alpha writes the infinite arithmetic sequence \[10, 8, 6, 4, 2, 0 ,\ldots.\]beta writes the infinite geometric sequence \[9, 6, 4, \frac{8}{3}, \frac{16}{9}, \ldots.\]gamma makes a sequence whose $n^{\text{th}}$ term is the product of the $n^{\text{th}}$ term of alpha's sequence and the $n^{\text{th}}$ term of beta's sequence: \[10\cdot 9 \quad,\quad 8\cdot 6\quad ,\quad 6\cdot 4\quad,\quad 4\cdot \frac83\quad,\quad 2\cdot \frac{16}{9}\quad,\quad \ldots.\]what is the sum of gamma's entire sequence?

If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million

Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.

The continuously compounding formula:

FV = PV* e^rt

Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.

Hence,

FV = 49* 2.7183^(0.0512*1) =51.57

Interest earned= 51.57-49=2.54

Hence, the university will earn an interest of $2.54 million.

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Answer:

15

Step-by-step explanation:

16c+4(-5)=220

16c-20=220

16c=240

C=15

Answer:

119º and 61º

Step-by-step explanation:

2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5

2x-15+3x+5=180

5x-10=180

5x=190

x=38

fill in x

2(38)-15

=76-15

=61

angle is 61

fill in x for angle 2

3(38)+5

=114+5

=119

angle 2 is 119

Using BODMAS we can conclude, Yes, both will give same result.

The rule used to solve mathematical expressions is known as the BODMAS rule. The order of operations for mathematical formulas requiring several operations is known as BODMAS. B. Brackets, O. Order of powers, D. Division, M. Multiplication, A. Addition, and S. Subtraction make up the acronym.

−9×(−9)−9

⇒ - 9 × 81

⇒ -729

⇒ [−9×(−9)]−9​

⇒ [81] -9

⇒ -729

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7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.

The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.

We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.

∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.

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Answer: About 65 minutes.

It changes an average of about 60 degrees Fahrenheit every half hour.

180     120      60    50

 0       30       60     65

Now it is about ten degrees until it's fifty. Since it takes thirty minutes to go down sixty degrees, divide sixty by ten to get six. Then divide thirty by six to get five. So, it should take about 65 minutes to cool down to 50 degrees.

It will take approximately 35 minutes for the custard to cool from 120°F to 50°F.

To determine how long it will take for the custard to cool to 50°F, we need to consider the rate at which it cools. From the given information, we know that the custard cools from 180°F to 120°F in 30 minutes.

To find the rate of cooling, we can calculate the temperature change per minute.

The temperature decreases by 180°F - 120°F = 60°F over 30 minutes. So, the rate of cooling is 60°F / 30 minutes = 2°F per minute. Now, let's use this rate to calculate how long it will take for the custard to cool from 120°F to 50°F.

The temperature difference between 120°F and 50°F is 120°F - 50°F = 70°F. To cool from 120°F to 50°F at a rate of 2°F per minute, it will take 70°F / 2°F per minute = 35 minutes.

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1. Based on the proportional relationship table created, 4.8 gallons of water will be in the fish tank after 3 mins.

2. 25 minutes.

3. The Constant of proportionality is: 1.6.

In a proportional relationship between variables x and y, the Constant of proportionality, k, is determined using any pair of values from the table as:

k = y/x.

The relationship is modelled as y = kx.

Constant of proportionality = k = y/x = 0.8/0.5

Constant of proportionality = k = 1.6

The equation for the relationship would be: y = 1.6x. Use the equation to complete the table:

For x = 1:

y = 1.6(1) = 1

For x = 3:

y = 1.6(3) = 4.8

For y = 40:

40 = 1.6x

40/1.6 = x

x = 25

The complete table is:

x             y              

0.5        0.8

1            1.6

3           4.8

25        40

1. Using the proportional relationship table, we can conclude that, 4.8 gallons of water will be in the fish tank after 3 mins.

2. Using the proportional relationship table, the time it would take to fill the tank with 40 gallons of water is: 25 mins.

3. Constant of proportionality = k = 1.6.

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Answer: $426.20

Step-by-step explanation:

The subtotal is [tex]299.99+191.96+99.99=\$ 591.94[/tex].

[tex](591.94)(0.8)=\$473.552\\\\(473.552)(0.9) \approx \$426.20[/tex]

Value of x for equation -3x + 1 + 10x = x + 4 is 1÷2.

Given equation,

-3x + 1 + 10x = x + 4

Shifting the variables to the left-hand side and constant to the right-hand side,

-3x - x + 10x = 4 - 1

Simplifying the equation,

10x - 4x = 3

6x = 3

x = 1÷2

When x from the right side shifts to the left side, its sign changes, and similarly, when 1 from the left side shifts to the right side, its sign changes.

x = 0.5

Therefore, value of x = 1÷2 that is 0.5

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area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is

(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2

hence, substituting the points (x1, y1)= (-2, 1);

( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get

area of triangle =

( -2(3-(-4)) + 0( -4 - 1) + 4(1-3))/2

(-14+0-8)\2

22\2

11 sq unit

Answer:

12.5

Step-by-step explanation:

there are eight triangles and one yellow so 1/8=12.5%

Answer: 12.5%

Step-by-step explanation:

There are 8 sections and 1 of them is yellow so 1 divided by 8 is 0.125 or 12.5%

Answer: y=7

Step-by-step explanation:

We need to combine like factors in this term by adding up all the exponents and copying the base.

No exponent implies the value of 1.

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Answer:

y =7

Step-by-step explanation:

Answer:

h = 6.36619772 cm

Step-by-step explanation:

h = (3 * v) / (πr2)

Answer:

h = 20 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )

given r = 9 and V = 540π , then

[tex]\frac{1}{3}[/tex] π × 9² × h = 540π

[tex]\frac{1}{3}[/tex] × π × 81h = 540π

27πh = 540π ( divide both sides by 27π )

h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm

Answer:

D

Step-by-step explanation:

Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

3(c) + 25

Step-by-step explanation:

Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?

2(25) + c

25c + 3

3(c) + 25

3(c + 25)

Answer:

108.333 km/hour

Step-by-step explanation:

See attached worksheet.

Answer:

First, 24 divided by 8 equals 3. this means you divide 12 by 3. you get 4. 4 cups of sugar will be used when 8 cups of flour are used.

The most appropriate choice for matrix and multiplicative inverse of matrix will be given by

B is the multiplicative inverse of A

What is a matrix and multiplicative inverse of matrix?

Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.

To learn about multiplicative inverse, it is important to know about identity matrix

[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.

Let A and B be two matrices

A is said to be a multiplicative inverse of B if AB = BA = I

Here,

A=   [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

AB =

[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

BA =

[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

So B is the multiplicative inverse of A

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For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

[tex]f(x) = x^{3} -9x^{2} +20x -12 \\[/tex]

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
[tex]\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2[/tex]

Now expanding, [tex]x^{2} -3x +2[/tex]

[tex]x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)[/tex]

Hence, [tex]x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)[/tex]

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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Answer: 100%-9/10= -0.8

Step-by-step explanation:

100%-9=-8

-8/10=-0.8

Answer: x^2-9x+20

Step-by-step explanation: you have to distribute (x-5) (x-4)

which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20

a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD

[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]

y=3.90cm

b)

[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]

x=40,27 cm

GOODLUCK.

The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.