;S] = [8;2]
To solve for L and S, we can use matrix algebra to isolate [L;S]:
[L;S] = [1 2; 1 -1]⁻¹ [8;2]
First, we need to find the inverse of the coefficient matrix [1 2; 1 -1]. The inverse is:
[1 -2; 1 1]/3
So we can substitute this into our equation:
[L;S] = [1 -2; 1 1]/3 [8;2]
[L;S] = [2;2/3]
So there are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.
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The complete question is:
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function
Answers
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
Answers
Explanation
Using combination
C(11, 3) = 11! / (3! (11-3)!) = 165
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.
Answers
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:
Problem 4.1
The table gives some sample data for two quantities, x and y, that are in a proportiona relationship. Complete the table.
Answers
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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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.
Answers
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.
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.
Answers
Use this to find your answer:
15 bags
There is 5 bbq
9 cheese
1 plain
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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The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Answers
Answer:
a)10
Step-by-step explanation:
(xx)=(2×2)=4
2(4)=8
8+2=10
answer: a) 10
SOMEONE PLS HELP ILL MARK BRAINLIEST
Answers
Answer:
see explanation below
Step-by-step explanation:
4. ∠A = 35, a = 8.9, find c
since side a is opposite to m∠A and c is the hypotenuse, we can use sin(∠A) = opp/hypo equation
5. sin(35) = 8.9/c
=> c = 8.9/sin(35) = 8.9/0.5736 = 15.516
6. 15.5
What is the value of
Select one:
OA. -39
OB. -3
OC. 3
OD. 21
26² +46-9
6+4
when b= -3?
Answers
twelve cans of dog food cost $16.80. How much is one can?
Answers
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)
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?
Answers
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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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
Answers
[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]
Find the sum of the first 33 terms of the following series, to the nearest integer. 13 , 22 , 31 , . . . 13,22,31,...
Answers
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
Please help will mark Brainly
Answers
For the function g, the vertex form equation is [tex]g(x) = -2(x - 5)^{2} + 9.[/tex]
What sort of equation would that be?In algebra, the idea of an equation is a logical assertion that shows the equivalence of several mathematical expressions. For instance, the equations 3x + 5 & 14, that are separated by the 'same' sign, make up the equation 3x + 5 = 14.
What about the meaning of the equation?A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equivalent. a meaningful noun. Equations are used when more than one factor has to be considered in order to fully understand or explain a situation.
Substituting the first point (7,1) into the equation for g(x), we get:
[tex]1 = a(7 - 5)^{2} + 9[/tex]
we get
[tex]-8 = 4a[/tex]
Dividing both sides by 4,
[tex]a = -2[/tex]
Now that we have found the value of a, we can write the equation for g(x) as:
[tex]g(x) = -2(x - 5)^{2} + 9[/tex]
Therefore, the equation in vertex form for the function g is [tex]g(x) = -2(x - 5)^{2} + 9[/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
Answers
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.
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
Answers
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.
Mateo y leo caminan para entrenar y encontrarse en un punto. Mateo camina 1/5 mas de lo que camina leo. Si entre los dos caminan 15Km, ¿ cuantos kilómetros recorre cada uno?
Answers
Answer:
Primero, podemos establecer las siguientes ecuaciones:
La suma de los kilómetros que caminan Mateo y Leo es igual a 15:
Mateo + Leo = 15
Mateo camina 1/5 más que Leo:
Mateo = Leo + 1/5Leo
Mateo = 6/5Leo
Podemos utilizar la segunda ecuación para despejar una de las variables en términos de la otra. Por ejemplo, despejando Leo:
Leo = 5/6Mateo
Luego, podemos sustituir esta expresión en la primera ecuación para obtener una ecuación con una sola variable:
Mateo + 5/6Mateo = 15
11/6Mateo = 15
Mateo = 15*6/11
Mateo = 8.18 Km
Finalmente, podemos utilizar una de las ecuaciones que relaciona a Mateo y Leo para obtener la distancia que recorre Leo:
Leo = 5/6Mateo
Leo = 5/6*8.18
Leo = 6.82 Km
Por lo tanto, Mateo recorre 8.18 Km y Leo recorre 6.82 Km.
Need help with short problem 2
Answers
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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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?
Answers
Answer:
thanks for the question
please mark me brainless
Find cos(β/2) and cot(β/2), if sin(β)= -(√(3)/2) and pi<β<(3pi/2)
Answers
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,
Simplify 14×5(13×2+13×5)
Answers
let me know if this helped!
\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 }
Answers
Step-by-step explanation:
The simplified expression is {3\tan^2\frac{3\pi^c}{4}}
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?
Answers
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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Solve by factoring (15 points)
g²+4g-32=0
A 9=32 or 28
B 9=4 or 8
C 9=2 or -16
D 9=4 or -8
Answers
g²+4g-32=0
A 9=32 or 28
B 9=4 or 8
C 9=2 or -16
D 9=4 or -8
[tex]g^{2} +4g-32=0[/tex]
[tex]g^{2} + 8g - 4g - 32=0[/tex]
[tex]g(g+8)-4(g+8) = 0[/tex]
[tex](g+8)(g-4) = 0[/tex]
[tex]g+8=0 \implies \bf g = -8[/tex]
[tex]g-4=0 \implies \bf g = 4[/tex]
[tex]\implies g = 4 \ or \ -8[/tex]
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.
Answers
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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