how are algebraic expressions used to represent and solve problems

Answer:

I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!

Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]

Add the square of the scaling factor s to the area of ​​the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of ​​the figure after dilation Ad. a d = s2a p .

To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of ​​the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]

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on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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Answer:

  -9447840

Step-by-step explanation:

You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.

The n-th term of a geometric sequence is ...

  an = a1·r^(n-1)

where a1 is the first term and r is the common ratio.

Using the given values, we have ...

  -160 = a1·(-1/3)^(11 -1)

  a1 = (-160)·(-3)^10 = -9447840

The first term is -9447840.

From the inventory ratios of  24 8, 33.4 and 53.8 of  Dunn and Bradstreet report. It can be concluded that

The problem is seeking expression of ratios in percentage

Ratios represents part or share of a whole while percentage refers to a fraction of hundred

Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up

= 24 8 + 33.4 + 53.8

= 108

Expressing as ratio 53.8 a percentage, we have

= 53.8/108 * 100

= 0.4981 * 100

= 49.81%

approximately 50%

We can therefore say that inventory of 53.8 or more is 50%

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The coordinates of the inflection points are (3, 0) and it concave upwards

From the question, we have the following parameters that can be used in our computation:

g(t) = t^2 - 27/t

Express properly

So, we have

g(t) = t² - 27/t

Calculate the second derivative

So, we have

g''(t) = 2 - 54/t³

Set the differentiated equation to 0

2 - 54/t³ = 0

So, we have

2t³ = 54

Divide by 2

t³ = 27

Take the cube roots

t = 3

Substitute t = 3 in g(t) = t² - 27/t

g(3) = 3² - 27/3

g(3) = 0

This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)

Recall that

g''(t) = 2 - 54/t³

Next, we check if the second derivative exist at t = 0,

g''(0) = 2 - 54/0³

g(0) = undefined

The undefined value implies that the graph has a vertical inflection point at t = 0

And as such, the graph of the function is concave upward

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The domain of the function whose graph shown in diagram is x ≤ 1.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

The domain of the function whose graph shown in diagram is x ≤ 1 as the value of x is less than 1.

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Answer:

A 0.9102

Step-by-step explanation:

A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.

The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.

A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.

A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.

Hence, the correlation coefficient is A, 0.9102

Answer:

she can fill 3 boxes completely and one book will be left over

Step-by-step explanation:

if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over

Answer:

Five hours after the museum opens, there are 36 visitors.

Step-by-step explanation:

V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.

A 90% confidence interval for the population mean is; CI = (163.355, 166.655)

The formula to find the confidence level here is;

CI = x' ± z(s/√n)

Where;

CI is confidence  level

z-score at confidence level

x' is sample mean

s is standard deviation

n is sample size

We are given;

Sample mean; x' = 165

Sample size; n = 20

standard deviation; s = 4.5

z at CL of 90% = 1.645

Thus;

CI = 165 ± 1.645(4.5/√20)

CI = 165 ± 1.655

CI = (163.355, 166.655)

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Producing written and visual content for social media can be divided into two items that can be developed as a one-person small business in a little amount of time.

Social media is internet communication that enables real-time information sharing and customer interaction. Social networking can help you: better connect with your audience. building online networks sell and publicise the goods and services you offer.

Social media's effects on business

The social media presence of businesses in order to boost visibility, engagement, positioning, and value creation for their intended audience has been facilitated by the digital revolution.

In order to help businesses establish their strategy in the digital environment, marketing and advertising agencies can quickly produce digital media such posters and catalogues in addition to advertising text as their core offerings.

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The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.

Simple Random Sampling Method:

Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.

Two-stage Cluster Sampling Method:

In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.

Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

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Answer:

19. Add

Step-by-step explanation:

10 - 7 =

13 - 10 =

16 - 13 =

16 + 3 =

5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.

5b) Under the lease, the customer saves $14,760.

5c) The lessee after returning the car has the following lease options:

6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.

6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.

6c) The monthly payment will be $567.26.

6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)

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Answer:

10. Yes
11. No
12. Yes
13. Yes
14. No
15. No

Step-by-step explanation:

Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.

10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.

Hope this helps.

Answer: To find the percent increase in pay, you can use the following formula:

percent increase = ((new pay - old pay)/old pay) * 100

Plugging in the values given in the question, you get:

percent increase = ((11.75 - 10.50)/10.50) * 100

= (1.25/10.50) * 100

= 0.119047619 * 100

= 11.9047619%

Therefore, the percent increase in pay is approximately 11.9%.

Step-by-step explanation:

Complete the puzzles with values -4, 0, -3 and 2

Since each row, column, and diagonal adds up to the same total.

For the 1st row, the total is:

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

That means each row, column, and diagonal will always adds up to 0.

3 + w + 1 = 0

w = -3-1

w = -4

w + y + 4 = 0

-4 + y + 4 = 0

y = 0

-1 + 4 + t = 0

3 + t = 0

t = -3

1 + h + t = 0

1 + h + (-3) = 0

h -2 = 0

h = 2

(Check the attached image for labeling)

Thus, complete the puzzle with the values accordingly

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On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so

[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]

The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.

Permutations refer to the arrangements of objects in certain order or way.

The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.

The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.

The probability is obtained as 1 / ₉P₃

where;

₉P₃ = 9! / (9 - 3)!

₉P₃ = 9! / 6!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

₉P₃ = 504

Hence, the probability = 1/504

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The liners function are not direct variation

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation.

For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation

If b is directly proportional to a, then k is the constant of variation and the value of k = b/a for all value of b and a

In the problem, the variables are compared as follows

feet = k * sec

k = feet / sec

For the first values, k = 33 / 3 = 11

For the second values, k = 36 / 6 = 6

since 11 ≠ 6 the function is not a direct variation

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If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.

The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

S1 probability = 0.6

F's likelihood is 0.40.

If the probability of S1 is given a value of 0.6, then

Probability of S2 then equals 0.4.

Using the table equation's payoff values as an exception.

EV=Σ

Each decision's expected value is calculated.

EV(Node 8) = 0.6 * 100 + 0.4 * 300

= 180

EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320

We chose the best value for node 4 from nodes 8 and 9.

The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.

The ideal anticipated value is determined to be 320.

Node 4's EV is 320.

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The number of Dvds owned by Maarissa is 45

The given parameters that will guide us in finding the number  of dvds owned by marissa are

Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.

Let the number of dvds owned by Marissa be x

Nymber of dvds owned by Kyle be y

This implies that  x+y = 66 ............................1

also, 2y + 3 = x ..................................................2

Substitute x = 2y + 3 in equation 1

= 2y + 3+y =66 Collecting like terms

⇒ 3y = 63

Making y the subject of the relation we have y=21

Recall that  2y + 3 = x

That means x = 2(21) + 3

x=45

Therefore Marrissa owns 45 dvds

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The required ratio is 1:2.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given that, A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions, it can be a shorter time between the first and second flashes than between the second flash and the third flash,  One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. The beacons are set 120 degrees apart along the rotation

If the second beacon is 120° after the first, then the first is 360° -120° = 240° after the second.

Therefore, the ratio of the times between beacons is =

120° : 240° = 1 : 2

Hence, the ratio is 1 : 2

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On solving the provided question, we can say that - here the value of exponential equation is 648/1296 = 0.5

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

So, the equation is

[tex]3(2x^3y^5)^3/ (2x^6y^3)^4[/tex]

and x=y=1

so, 648/1296 = 0.5

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The transformation in the graph is 1 units vertically downwards.

The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.

Let the function f(x) and g(x) are two real functions.

And  g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

The function f(x) = eˣ,

and the function g(x):

g(x) = f(x)-1= eˣ-1.

The graph of both the functions are given in the attached images.

For the base function f (x) and a constant k, the function given by

The transformations in the graph is defined by:

g (x) = f (x) + k, where k is real numbers.

Function can be sketched by shifting f (x), k units vertically.

The value of k determines the direction of the shift. Specifically,

if k > 0, the base graph shifts k units upward, and

if k < 0, the base graph shifts k units downward.

Here, k = -1

And the graph of g(x) is the graph of f(x) is shifted down 1 unit.

Therefore, the f(x) is shifted to 1 unit downward.

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Answer:

Step-by-step explanation:

-12