The height, h, in metres, of a weather balloon above the ground after seconds can be modelled by the function h(t) = -2t³ + 3r² + 149t + 410, for 0 ≤ t ≤ 10. When is the balloon's height 980 m above the ground? Use intervals/factors method to justify your answer.

Answer:

Step-by-step explanation:

First, write down your equations (wherein apples are represented by x and oranges by y)

8x + 7y = 18.85

2x + 10y = 12.88

From here, we will solve by substitution.

First, we will have to isolate a variable.

2x + 10y = 12.88         Subtract

2x = -10y + 12.88        Divide

x = -5y + 6.44

Now substitute

8 ( -5y + 6.44) + 7y = 18.85    Distribute

-40y + 51.52 + 7y = 18.85      Combine like terms

-33y = -32.67                         Solve

y = 0.99 or 99 cents per pound of oranges

Substitute once more to find x

2x + 9.90 = 12.88         Subtract

2x = 2.98                      Solve

x = 1.49 or $1.49 per pound of apples

It's never a bad idea to check your answer

2(1.49) + 10(0.99) = 12.88      Solve

2.98 + 9.90 = 12.88               Confirm

Answer:

Step-by-step explanation:

18=18+x-x*x/x

Answer:

1/2 make a sketch of the corresponding triangle

Step-by-step explanation:

We need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

In Example 5.4, we have the following:

The stock price at time t, St, is modeled as a geometric Brownian motion with constant drift and volatility, such that dSt = μSt dt + σSt dWt, where μ is the drift rate, σ is the volatility, and dWt is a Wiener process increment.

Taking the natural logarithm of both sides, we get d ln(St) = (μ - 0.5σ^2)dt + σdWt.

Letting Xt = ln(St), we have dXt = (μ - 0.5σ^2)dt + σdWt.

From the problem statement, we have that Xi = ei, where ei ~ N(0,1) for i = 1, 2, ..., n, where n is the number of time steps.

We want to find values of μ and σ such that Mn = exp(1/n Σi=1^n Xi) = exp(1/n Σi=1^n ei) = exp(1/n En) is a martingale, where En is the average of the N(0,1) random variables.

Using the fact that exp(a+b) = exp(a)exp(b), we have:

Mn+1 = exp(1/(n+1) Σi=1^(n+1) Xi) = exp(1/(n+1) Σi=1^n Xi)exp(Xn+1)

For Mn+1 to be a martingale, we need:

E[Mn+1 | Fn] = Mn

where Fn is the filtration up to time n. Since Xi are independent and identically distributed, we have:

E[Mn+1 | Fn] = E[exp(1/(n+1) En+1 + 1/(n+1) Σi=1^n ei) | Fn] = Mn exp(1/(n+1) E[en+1])

where en+1 ~ N(0,1). Note that E[en+1] = 0 and Var[en+1] = 1.

Thus, we need:

Mn exp(1/(n+1) E[en+1]) = Mn

or equivalently:

exp(1/(n+1) E[en+1]) = 1

Taking the logarithm of both sides, we get:

1/(n+1) E[en+1] = 0

or:

E[en+1] = 0

Therefore, we need μ - 0.5σ^2 = 0, or equivalently:

μ = 0.5σ^2

This is the same condition as in Example 5.4, which ensures that the lognormal stock prices follow a martingale.

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The function in the values menu would you use to summarize the data is SUM

Because

I would use the SUM function to figure out how much box office revenue each genre earned. In the pivot table, the SUM function would add the total revenue separately for each genre.

This function, as clear from the name, is used to add all the values provided as arguments and to display the result in the cell-containing function. Argument Type All Numbers Return Type Number. Syntax = SUM(number 1 , number2, ).

The SUM function will sum hardcoded values and numbers that result from formulas. If you need to sum a range and ignore existing subtotals, see the SUBTOTAL function.

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Answer:

Area = 1,344 cm²

Step-by-step explanation:

First, find the value of x and the numerical side length of all sides of the triangle before finding the area.

Thus:

Perimeter of a triangle = sum of all its side

Therefore,

(6x - 44) + (2x - 20) + (3x + 24) = 224

Solve for x

6x - 44 + 2x - 20 + 3x + 24 = 224

Add like terms

11x - 40 = 224

Add 40 to both sides

11x = 224 + 40

11x = 264

Divide both sides by 11

x = 24

Find the measurement of each side length by plugging in the value of x:

Hypotenuse = 6x - 44 = 6(24) - 44 = 100 cm

Height = 2x - 20 = 2(24) - 20 = 28 cm

Base = 3x + 24 = 3(24) + 24 = 96 cm

Find the area:

Area = ½×base×height

Plug in the values

= ½×96×28

Area = 1,344 cm²

Answer:

(12-3)/1.5= 6

Step-by-step explanation:

You subtract $3 from $12 for the first fee and then divide $9 by $1.50 to find how many hours you can stay.

Answer:

(12 - 3) ÷ 1.5 = 6

Answer:

$3.45

Step-by-step explanation:

the large salad costs 1.40 more

large salad = 4.85

small salad = 4.85 - 1.40

small salad costs $3.45

Answer:

3.45$ is the price of small salad as it costs 1.40$ less than large salad

Step-by-step explanation:

i hope you find it helpful, have a nice day

Answer:

3) fifty seven and three tenths

4) 1, 2, 4, 8, 16

5) No, she would have only 60 pictures in the album. When she has 80 pictures in total. 15×4=60

Step-by-step explanation:

Hope this Helps!!

:)

Step-by-step explanation:

this is your answer hope this may help you

Number of license plates = 24 x 24 x 7 x 7 x 7

= 197568

Step-by-step explanation:

Ratio of adults to children= 7:3

Total no. Of people at the cricket match:150

To find the value of the ratios, 7x+3x=150 ; 10x=150 ; x=150/10:15

So, 7:3 is 7(15) adults to 3(15) children,

Total no. Of adults: 105

Total no. Of children: 45

So, as per the question, the no. Of children that attended the cricket match is 45

Answer:

a= 80

b= .25

Step-by-step explanation:

We know that a has to equal 80 because

\(a(b)^0=80\\a=80\)

We can then just solve for b

\(80(b)^1=20\\b=\frac{20}{80} \\b=.25\)

Answer:

Uhhh

Step-by-step explanation:

Answer:

9/40

Step-by-step explanation:

Tan of an angle equals the length of the side opposite the angle divided by the length of the leg adjacent to the angle. Thus, for angle C, AB is opposite it, which is 9, and although both CA and CB are adjacent, adjacent typically refers to the leg, not the hypotenuse, so we want CB, which is 40. Opposite/Adjacent = 9/40

Answer:

Step-by-step explanation:

\(\sf 5(x - 10) = 30 - 15x\)

\(\sf 5x-50=30-15x\)

\(\sf 5x-50+50=30-15x+50\)

\(\sf 5x=-15x+80\)

\(\sf 5x+15x=-15x+80+15x\)

\(\sf 20x=80\)

\(\sf \frac{20x}{20}=\frac{80}{20}\)

\(\sf x=4\)

Step-by-step explanation:

It is so simple Hope u understand

Answer:

Step-by-step explanation:

Sum = -5

Product = 2*(-3) = -6

Factors = -6 , 1   {-6 + 1 = -5  & -6 *1 = -6}

2m² - 5m -3 = 0

2m² - 6m + m -3 = 0

2m(m - 3) + (m -3) = 0

(m -3)(2m + 1) = 0

m - 3 =  0    or 2m + 1 = 0

    m = 3      or 2m = -1

                          m = -1/2

Ans: m = 3 , (-1/2)

Answer:

Below

Step-by-step explanation:

See image below on how to find  h = height

 then you have two legs of a right triangle   5 and   26

L^2 = 5^2 + 26^2        via Pythagorean Theorem

L = sqrt(701) = 26.5 ft

The length of each leg of the isosceles triangle is 26 ft.

A triangle is a three-sided polygon that consists of three edges and three vertices.

An isosceles triangle has area of 130 ft²

The base is 10 ft

We have to find the length of the legs

We know that in an isosceles triangle two sides are equal

The area of a triangle is given by the formula:

Area = (1/2)× base × height

Since the triangle is isosceles, we know that the height (or altitude) of the triangle is also the length of one of the legs.

Let h be the height of the triangle (and also the length of one of the legs). Then we have:

130 = (1/2) × 10 × h

Simplifying, we get:

130 = 5h

Dividing both sides by 5, we get:

h = 26

Therefore, the length of each leg of the isosceles triangle is 26 ft.

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Answer:

w=1/15

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

9−7w=8w+8

9+−7w=8w+8

−7w+9=8w+8

Step 2: Subtract 8w from both sides.

−7w+9−8w=8w+8−8w

−15w+9=8

Step 3: Subtract 9 from both sides.

−15w+9−9=8−9

−15w=−1

Step 4: Divide both sides by -15.

−15w/−15 = −1/−15

w = 1/15

Answer:

B

Step-by-step explanation:

x > 1

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:

x=t+p

Step-by-step explanation:

x-p=t

x=t+p

Answer:

The answer is A

The experimental and theoretical probability for each result are:

                                    Theoretical  Experimental

P(5)                                      1/6              7/40

P( 1 or 6)                               1/3              7/20

P(no more than 4)                2/3             21/40

P(greater than 2)                  2/3                7/10

Probability determines the chances that an event would happen. Experimental probability is the probability of an event happening based on the result of an experiment that has been carried out multiples time.

Theoretical probabilities:

P(5) = number of sides with 5 / total number of sides = 1/6

P( 1 or 6)  = number of sides with 1 / total number of sides + number of sides with 6 / total number of sides  = 1/6 + 1/6 = 1/3                  

P(no more than 4)   = number of sides that is no more than 4 / total number of sides  = 4/6 = 2/3

P(greater than 2) = number of sides greater tha 2 / total number of sides   = 4/6 = 2/3      

Experimental probabilities:

P(5) =  number of times there was a result of 5 / total number of times the die was rolled = 7/40

P( 1 or 6) = (number of times there was a result of 1 / total number of times the die was rolled) + (number of times there was a result of 6 / total number of times the die was rolled )

2/40 + 12/40 = 14/40 = 7/20    

P(no more than 4) = sum of results no more than 4 / total number of times the die was rolled = ( 2 + 10 + 5 + 4) = 21/40

P(greater than 2) = sum of results greater than 2 / total number of times the die was rolled = (7 + 12 +5 + 4) / 40 = 28/40 = 14/20

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Answer:

5. $16.8 6.$16.7 7. 4 costumes 8. no because the slope isn't one 9. 28.8

Step-by-step explanation:

For number 5 you would divide the 90 miles by the two gallons of gasoline used which gives you 45. Your car is using one gallon of gas every 45 miles.

If your trip is going to be 270 miles long then you would divide the 270 by 45 to see how many gallons you would use. You would end up using 6 gallons.

Finally you would multiply the 6 by $2.80 to get $16.80

You would spend $16.80

Answer:

P(≥ 4) = 0.44

Step-by-step explanation:

The experimental probability of landing on a number greater than or equal to 4 can be calculated by adding the frequency of outcomes 4, 5, and 6 and dividing by the total number of trials.

The frequency of outcomes 4, 5, and 6 is 6 + 9 + 7 = 22.

The experimental probability of landing on a number greater than or equal to 4 is 22/50 = 0.44.

So, the answer is B. P(≥ 4) = 0.44.

Answer:

P(≥ 4) = 0.44  

Step-by-step explanation:

I took the test and it was right!

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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The year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

To calculate the rate of inflation and the Consumer Price Index (CPI) change from year 1 to year 2, we need to follow these steps:

Step 1: Calculate the inflation rate:

Inflation Rate = (Year 2 CPI - Year 1 CPI) / Year 1 CPI

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = (Year 2 Basket Price / Year 1 Basket Price) * 100

Let's calculate the values:

Year 1 Basket Price = $25.00

Year 2 Basket Price = $25.50

Step 1: Calculate the inflation rate:

Inflation Rate = ($25.50 - $25.00) / $25.00

Inflation Rate = $0.50 / $25.00

Inflation Rate = 0.02 or 2%

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = ($25.50 / $25.00) * 100

Year 2 CPI = 1.02 * 100

Year 2 CPI = 102

Therefore, the year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

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The arc length of the sector is 7.065 approximately 7.1 cm. Then the correct option is D.

It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

The central angle of π/2 radians in a circle with a radius of 4.5 cm.

Then the arc length will be

\(\rm Arc \ length = \dfrac{\pi /2}{2 \pi} * 2*\pi * 4.5\\\\\\Arc \ length = \dfrac{1}{2} * 3.14*4.5\\\\\\Arc \ length = 7.065\)

Then the arc length is 7.065 approximately 7.1 cm. Then the correct option is D.

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Answer:

D is the answer

Step-by-step explanation:

No Reason just try it out

Answer:

A

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

it's Y over X

I also took this test on edge :)