The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below.

Alternative Text

Part A
What are the actual dimensions of the pool? Enter your answers in the boxes.

Blueprint: 10 in. Actual:

ft

Blueprint: 20 in. Actual:
ft


Part B
How much would it cost to buy a cover for the pool that costs $0.30 per square foot? Enter your answer in the box.

It will take 1.7 hours (or 1 hour and 42 minutes) for the park keepers to complete both pruning and weeding.

What is expression ?

Expressions can be used to represent mathematical operations or relationships, such as addition, subtraction, multiplication, division, and exponentiation. They can also be used to represent algebraic equations, inequalities, and functions.

Let's first find the rate at which each activity is completed.

For weeding:

2 park keepers can weed 2 flowerbeds in 1 hour, which means they can weed 1 flowerbed in 1/2 hour (or 0.5 hours)

Therefore, each park keeper can weed 1 flowerbed in 1 hour

For pruning:

3 park keepers can prune 6 trees in 2 hours, which means they can prune 1 tree in 1/3 hour (or 0.33 hours)

Therefore, each park keeper can prune 2 trees in 1 hour

Now, let's see how much work can be done in 1 hour with 5 park keepers:

They can weed 5 flowerbeds (since each park keeper can weed 1 flowerbed in 1 hour)

They can prune 10 trees (since each park keeper can prune 2 trees in 1 hour)

Since there are 13 trees to prune, it will take 1.3 hours (13 trees / 10 trees per hour = 1.3 hours) to complete the pruning.

After the pruning is done, there are still 2 flowerbeds to weed. Since 5 park keepers can weed 5 flowerbeds in 1 hour, it will take 0.4 hours (2 flowerbeds / 5 flowerbeds per hour = 0.4 hours) to complete the weeding.

Therefore, the total time to complete both activities is:

1.3 hours (pruning) + 0.4 hours (weeding) = 1.7 hours

Therefore, it will take 1.7 hours (or 1 hour and 42 minutes) for the park keepers to complete both pruning and weeding.

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The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.

To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.

The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:

Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...

Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:

First, we find the values of the function and its derivatives at x = 0:

f(0) = sin(0) = 0

f'(x) = cos(x), so f'(0) = cos(0) = 1

f''(x) = -sin(x), so f''(0) = -sin(0) = 0

f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1

Using these values, we can write the Maclaurin polynomial:

P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!

Simplifying further, we have:

P3(x) = x - (x^3) / 6.

Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:

P3(x) = x - (x^3) / 6.

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The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

The cost of orange juice is $3 per jug

Step-by-step explanation:

A unit rate is a rate where the second quantity is one unit.

Answer:$6 x the number of hours he works + $7.50 times the number of hours he works has to be less than or equal to (≤) 15 hours. The number of hours he works has to be more than or equal (≥) to $75. Great job choosing the correct answer!

Step-by-step explanation:

Answer:

  1

Step-by-step explanation:

The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.

  343 = 7·7·7 = 7³

The value of k is the power of 7 in the factorization of 343, so we have ...

  k = 3

and ...

  343/7³ = 1

The remainder when this ratio is divided by 7 is ...

  1 mod 7 = 1

The remainder when 343/7^k is divided by 7 is 1.

Answer: The radius is about 50.2 m.

Step-by-step explanation: The formula to find the circumference of a circle is 2\(\pi\)r. We know the radius is 8 and that you need to use 3.14 as pi so: 2×3.14×8 = 50.2

Answer:

50.24

Step-by-step explanation:

circumference of a circle formula :\(\pi\)D

D=diameter

radius x 2 =diameter

8 x 2 =16

16x\(\pi\)=50.24

have a nice day!!

Answer:

Image result for what event started the 100 years war

The Hundred Years' War was fought between France and England during the late Middle Ages. It lasted 116 years from 1337 to 1453. The war started because Charles IV of France died in 1328 without an immediate male heir

Step-by-step explanation:

So it would be C

Answer:

Philip VI took English land

Step-by-step explanation:

"By convention, the Hundred Years' War is said to have started on May 24, 1337, with the confiscation of the English-held duchy of Guyenne by French King Philip VI." - Encyclopedia Britannica

Answer:

$39.36

Step-by-step explanation:

Since its 20% off that means we still have a remaining 80% so first multiply 0.8 to the 82

82x0.8= 65.6

Since there is a additional 40% off multiply by 0.4 to get the discount amount

65.6x0.4= 26.24

Subtract the discount from the price

65.6-26.24= 39.36

Answer:

20 square units

Step-by-step explanation:

this shape contains a 4 x 4 square and 8 triangles

.

area if the square = 16

.

area of the triangles= (1 x 1 / 2) x 8 = 4

.

total, 16 + 4 =20

Answer:

45⁰

according to question the answers is given here in the image / attachment . please follow these steps.

this is my attachment answer hope it's helpful to you

Answer:

2

Step-by-step explanation:

When give two points, we can use the slope formula

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

    = ( 4- -2)/(4-1)

    = ( 4+2)/(4-1)

    = 6/3

     = 2

Answer:

2

Step-by-step explanation:

When give two points, we can use the slope formula

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

    = ( 4- -2)/(4-1)

    = ( 4+2)/(4-1)

    = 6/3

     = 2

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

d/dt[u(t)·v(t)] = u(t)·v′(t) + v(t)·u′(t) is the derivative rule for the function and ddt(u⋅v)|t=0 = 11 is the evaluated value.

Let's use the Product Rule to differentiate u(t)·v(t), d/dt[u(t)·v(t)] = u(t)·v′(t) + v(t)·u′(t).

Using the Product Rule,

d/dt[u(t)·v(t)] = u(t)·v′(t) + v(t)·u′(t)

ddt(u⋅v) = u⋅v′ + v⋅u′

Given that u and v are differentiable functions at t=0 with u(0)=⟨0,1,1⟩, u′(0)=⟨0,7,1⟩, v(0)=⟨0,1,1⟩,

and v′(0)=⟨1,1,2⟩, we have

u(0)⋅v(0) = ⟨0,1,1⟩⋅⟨0,1,1⟩

=> 0 + 1 + 1 = 2

u′(0) = ⟨0,7,1⟩

v′(0) = ⟨1,1,2⟩

Therefore,

u(0)·v′(0) = ⟨0,1,1⟩·⟨1,1,2⟩

= 0 + 1 + 2 = 3

v(0)·u′(0) = ⟨0,1,1⟩·⟨0,7,1⟩

= 0 + 7 + 1 = 8

So, ddt(u⋅v)|t=0

= u(0)⋅v′(0) + v(0)⋅u′(0)

= 3 + 8 = 11

Hence, d/dt[u(t)·v(t)] = u(t)·v′(t) + v(t)·u′(t) is the derivative rule for the function and ddt(u⋅v)|t=0 = 11 is the evaluated value.

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The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer:

eef the points thanks man

thanks

Step-by-step explanation:

Answer:

Answer:

eef the points thanks man

thanks

Step-by-step explanation:

Step-by-step explanation:

Answer:

I do it for the point haha

Step-by-step explanation:

you silly elf he

Answer:

A rectangle is a good, simple shape to begin with. The area of a rectangle is equal to the product of the length of its base and the length of its height. The height is a segment that is perpendicular to the base. For a rectangle, the base and height are often called the "length" and the "width", and sometimes the height is referred to as the "altitude."

Step-by-step explanation

Mark me as brainiest

Answer:

B

Step-by-step explanation:

$500 a week x 50 weeks in a year = $25,000 a year

$27,500 > $25,000

HOPE THIS HELPED

Answer:  \(\bold{G(t)=356e^{-0.59413t}}\)

Step-by-step explanation:

Use the decay formula: \(P=P_oe^{kt}\)   where

Given: P = 44.5, P₀ = 356, k = unknown, t = 210 minutes (3.5 hours)

\(44.5=356e^{k(3.5)}\\\\\\\dfrac{44.5}{356}=e^{3.5k}\\\\\\0.125=e^{3.5k}\\\\\\ln(0.125)=3.5k\\\\\\\dfrac{ln(0.125)}{3.5}=k\\\\\\-0.59413=k\)

Input P₀ = 356 and k = -0.59413 into the decay formula

              \(\large\boxed{P=356e^{-0.59413t}}\)

Answer:

(-10, 6)

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Answer:

1.83

Step-by-step explanation:

1.78 + 5 cm

because it says she is taller so you add both

Height of Amy who is 5 cm taller than Jack is 1.83 meters.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Jack is 1.78 m tall and Amy is 5 cm taller than Jack.

Therefore, The sum of the height of Jack and 5 cm more is the height of

Amy.

Therefore,

178 cm + 5 cm = 183 cm is the height of Amy. (1m = 100 cm)

So, 183 cm is equal to 1,83 meters.

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The lengths of the sides of the rectangles are;

a. (2•x + 3) and (x + 2)

b. (6•x + 2) and (x + 1)

c. (x + (2 + √3)) and (x + (2-√3))

The given functions are presented as follows;

a. 2•x² + 7•x + 6

By factoring of the above function we have;

2•x² + 7•x + 6 = (2•x + 3) × (x + 2)

The lengths of the sides of the rectangle are therefore;

b. 6•x² + 7•x + 2

The above function can be factored as follows;

6•x² + 7•x + 2 = (6•x + 2) × (x + 1)

The rectangle side lengths are;

c. x² + 4•x + 1

Using the quadratic formula, the above function can be factored to give;

x² + 4•x + 1 = (x + (2 + √3)) × (x + (2-√3))

The sides of the rectangle are therefore;

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Answer:

We know that:

Also:

We are given:

Compare the values of PQ

Proved

Answer:

8

Step-by-step explanation:

4 x 2.

Answer:

still need it?..........

If a team at a factory collected data on the number of nonconforming parts to construct an np-chart then the average fraction has been mentioned below.

The term "average" refers to the mean or centre tendency of a group of data. In other words, it serves as a gauge for the average or median value among a group of numbers. This may be computed by adding up all of the set's values and dividing the result by the total number of values. As an illustration, the average would be (1 + 2 + 3 + 4 + 5) / 5 = 3  if given numbers were 1, 2, 3, 4, and 5.

Average fraction may also be used to represent the expected value or usual outcome of a random variable. For example, if we flip a coin and assign a value of 1 to heads and a value of 0 to tails, the average of the potential outcomes.

How to solve?

= 0.2 and the standard deviation was s = 0.1.

Based on this information, the team can construct an np-chart to monitor the process and identify any potential issues.

The np-chart plots the number of nonconforming parts in each sample against the sample number.

The average fraction nonconforming (p) is indicated by a horizontal line on the chart, and any points that fall outside the upper and lower control limits, which are determined by the standard deviation (s), are considered to be out of control and require further investigation.

This allows the team to monitor the process and take corrective action if necessary to ensure that the number of nonconforming parts remains within acceptable limits.

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Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

To solve the system of equations by elimination, we'll need to eliminate one of the variables.

\(Here's how to solve each system of equations:6x + 5y = 46x − 7y = −20\)

To eliminate x, we will multiply the first equation by 7 and the second equation by 6.

\(This gives us:42x + 35y = 28636x − 42y = −120\)

\(Now we will add the two equations together:78y = 166y = 166/78y = 83/39\)

Now we will substitute the value of y into one of the original equations to find x.

\(We'll use the first equation:6x + 5y = 46x + 5(83/39) = 46x = (234/39) - (415/39)6x = -181/39x = (-181/39) ÷ 6x = -181/234\)

\(Therefore, the solution of the system of equations is x = -181/234, y = 83/39(x+2)² + (y-2)² = 1y = - (x+2)² + 3\)

To solve this system of equations, we will substitute y in the first equation by the right-hand side of the second equation.

\(This gives us:(x+2)² + (- (x+2)² + 3 - 2)² = 1(x+2)² + (-(x+2)² + 1)² = 1(x+2)² + (x+1)² = 1x² + 4x + 4 + x² + 2x + 1 = 1 2x² + 6x + 4 = 0 x² + 3x + 2 = 0  (Divide by 2) (x+2)(x+1) = 0x = -1, x = -2.\)

\(We will now use the second equation to find the values of y:y = -(x+2)² + 3When x = -1: y = -(-1+2)² + 3 = -1When x = -2: y = -(-2+2)² + 3 = 3\)

Therefore, the solutions of the system of values are (-1, -1) and (-2, 3).

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