In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°. Find the area of ΔRST, to the nearest square inch

Answer:

Distance rode = 6 miles

Step-by-step explanation:

distance from home = 2 miles

remaining distance =  4 miles

The distance rode = 4 + 2 = 6 miles

9514 1404 393

Answer:

Step-by-step explanation:

a) The 36000 -23000 = 13000 difference in salary is being made up at the rate of 3000 -2000 = 1000 per year. It will take 13000/1000 = 13 years for the salaries to be the same.

__

b) After 13 years, the salary will be ...

  23000 +13(3000) = 23000 +39000 = 62,000 . . . dollars

  36000 +13(2000) = 36000 +26000 = 62,000 . . . dollars

Answer:

after the first company, her salary would be 48000 in 5 years

after the second company, her salary would be 48000 in 4 years

Step-by-step explanation:

The hexadecimal system numbering system is base 16; in other words, 16 numerals are used to express any given number.

In this system, 16 numerals are used to represent any given number. The numerals used in this system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, where A represents 10, B represents 11, and so on, up to F, which represents 15.

This system is commonly used in computer science, as it is more compact than the decimal system, and allows for easier conversion between binary and decimal systems. In the hexadecimal system, each digit represents a power of 16, just as each digit in the decimal system represents a power of 10.

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Answer:

\(\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution : \:-10x + 42}}}}}}}}\)

Step-by-step explanation:

\(\sf{-3(2x + 1) - 4x + 45}\\\\\sf{Multiply \: the \: numbers : -3(2x + 1)}\\\\\sf{=( -3 * 2x) +( -3*1 )- 4x + 45}\\\sf{= -6x - 3 - 4x + 45}\\\\\sf{Rearrange \: the \: terms \: and \: do \: the \: operations} \\\\\sf{= -6x - 4x - 3 + 45}\\=\large{\boxed{\tt{ -10x + 42}}}\\\)

_______

Hope it helps!

\(\mathfrak{Lucazz}\)

a.) Suppose you have 500 feet of fencing to enclose a rectangular plot of land that borders on a river. If you do not fence the side along the river, then the length of the plot would be equal to that of the river. Suppose the length of the rectangular plot is x and the width is y.

So, the fencing required would be 2x + y = 500. y = 500 − 2x. The area of the rectangular plot would be xy.

Substitute y = 500 − 2x into the equation for the area.

A = x(500 − 2x) = 500x − 2x²

Now, differentiate the above equation with respect to x.

A = 500x − 2x²

dA/dx = 500 − 4x

Set dA/dx = 0 to get the value of x.500 − 4x = 0or, 500 = 4x

So, x = 125

Substitute x = 125 into y = 500 − 2x to get the value of y.y = 500 − 2x = 250 ft

The maximum area is A = xy = 125 × 250 = 31,250 sq. ft.

b.) Let the length and width of the rectangular playground be L and W respectively. Then, the perimeter of the playground is L + 3W. Given that 900 feet of fencing is used, we have:

L + 3W = 900 => L = 900 − 3W

Area = A = LW = (900 − 3W)W = 900W − 3W²

dA/dW = 900 − 6W = 0W = 150

Substitute the value of W into L = 900 − 3W to get:

L = 900 − 3(150) = 450 feet

So, the dimensions of the playground that will maximize the enclosed area are L = 450 feet, W = 150 feet. The maximum area is A = LW = 450 × 150 = 67,500 square feet.c.)

Let x be the number of $1 increments. Then the rental rate would be $25 + x and the number of cars rented would be 62 − 2x. Hence, the revenue would be (25 + x)(62 − 2x) = 1550 − 38x − 2x²

Differentiating with respect to x, we get dR/dx = −38 − 4x = 0or, x = −9.5. This value of x is not meaningful as rental rates cannot be negative. Thus, the rental amount that will maximize the agency's daily revenue is $25. The maximum daily revenue is R = (25)(62) = $1550.

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According to the information we can conclude that the maximum area for the plot is 15,625 square feet (part a). Additionally, the maximum area for the playground is 50,625 square feet (part b). Finally the maximum daily revenue is $975 (part c).

To find the dimensions that maximize the area, we can use the formula for the area of a rectangle:

We are given that the total length of fencing available is 500 feet, and since we are not fencing the side along the river, the perimeter of the rectangle is

Solving for L, we have

Substituting this into the area formula, we get

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 125 feet, and the length is also 125 feet. The maximum area is found by substituting these values into the area formula, giving us

Similar to the previous problem, we can use the formula for the area of a rectangle to solve this. Let the width of the playground be w, and the length be L. We have

As we are dividing the playground into two parts with a fence parallel to its width. Solving for L, we get

Substituting this into the area formula, we have

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 225 feet, and the length is also 225 feet. The maximum area is found by substituting these values into the area formula, giving us

Let x be the rental rate in dollars. The number of cars rented can be expressed as

Since for each $1 increase in rate, two fewer cars are rented. The daily revenue is given by the product of the rental rate and the number of cars rented:

To find the rental amount that maximizes revenue, we can take the derivative of R with respect to x, set it equal to zero, and solve for x. The resulting rental rate is $22. Substituting this into the revenue formula, we find the maximum daily revenue to be

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Answer:

d

Step-by-step explanation:

Answer: x = -2

Step-by-step explanation:

-6x = 5x + 22

-11x = 22

x = -2

The number of students in the school given the number of people that attended the dance is 128.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

Number of students = number of students at the dance / percentage that attended the dance

32 / 25%

32 / 0.25 = 128

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\( \sqrt{25} = 5 \\ \sqrt{16 } = 4 \\ \sqrt{49} = 7\)

5+4-7 = 9-7 = 2

Our Answer 2

Answer:

The answer is 2

Step-by-step explanation:

√25 = 5

√16 = 4

√49 = 7

Now,

√25 + √16 - √49

5 + 4 - 7

9 - 7 = 2

Thus, The answer is 2

-TheUnknownScientist

Step-by-step explanation:

*change density to kg per cubic meter

*change volume to cubic meter

*rearrange the formula to solve for mass

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

A pentagonal prism is a prism with five rectangular sides and two top and bottom pentagonal bases. With 7 faces, 10 vertices, and 15 edges, it is a particular form of heptahedron. A pentagonal prism can have five sides due to its pentagonal bases. The pentagonal prism is also called Five-sided polygon prism in other name.

The pentagonal prism is a prism with five rectangular sides and two pentagonal base

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Answer:

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

Step-by-step explanation:

hope this helped!

The percent change in River depth is 4%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this situation, in 1846 the depth of the River was 5 feet deep. In 1847 it dropped to 3.1 feet. This year, 1848 it rose to 5.2 feet.

The percentage change from 1846 to 1848 will be:

= (5.2 - 5) / 5 × 100

= 0.2/5 × 100

= 4%

The percentage is 4%.

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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The point is on second quadrant.

P(x, y) is on the unit circle

radius of the circle must be 1

The equation x² + y² = r²

\(y=\frac{2}{3}\), r =1

\(x^{2} (\frac{2}{3}) ^{2}= 1^{2}\)

\(x^{2} +\frac{4}{9} =1\)

\(x^{2} =1-\frac{4}{9}\)

\(x^{2} =\frac{5}{9}\)

\(x=\sqrt{\frac{5}{9} }\)

x = ±\(\sqrt{\frac{5}{9} }\)

x- c00rdinate is negative = - \(\sqrt{\frac{5}{9} }\)

P(x, y) = \((-\sqrt{\frac{5}{9} }, \frac{2}{3})\)

Therefore, the point is on second quadrant.

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Answer:

125.

Given:

Step-by-step explanation:

As given in the question that the ratio is already given,

therefore,

1. The ratio of tourist of to locals

the ratio of tourist to local is 4:5

\(\frac{tourist}{locals}\)=\(\frac{4}{5}\)

2. Attendance of locals at the opening

here are 100 tourist at the opening

\(\frac{100}{locals} =\frac{4}{5}\)

locals= 125

locals are 125 in attendance.

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125 is the attendance of locals

The ratio of tourists to locals is 4:5

Tourists / Locals = 4 / 5

There are 100 tourists at the opening of the new museum

100 / locals = 4/5

locals = 500/4

locals = 125

The attendance of locals is 125.

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0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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Step-by-step explanation:

I hope this helps..........

The entry required to account for the change in office supplies would depend on the accounting method used. Assuming the company follows the periodic inventory system, where office supplies are expensed as they are used, the entry would be as follows:

At the beginning of the period:

Debit: Office Supplies Expense - $4,000

Credit: Office Supplies - $4,000

At the end of the period:

Debit: Office Supplies - $3,900

Credit: Office Supplies Expense - $3,900

Explanation:

1. At the beginning of the period, the company records the office supplies as an asset (Office Supplies) and recognizes an expense (Office Supplies Expense) for the same amount. This reduces the value of the asset and reflects the cost of supplies used during the period.

2. At the end of the period, when it is determined that $3,900 worth of supplies remains, the company adjusts the office supplies account by reducing it by the remaining amount. This adjustment is necessary to reflect the correct value of supplies on hand at the end of the period.

The entry ensures that the net effect of the transactions is an expense of $100 ($4,000 - $3,900), which represents the cost of supplies consumed during the period.

The value we can use in the series is \($\sum_{k=0}^\infty 1/k^8\).

To check the convergence we consider two series as

Series 1: \($\sum_{k=0}^\infty \frac{k^8}{5(3-6k+3k^6)^2}$\)

Series 2: \($\sum_{k=0}^\infty \frac{k^8 + k^3 + 4k}{5(3-6k+3k^6)^2}$\)

We employ the p-test, which indicates that the series converges if the ratio of succeeding entries in a series approaches a number less than 1. The ratio of successive terms for Series 1 approaches 1, indicating that Series 1 diverges.

We can infer that Series 2 also diverges because Series 1, which is smaller than Series 2, likewise diverges.

Thus, the given series also diverges.

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Answer:

9c

Step-by-step explanation:

16+25=41

50-41=9

fnfnx

Domain of the radical function of the form f(x) = √(ax + b) + c is given by the solution of the inequality ax + b ≥ 0 and the range is the all possible values obtained by substituting the domain values in the function.

We know that the general form of a radical function is,

f(x) = √(ax + b) + c

The domain is the possible values of x for which the function f(x) is defined.

And in the other hand the range of the function is all possible values of the functions.

Here for radical function the function is defined in real field if and only if the polynomial under radical component is positive or equal to 0. Because if this is less than 0 then the radical component of the function gives a complex quantity.

ax + b ≥ 0

x ≥ - b/a

So the domain of the function is all possible real numbers which are greater than -b/a.

And range is the values which we can obtain by putting the domain values.

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Answer:80.029

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Isolate M

Divide -5

Answer:

a

Step-by-step explanation:

Answer:

y=-1/3x-1 I believe

Step-by-step explanation:

The Y intercept is where the line meets the Y line, which crosses at -1 and for slope, find a point and do rise/run. This question goes down 1 and to the right 3 so -1/3

Answer:

20,000×17 gives 340,000

340,000×68 which gives 23,120,000

Answer:

\( -2 \: \: 4\)

Step-by-step explanation:

-2 4 is not an equivalent equation

Answer:

c

Step-by-step explanation:

duh

The value of l such that the rectangle and trapezium have the same area will be 18 feet.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

The perimeter of the rectangle = 2( length + width).

As per the given,

Area of rectangle = area of a trapezoid

9 x l = (1/2)(24 + 12)9

9l = 162

l = 18 feet

Hence "The amount of l that must be present for the rectangle and trapezium to share the same area is 18 feet.".

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