The total cost charged for a day of fun at Aussie World consists of an entry fee of $15 and a rate of $3 per ride. Write the rule for the total cost, C, where r rides are taken.

Recall the binomial theorem.

[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is

[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]

Observe that

[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]

[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]

When we multiply these by [tex]8-9x[/tex],

• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]

• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]

and the sum of these terms is

[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]

2. The binomial expansion is

[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]

We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :

[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]

Answer:

J

Step-by-step explanation:

Answer:

Domain is 1 and 7 and range is -5and -4

Step-by-step explanation:

because domain is a first group element and range is a second element of a set

The formula for Observed Score is; Observed score (X) = True score (T) + measurement error (e)

The formula for Observed Score is;

Observed score (X) = True score (T) + measurement error (e)

1) True score is the score that would be obtained if an individual took a test an infinite amount of times and those test scores were averaged. The concept of true score is theoretical because you can't give someone something an infinite number of times.

2) Standard error of measurement is the standard deviation of multiple test scores (how far the sample mean of the data is likely to be from the true population mean).

The less random error (e) in the measure, the more the observed score X approximates the true score T.

Thus;

Observed score = True Score + Error

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Based on the scale, the actual length of the Golden Gate Bridge is  68,600 inches.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension. An example of a scale drawing is a map.

The scale of a drawing is usually written in this format -  length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 : 19,600. This scale means that 1 inch of the postcard represents 19.600 of the original Golden Gate Bridge.

Actual length of the Bridge = scale x length of the bridge in the postcard

19,600 x 3.5 = 68,600 inches

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Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).

The amount that was above $200 that she found can be x which means that the greater side of the inequality is:

= 200 + x

She then gave away $80:

= 120 + x

She gave away 1/3 of the money so the amount left is:

= 2/3 x (120 + x)

The lesser side of the inequality:

(x + 2) - 200 = x

So then:

((120 + x) x 2) / 3 > x

240 + 2x > 3x

240 > x

x < 240

The interval that shows the possible values of the original pile of money is therefore:

( 200, 440)

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The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.

It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.

On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;

x² +4x -x -4 = 0

(x+4) (x-1) = 0

Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.

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Hello, the solution of the geometry problem is in this photo.

AOC = 136°

BOC = 44°

Answer:

PQ = 20 cm

QR = 15 cm

Step-by-step explanation:

The area of the barn quilt is 3 sq.ft.

The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.

Number of boys are practicing hitting the ball = 4

Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]

1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.

Area of the barn quilt = 1 1/3*2 1/4

                                  = 4/3*9/4

                                  = 3 sq. ft.

2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.

Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5

                                                                                 = 1/5 of a cup

3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.

Number of boys practicing hitting the ball = 6*2/3 = 4

4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.

Number of bags of lemon used on Tuesday = 7/5*5/4

                                                                     = 7/4

                                                                     = 1 and 3/4 bags

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Answer:

  67.5 cm²

Step-by-step explanation:

The figure can be decomposed into figures whose area formulas you know.

As the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the parallel bases, and h is the height.

The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...

  A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²

The area of a rectangle is given by the formula ...

  A = LW

where L and W represent the length and width, respectively.

The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...

  A = (15 cm)(3 cm) = 45 cm²

The total area of the figure is the sum of the areas of the trapezoid and rectangle:

  A = (22.5 cm²) + (45 cm²) = 67.5 cm²

The are of the figure is 67.5 cm².

The magnitude of the resulting vector, u - v, is approximately 5.83

and its angle of direction is approximately 59.04°.

We want to subtract vector v from vector u.

We are given;

v = <2, -3> = 2i - 3j

u = <5, 2> = 5i + 2j

u - v = 5i + 2j - (2i - 3j)

= 5i + 2j - 2i + 3j

= 3i + 5j

Resultant vector = √(3² + 5²)

Resultant vector = √34 ≈ 5.83

Angle of direction of resultant vector is;

tan θ = (5/3)

θ = tan⁻¹(5/3)

θ = 59.04°

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Y receives $30000 less than if the profit were divided in proportion to how much they invested.  

In a proportional tax system, everyone is compelled to pay the same amount of taxes as a percentage of their income.

Profit will Divide into 4 equal parts.

The total Profit for the month is  = $120,000

The party will receive a sum of = $30,000

This shows that Y also receive the same amount

Y = $30,000 (Profit received)

Now

If the Profits were divided in proportion to the investments made .

The proportion on investment made by Y.

The total investment made = $12000+$6000+$25000+$7000

                                            = $50000

Out of this the Amount invested by Y = $25000

The Proportional Profit of Y.

=  (25000/ 50000) x 120000                      

= $60,000

So Y receives 60000 - 30000

                       = 30000

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(3x² - 7x + 14) + (5x² + 4x - 6)

Match 3x² and 5x² to get 8x².

Combine −7x and 4x to get −3x.

Subtract 6 from 14 to get 8.

Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".

(2x² - 5x -3) + (-10x² + 2x + 7)

Combine 2x² and -10x² to get −8x².

Combine −5x and 2x to get −3x.

Add −3 and 7 to get 4.

Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".

(12x² - 2x - 13) + (-4x² + 5x +9)

Combine 12x² and -4x² to get 8x².

Combine −2x and 5x to get 3x.

Add −13 and 9 to get −4.

Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".

It looks like the function might be defined by

[tex]f(x) = \begin{cases} 3a{}x + b & \text{if } x > 1 \\ 11 & \text{if } x = 1 \\ 5a{}x - 2b & \text{if } x < 1 \end{cases}[/tex]

To ensure continuity at [tex]x=1[/tex], we need both one-sided limits to exist and have the same value.

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} (5a{}x - 2b) = 5a - 2b[/tex]

[tex]\displaystyle \lim_{x\to1^+} f(x) = \lim_{x\to1} (3a{}x + b) = 3a + b[/tex]

Both limit values must be equal to [tex]f(1) = 11[/tex], so that

[tex]\begin{cases} 5a - 2b = 11 \\ 3a + b = 11 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](5a - 2b) + 2 (3a + b) = 11 + 2\cdot11 \implies 11a = 33 \implies \boxed{a=3}[/tex]

Solving for [tex]b[/tex], we get

[tex]5\cdot3 - 2b = 11 \implies -2b = -4 \implies \boxed{b=2}[/tex]

The order of magnitude for total attended for a high school football team is 3

The given parameters are:

Average number of fan = 1000

Number of home games = 5

The total number of fans in the 5 games is:

Total number of fans = Average number of fan * Number of home games

Substitute known values in the above equation

Total number of fans = 1000 * 5

Express 1000 as 10^3

Total number of fans = 10^3 * 5

Rewrite the equation as:

Total number of fans = 5 * 10^3

The power of 10 represents the order of magnitude

Since the power of 10 is 3, the order of magnitude is 3

Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3

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The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

For given question,

We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]

We need to determine whether the sequence converges or diverges.

From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]

We use Ratio Test.

According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.

Consider,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]

Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

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Stephen read about 9 pages more each week.

What is a linear equation in math?

If stephen reeds 278 pages in 7 week ,

To find number of pages read in 1 week, divide 278 by 7

                    = [tex]\frac{278}{7}[/tex]  ⇒ 39.71

Another person reads 31 pages each week.

So stephen reads allmost 40  per week and alice 31.

Then, we need to find the difference between them

Difference = 40 - 31 = 9

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The area and perimeter of the picture is 576 inches square and 96 inches respectively

Given that each frame is a rectangle and four frames makes up the picture

Note that the picture takes the shape of a square

Let's find the total perimeter

Perimeter of the picture = sum of the four rectangular frame perimeters

Perimeter = 24 + 24 + 24 + 24

Perimeter = 96 inches

Formula for area of a square = a^2

Where 'a' is the length of the side  = 24 inches

Substitute the value of 'a'

Area of the picture = 24^2

Area of the picture = 576 inches square

Thus, the area and perimeter of the picture is 576 inches square and 96 inches respectively.

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Answer:

60m3

Step-by-step explanation:

my son got the right anser

Answer:

60m^3

Step-by-step explanation:

The formula for volume of a rectangular prism is height*width*depth

We can see two distinct shapes here

First, we find the volume for the bigger shape

We can see the measurements that pertain to it...

Width is 6m, depth is 3m, and height is also 3m

Multiply those three, you get 54m^3

Now the smaller shape...

1m in width, 2m in height, and 3m in depth

Multiply those, get 6m^3

Add the two shapes together, 54+6=60m^3

Answer:

1st option

Step-by-step explanation:

to find f(g(x)) substitute x = g(x) into f(x) , that is

f(g(x))

= f(4x - 5)

= 2(4x - 5) + 1 ← distribute parenthesis

= 8x - 10 + 1

= 8x - 9

One can prove congruence through transformation if they have the same shape and size.

The congruency postulates include:

In geometry, it should be noted that two figures are congruent if they have the same shape and size.

In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).

It should be noted that the congruence postulate is used to illustrate that the triangles are equal.

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Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: [tex]a*\frac{x}{100}[/tex] where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: [tex]\frac{96}{100} = 0.96[/tex]. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

[tex]0.96T = 72,000[/tex]

To find the original value of T, we simply divide both sides by 0.96

[tex]T = 75,000[/tex]

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

[tex]1000P = T[/tex]

Substitute 75,000 as T

[tex]1000P = 75,000[/tex]

Divide both sides by 1,000

[tex]75=P[/tex]

This means she sold each for 75

Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

Answer: 147.2 miles

Step-by-step explanation:

We can answer this by knowing the formula [tex]speed=\frac{distance}{time}[/tex]. Here, the speed is 46 miles/hour and the time is 3.2 hours. Let's put these values into the formula and solve for distance.

[tex]46=\frac{distance}{3.2}\\46*3.2=\frac{distance}{3.2}*3.2\\d=147.2[/tex]

Alex traveled 147.2 miles.

The expected value or mean of binomial distribution is also increased by increasing the number of trials.

The standard deviation of binomial distribution is also increased by increasing the number of trials.

According to the question

There is binomial experiment.

The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.

We all know,

In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.

The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].

From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.

Thus we can say that

If the number of trials is increasing, then the expected value is also increasing.

From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.

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The minimum number of books required to be equally distributed among the students are 1,440 books.

To find the minimum required books so that they can be equally distributed:

The number of students in three sections of class 6th are 32, 36, and 40.

Now, find the LCM od 32, 36, and 40.

The LCM od 32, 36, and 40 will be 1,440.

Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.

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