The better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.
What is discount?We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods.
Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory.
Given that, a can of Tab costs R7, 20 at Timber City.
Then 6 packs will cost = 6(720) = R4320
At promotion the cost is R3960 the discount offered is:
D = R4320 - R3960
D = R360
At campus Canteen a can of tab is for R7, 50.
6 packs = 6(750) = R4500
Discount = 4500 - 3900 = R600
Hence, the better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.
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Write down the reciprocal of the following fractions
4
Answer: 4/1 is 1/4 but what are the 4 fractions your talking about?
Step-by-step explanation:
Write an equation for the quadratic graphed below
x-intercepts: (-2,0) and (1,0). y-intercept: (0,-2)
A quadratic function with x-intercepts as (-2,0) and (1,0) and y-intercept as (0,-2) is y = x² + x - 2.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
It is given that the x intercepts of the quadratic function are (-2,0) and (1,0).
The y intercept of the quadratic function is (0,-2).
Let the equation of the given quadratic be y = ax² + bx + c.
As the given quadratic has x intercepts as (-2,0) and (1,0) and y intercept as (0,-2).
This implies that the quadratic function is passing through the points (-2,0), (1,0) and (0,-2).
So, the points (-2,0), (1,0) and (0,-2) must satisfy the equation of the quadratic function.
As the point (-2,0) satisfy the equation of the quadratic function -
y = ax² + bx + c
0 = a(-2)² + b(-2) + c
0 = 4a - 2b + c ..... (1)
As the point (1,0) satisfy the equation of the quadratic function -
y = ax² + bx + c
0 = a(1)² + b(1) + c
0 = a + b + c ..... (2)
As the point (0,-2) satisfy the equation of the quadratic function -
y = ax² + bx + c
-2 = a(0)² + b(0) + c
-2 = c ..... (3)
Substitute the value of c in equation (1) -
0 = 4a - 2b - 2
2 = 4a - 2b ...... (4)
Substitute the value of c in equation (2) -
0 = a + b - 2
2 = a + b ...... (5)
Multiply equation (5) by 2 -
4 = 2a + 2b ...... (6)
Add equation (4) and (6) -
2 + 4 = 4a - 2b + 2a + 2b
6 = 6a
a = 1
Substitute the value of a in equation (5) -
2 = 1 + b
b = 2 - 1
b = 1
The values are a = 1, b = 1 and c = -2.
Now substitute the value of a, b and c in the quadratic function.
y = ax² + bx + c
y = (1)x² + (1)x + (-2)
y = x² + x - 2
Therefore, the quadratic function is y = x² + x - 2.
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PLEASE HELP!!!!!!!!!!!
What are the benefits and limitations of quadratic models in real world applications such as bridge design?
The benefits of using quadratic models in real-world applications include: -They are versatile and can be used for a variety of problems.
Why are Quadratic Models important?Researchers may find the quadratic model to be a useful data analytic approach for helping them identify the combined impacts of achievement goals on academic accomplishment.
We anticipate that future studies on the impact of academic achievement goals will frequently use the quadratic model to analyze their data.
Situations that can be approximated by quadratic functions include tossing a ball, firing a cannon, jumping off a platform, and hitting a golf ball.
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A researcher is funded to obtain an estimate for the population proportion of smokers who have tried using e-cigarettes. She plans to interview 100 smokers. Previous studies have estimated that 20% of smokers have tried e-cigarettes.
The researcher decides to present the 99% confidence interval. What is the best interpretation for this interval?
A. She is 99% confident that the sample proportion is within the interval.
B. There is 99% likelihood that another sample of 100 will have an overlapping confidence interval.
C. She is 99% confident that the population parameter is within the interval.
D. There is a 1% probability that the population parameter is higher than the interval.
The best interpretation for this interval is that "She is 99% confident that the population parameter is within the interval" (option C).
What is the meaning of confidence interval?In statistics and related fields, the confidence interval refers to a percentage that determines the population fits the interval set. Due to this, a high confidence rate is considered to be positive.
What does the confidence interval mean in this case?In this case, the confidence interval implies that the researcher is 99% confident that the population parameter is within the interval (option C)
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Volume of Cylinders, Cones, and Spheres
1
2
The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?
○ 3² cm³
π
O 87 cm³
○ 64 cm³
O 167 cm³
Answer:[tex]\frac{32\pi }{3} cm^{3}[/tex]
Step-by-step explanation:
Since the diameter is 4 cm, we know the radius is 2 cm since diameter = 2 x radius. The formula for a sphere's volume is [tex]\frac{4\pi }{3}[/tex]×[tex]r^{3}[/tex], so by plugging in 2 we get [tex]\frac{4\pi }{3}[/tex]×[tex]2^{3}[/tex] = [tex]\frac{4\pi }{3}[/tex] x 8 = [tex]\frac{32}{3}[/tex] [tex]\pi[/tex] [tex]cm^{3}[/tex]
A store bought a hand-crafted toy chest at a cost of $921.60 and marked it up 115%. Sebastian bought it and paid 2% sales tax. What was his total cost
Square has a perimeter of 36 find the area
Answer:
A = 81 units²
Step-by-step explanation:
the sides of a square (s) are congruent
given perimeter = 36 , then
s = 36 ÷ 4 = 9
the area (A) of a square is calculated as
A = s²
then
A = 9² = 81 units²
A random sample of 223 students were asked if they owned a pet or not. The following contingency table gives the two-way classification of their responses.
The probabilities of the random sample of 223 students are solved
P ( male ) = 0.475
P ( female ) = 0.525
P ( male | pet ) = 0.538
P ( female | no pet ) = 0.547
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the total number of students be = 223 students
Let the total number of male students be = 49 + 57 = 106 students
Let the total number of female students be = 64 + 53 = 117 students
Now , the equation will be
Let the number of male students who own a pet = 57 students
Let the number of male students who does not own a pet = 49 students
And ,
Let the number of female students who own a pet = 53 students
Let the number of female students who does not own a pet = 64 students
The probability of choosing a male student P ( male ) = number of male students / total number of students
The probability of choosing a male student P ( male ) = 106 / 223
The probability of choosing a male student P ( male ) = 0.475
And ,
The probability of choosing a female student P ( female ) = number of male students / total number of students
The probability of choosing a female student P ( female ) = 117 / 223
The probability of choosing a female student P ( female ) = 0.525
And ,
Probability of choosing a male student who owns a pet P ( male | pet ) = number of male students who own a pet / number of male students
P ( male | pet ) = 57 / 106
P ( male | pet ) = 0.538
The probability of choosing a female student who does not own a pet is P ( female | no pet ) = number of female students who does not own a pet / number of female students
P ( female | no pet ) = 64 / 117
P ( female | no pet ) = 0.547
Hence , the probabilities are solved
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evaluate the integral below by interpreting it in terms of areas in the figure. the areas of the labeled regions are
The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
R1 = 4, R2 = 5, R3 = 6
The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
The integral is given by:
∫ (R1 + R2 + R3) dA
where R1, R2, and R3 are the areas of the labeled regions in the figure.
By interpreting the integral in terms of areas, we can calculate the value of the integral. The integral evaluates to 11, which is the sum of the areas of the three regions (R1 + R2 + R3 = 4 + 5 + 6 = 11).
The complete question is :
Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A = 3, B = 4, C = 5, and D = 6.
∫DBCA x dA
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Write the decimal number in words 17.43
Rosa is using a recipe that serves six and uses one and three quarters cups of pasta. Choose the amount of pasta she will use if she wants to make eight servings. (2 points)
two and one third cups
three and three quarters cups
four and one quarter cups
two and one quarter cups
Answer: To calculate the amount of pasta needed for eight servings, we need to multiply the original amount of pasta in the recipe by 8/6.
So, 1.75 cups * 8/6 = 2.3 cups of pasta.
Therefore, Rosa will use 2.3 cups or four and one quarter cups of pasta if she wants to make eight servings.
Step-by-step explanation:
Consider Functions: Consider a square with side of length s, diagonal of length d, perimeter P, and area A.a) Write A as a function of s.b) Write s as a function of A.c) Write s as a function of d.d) Write d as a function of s.e) Write P as a function of s.f) Write s as a function of P.g) Write A as a function of P.h) Write d as a function of A.
For square, Functions will be A=s², s=√A, s=√(d²/2), d=√2s², p=4s, s=p/4, A=(p/4)², d=√2A.
What exactly is a function?
A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a co-domain, as well as a range. In general, a function is denoted as f(x), where x represents the input. A function's generic representation is y = f. (x).
In mathematics, there are several types of functions. Some examples include:
When there is a mapping for a range for each domain between two sets, this is referred to be an injective function or a one to one function.
Surjective functions, also known as Onto functions, are used when more than one element is transferred from domain to range.
Polynomial function: A function made up of polynomials.
Inverse Functions: A function that may be used to inverse another function.
Now,
As given square with side of length s, diagonal of length d, perimeter P, and area A.
and Area=side²
Perimeter=4*side
diameter²=side²+side²
then A=s² and s=√A, s=√(d²/2) and d=√2s², p=4s and s=p/4, A=(p/4)², d=√2A.
Hence,
For square, Functions will be A=s², s=√A, s=√(d²/2), d=√2s², p=4s, s=p/4, A=(p/4)², d=√2A.
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CAN SOMEONE HELP WITH THIS?✨
4966.5
Step-by-step explanation:
Starting at finding out how the population will increase in 3 years we take 3 and divide it by 4. This produces an increase of 75% every 3 years. If we multiply 2838 by 75% we get 2128.5. If we add it back to 2838, we get 4966.5
Verify that the indicated function y p(x) is an explicit solution of the given first-order differential equation.
(y-x)y' =y-x+ 2; y=x+2√x+3
When y = x + 2√x +3,
y'= -x+2
Thus, in terms of x,
(y - x)y' =
y-x+2=
Since the left and right hand sides of the differential equation are equal when x + 2√x + 3 is substituted for y, y = x + 2√x + 3 is a solution.
Proceed as in Example 6, by considering p simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering p as a solution of the differential equation, give at least one interval I of definition.
O(-6, -3)
O(-3,00)
(-∞, -3)
x.
(-6, 3)
O[-3, 3]
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[tex]y=\frac{2x\pm\sqrt{5x^2-(4x^2-16x+4\bar{c})} }{2(1)}[/tex]Solve the given DE, [tex](y-x)\frac{dy}{dx} =y-x+2[/tex].
Rewriting,
=> [tex](y-x)\frac{dy}{dx} =y-x+2[/tex]
=> [tex](y-x)dy =(y-x+2)dx[/tex]
=> [tex]-(y-x+2)dx+(y-x)dy =0[/tex]
=> [tex](-y+x-2)dx+(y-x)dy =0[/tex]
Check to see if this is an exact DE by taking the partial derivative of M with respect to y and N with respect to x.
[tex]M=(-y+x-2)dx[/tex]
=> [tex]M_{y} =-1[/tex]
[tex]N=(y-x)dy[/tex]
=> [tex]N_{x}=-1[/tex]
[tex]M_{y} =N_{x}[/tex], so this is an exact DE. Now integrate M with respect to x and N with respect to y.
[tex]\int\ ({-y+x-2)} \, dx[/tex]
=>[tex]-xy+\frac{x^2}{2}-2x[/tex]
[tex]\int\ ({y-x)} \, dy[/tex]
=> [tex]=\frac{y^2}{2} -xy[/tex]
So we can say the solution to the given DE is, [tex]\frac{x^2}{2}+\frac{y^2}{2}-xy-2x=c[/tex].
Find the equation of the line intersecting the graph of [tex]y=x^{3} - x+4[/tex] at x=-2 and x = 2
The equation of the line secant to the cubic equation y = x³ - x + 4 is equal to y = 3 · x + 4.
How to derive the equation of a line secant to a curve
In this problem we find the case of a cubic equation that is intersected twice by a line, that is, a secant line. According to analytical geometry, lines are described by equations of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Where the slope of the line is determined by secant line formula:
m = Δy / Δx
First, determine the slope of the secant line:
x = - 2
y = (- 2)³ - (- 2) + 4
y = - 2
x = 2
y = 2³ - 2 + 4
y = 10
m = [10 - (- 2)] / [2 - (- 2)]
m = 3
Second, calculate the intercept of the linear function:
b = y - m · x
b = 10 - 3 · 2
b = 10 - 6
b = 4
Third, write the equation of the secant line:
y = 3 · x + 4
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Anna is considering writing and publishing her own book She estimates her revenue equation as R = 6.56x and her cost equation as C = 10.063 + 1.09x where x is the number of books she sells. Find the minimum number of books she must sell to make a profit
Anna must sell atleast ? books to make a profit.
Anna must sell at least approximately 1.845 books to make a profit.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
We can find the minimum number of books Anna must sell to make a profit by setting the revenue equal to the cost and solving for x.
That is, we want to find the value of x where R = C:
6.56x = 10.063 + 1.09x
5.47x = 10.063
x = 10.063 / 5.47
x = approximately 1.845 books
Hence, Anna must sell at least approximately 1.845 books to make a profit.
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A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is
�
(
�
)
P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
What is
�
(
�
)
P(B)P, left parenthesis, B, right parenthesis, the probability that the second student is a girl?
What is
�
(
�
and
�
)
P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first student is a boy and the second student is a girl?
P(A) = 1/2, P(B) = 3/4, and P(A and B) = 3/8, where A is the event that the first student is a boy and B is the event that the second student is a girl.
The total number of possible outcomes in this scenario is 4C2, which is equal to 6. These outcomes are AB, AC, AD, BC, BD, and CD, where A represents Franklin and B, C, and D represent Sandra, Marta, and Jane, respectively.
The probability that the first student is a boy is P(A) = 1/2, since there are two boys and four students total.
The probability that the second student is a girl is P(B) = 3/4, since there are three girls and four students total.
The probability that the first student is a boy and the second student is a girl is P(A and B) = 1/2 x 3/3 = 3/8, since the probability of the first student being a boy is 1/2 and the probability of the second student being a girl is 3/4 (after one girl has already been chosen as the first student).
Therefore, the probability that the first student is a boy is 1/2, the probability that the second student is a girl is 3/4, and the probability that the first student is a boy and the second student is a girl is 3/8.
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A company believes it has a 40% chance of being successful on bidding a contract that yields a net profit of $30,000. Assume it costs $5,000 in consultant fees to prepare the bid. What is the expected gain or loss for the company if it decides to bid on the contract?
Answer:
Joe mum so gaeee
Step-by-step explanation:
your answer is 1000
If the lengths of two adjacent sides of a parallelogram area a and b, and if the acute angle formed by these two sides is theta, show that the product of the lengths of the two diagonals is given by the expression (a^2 + b^2)^2 - 4a^2b^2cos^2theta
√(a² + b²)² - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.
An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.
we have AB as a, AD as b and the angle between them is theta.
So using the cosine rule, we have
BD = √a² + b² - 2abcosθ
So now consider the triangle ABC
Here AB is a, BC is b and the angle is 180-theta
So using cosine rule, we get AC as
AC = √a² + b² - 2abcosθ( 180 - θ )
AC = √a² + b² - 2ab(-cosθ )
AC = √a² + b² - 2abcosθ
Now we have the two diagonals AC and BD. So multiplying, we get
AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ
Simplifying, we get
AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)
AC × BD = √(a² + b²)² - (2abcosθ)²
AC × BD = √(a² + b²)² - 4a²b²cos²θ
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Consider the rabbit pairs that illustrate the pattern in the Fibonacci sequence. These rabbits produce exactly 1 pair of new rabbits after reaching maturity at age 2 months. Imagine that the rabbits and all their offspring live forever. Also, imagine the field the rabbits live in can expand in size so that its side length is exactly equal to the number of pairs of rabbits living in the field. What is the side length of the field at the end of two years? Explain and show your work
The side length of the field after two years (24 months) would be 46368.
How to determine the side length of the fieldThe Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
To determine the side length of the field after two years, we can calculate the number of rabbit pairs after two years.
At the end of the first month, there is 1 pair of rabbits.
At the end of the second month, there are 1 + 1 = 2 pairs of rabbits.
At the end of the third month, there are 1 + 1 = 2 pairs of rabbits.
At the end of the fourth month, there are 2 + 1 = 3 pairs of rabbits.
At the end of the fifth month, there are 3 + 2 = 5 pairs of rabbits.
At the end of the sixth month, there are 5 + 3 = 8 pairs of rabbits.
At the end of the seventh month, there are 8 + 5 = 13 pairs of rabbits.
At the end of the eighth month, there are 13 + 8 = 21 pairs of rabbits.
At the end of the 24th month, there are fibonacci(24) = 46368 pairs of rabbits.
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a) Use the Intermediate Value Theorem to show that the following equation has a solution on the given interval.b) Use the graphing utility to find all the solutions to the equation on the given interval.c) Illustrate your answers with an appropriate graph.
let a where b and c are square. show that a is invertible if and only if both b and c are invertible.
The square matrix A is invertible, i.e., inverse of A is exist, if and only if the inverse of matrices B and C exists.
We have a matrix A such that
[tex]A = \begin{bmatrix} B & 0 \\0 & C \\ \end{bmatrix}[/tex]
where, B and C are square matrices. We have to prove or show that matrix A is invertible iff B and C are invertible. We shall prove it by using the inverse and determinant of matrices. The determinant is a scalar value which is associated with the square matrix. If X is a matrix, then the determinant of a matrix is denoted by |X|. Inverse of matrix A is calculated by using formula as below,
A = adj(A)/|A|. As we see a matrix A is invertible if and only if it has non-zero determinant. Also for a diagonal matrix its determinant is product of diagonal entries here diagonal entries are again matrices so |A|=|B|×|C|. From here we can clearly says |A| ≠ 0 if and only if |B| ≠ 0 and |C| ≠ 0. Hence, the matrix A is invertible iff B and C are invertible.
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Complete question :
Let A = [ B, 0 ; 0, C], where B and C are square. show that A is invertible if and only if both B and C are invertible.
Luciano walked 7/18 mile on Saturday morning. On Sunday, she walked 5/9 mile. How much more did she walk on Sunday than on Saturday. Shade the box next to any answer.
The distance Luciano walked more on Sunday is given by the equation A = ( 1/6 ) of a mile
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the distance Luciano walked more on Sunday be A
Now , the equation will be
The distance walked by Luciano on Sunday = ( 5/9 ) mile
The distance walked by Luciano on Saturday = ( 7/18 ) mile
So , the distance Luciano walked more on Sunday A = distance walked by Luciano on Sunday - distance walked by Luciano on Saturday
Substituting the values in the equation , we get
The distance Luciano walked more on Sunday A = ( 5/9 ) - ( 7/18 )
On simplifying the equation , we get
The distance Luciano walked more on Sunday A = ( 10 - 7 ) / 18
The distance Luciano walked more on Sunday A = 3/18 miles
The distance Luciano walked more on Sunday A = 1/6 miles
Hence , the equation is A = 1/6 of a miles
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In formally proving that lim…….
The value of m in the limit is (-13 + sqrt(169 + 4ε)) / 2, where -84.875 < ε < 1.
What is the value of mTo prove that lim as x approaches 6 of (x^2+x) = 42, we need to find a δ > 0 such that if 0 < |x - 6| < δ, then |(x^2+x) - 42| < ε, where ε > 0 is arbitrary.
We can start by working with the expression |(x^2+x) - 42| and trying to bound it by ε. We have:
|(x^2+x) - 42| = |x^2 + x - 6^2 - 6 + 36| = |(x-6)(x+7)|.
To get a bound on |(x-6)(x+7)|, we can assume that 0 < |x - 6| < δ, where δ > 0 is some quantity we need to determine. This means that:
|x-6| < δ.
We can then use the triangle inequality to bound |x+7| as follows:
|x+7| <= |x-6| + |13| < δ + 13.
Thus, we have:
|(x-6)(x+7)| <= |x-6|*|x+7| < δ(δ+13).
Now, we want to choose δ such that δ(δ+13) < ε. Let's choose:
δ = min(ε/m, 1),
where m is some constant we need to determine. We want to make sure that this choice of δ satisfies δ(δ+13) < ε.
Substituting δ = min(ε/m, 1) into the inequality δ(δ+13) < ε, we get:
min(ε/m, 1)(min(ε/m, 1) + 13) < ε.
Simplifying this inequality gives:
min(ε/m, 1)^2 + 13min(ε/m, 1) - ε < 0.
Since we want to choose the smallest possible value of δ that satisfies this inequality, we want to choose m to be the largest value that satisfies this inequality.
The discriminant of the quadratic equation is:
b^2 - 4ac = 13^2 + 4ε.
Since ε > 0, we know that the discriminant is positive, so there are two roots to the quadratic equation. The largest root is:
(-13 + sqrt(169 + 4ε)) / 2.
So, we can choose:
m = (-13 + sqrt(169 + 4ε)) / 2.
Then, we have:
min(ε/m, 1) = ε/((-13 + sqrt(169 + 4ε)) / 2).
Substituting this value of δ into the inequality δ(δ+13) < ε, we get:
ε^2 / (13 - sqrt(169 + 4ε)) < ε.
This simplifies to:
ε < 13 - sqrt(169 + 4ε).
Squaring both sides and rearranging, we get:
4ε^2 + 338ε - 1444 < 0.
This quadratic inequality holds if and only if:
(-338 - sqrt(338^2 + 441444)) / (24) < ε < (-338 + sqrt(338^2 + 441444)) / (24).
Simplifying this gives:
-84.875 < ε < 1.375.
Thus, we have found that if we choose:
m = (-13 + sqrt(169 + 4ε)) / 2,
where:
-84.875 < ε < 1.
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Your goal is to have $17500 in your bank account by the end of 9 years. If the interest rate remains constant at 4% and you want to make annual identical deposits, how much will you need to deposit in your account at the end of each year to reach your goal? a. 1984.36
b. 1653.63
c. 1157.54
d. 1488.27
The annual deposits that needs to be made is for amount $2352.94.
What is annuity?
Annuity refers to an equal series of future cash flows which are received or paid periodically. Future value of annuity is the value of the annuity at the end of the series whereas present value is the value of the annuity at the beginning of the series.
The annuity value can be calculated as -
Future value of annuity = Annuity x (1 - (1 + Rate)^-Number of years) / Rate
The values are given as -
Future value of annuity = $17500.00
Annuity = Identical annual deposits
Rate = 4% = 0.04
Number of years = 9
Substitute the values into the equation -
17500 = Annuity x (1 - (1 + 0.04)^-9 ) / 0.04
Annuity identical deposits = 17500 x 0.04 / ((1.04)^-9)
Annuity identical deposits = 700 / (1 - 0.7025)
Annuity identical deposits = 700 / 0.2975
Annuity identical deposits = 2352.94
Therefore, the value is obtained as $2352.94.
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Todd keeps his 4-room house very clean. It takes 1 hour and 36 min to clean his whole house. How long does it take him to clean one room?
Answer:
24 min
Step-by-step explanation:
1 hr 36 min = 96 min
96 min / 4 = 24 min
Which expression is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) )?
The expression that is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) ) is option D. (1 + cos(x))(sin (x))
How are the expressions equivalent?The expression (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) is equivalent to (1 + cos(x))(sin (x)) because of the double angle identity for tangent.
The double angle identity states that tangent of 2 times an angle is equal to 2 times the tangent of that angle divided by 1 minus the square of the tangent of that angle. In other words,
tan(2θ) = 2tan(θ)/(1 - tan2(θ))
In this expression, we have tangent of x/2, so substituting θ = x/2 gives us:
tan(x) = 2tan(x/2)/(1 - tan2(x/2))
Since cos(x) = 1 - 2sin2(x/2), we can simplify the expression to:
(1 + cos(x))2tan(x/2) = (1 + 1 - 2sin2(x/2))2tan(x/2) = (2 - 2sin2(x/2))(2sin(x/2)/(1 - sin2(x/2)))
Expanding the product of the two factors gives us the final result:
(1 + cos(x))2tan(x/2) = (2 - 2sin2(x/2))(sin(x)) = (1 + cos(x))(sin(x))
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I’m not sure how to answer these questions can someone help pls
Answer:
Greatest common factor for 14/16 is 2
Greatest common factor for 3/12 is 3
Greatest common factor for 16/28 is 4
So to simplify 14/16 it is 7/8
To simplify 3/12 it is 1/4
To simplify 16/28 it is 4/7
Step-by-step explanation:
Construct a know-show table for each of the following statements and then write a formal proof for one of the statements.
(a) If m is an odd integer, then m + 1 is an even integer.
(b) If x is an even integer and y is an odd integer, then x + y is an odd integer
(c) If m is an even integer, then 3m^2 + 2m + 3 is an odd integer.
Step-by-step explanation:
(a)
If m is an odd integer, then m + 1 is an even integer.
m (odd integer) m + 1 (even integer)
1 2
3 4
5 6
... ...
Proof:
Suppose m is an odd integer. We can write m as 2n + 1 for some integer n. Then,
m + 1 = (2n + 1) + 1 = 2n + 2
Since 2n + 2 is clearly an even integer, it follows that m + 1 is an even integer if m is an odd integer.
(b)
If x is an even integer and y is an odd integer, then x + y is an odd integer
x (even integer) y (odd integer) x + y (odd integer)
0 1 1
2 3 5
4 5 9
... ... ...
Proof:
Suppose x is an even integer and y is an odd integer. We can write x as 2n and y as 2m + 1 for some integers n and m. Then,
x + y = 2n + (2m + 1) = 2(n + m) + 1
Since n + m is clearly an integer, it follows that x + y is an odd integer if x is an even integer and y is an odd integer.
(c)
If m is an even integer, then 3m^2 + 2m + 3 is an odd integer.
m (even integer) 3m^2 + 2m + 3 (odd integer)
0 3
2 27
4 99
... ...
Proof:
Suppose m is an even integer. We can write m as 2n for some integer n. Then,
3m^2 + 2m + 3 = 3(2n)^2 + 2(2n) + 3 = 12n^2 + 4n + 3
Since 12n^2 + 4n + 3 is clearly an odd integer, it follows that 3m^2 + 2m + 3 is an odd integer if m is an even integer.
A spherical boulder is 24 feet in diameter and weighs almost 6 tons find the volume
The volume of the spherical boulder is 7234.56 cubic feet.
What is the diameter?
A line connecting the center and the circumference at its opposite ends is called the diameter. Its length is double that of the circle's radius.
The formula for the volume of a sphere is [tex]V=\frac{4}{3}\pi r^{3}[/tex].
Given the diameter of the sphere is 24 feet.
therefore radius is equal to 12 feet.
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi (12)^{3} \\V=\frac{4}{3} *3.14*1728\\V=7234.56[/tex]
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