Carry your intermediate computations
to at least four decimal places, and round your answer to at least one decimal place.

The peripheral angle above the arc would be:

160 / 2 = 80 degrees.

The peripheral angle above a circular arc is equal to the central angle subtended by the arc divided by 2.

The central angle of a circle is 360 degrees, so if the arc represents 4/9 of the circle, the central angle subtended by the arc would be:

360 * (4/9) = 160 degrees

The peripheral angle above the arc would be:

160 / 2 = 80 degrees.

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The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: Ramon's path passes through the co-ordinates  (2,1)

and (0,−2) while Malika's passes through  (0,3)

and (−2,0)

Thus using the two point of a line to construct the linear equations we get

Ramona's path is y=1.5x−2

Malika's path is y=1.5x+3

Now solving for the two equations we get

1.5x-2=1.5x+3

-2=3 which is not  possible

Hence, The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.

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Step-by-step explanation:

n + (n+1) + (n+2) = 417

3n + 3 = 417

3n = 414

n = 138

so, the 3 integers are

138, 139, 140

Answer:

138

Step-by-step explanation:

n,n+1,n+2

so 3n+3=417

3n=414

n=138

The number that probably is an irrational number is 1.6490221...

An irrational number is a number that cannot be expressed as a finite decimal or a fraction.

The number 0 is not irrational.

The number 1.6490221... is an example of a decimal that goes on forever, which is the characteristic of an irrational number.

The number 3/4 can be expressed as a fraction and is therefore not irrational.

The number -5 is not irrational.

Therefore, the answer is 1.6490221..., which is probably an irrational number.

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Step-by-step explanation:

The original price was 150 / (1 - 0.75) = $600.

The height of the pumpkin is 5.7 m.

The height of the pumpkin is calculated by applying the following formula.

y = -0.1x² + 4.9x

where;

y = 0.9x

Now, our new equation becomes;

0.9x = -0.1x² + 4.9x

re-arrange the equation, and solve for x

0.1x² = 4.9x - 0.9x

0.1x² = 4

x² = 4 / 0.1

x² = 40

x = √ ( 40 )

x = 6.32

The height of the pumpkin = 0.9x = 0.9 x 6.32 = 5.7 m

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Answer:

1.9 percent

Step-by-step explanation:

95 boys + 64 girls = 159 total honor roll students

To quickly find percentages of numbers, think of the current number as 100%, or 1.00. Then, go from there to find the number to multiply to get the percentage you need.

For example, a 25% decrease in the number of girls means the new number will be 75% of the old number, so we multiply the number of girls by 0.75 to get the new number of girls. 64*0.75 = 48.

Same with the boys, 95 boys is 100%, but this year the number increased by 20%, so we need to find 120% of the number, so we multiply it by 1.20. 95*1.20 = 114

To answer this question, we need to know by what percent the total number of honor students increased by, so we need to know the new total number. 48+114 = 162

To find out what percent 162 is out of 159, we divide them. 162 / 159 = 1.0188, or 101.9 percent if you round to the nearest tenth. So, the number of students increased by 1.9%.

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The equation to model the situation will be written as y = 14 × (0.58)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

Assume an exponential function has a starting value of 14 and a decay rate of 42%. Then the equation is given as,

y = 14 × (1 - 0.42)ˣ

y = 14 × (0.58)ˣ

The equation to model the situation will be written as y = 14 × (0.58)ˣ.

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Answer:

It's the second one because -3x3-5 equals -14

The approximate lateral area of the cone is equal to 200.96 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

16π = πr²

Radius, r = √16

Radius, r = 4 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 4 × 16

Lateral surface area of a cone, LSA = 200.96 cm².

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Answer:

201 beause you are rounding to the nearest whole number

Step-by-step explanation:

The measure of x use Pythagorean Theorem

1. x= 15

Th Pythagorean theorem only applies to right triangles. This is the same as explained in the Pythagorean Theorem Module which states that for each right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other side or the sides of the right angle.

Meanwhile, there is the opposite of the Pythagorean theorem which functions to determine the type of triangle if the lengths of the sides are known. The types of triangles include:

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if the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.

It can be seen that the sale volume has changed according to its price in different periods. The values have been reported in the following table. This company is going to launch a new product and the price needs to be decided based on the market analysis. Determine the appropriate price for the newly developed electric bicycle with the aim of maximizing the company’s profit. The demand for new products has a direct relationship with its price.

Table 1- Demands of an electric bicycle based on a price level according to previous experiences

Price (£)  Demand

1150  415

1185  405

1210  390

1235  380

1260  345

1285  302

1310  270

1335  255

1360  246

1385  240

1410  230

1435  222

1460  216

1485  214

1510  210

1540  200

The main objective of the company is to maximize profit regarding to the new product. It is assumed that the unit production and supply cost of each electric bicycle is £740, so the profit of each unit will be (the sale price – unit production cost).

Determine the optimal demand

Compute the optimal profit.

Interpret the results.

If the supply cost of each electric Bicycle is £250 and then £950 determine the optimal price and interpret the results appropriately.

Suppose that the supply cost is £950 and the company has decided to set the price less than £1300, then what will be the optimal price? Interpret the results

To find the optimal price, we need to find the price that maximizes the company's profit. Profit is calculated as (sale price - unit production cost), and we have been given the unit production cost as £740. So, the profit function can be written as:

Profit = (sale price - £740) * demand

Using the data in the table, we can plot the demand as a function of price and then calculate the profit for each price level:

Price (£) Demand Profit (£)

1150 415 121,750

1185 405 133,650

1210 390 141,600

1235 380 146,200

1260 345 140,100

1285 302 113,640

1310 270 75,600

1335 255 67,170

1360 246 66,480

1385 240 66,600

1410 230 63,700

1435 222 62,820

1460 216 62,160

1485 214 62,370

1510 210 61,500

1540 200 59,200

From the table, we can see that the maximum profit is obtained at a price of £1210, which gives a profit of £141,600. The optimal demand at this price is 390 units.

Interpretation: The company can maximize its profit by setting the price of the electric bicycle at £1210, and the optimal demand at this price is 390 units. The company can earn a profit of £141,600 if it sells 390 electric bicycles at this price.

If the supply cost of each electric bicycle is £250, then the profit function becomes:

Profit = (sale price - £250 - £740) * demand

Profit = (sale price - £990) * demand

Using the same method as before, we can calculate the profit for each price level:

Price (£) Demand Profit (£)

1150 415 157,450

1185 405 169,950

1210 390 177,300

1235 380 181,300

1260 345 174,150

1285 302 146,890

1310 270 110,250

1335 255 96,525

1360 246 95,040

1385 240 95,400

1410 230 92,400

1435 222 91,512

1460 216 90,720

1485 214 91,422

1510 210 89,100

1540 200 85,600

The maximum profit is obtained at a price of £1210, which gives a profit of £177,300. The optimal demand at this price is 390 units.

Interpretation: If the supply cost of each electric bicycle is reduced to £250, then the optimal price remains the same as before at £1210. However, the maximum profit increases to £177,300, which is an increase of £35,700 compared to the previous scenario.

If the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.

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Answer:

She would have to pay $17.50 for 35 songs.

Step-by-step explanation:

We have the amount it costs per song (0.50), and we have the amount of songs that she wants to buy (35). If we multiply 35 the amount of songs by 0.50 the price per song, we will have a grand total of $17.50.

35 * 0.50 = 17.50

-Hope this helped

Answer: IT IS EZ IT JS 67 AND 194

Step-by-step explanation

Answer: it think 10

Step-by-step explanation:

and Get some sleep bro

Answer: 10

Step-by-step explanation:

5+5=10

Answer:

Step-by-step explanation:

-2x+0.25>6.25

-2x>6

Swap the sign when you divide or multiply by a negative in an inequality.

x<-3

Option #1

1km would be represented by 4cm on a  1 : 25000 scale map.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.

We know 1 km = 1×100000 = 100000 cm.

So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.

Now, Again 1 km = 100000 cm,

So, 1km will be represented by 100000/25000 = 4 cm.

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Answer: x=12

Step-by-step explanation:

[tex]5(x+6)=8x-6[/tex]

On the left side of the equation, open the parentheses:

[tex]5x+30=8x-6\\\\5x+30-5x=8x-6-5x\\\\30=3x-6\\\\30+6=3x-6+6\\\\36=3x[/tex]

Divide both parts of the equation by 3:

[tex]12=x[/tex]

[tex]Thus,\ x=12[/tex]

Answer:

Step-by-step explanation:

The experimental probability of getting a Twix is 3/5 or 60%.

The probability of rolling 3 sixes to the nearest thousandth is 0.556.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Using binomial distribution.

[tex]^nC_r P^cQ^{n - r}[/tex]

Now,

Probability of getting a six = 1/6

P = 1/6

Probability of not getting a six = 5/6

Q = 5/6

Now,

n = 5 and r = 3

So,

[tex]^nC_r P^rQ^{n - r}[/tex]

= [tex]^5C_3(1/2)^3(5/6)^2[/tex]

= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)

= 10 x 1/8 x 25/36

= 5/9

= 0.556

Thus,

The probability of rolling 3 sixes is 0.556.

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Answer:

Step-by-step explanation:

The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.

Arithmetic succession or arithmetic sequential is a numerical series in which the difference between subsequent terms is uniform.

Let's check all the options, then we have

A.  {-6, 1, 8, 15, 22,...}, then the common difference is given as,

d = 1 - (-6) = 8 - 1 =

d = 7 =  7

B.  {64, 32, 16, 8, 4,...}, then the common difference is given as,

d = 32 - 64 = 16 - 32
d = -32 ≠ - 16

C.  {1, 2, 4, 8, 16,...}, then the common difference is given as,

d = 1 - 2 = 2 - 4

d = - 1 ≠ - 2

D.  {1, 3, 6, 10, 15,...}, then the common difference is given as,

d = 1 - 3 = 3 - 6

d = - 2 ≠ - 3

The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.

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The inequality that can be used to represent the number of topsoil and mulch Sam can carry is, 40x + 20y ≤ 480

And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that:

Weight of top soil = 40 pounds

Weight of mulch = 20 pounds

Total weight Sam can carry = 480 pounds

Now, Let number of bags of top but soil = x

And, The number of weight of mulch = y

Hence, The inequality is,

⇒ 40x + 20y ≤ 480

Therefore, the inequality that can be used to represent the number of topsoil and mulch Sam can carry is 40x + 20y ≤ 480

And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.

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Answer:

I doubt I'm wrong but it's D

Answer: 79

Step-by-step explanation: The weighted average for the scores can be calculated as follows:

Lab score: 94 x 0.23 = 21.62

First major test: 89 x 0.215 = 19.135

Second major test: 63 x 0.215 = 13.495

Final exam: 73 x 0.34 = 24.82

Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976

Rounding to the nearest whole number, the weighted average is 79.

Answer:

103,847

103,847.0

Step-by-step explanation:

Step 1: Multiply the two numbers: 573.06 x 184.25 = 106,157.45

Step 2: Round the answer to four significant figures: 106,200

The snowfall change is plotted on the graph attached with the answer below.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that Peter recorded the snowfall each winter in New York for the last 4 years. He predicts that the snowfall change from year 4 to year 5 will be twice as much as the change was from year 3 to year 4.

Let the snowfall in years 3 to 4 is (2,0) so it will be in year 4 to 5 will be (4,0). Plot the two points on the graph. The graph is attached with the answer below for better understanding.

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Inverse of function f(x) is f⁻¹(x) = x³/125 - 7

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f⁻¹ or F⁻¹.

Given function,

f(x) =  5∛(x + 7)

f⁻¹(x) = 5∛(f(x) + 7)

Cubing both sides

x³ = 5³(f(x) + 7)

x³ = 125 (f(x) + 7)

f(x) + 7 = x³/125

f(x) = x³/125 - 7

Hence,  f⁻¹(x) = x³/125 - 7 is inverse of function f(x).

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The solution of the given equation is x= 5 and x = -8.

An algebraic equation of the second degree in x is a quadratic equation. First, there must be a term other than zero in the coefficient of x^2 for an equation to be a quadratic equation. The x^2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.

The given equation is x = √40 - 3x.

Square on both sides of the equation:

x^2 = (√40 - 3x)²

x² = 40 - 3x

Regroup to one side of the equation:

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x + 8) - 5 (x+8) = 0

(x - 5)(x + 8) = 0

Equate each term to 0:

x - 5 = 0

x= 5

x+ 8 = 0

x = -8

Hence, the solution of the given equation is x= 5 and x = -8.

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