3. A hot air balloon travels 18 miles in 3 hours. At this rate, how many miles will the
3
hot air balloon travel in 2 hour?
4
A. 4.5 miles
B. 6 miles
C. 11.5 miles
D. 13.5 m

Answer:

240

Step-by-step explanation:

We need to find the coeffeicent of the binomial expansion of

[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} [/tex]

Note that

[tex] - 2 {x}^{ - 2} = - \frac{2}{ {x}^{2} } [/tex]

The binomial theorem states that

[tex](x + y) {}^{n} = x {}^{n} y {}^{0} + \binom{n}{1} x {}^{n - 1} y + \binom{n}{2} x {}^{n - 2} y {}^{2} ....... + x {}^{0} y {}^{n} ( \binom{n}{n} )[/tex]

Using this, we let expand our series

[tex]( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} = x {}^{30} + \binom{10}{1} ( {x}^{27} 2 {x}^{ - 2} ) + \binom{10}{2} {x}^{24} 2x {}^{ - 4} + \binom{10}{3} {x}^{21} 2x {}^{ - 6} + \binom{10}{4} {x}^{18} 2x { }^{ - 8} + \binom{10}{5} x {}^{15} 2x {}^{ - 10} + \binom{10}{6} x {}^{12}2 x {}^{ - 12} + \binom{10}{7} x {}^{ 9} 2x {}^{ - 14} + \binom{10}{8} x {}^{ 6} 2x {}^{ - 16} + \binom{10}{9} ( {x}^{3} )2x {}^{ - 18} + 2x {}^{ - 20} [/tex]

[tex] \frac{1}{ {x}^{5} } = x {}^{ - 5} [/tex]

So what term in the series eqaul x^-5.

That term is the 10 choose 7 term.

[tex] \binom{10}{7} {x}^{9} 2x {}^{ - 14} [/tex]

Because

[tex] = \binom{10}{7} 2x {}^{ - 14} {x}^{9} = \binom{10}{7} 2 {x}^{ - 5} [/tex]

So we need to compute 10 choose 7.

That equals

10!/3!(7!)= 10×9×8/6= 720/6=120.

So we get

[tex]120(2) {x}^{ - 5} [/tex]

[tex]240 {x}^{ - 5} [/tex]

So the coeffceint u

is 240

Answer:

D. 201.1

Step-by-step explanation:

We see that the radius o the given circle is 16, so we do 16^2*pi

then we multiply that be 90/360

which rounds to 201.1

Answer/Step-by-step explanation:

GIven;

A customer in Maine orders a Dog Treat Bundle for $34.80.

The sales tax in Maine is 5.5%.

To Find;

How much sales tax is collected on the order?

Solve;

$34.80 * 5.5% = 1.914

Round: 1.914 = 1.91 [Sales tax added]

$34.80 + 1.91 = 32.89 [Total]

Hence, $1.91 sales tax is added and $32.89 is the total (include sales tax)

~Learn with lenvy~

Answer: a6=70

Step-by-step explanation:

we know that

In the Arithmetic Sequence the formula is:

an= a1 + d(n−1)

where

a1 is the first term

d is the common difference

n is the number of terms

in this problem

a1=5

a2=18

a3=31

a4=44

a5=57

so

d=a2-a1 or a3-a2 or a4-a3 or a5-a4

d=57-44----> 13

find a6

a6= a1 + d(n−1)

n=6

d=13

a1=5

a6=5+13*(6-1)----> a6=5+13*5----> a6=70

Answer:

Answer:

Last option

Step-by-step explanation:

In order to manipulate a, you have to divide by 3 on both sides.

Answer:

You must know all forms of additional payment and expenses, like medical bills and community expenses that can happen at any given time.

                                              ~Hope it helps~

                                                  ~Be great~

Answer:

6 6

---- ÷ ---

16 10

Step-by-step explanation:

equals 5/8

Answer:

10.7

Step-by-step explanation:

the tenth place is the first number that comes after the decimal so, that is the number you are rounding. We take a look following that number and it it is equal to or greater than 5, (which it is), we round up one number.

Answer:

10.7

Step-by-step explanation:

Any number between 1-4 rounds down and 5-9 rounds up, so here you will round up. I've included the decimal places as well below. The number after the decimal point is the tenth's place.

Good luck! Hope this helps

Answer: -0.383

Step-by-step explanation:

Since this is on the unit circle, the cosine is equal to the x coordinate and the sine is equal to the y coordinate.

Since cot = 1/tan = cos/sin, the approximate value is (-0.358)/(0.934), which is about -0.383.

Answer:

1. YES

1. YES2. YES

1. YES2. YES3.YES

4.NO

Hope it helps

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Learn more about scale factors here :

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Answer:

1 foot

Step-by-step explanation:

you multiply 5 1/4 inches by two, you would get 10 1/2 inches. if 2 inches equals 1 foot then 5 inches would equal 10 inches and 1/4 would equal 1/2. If you put those numbers together, you get 10 1/2 inches. Therefore the answer is 2 inches = 1 foot. 

Answer:

97.79ft

Step-by-step explanation:

Adding the area of every side together gets the surface area of the whole shape.

The semi-annual payment is $1662.47

Given : A 3 year loan of $8,561 at 9.1% compounded semi-annually.

We have to determine the semi annual payment.

We know,

[tex]P=\dfrac{PV.r}{1-(1+r)^{-n}}[/tex]

Where PV is present value of loan.

r is rate of interest

n is time period.

Given loan is calculated semi annually,

So PV = $ 8561

r=9.1 % =9.1/200

and time period is 3 years = 6 number of period as semi annually.

Thus, Substitute,

We get,

[tex]P=\dfrac{8561(\dfrac{9.1}{200})}{1-(1+\dfrac{9.1}{200})^{-6}}[/tex]

[tex]P=1662.47[/tex]

Hence the semi-annual payment is $1662.47

To know more about Amount follow

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Answer:

Step-by-step explanation:

Givens

pi = 3.14

d = 3.8

r = d/2

r = 3.8/2 = 1.9

Formula

V = (4/3) * pi * r^3

Solution

V = (4/3) * 3.14 * 1.9^3

V = 4/3 * 3.14 * 6.859

V = 28.7163

Answer:

D. The trinomial is equivalent to (x+2)(x-1)

Step-by-step explanation:

1. Factor out the common term x:

= x(x^2+x-2)

2. Factor the equation:

= x(x - 1)(x + 2)

From this, we can see that because the equation was factorable, it is not prime. Option B is not completely factored, so it is incorrect. The final ordered pair shown in Option C is has (x + 1), when it should be (x - 1), so it is also incorrect. Option D is the true statement.

Answer:

[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]

Step-by-step explanation:

[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]

Answer:

second one down

4 860 000 000 000

Step-by-step explanation:

count out 12 zeros after the 4 and you will find the one in decimal notation

The decimal notation for the given scientific notation is 4860000000000. (option b)

The decimal notation is an alternate method to represent the fractional value. It means that it is the fractional representation using base 10. The fractions can be converted into decimals and vice versa.

Given is a scientific notation, 4.86 × 10¹², we need to convert it into a decimal notation,

4.86 × 10¹²

= 4.86 × 10,000,000,000,000

= 4.86 × 100 × 100000000000

= 486 × 100000000000

= 48600000000000

Hence, the decimal notation for the given scientific notation is 4860000000000. (option b)

Learn more about decimal notation, click;

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Answer:

  (b)  64 sq. in.

Step-by-step explanation:

The shaded area is the difference between the overall area and the areas of the cutout corners.

The overall area is 10 in by 10 in, so is ...

  A = s² = (10 in)² = 100 in²

The area of the cutout at each of the four corners is ...

  A = s² = (3 in)² = 9 in²

So, the total area of the four cutouts is ...

  cutout area = 4 × 9 in² = 36 in²

The remaining area is then ...

  100 in² -36 in² = 64 in²

Step-by-step explanation:

what number you need help with

25/100

Step-by-step explanation:

if he has a fraction of a bar graph it is 25% if that grah so in other words 25% as a fraction is 25/100

Answer:

[tex]\fbox{Gradient of curve = -6}[/tex]

Step by step explanation:

Given:

Equation of curve ↦ xy = 6

Point ↦(1,6)

To find:

The gradient of curve = ?

Solution:

[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]

Taking log both the side,

[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]

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Answer:

1/3 probability

Step-by-step explanation:

The probability that you flip heads is 1/2, one heads out of two possible (heads and tails).

The probability that you draw a purple marble is 2/3, two purples and three total (2 p +1 w).

To find the probability of both happening, multiply the probabilities together:

(1/2) * (2/3) = (2/6) = (1/3)

Answer:

Step-by-step explanation:

Let

The equations as per question are below

Crazy Curly's

Bill's Beauties

Solve the system by substitution

Answer:

805.5 out of 900

Step-by-step explanation:

A test is out of 100 and because there are 9 tests: 9 x 100 which equals 900.

To get the average we add up each test mark and divide by the number of tests. The same can be applied here but reversed. So because there were 9 tests we can multiply 89.5 by 9 which gives us 805.5. Beverly scored 805.5 marks out of 900 which makes her average 89.5% for 9 tests.

Answer:

4:55 hrs :)

Step-by-step explanation:

1:30 hours + 40 min + 40 min + 2:05 

1:30 hrs + 1:20 hrs + 2:05 hrs

2:50 hrs + 2:05 hrs

4:55 hrs

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