On Wednesday evening Sonto spent hour doing homework, 45 minutes doing housework, 1 hour visiting friends and 1 hours watching television. Write this information as a ratio.
​

The explicit Sequence is [tex]a_n = 3. 6^{n-1[/tex].

The 10 term of the sequence is 3,023,308.

A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value.

Given:

3, 18, 108, 648, ...

First term, a= 3

common ratio, r= 18/3

                          = 6

Now, using geometric sequence

[tex]a_n = a. r^{n-1[/tex]

So, the explicit function is

[tex]a_n = 3. 6^{n-1[/tex]

let us find the fifth term

[tex]a_5[/tex] = 3. [tex]6^4[/tex]

    = 3888

and, the 10 term of the sequence is

[tex]a_5[/tex] = 3. [tex]6^9[/tex]

    = 3,023,308

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Answer: x is equal to 0.88

Step-by-step explanation:

To solve for x, we can start by simplifying both sides of the equation:

89(54x - 36) + 2 = -34(-40 + 16x) + 90x

First we can simplify the left side of the equation:

89(54x - 36) + 2 = 4846x - 3204 + 2 = 4846x - 3202

Now we can simplify the right side of the equation:

-34(-40 + 16x) + 90x = -34(16x - 40) + 90x = -544x + 1360 + 90x = -454x + 1360

Now we can set the left side of the equation equal to the right side and solve for x:

4846x - 3202 = -454x + 1360

Now we can add 454x to both sides and subtract 1360 from both sides

5,300x = 4660

x = 4660/5300

x = 0.88

Therefore, x is equal to 0.88

Answer:

0.86

Step-by-step explanation:

89(54x-36)+2=-34(-40+16x)+90x

4806x-3204+2=1360-544x+90x

4806x+500x-90x=3204-2+1360

5260x=4562

x= 4562/5260

x=0.86

Answer:

[tex]4x+7-\frac{-5}{x+7}[/tex]

Step-by-step explanation:

divde:

[tex]\frac{4x^{2}+35x+44 }{(x+7)} simplify=4x+ \frac{7x+44}{x+7} \\divide: 4x+ \frac{7x+44}{x+7} \\ simplify= 7+\frac{-5}{x+7} \\\\answer: 4x+7\frac{-5}{x+7}[/tex]

The perimeter of the triangle is  40.42 cm

The height of the triangle is 14 cm

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

The length of the base is 9.5 cm

The total area of the triangle is 66.5 cm²

We know,

Area = (1/2)*base * height

⇒ 66.5 = (1/2)*9.5* h

⇒h = 14 cm

The height is 14 cm

By using Pythagoras theorem  

hypotenuse = √{(base)² + (height)²} = √{(9.5)² + (14)²}  = 16.92 cm

The hypotenuse is 16.92 cm

The perimeter of the triangle is height + base + hypotenuse = 14 + 9.5 + 16.92 = 40.42 cm

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Using the concept of solving equation, (a) after four months, the total cost would be the same and (b) total cost for each club A and B are: 105.

Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

Let, x be the number of months of membership

y be the total cost

Club A : y = 20x + 25 ......... (i)

Club B : y = 23x + 13 ........... (ii)

Because we know that the prices, y would be equal, we can set the two equations equal to each other.

20x + 25 = 23x + 13

or, 3x = 12

or, x = 4

So, after four months, the total cost would be the same.

Total cost for each club A and B are: 105.

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Answer:

m = 5 and n = 6

Step-by-step explanation:

In a parallelogram, opposite sides of the figure are congruent (equal to each other).

This means that 3m - 7 = m + 3 and 2n + 12 = 4n

We can now solve for the variables

3m - 7 = m + 3

==> add 7 to both sides

3m = m + 10

==> subtract 2 from both sides

2m = 10

==> divide both sides by 2

m = 5

2n + 12 = 4n

==> subtract 2n from both sides

12 = 2n

==> divide both sides by 2

6 = n

Answer:

n=6,m=2

Step-by-step explanation:

4n=2n+12

2n =12

n=6

m+3=3m-1

4=2m

m=2

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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When a quadratic equation is graphed, a parabola is produced, whereas a linear equation results in a straight line.Consequently, (1, 3) and are the answers to the system of equations (-5, -3)

In the following respects, quadratic equations differ from linear equations:When a quadratic equation is graphed, a parabola is produced, whereas a linear equation results in a straight line.In contrast to the slope of a linear polynomial, a quadratic polynomial's slope is dynamic.

(1, 3) and are the answers to the system of equations (-5, -3)

Considering the subsequent features

Y=x^2+5x-3

Y-x=2; y = x + 2

The result of equating both outputs is

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Formulation factorization

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Remember that y=x+2

y = 3 and -3

Consequently, (1, 3) and are the answers to the system of equations (-5, -3)

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Evaluation of the  amount is 42.78.

Evaluated; assessing Identify or set the value of anything by using a transitive verb to determine its importance, value, or condition, generally by meticulous analysis and research.

The act of evaluating or determining the standard, significance, quantity, or worth of something: It will be necessary to wait until all the data has been gathered before evaluating this new medicine.

Process, impact, result, and summative assessment are the four primary forms of evaluation.

$32.01

$0.76

$10.00

Evaluation of the  amount is

32.01 + 0.76 + 10.00 = 42.78.

Evaluation of the  amount is 42.78.

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need more info. add the question in but try the whole question.

a.  An inequality to represent how long the family should drive on the first day :

n ≥ 11.

b. the family should drive 11 hours.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

To get to the beach for vacation,

Cheng's family must drive at least 660 miles on the first day.

They are traveling at a constant speed of 60 miles per hour.

The total time  = 660 / 60 = 11 hours.

That means, the family should drive 11 hours.

An inequality to represent how long the family should drive on the first day :

n ≥ 11.

Therefore, inequality is n ≥ 11. And family should drive 11 hours.

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Answer:

Step-by-step explanation:

6

Answer:

17 gal.

Step-by-step explanation:

You can solve this using unitary method.

168 mi ---- 4 gal.

714 mi ---- 714 mi x 4 gal. /168 mi = 17 gal.

Answer: So in the image here, you are able to use the point thingamajig so here are the coordinates you would graph

(-2,-1)

(2 , 1 )

(4 , 2 )

(6 , 3 )

but after that i have no idea on what the inverse and direct operations are!

but i hope ^ that helps!!!

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer:

16 degrees

Step-by-step explanation:

90-74=16. Because the whole is 90 degrees, So you subtract it from the 74 degrees and you get your answer

The length of EF is 10.63 units.

The formula to find the distance between the two points is usually given by d=√((c – a)² + (d– b)²).

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Given:

From the graph the coordinates of E( -3, -4) and F(4, 4).

Using Distance Formula

EF = √ (4 - (-3))² + ( 4 -(-4))²

EF = √ (4+ 3)² + (4+4)²

EF = √ 7² + 8²

EF = √ 49 + 64

EF = √113

EF = 10.63 units

Hence, the length of EF = 10.63 units

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A pair of functions that are inverses of each other include the following: B. f(x) = 4x³ + 5 and g(x) = ∛[(x - 5)/4].

In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:

f(x) = y = ∛(x + 3) - 5

x = ∛(y + 3) - 5

x + 5 = ∛(y + 3)

Taking the cube of both sides of the function, we have:

(x + 5)³ = y + 3

g(x) = y = (x + 5)³ - 3 (Not an inverse of f(x)).

From the second answer option, we have the following:

f(x) = y = 4x³ + 5

x = 4y³ + 5

x - 5 = 4y³

Dividing both sides of the function by 4, we have the following:

y³ = (x - 5)/4

Taking the cube root of both sides of the function, we have:

g(x) = y = ∛[(x - 5)/4] (An inverse of f(x))

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The number that replaces the question mark is 5.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented by a symbol, such as a numeral or word. Numbers are used in various ways, including counting, measuring, and labeling. They can also be used to represent relationships between objects and ideas, and to measure the size, volume, and distance of objects.

This is because the pattern of the sequence is to add the two numbers that are next to each other together to get the next number. In the sequence, the two numbers that are next to the question mark are 6 and 7. When 6 and 7 are added together, the result is 13. Since 13 is greater than 12, the next number in the sequence must be 5.

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Answer:

0.413333333

Step-by-step explanation:

hope this helps

Answer:

0,39 because if you do 0.496÷1.2=0,3908333333 and If you round up is 0,39

Answer:

The final answer is 7.

Step-by-step explanation:

Since the question states that Little's law can be applied to any single part of the store (for example, just the checkout line), then the average number of shoppers,

�

, in the checkout line at any time is

�

=

�

�

, where

�

is the number of shoppers entering the checkout line per minute and

�

is the average number of minutes each shopper spends in the checkout line.

Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line. However, this needs to be converted to the number of shoppers per minute (in order to be used with

�

=

5

). Since there are 60 minutes in one hour, the rate is

84

shoppers

per

hour

60

minutes

=

1.4

shoppers per minute. Using the given formula with

�

=

1.4

and

�

=

5

yields

�

=

�

�

=

(

1.4

)

(

5

)

=

7

Therefore, the average number of shoppers,

�

, in the checkout line at any time during business hours is 7.

Answer:200 bucks

Step-by-step explanation:

This is because the point (1,4) is on the line.

Plugging x = 1 into y = 4x leads to y = 4.

Plugging x = 3 into that equation leads to y = 12; which explains why the point (3,12) is also on the line.

Answer:

31

Step-by-step explanation: 0.62*50=31

Answer:

I'd say about 31 Kilometers. (Sorry if I'm wrong!)

The algebraic property used for the expansion of the algebraic expression is; Distributive Property.

There are different algebra properties such as Associative property, Identity Property, Inverse property, Distributive property, commutative property.

The examples of these algebra properties are;

1) Associative Property; a + ( b + c ) = ( a + b ) + c

a( b c ) = ( a b ) c

2) Commutative property; a + b = b + a

3) Identity Property;

a + 0 = a and a ⋅ 1 = a

4) Inverse Property;

a + ( − a ) = 0 and a ⋅ 1 a = 1

5) Distributive Property;
a ( b + c ) = a b + a c

We are given the expression;

15x - 20xy as 5x(3 - 4xy)

From the earlier properties explained, this is clearly an example of distributive property.

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21.36 ft high up the wall is her friend.

An equation is a mathematical statement that two expressions are equal. It usually consists of two expressions separated by an equals sign (=). An equation can be used to describe the relationship between two variables, such as the distance and time it takes for an object to travel. Equations can also be used to solve for unknown variables.

Draw a diagram:

12ft
|\
| \
|  \
|   \
|    \
|     \
|      \
|_______\
56°    Friend

Create an equation:

tan (56°) = h/12

Solve for h:

h = 12 * tan (56°)
h = 21.36 ft

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Answer: [ln((4xy^2)/((x^2y)^2))]

Written as: ㏑((4xy²)/(x²y)²)

Step-by-step explanation:

ln(4xy^2)-2ln(x^2*y)

ln(4xy^2)-ln((x^2*y)^2)

ln(4xy^2)+[ln((x^2*y)^2)]*-1

[ln((4xy^2)/((x^2y)^2))]

Answer:

see below

Step-by-step explanation:

Given expression to us is ,

[tex]\longrightarrow ln (4xy^2)- 2ln(x^2y)\\[/tex]

Using identity

[tex]\longrightarrow ln (4xy^2) + (-2)ln (x^2y)\\[/tex]

[tex]\longrightarrow ln (4xy^2) + ln (x^2y)^{-2}\\[/tex]

simplify,

[tex]\longrightarrow ln(4xy^2) + ln (x^{2(-2)} y^{-2})\\[/tex]

using identity,

[tex]\longrightarrow ln(4xy^2)+ ln\bigg( \dfrac{1}{x^4 y^2}\\ [/tex]

using identity ,

[tex]\longrightarrow ln\bigg( xy^2\times \dfrac{1}{x^4y^2}\bigg)\\ [/tex]

simplify,

[tex]\longrightarrow ln\bigg(\dfrac{2}{x^3}\bigg)\\[/tex]

[tex]\longrightarrow \boxed{ ln \ (2x^{-3})}[/tex]

and we are done!

The solution to the algebra word roblem is; After 1 months, there will be 10 of each on staff.

We are given;

Initial number of junior residents = 9

Initial number of senior residents = 6

Rate of hiring  junior residents = 1 per month

Rate of hiring  senior residents = 4 per month

If number of months is x, then we have that;

9 + x = 6 + 4 x

Rearranging, we have;

4x - x = 9 - 6

3x = 3

x = 3/3

x = 1 months

Thus;

9 + x = 9 + 1

= 10 staff

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All of your answers are correct so far.

4. Line L is y=-2x-3. Line M is y=-2/3x+1

5. The solution is x=-3, y=3

6. Point P represents the answer to the equations.

8. Inequalities:

Line L: y>-2x-3

Line M: y<-2/3x+1

9. -3, 3

a) The amount of the monthly mortgage payment is 843.86

b) The total amount of interest Ato Liku that will pay over the life of the mortgage is 104,000

c) The amount of the mortgage Ato Liku will have paid after 10 years is 101,263.20

a) To determine the amount of the monthly mortgage payment, we need to use the formula for the monthly mortgage payment (also known as the loan payment formula):

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where M is the monthly mortgage payment, P is the principal (the remaining balance after the down payment), i is the monthly interest rate (12%/12 = 1%), n is the number of payments (30 years x 12 months/year = 360 payments), and ^ denotes exponentiation.

P = 250,000 x (1-.20) = 200,000

n = 30 x 12 = 360

i = 0.12/12 = 0.01

M = 200,000 [ 0.01(1 + 0.01)^360 ] / [ (1 + 0.01)^360 - 1]

M = 843.86

b) To determine the total amount of interest Ato Liku will pay over the life of the mortgage, we can subtract the original loan amount (200,000) from the total amount of the payments over the life of the loan:

total interest = total payments - original loan amount

total payments = M x n = 843.86 x 360 = 304,000

total interest = 304,000 - 200,000 = 104,000

c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we need to multiply the monthly mortgage payment by the number of payments made after 10 years.

10 years x 12 months/year = 120 months

Mortgage paid after 10 years = 843.86 x 120 = 101,263.20

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Their ages Mario is four years old, while Martina is five.

If a person is "x" years old now, then "n" years from now, that person will be "x + n" years old. The age of this would be equal to x - n years n years ago.

Mario is four years old, while Martina is five.

Explanation:

2x -y = 6 adding two to the number 4x -2y = 12

3x + 2y = 23

The sum of the two figures

4x - 2y = 12

3x + 2y = 23

7x = 35 by 7 multiply both sides.

Marina is x years old.

2x - y = 6 Put 5 in place of x, then figure out y.

2(5) -y = 6

10 -y = 6 From both sides, deduct 10

-y = -4 Divide the two sides by -1.

Mario has a value of 4.  

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