The first four terms of an arithmetic sequence are given.

27, 32, 37, 42, ...

What is the 60th term of the sequence?

Answer:

a.) 10

b.) -2

c.) 6

d.) y = 6

e.) T = π

f.) y = -6cos(2t) + 4

Step-by-step explanation:

a.) Max value is the highest value in the y-axis. It peaks at y=10

b.) Min value is the lowest value in the y-axis. Peaks at y=-2

c.) Amplitude is how high the peak is from the midpoint. It could be found by taking the average of the peaks. (10 - (-2))/2 = 6

d.) y = 6

e.) T = π

f.) General equation for a sinusoidal wave is

y = Acos(ωt - Ф) + k

y = Acos((2π/T)t - Ф) + k

The graph started at it's min, so the amplitude must had been fliped upsidedown because it normally starts at the max. Therefore I must make my equation negative to flip it.

y = -Acos((2π/T)t - Ф) + k

y = -(6)cos((2π/(π))t - (0)) + (4)

y = -6cos(2t) + 4

Final answer:

The length of the rectangle increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially when the area is increasing at 8 square meters per hour and the width at 0.4 meters per hour.

Explanation:

To find how quickly the length of the rectangle increases, given that the area increases at a rate of 8 square meters per hour and the width increases by 40 centimeters (0.4 meters) per hour, we can use the area formula for a rectangle (Area = length × width). The rate of change of the area with respect to time (ΔA/Δt) can be related to the rates of change of the length and width with respect to time (ΔL/Δt and ΔW/Δt respectively) by the product rule for differentiation if we consider length and width as functions of time.

Initially, the area A is 10m × 7m = 70m². When the area is increasing at 8m²/h and the width is increasing at 0.4m/h, we can write the relation as follows:

ΔA/Δt = ΔL/Δt × W + L × ΔW/Δt

Substituting the given values and solving for the rate of change of the length (ΔL/Δt):

8 = ΔL/Δt × 7 + 10 × 0.4

8 = 7ΔL/Δt + 4

7ΔL/Δt = 4

ΔL/Δt = 4/7 m/h

Therefore, the length increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially.

Answer:

$2925

Step-by-step explanation:

To find the cost, we need to get the area of the triangular sale. This can be obtained by using the area of a triangle.

This is A = 1/2 * b * h

Where in this case, b = 12ft and h = 25ft

The area is thus 1/2 * 12 * 25 = 150sq.ft

Now we know that 1sq.ft is $19.50, 150 will be 150 * 19.5 = $2925

The letter e is used for continuous compound, it is raised by the interest rate times the amount of time.

The formula would be 1200e^0.16t

The answer is C

Answer:

The maximum revenue is $1,20,125 that occurs when the unit price is $155.

Step-by-step explanation:

The revenue function is given as:

[tex]R(p) = -5p^2 + 1550p[/tex]

where p is unit price in dollars.

First, we differentiate R(p) with respect to p, to get,

[tex]\dfrac{d(R(p))}{dp} = \dfrac{d(-5p^2 + 1550p)}{dp} = -10p + 1550[/tex]

Equating the first derivative to zero, we get,

[tex]\dfrac{d(R(p))}{dp} = 0\\\\-10p + 1550 = 0\\\\p = \dfrac{-1550}{-10} = 155[/tex]

Again differentiation R(p), with respect to p, we get,

[tex]\dfrac{d^2(R(p))}{dp^2} = -10[/tex]

At p = 155

[tex]\dfrac{d^2(R(p))}{dp^2} < 0[/tex]

Thus by double derivative test, maxima occurs at p = 155 for R(p).

Thus, maximum revenue occurs when p = $155.

Maximum revenue

[tex]R(155) = -5(155)^2 + 1550(155) = 120125[/tex]

Thus, maximum revenue is $120125 that occurs when the unit price is $155.

Answer:

X = 3/5

Step-by-step explanation:

2/x=4/5x+2

Find the LCM of the denominator 5x and 1

2/x =4/5x + 2/1

2/x = (4 + 10x)/5x

Cross multiply the equation

2× 5x = (4+ 10x) × x

10x = 4x + 10x^2

Collect like term of the mixed number

10x - 4x = 10x^2

6x = 10x^2

Divide both side by 2x

6x/2x = {10x^2 } / 2x

3 = 5x

Divide both side by the coefficient of x

3/5 = 5x/5

X = 3/5

Answer:

break even units for both the cases will be 5

Step-by-step explanation:

Data provided in the question:

For the case 1

Variable cost = $20 each

Selling cost = $50

Rent for the booth fair = $150

Now,

Let break even units be x

At break even

Total cost = Total revenue

Thus,

$20x + $150 = $50x

or

$50x - $20x = $150

or

$30x = $150

or

x = 5

Case 2

Variable cost = $15 per unit

Thus,

At break even

Total cost = Total revenue

Thus,

$15x + $150 = $50x

or

$50x - $15x = $150

or

$35x = $150

or

x = 4.28 ≈ 5

The break even point will still remain the same.

The break-even point is calculated by setting total cost equal to total revenue and solving for the number of units produced and sold (denoted as 'units').

Given the current variable cost per unit ($20), the sale price per unit ($50), and the fixed cost (booth rent - $150), we can set up the equation as follows:

Total Cost = Fixed cost (booth rent) + variable cost per unit * units
Total Revenue = sale price per unit * units

Setting these two equal to each other, we get:

150 + 20*units = 50*units

By rearranging this equation, we find:

units = 150 / (50 - 20)

This calculates out to 5 units. Therefore, Ray needs to sell 5 units to break even with his current costs.

If Ray is able to reduce his variable cost to $15 per unit, we will repeat the same calculation with the new variable cost:

units = 150 / (50 - 15)

This calculates out to approximately 4.29 units. Since Ray cannot sell a fraction of a unit, he would have to sell 5 units to fully cover his costs, but he would begin to make a profit sooner than with his current variable cost. In fact, from the 5th unit sold, part of the revenue would go towards profit. Therefore, with the reduced variable cost, his break-even point would be closer to 4 units, but practically still 5 units.

In conclusion, with his current costs, Ray's break-even point is at 5 units. If he is able to reduce his variable cost to $15 per unit, his break-even point would theoretically be lower at approximately 4.29 units, but practically still would round up to 5 units.

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Answer:

The value of [tex]x=8[/tex].

Step-by-step explanation:

Given:

[tex]\frac{x+3}{x}-\frac{x+1}{x+4}=\frac{5}{x}[/tex]

We need to solve this equation.

Solution:

First combining equation having same denominators we get;

[tex]\frac{x+3}{x}-\frac{5}{x}=\frac{x+1}{x+4}[/tex]

Now denominators are common so we will solve the numerators we get;

[tex]\frac{x+3-5}{x}=\frac{x+1}{x+4}\\\\\frac{x-2}{x}=\frac{x+1}{x+4}[/tex]

Now by cross multiplication we get;

[tex](x-2)(x+4)=x(x+1)[/tex]

Now Applying distributive property we get;

[tex]x^2+4x-2x-8=x^2+x\\\\x^2+2x-8=x^2+x[/tex]

Now Combining the like terms we get;

[tex]x^2+2x-x^2-x=8\\\\x=8[/tex]

Hence on solving we get the value of [tex]x=8[/tex].

Answer:

He drive 1,400 miles last month all together.

So, option B) 1,400 is the correct answer.

Step-by-step explanation:

Given:

Alex has a truck. 42% of the miles he drove last month were for work.

If Alex drove 588 miles for work.

Now, to find miles he drive last month all together.

Let the miles he drive last month all together be [tex]x.[/tex]

42% of the miles he drove last month were for work.

Alex drove 588 miles for work.

Now, to get the miles he drive last month all together we put an equation:

[tex]42\%\ of\ x=588[/tex]

[tex]\frac{42}{100} \times x=588[/tex]

[tex]0.42\times x=588[/tex]

[tex]0.42x=588[/tex]

Dividing both sides by 588 we get:

[tex]x=1400\ miles.[/tex]

Therefore, he drive 1,400 miles last month all together.

So, option B)  1,400 is the correct answer.

Answer:

The answer is 1,400  

Step-by-step explanation: If you do 1,400x42%=588 So the answer is 1400!!!!!

Answer:The number of ounces of cereals left in the box is 3

Step-by-step explanation:

Tina and Joey share a 18-ounce box of cereal. By the end of the week, Tina has eaten 1/6 of the box. This means that the amount of cereal that Tina ate is

1/6 × 18 = 3 ounce

Also, by the end of the week, Joey has eaten 2/ 3 of the box of cereal. This that the amount of cereal that Joey ate is

2/3 × 18 = 12 ounce

The number of ounces of cereals left in the box would be

18 - (12 + 3) = 18 - 15

= 3

Height  of the rock wall is 52.2 ft.

Step-by-step explanation:

These two triangles are similar, so using the similarity ratio, we can write as,

Δ HTV ~ Δ JSV

Now we can write the ratio as,

HT/TV = JS/SV

5.8/4 = x/36

Rearranging the equation to get x as,

x = 36 × 5.8 /4

 = 52.2 ft

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine tan m∠A, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan A = √32/2 = (√16 × √2)/2

Tan A = (4√2)/2

Tan A = 2√2

The value of tan A is in the simplest radical form  [tex]2\sqrt{2}[/tex].

The exact value of tanA in the simplest radical form.

The value of tan A is determined by using the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\[/tex]

Where Perpendicular = [tex]\sqrt{32}[/tex] and Base = 2

Substitute all the values in the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\TanA = \dfrac{\sqrt{32}}{2}\\\\TanA = \dfrac{4}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\TanA = 2\sqrt{2}[/tex]

Hence, The value of tan A is [tex]2\sqrt{2}[/tex].

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Answer:

55 because if u take the 6 and 3 and multiply then subtract 4 and whatever you get that's your answer same with the others

Answer:

1. the answer is x=1/3y+1 y=3x−3

Step-by-step explanation:

Answer:

[tex]m\angle H = 44.4\°[/tex].

Step-by-step explanation:

Given:

In Right Angle Triangle GIH

∠ I = 90°

GI = 7    ....Side opposite to angle H

GH = 10  .... Hypotenuse

To Find:

m∠H = ?

Solution:

In Right Angle Triangle ABC ,Sine Identity,

[tex]sin \ H = \frac{Oppsite\ side\ to\ \angle H}{Hypotenuse}[/tex]

Substituting the values we get;

[tex]sin\ H = \frac{7}{10} = 0.7[/tex]

Now taking [tex]sin^{-1}[/tex] we get;

[tex]\angle H = sin^{-1}\ 0.7 = 44.427[/tex]

rounding to nearest tenth we get.

[tex]m\angle H = 44.4\°[/tex].

Hence [tex]m\angle H = 44.4\°[/tex].

Answer:

MA

Step-by-step explanation:

Answer:

$4300.

Step-by-step explanation:

Let x represent amount of money invested in each account.

We have been given that equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5.        

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex], where,

I = Amount of interest after t years,

P = Principal amount,

r = Annual interest rate.

Since principal for each amount is equal and time is equal to 1 year, so we can represent our given information in an equation as:

[tex]1225.5=x(0.07+0.09+0.125)(1)[/tex]

[tex]1225.5=x(0.285)[/tex]

[tex]x=\frac{1225.5}{0.285}[/tex]

[tex]x=4300[/tex]

Therefore, an amount of $4300 is invested in each account.

Final answer:

The amount invested in each of the three accounts with different interest rates, which together yield a total interest income of $1,225.5, is $4,300 in each account.

Explanation:

To solve for the amount invested in each account, we need to set up an equation that represents the total interest income from the accounts.

Letting x represent the amount invested in each account, we can say that the interest from the first account at 7% is 0.07x, the second account at 9% is 0.09x, and the third account at 12.5% is 0.125x. The total interest income is the sum of these individual interests, which equals $1,225.5. Hence, the equation to solve is:

0.07x + 0.09x + 0.125x = 1,225.5

Combining like terms gives:

0.285x = 1,225.5

Dividing both sides by 0.285 gives us:

x = 1,225.5 / 0.285

x = 4,300

Therefore, the amount invested in each account is $4,300.

Answer:

y=1/3x-1

Step-by-step explanation:

A(0,-1)=(x1,y1) x1=0,y1=-1

B(3,0)=(x2,y2) x2=3, y2=0

m=(y2-y1)/(x2-x1)

m=(0-(-1))/(3-0)

m=1/3

y-y1=m(x-x1)

y-(-1)=1/3(x-0)

y+1=1/3*x

y=1/3*x-1

Answer:

Use math in healthcare career: In healthcare career one must translate medication orders into the right doses and number of pills to administer.

Step-by-step explanation:

Consider the provided information.

Math in healthcare career play significant role one should must know the units of the measurement for temperature, blood pressure, pulse rate, breathing rate etc.

In healthcare career one must translate medication orders into the right doses and number of pills to administer.

For example, If a doctor recommends a 100 gram of a drug every 6 hours and the hospital has 50 milligram pills, then you need to give two pills every 6 hours. Because 50 milligram times 2 is 100 milligram.

Math is vital in a healthcare career for tasks such as dosage calculations, interpreting vital signs, and handling medical billing. Proper math skills ensure accuracy and safety. Mastery in math will enhance your ability to provide effective patient care.

You asked how you will use math in your healthcare career. Math is essential in healthcare for various day-to-day operations. Here are some specific examples:

In conclusion, math is a vital skill in the healthcare field. Its applications range from dosage calculations to interpreting vital signs, and even handling billing. Mastery of math in your healthcare career will enable you to provide safe and effective patient care.

The measure of the angle R is [tex]m \angle R=69.4[/tex]

Explanation:

It is given that the lengths of the triangle are PQ = 8 and QR = 3

To find the angle of R using the opposite and adjacent side, we shall use the tangent formula.

[tex]\tan \theta=\frac{o p p}{a d j}[/tex]

where opp = 8 and adj = 3

Thus, substituting these values in the formula, we get,

[tex]\tan \theta=\frac{8}{3}[/tex]

Multiplying both sides by [tex]tan^{-1}[/tex], we get,

[tex]\theta=tan^{-1} (\frac{8}{3})[/tex]

Dividing, we get,

[tex]\theta=69.44[/tex]

Rounding off to the nearest tenth, we have,

[tex]\theta=69.4[/tex]

Thus, the measure of the angle R is [tex]m \angle R=69.4[/tex]

Answer:

{x| x∈R, x > -2}

Step-by-step explanation:

You solve the inequality just like you would solve an equality.

Everything that has the x on the left side, everything without x on the right side.

Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than

So

[tex]10 < x + 12[/tex]

[tex]-x < 12 - 10[/tex]

[tex]-x < 2[/tex]

Multiplying by -1

[tex]x > -2[/tex]

So the correct answer is:

{x| x∈R, x > -2}

{x| x∈R, x > -2}

Step-by-step explanation:

You solve the inequality just like you would solve an equality.

Everything that has the x on the left side, everything without x on the right side.

Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than

So

Multiplying by -1

So the correct answer is:

{x| x∈R, x > -2}

Answer / Step-by-step explanation:

Given the statement:

∃x∈D,(P(x)∧Q(x)) and (∃x∈D,P(x))∧(∃x∈D,Q(x)) ,

Then,

(a), The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement.

That is:

(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y))

Where  

(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y)) implies that P(x) is true for some element x in D and Q(y) is true for some element y in D. However, x and y are not necessary the same element and thus, we cannot be sure that  

P(x) ∧ Q(x) or P(y) ∧ Q(y) is true.

Moreover, if P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y,

Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement  

∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.

(b)

If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y, then Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement  

∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.

So in summary, we can say for:

(a) the statement does not contain the same truth value.

(b) The statement depicts there is such a choice in the first place.

In this exercise we have to use the knowledge of sets to identify which of the statements is true and false, thus we can state that:

A) the statement does not contain the same truth value.

B) The statement depicts there is such a choice in the first place.

Then, the first statement says that:

A)The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement. That is:

[tex](\exists \ x \in D,P(x)) \wedge ( \exists \ x\in D,Q(x)) = (\exists \ x \in D,P(x)) \wedge (\exists \ y \in D,Q(y))[/tex]

Where the equation above implies that P(x) is true for some element x in D and Q(y) is true for some element y in D.

However, x and y are not necessary the same element and thus, we cannot be sure that   is true.

If P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x)[/tex] is false and [tex]P(y) \wedge Q(y)[/tex] is also false.  

B) If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x) \ or \ P(y) \wedge Q(y)[/tex] is also false.

Moreover, there is no other known element (z) such that is true and thus the statement.

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Answer:

Step-by-step explanation:

(24.50+11 d)*(107/100)=108.61

24.50×107+1177 d=10861

1177 d=10861-24.50×107

=10861-2621.50

=8239.50

d≈7 days

Final answer:

The equation that can be used to determine the number of days d the car was rented is: $108.61 = $24.50 + ($11 * Number of days). By solving this equation, we find that the car was rented for 7 days.

Explanation:

To determine the number of days the car was rented, we can use the equation:

Total cost = Cost of renting a car + (Cost per day * Number of days)

In this case, the cost of renting a car is $24.50 and the cost per day is $11. The sales tax is 7%.

The equation becomes:

$108.61 = $24.50 + ($11 * Number of days)

Now, we can solve for the number of days:

Subtract $24.50 from both sides of the equation: $108.61 - $24.50 = $11 * Number of days

Calculate the difference: $84.11 = $11 * Number of days

Divide both sides of the equation by $11: Number of days = $84.11 / $11

Round the result to the nearest whole number: Number of days = 7

Answer:

The solution is (5, −2)

Step-by-step explanation :

x + y = 3 => y = 3 - x

                  y = x - 7  } =>

=> 3 - x = x - 7 => 3 + 7 = x + x => 2x = 10 => x = 5

x + y = 3

5 + y = 3

y = 3 - 5

y = - 2

Answer:

I feel bad for you I really would like to help you but I haven't even learn that stuff yet

The solution is in the attachment

The height of the rose after 10 weeks was approximately 7.714 inches. This is calculated by multiplying the original height of the rose (5.8 inches) by 1 1/3 (converted to a decimal as 1.33).

The subject of this question is Mathematics, and it involves performing multiplication to find the height of the rose after 10 weeks. Given that the height of the rose was 5.8 inches originally, and after 10 weeks, the height was 1 1/3 times the original height, we can calculate the new height as follows:

So, 5.8 inches * 1.33 = 7.714 inches.

Therefore, the height of the rose after 10 weeks was approximately 7.714 inches.

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Question refers to below content.

Three gallons of paint are used to paint 16 wooden signs. How many wooden signs can be painted with one gallon of paint?? Between what two whole numbers does the number lie?

Answer:

[tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.

The answer lies between number 5 and 6.

Step-by-step explanation:

Given:

Amount of paint = 3 gallons

Number of wooden signs = 16

We need to find the Number of wooden signs can be painted with 1 gallon of paint.

Solution:

Now we know that;

3 gallons of paint = 16 wooden signs painted

1 gallon of paint =  Number of wooden signs can be painted with 1 gallon of paint.

By using Unitary method we get;

Number of wooden signs can be painted with 1 gallon of paint = [tex]\frac{16}{3} \ \ Or \ \ 5 \frac{1}{3}[/tex]

Hence [tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.

Now we can say that;

[tex]5 \frac{1}{3}[/tex]  lies between 5 and 6.

Hence The answer lies between number 5 and 6.

Answer:

Step-by-step explanation:

7,300 = 5,500 + 300x

7,300 - 5,500 = 300x

1,800 = 300x

x = 6

Answer:

greater than or equal to 6

Step-by-step explanation:

i just took the plato test

Answer:

66500

Step-by-step explanation:

114000:total budget

12:total bungalows

9500:budget for each bungalow

7: unfinished bungalows

66500: remaining budget for unfinished bungalows

hope this helped and good luck :D

The remaining budget for unfinished bungalows is $66500

The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')

Given that, A total of $114,000 will be evenly spent to build 12 Bungalows, the first 5 bungalows have been completed and paid. We need to find the amount available for the remaining bungalows.

Amount used in each bungalow;

114000/12 = $9500

Therefore, each bungalow will need $9500

Amount used = $9500 × 5 = $47500

Amount remaining for remaining bungalows = $114,000 - $47500 = $66500

Hence, $66500 is remaining budget for unfinished bungalows.

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Answer: the number of slices that each person will get is 4 4/9

Step-by-step explanation:

Antonio ordered 5 large pizzas, which have a total of 40 slices.

He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, it means that the pizza would be divided among 9 people(Antonio and 8 friends = 9 people).

The number of slices that each of them will get would be

40/9 = 4 4/9 slices

Answer:

179.2km

Step-by-step explanation:

The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.

This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km

Hence, each adult in the family drove a distance of 179.2km