Answers
The sequence pattern for 3¹/₃, 3¹/₄, 3¹/₅, ...... is; f(n) = 3 + 1/(2 + n)
How to find the sequence pattern?We are given the sequence;
3¹/₃, 3¹/₄, 3¹/₅, ......
Now, we can see that;
First term is 3¹/₃.
However, for the second term, 1 has been added to the denominator.
Thus, we can suggest that the sequence pattern here is;
f(n) = 3 + 1/(2 + n)
where n is the nth term.
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Related Questions
evaluate the expression 27 (36)
Answers
The value of the expression is 972
How to evaluate the expression?The expression is given as:
27(36)
Express 36 as 18 + 18
27(18+ 18)
Expand
486+ 486
Evaluate the sum
972
Hence, the value of the expression is 972
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Question 3
Show work and solve 3 = 5*+1 using change of base formula.
Answers
Answer: [tex]x=\frac{\log (3/5)}{\log 5}[/tex]
Step-by-step explanation:
[tex]3=5^{x+1}\\\\\log_{5} 3=x+1\\\\x=\log_{5} 3-1\\\\x=\log_{5} 3-\log_{5} 5\\\\x=\log_{5} \left(\frac{3}{5} \right)\\\\x=\frac{\log (3/5)}{\log 5}[/tex]
For problems 13-19, transcribe the following expressions: (Write it out.)
Example: z + 4 = z plus 4
13. st
14. 6/t - 4
15. 20 + t 2
16. 50 - x
17. x - y 2
18. 24/12 + 12
19. xy - 16
Answers
The transcribe expression is the expression of the equation in words.
How to transcribe expression?The expression can be transcribe as follows;
1. st = s multiply by t
2. 6 / t - 4 = 6 divided by t minus 4
3. 20 + t² = 20 plus t squared.
4. 50 - x = 50 minus x
5. x - y² = x minus y squared.
6. 24 / 12 + 12 = 24 divided by 12 plus 12
7. xy - 16 = x multiply by y minus 16
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Suppose that $6500 is placed in an account that pays 12% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
Answers
The amount after 1 year is $7280 and the amount after two year is $8153.
Given that $6500 is placed in an account that pays 12% interest compounded each year.
Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.
Compounded interest=12%
Principal amount=$6500
Time period = 1 year
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years
Here P=6500, r=12%, n=1, t=1
Substitute these values in the formula, we get
A=6500(1+(0.12/1))¹⁽¹⁾
A=6500(1+0.12)¹
A=6500×1.12
A=7280
Now we have to calculate for two years.
That is if n=2 , then
A=6500(1+(0.12/1))¹⁽²⁾
A=6500(1+0.12)
A=6500×1.2544
A=8153.6
Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
Answers
The width of the cooling tower at the base of the structure is 40 meters.
Width of the cooling towerGiven equation
x²/400 -(y-90)²/1600=1
Solving for the width
Cooling tower width =2√400
Cooling tower width=2×20
Cooling tower width=40 meters
Therefore the correct option is D. 40 meters.
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Answer:
40
Step-by-step explanation:
in the diagram , what is the value of x
Answers
The value of x from the given diagram is 100 degrees
Sum of interior angleFrom the given diagram, we will use the theorem "angle at the vertex is half that at the centre.
<50 = 1/2 x
Cross multiply
50 * 2 = x
x = 50 * 2
x = 100 degrees
Hence the value of x from the given diagram is 100 degrees
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If x^y = z is there any way to find y if you know x and z?
Answers
We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
How to solve for y?The expression is given as:
x^y = z
The above expression is an exponential expression.
Start by taking the logarithm of both sides
y log(x) = log(z)
Divide both sides by log(x)
[tex]y = \log_x(z)[/tex]
Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
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Assume that Hogan Surgical Instruments Co. has $2,500,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 18 percent, but with a high-liquidity plan, the return will be 14 percent. If the firm goes with a short-term financing plan, the financing costs on the $2,500,000 will be 10 percent, and with a long-term financing plan, the financing costs on the $2,500,000 will be 12 percent.
Answers
The the anticipated return after financing cost with the most aggressive asset financing mix is $200000.
Most aggressive
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $450,000 + (-$250,000)
Anticipated return = $200,000
Most conservative
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Long-term financing = –$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $350,000 + (-$300,000)
Anticipated return = $50,000
Moderate approach
Low liquidity = $2,500,000 *18%
Low liquidity = $450,000
Long-term financing =–$2,500,000 * 12%
Long-term financing = -$300,000
Anticipated return = $450,000 + (-$300,000)
Anticipated return = $150,000
Moderate approach
High liquidity = $2,500,000 *14%
High liquidity = $350,000
Short-term financing = -$2,500,000*10%
Short-term financing = -$250,000
Anticipated return = $350,000 + (-$250,000)
Anticipated return = $100,000
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Complete question:
a. Compute the anticipated return after financing cost with the most aggressive asset financing mix.
b. Compute the anticipated return after financing cost with the most conservative asset financing mix.
c. Compute the anticipated return after financing cost with the two moderate approaches to the asset financing mix.
Kathy and Linda both accepted new jobs at different companies. Kathy's starting salary is $31,500 and Linda's starting salary is $33,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers. A website that collects salary information from a sample of employees for a number of major employers reports that Kathy's company offers a mean salary of $42,000 with a standard deviation of $7,000. Linda's company offers a mean salary of $45,000 with a standard deviation of $6,000. Find the z-scores corresponding to each woman's starting salary.
Answers
1. The z-scores corresponding to Kathy's starting salary is -1.5
2. The z-scores corresponding to Linda's starting salary is -2
z-scorez = (x - μ) / σ
Where
z is the s-scorex is the scoreμ is the mean σ is the standard deviation1. How to determine the z-score for Kathy's starting salaryStarting salary (x) = $ 31500Mean salary (μ) = $ 42000Standard deviation (σ) = $ 7000z-score for Kathy's starting salary (z) =?z = (x - μ) / σ
z = (31500 - 42000) / 7000
z-score for Kathy's starting salary = -1.5
2. How to determine the z-score for Linda's starting salaryStarting salary (x) = $ 33000Mean salary (μ) = $ 45000Standard deviation (σ) = $ 6000z-score for Linda's starting salary (z) =?z = (x - μ) / σ
z = (33000 - 45000) / 6000
z-score for Linda's starting salary = -2
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Which is the graph of f(x) = (4)×?
Answers
See the graph in the attached image.
A -foot pole is supporting a tent and has a rope attached to the top. The rope is pulled straight and the other end is attached to a peg one foot above the ground. The rope and the pole form an angle that measures , as shown below. The pole, the rope, and an imaginary line that runs across the ground from the top of the peg to the pole form a right triangle. The hypotenuse is unknown. The pole is adjacent to the 35-degree angle, and it is labeled 10 feet. The 10 foot measurement includes the height of the 1 foot peg. The imaginary line that runs across the ground is opposite the 35-degree angle, and it is not labeled. Which expression shows the length of the rope?
Answers
An expression which shows the length of this rope is: 10/cos35 ≈ 12.2 feet.
How to determine the length of this rope?In order to determine the length of this rope, we would apply the law of cosine because both the rope and apple formed an angle that are adjacent in a right triangle:
cos(θ) = Adj/Hyp
Where:
Adj is the adjacent side of a right triangle.Hyp is the hypotenuse of a right triangle.θ is the angle.Substituting the given parameters into the formula, we have;
cos(35) = 10/Hyp
Hyp = 10/cos35
Hyp = 12.2 feet.
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Tom's Sports Wear is a retailer of sports hats located in Atlanta, Georgia. Although Tom's carries numerous styles of sports hats, each hat has approximately the same price and invoice purchase cost, as shown below. Sales personnel receive large commissions to encourage them to be more aggressive in their sales efforts. Currently the economy of Atlanta is really humming, and sales growth at Tom's has been great. However, the business is very competitive, and Tom has relied on its knowledgeable and courteous staff to attract and retain customers, who otherwise might go to other sports wear stores. Also, because of the rapid growth in sales, Tom is finding it more difficult to manage certain aspects of the business, such as restocking of inventory and hiring and training new salespeople.
Sales price $ 31.00
Per-unit variable costs:
Invoice cost 17.05
Sales commissions 4.05
Total per-unit variable costs $ 21.10
Total annual fixed costs:
Advertising $ 23,100
Rent 28,200
Salaries 124,200
Total fixed costs $ 175,500
The annual breakeven point in unit sales is calculated to be:
Answers
The annual breakeven point is $550157
Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.
The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.
The sales price is $31 and the total variable cost is $21.10.
Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get
Contribution margin= Sales price-Total sales price
Contribution margin=31-21.10
Contribution margin=9.9
Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get
contribution margin ratio=contribution margin/Sales price
contribution margin ratio=9.9/31
contribution margin ratio=0.319
contribution margin ratio=31.9%
Furthermore, we will find the break-even point, we get
Break-even point=Fixed cost/contribution margin
Break-even point=175500/9.9
Break-even point=17727.27
Now, we will find the break-even sales in dollars, we get
Break-even sales=Fixed cost/contribution margin ratio
Break-even sales=(175500/31.9)×100
Break-even sales=550157
Hence, the annual breakeven point in unit sales is calculated to be $550157.
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Tom has 7 hamsters. If each hamster weighs 11 pounds, how much weight is there in total?
Answers
Answer:
7
Step-by-step explanation:
7x11=77
Triangle abc has vertices at A(-6, 3) , B(3, 5) and C(1, -4). Show that triangle abc is isosceles and find the area of this triangle.
Answers
Using the formula for the distance between two points, it is found that:
Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.The area is of 38.63 units squared.What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we use the formula to find the lengths for each side of the triangle.
For example, side AB has length given by the distance between (-6,3) and (3,5), hence:
[tex]AB = \sqrt{(-6 - 3)^2 + (3 - 5)^2} = 9.22[/tex]
Side AC has length given by:
[tex]AC = \sqrt{(-6 - 1)^2 + (3 - (-4))^2} = 9.9[/tex]
Side BC has length given by:
[tex]BC = \sqrt{(3 - 1)^2 + (5 - (-4))^2} = 9.22[/tex]
Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.
What is the area of a triangle?The area of a triangle is given by half the length of the base multiplied by the height.
The midpoint of side BC, of length of 9.22 units, is of (2,0.5). The height is the distance of this point from point A, hence:
[tex]d = \sqrt{(-6 - 2)^2 + (3 - 0.5)^2} = 8.38[/tex]
Hence the area is:
A = 0.5 x 9.22 x 8.38 = 38.63 units squared.
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find HM if HG=18, FM=5, and EM=9
Answers
Answer:
HM = 3 or HM = 15
Step-by-step explanation:
The product of segment lengths is the same for both chords.
SetupFM·EM = GM·HM
GM +HM = 18
Substituting for GM, we have ...
FM·EM = (18 -HM)·HM
5·9 = (18 -HM)·HM
SolutionEffectively, we want two factors of 45 that have a total of 18. Looking at the factors of 45, we have ...
45 = 1·45 = 3·15 = 5·9
The totals of these pairs are 46, 18, 14. The factor pair we're looking for is 3·15.
Either of these factors could be HM. The other will be GM.
There is nothing in the problem description that suggests the length of HM relative to other lengths on the diagram. (We know the diagram is not to scale.) So, there are two possible solutions:
HM = 3 or HM = 15
una persona compra un terreno a crédito pagadero en 5 año. El primer año paga 5000$. Si cada año paga 10% más que el anterior; calcula cuanto pagará en el quinto año y cual es el importe del terreno
Answers
El pago en el quinto año sera de $7,320.50, y el importe total es de $30,525.50
¿Cual es el importe en el quinto año?Sabemos que el importe inicial es $5,000, cada año paga 10% más que el anterior.
Entonces se hacen 5 pagos, y el pago que se hace en cada año esta dado por la ecuación exponencial:
[tex]P(x) = \$5000*(1.10)^{x - 1}[/tex]
Donde x es el número del año.
Entonces en el año número 5, el pago será:
[tex]P(5) = \$5000*(1.10)^{5 - 1} = \$7,320.50[/tex]
¿Cuanto es el importe total?
Está dado por:
[tex]T = P(1) + P(2) + P(3) + P(4) + P(5)\\\\T = \$5000*( 1 + (1.10)^1 + (1.10)^2 + (1.10)^3+ (1.10)^4) = \$30,525.50[/tex]
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If a cylinder has a height of 12 feet and a radius of 4 feet, what is its surface area (in square feet)? What is its volume (in cubic feet)? (Round your answers to two decimal places.)
Answers
The volume of the cylinder is 602.88 ft³.
The surface area of the cylinder is 301.44 ft²
How to find the volume and surface area of a cylinder?volume of a cylinder = πr²h
volume of a cylinder = 3.14 × 4² × 12
volume of a cylinder = 3.14 × 16 × 12
volume of a cylinder = 602.88 ft³
Surface are of a cylinder = 2πr(r + h)
Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)
Surface are of a cylinder = 25.12(12)
Surface are of a cylinder = 301.44 ft²
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please help me i included the images of the questions, ill give brainliest
Answers
Answer:
1: r^5, 2: st^2, 3: qr, 4: 1, 5: m, 6: x, 7: 1/z, 8: a, 9: d^4f^2 10: 1, 11: cd^2, 12: b, 13: 1, 14: st^2, 15: 1/mn.
Step-by-step explanation:
1 explanation: Cancel the common factor of r^6 and r.
2 explanation: Simplify the expression.
3 explanation: simplify the expression.
4 explanation: Simplify the expression.
5 explanation: simplify the expression.
6 explanation: Cancel the common factor of x^2 and x.
7 explanation: Cancel the common factor of z^4 and z^5.
8 explanation: Cancel the common factor of a^2 and a.
9 explanation: simplify the expression.
10 explanation: simplify the expression.
11 explanation: simplify the expression.
12 explanation: simplify the expression.
13 explanation: simplify the expression.
14 explanation: simplify the expression.
15: simplify the expression.
SOLVE AND EXPLAIN HOW TO SOLVE
Answers
Answer:
4.13
Step-by-step explanation:
Using sine ratio where it states that sine of a measurement is equal to ratio of opposite of measurement to hypotenuse (slant side/side with slope)
From the question, our opposite is x, hypotenuse is given as 15 units and the measurement is 16°. Apply the formula:
[tex]\displaystyle{\sin 16^{\circ} = \dfrac{x}{15}}[/tex]
Move 15 to multiply sin(16°):
[tex]\displaystyle{15\sin 16^{\circ} = x}[/tex]
Go ahead and input the value in a calculator since it's not a special triangle - a measurement that can be found using hand method - after you find the value, round it to 2 decimal places:
[tex]\displaystyle{x = 4.13456033...}[/tex]
Therefore, after rounding to 2 decimal places, the answer is:
[tex]\displaystyle{x=4.13}[/tex]
Therefore, the value of x is 4.13 units.
Using the table, what is the average daily balance of the credit card for the July 1 - July 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Day 1112126 Activity − Payment Purchase Payment Adjustment −−500+750−700 Closing Balance 2500200027502050
To solve, multiply each closing balance by the number of days at that balance, add all of these together and then divide by the total number of days in the billing period.
($2500×10)+($2000×10)+($2750×5)+($2050×6)31≈$2291.94
Answers
The average daily balance of the credit card is 2291.94
What is the average daily balance?
The average daily balance can be determined by dividing the total daily balance of month by numbers of days in month.
We can find average daily balance as shown below:
Average daily balance = total balance of the month/total number of days in the month
Total balance = (2500*10) +(2000*10) +(2750*5) +(2050*6)
= 25000+20000+13750+12300
= 71,050
Number of days = 31
Average daily balance = 71,050/31
= 2291.9354
Round to the nearest cent
= 2291.94
Hence, the average daily balance of the credit card is 2291.94
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For each of the following equivalence relations, describe the corre-
sponding partition. Your description of each partition should have no redundancy,
and should not refer to the name of the relation.
Answers
The description of the corresponding partition is given as follows:
The infinite classes can be defined as:
At equal distance of x from point [1,2]
Where x can vary from o to infinity.
What is a corresponding partition?The analogous partition, commonly known as "the set of equivalence classes," is the set A/R, the elements of which are the subsets of A satisfying the following:
For every a∈A there is some B∈A/R such that a∈B.
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Determine the function f(x)= kx+m if f(x-1)-f(x)=2 and f(-2)=1-m
Answers
[tex]f(x) = kx + m \\ f(x - 1) = k(x - 1) + m[/tex]
[tex]f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2[/tex]
[tex]f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2} [/tex]
[tex]f(x) = - 2x - \frac{3}{2} [/tex]
Following a group of truck drivers and noting the number of miles traveled for one year refers to which type of statistical study?
Answers
Considering that the data is only noted and not changed, this is an example of an observational study.
What are observational and experimental studies?Experimental study: In an experimental study, there is an intervention in a sample, and it's effect is studied.Observational study: In an observational study, the sample is just analyzed, without any intervention.In this problem, the data, which is the number of miles traveled, is only analyzed, no interventions are made, hence this is an example of an observational study.
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that any pair of congruent triangles is similar True or false.
Answers
Answer:
yes it's true no problem sir
Tim Worker is checking his earnings statement. His weekly earnings are $520.00. If he claims two exemptions, how much tax is withheld? 18.73 15.40 17.65 16.48
Answers
The tax that will be withheld is D. $16.48.
How to calculate the tax?From the information, it was stated that Tim Worker is checking his earnings statement and that his weekly earnings are $520.00.
The tax that will be withheld will be:
= 3.16% × $520
= $16.48
In conclusion, the correct option is D.
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Multiply –8m(–6m – 7).
–14m2 – 15m
48m2 + 56m
–14m – 15
48m + 56
Answers
Answer: 48m2 + 56m
Step-by-step explanation:
Answer:
Answer B
Step-by-step explanation:
Shawn averages 10,142 steps every day. If there were 31 days in the month, about how many steps did he take in that month.
Answers
Answer:
314402 steps
Step-by-step explanation:
10142 x 31
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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-275+156-(-293)-157 = 17
ME PUEDEN DAR EL PROCEDIMIENTO
PLIS
Answers
The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation
Evaluation-275+156-(-293)-157 = 17
Using BODMAS
b - bracketo - offd - divisionm - multiplicationa - additions - subtraction-275+156-(-293)-157 = 17
= -275 + 156 + 293 - 157
= 17
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Need help with defining this question.
Answers
Answer: 19
Step-by-step explanation:
[tex]F(5)=5^2 - 2(5)+4=19[/tex]