How is math used in making murals?(subject:Collage and Career readiness)

When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.

What is a graph?

We use the term graph to describe the presentation of data by the use of cartesian coordinates. The coordinates are usually the x and the y coordinates and the data that is plotted is the dependent and the independent variable.

Now when we have a variable whose value lies so much apart from the rest of the values, we call this an outlier. When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.

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The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Analyzing the coordinates being provided, the scale factor is found to be 0.5, hence the image of point A(12,4) under the same dilation and the center of dilation as origin is A'(6,2).

A dilation is a transformation in Euclidean space that enlarges or reduces all the points in a figure by a scale factor. In the example given, the dilation maps (6, 10) to (3, 5) with a scale factor of 0.5, and the center of dilation is the origin (0,0). The image of a point A(x,y) under this dilation would be A'(x*0.5, y*0.5). It means the point is scaled down by 0.5 in both x and y coordinate.

The dilation described above can be used in real-world applications such as image processing, where it can be used to reduce the size of an image without losing important details, or to enlarge an image without introducing distortion. It can also be used in architectural design to create smaller or larger versions of floor plans and blueprints. Additionally, it can be used in cartography to change the scale of maps without altering the shape of the features on the map.

Analyzing the given dilation map , mapped from (6,10) to (3,5) ,the center of the dilation being origin. We can see that the scaling factor is 0.5.

So , using the same dilation for point A(12,4), The image of A will be,

A'(12*0.5,4*0.5) = A'(6,2)

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3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

The answer is (2x+y)(2x-3)

Step-by-step explanation:

I learned this on ixl, its kind of hard to explain.

\(

6+5\sqrt{249}-2x=7 \\

-2x=7-6-5\sqrt{249} \\

-2x\approx-77.9 \\

x\approx\frac{-77.9}{2}\approx38.95

\)

Hope this helps.

\(\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}\)

Answer:

y=-x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-2))/(3-1)

m=(-4+2)/2

m=-2/2

m=-1

y-y1=m(x-x1)

y-(-2)=-1(x-1)

y+2=-x+1

y=-x+1-2

y=-x-1

Answer:

There are 1650 child visitors and 550 adult visitors

Step-by-step explanation:

Use this step by step that was already used before to answer this, it's a png file.

A system of linear equations that represents this situation is,

⇒ x + y = 2200

⇒ 6x + 9y = 14,850

Where, x represent the cost of a ticket for a child and let y represent the cost of a ticket for an adult.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Zoo admission costs $6 for children and $9 for adults.

And, On Monday, 2200 people visit the zoo and the zoo collects $14,850 in admissions.

Let x represent the cost of a ticket for a child and let y represent the cost of a ticket for an adult.

Hence, We can formulate;

A system of linear equations that represents this situation is,

On Monday, 2200 people visit the zoo.

So, we get;

⇒ x + y = 2200 .. (i)

And, Zoo admission costs $6 for children and $9 for adults and the zoo collects $14,850 in admissions.

So, We get;

⇒ 6x + 9y = 14,850 .. (ii)

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Hi!

The coefficient of x is known as the slope, and that can be represented as rise/run, and in this example is it 1/4, therefore your rise is 1.

Hope this helps! :D

Answer:

Step-by-step explanation:

We know that:

Let's compare the slope and its formula.

Work:

Hence, the rise of the slope is 1.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

It would be a lot of bavgeria

Answer:

450000

Step-by-step explanation:

125×(60×60)

=125×3600

=450000

Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

Answer:

To solve this problem, we need to subtract the cost of the book and the total amount donated to charities from the total amount of cash Katye received for her birthday. Here are the steps:

Add up the value of the gifts Katye received:

Total value of gifts = (value of gift 1) + (value of gift 2) + ... + (value of gift 15)

Add up the value of the cash Katye received:

Total cash = $100

Subtract the cost of the book from the total cash:

Cash remaining after buying the book = $100 - $23

Determine the maximum number of $10 donations that Katye can make:

Maximum number of $10 donations = (cash remaining after buying the book) / $10

Multiply the maximum number of donations by $10 to get the total amount donated:

Total amount donated = (maximum number of $10 donations) x $10

Subtract the cost of the book and the total amount donated from the total cash:

Cash remaining = $100 - $23 - (total amount donated)

The final answer will be the cash remaining after these calculations

The ticket price that would maximize the total revenue would be $ 23.

Given that a football team charges $ 30 per ticket and averages 20,000 people per game, and each person spend an average of $ 8 on concessions, and for every drop of $ 1 in price, the attendance rises by 800 people, to determine what ticket price should the team charge to maximize total revenue, the following calculation must be performed:

Therefore, the ticket price that would maximize the total revenue would be $ 23.

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Answer:

Find 10% Then half it to find 5%. Times what 10% is by 2 and then add the 5%. Or find out what goes into 24 4 times as it's 25% off and 25 goes into 100 4 times.

Step-by-step explanation:

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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The expected value of the random variable D is 6.. This gives us the following equation :E[D] = 0(1/6) + 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6)

The expected value of the random variable D, E[D], can be calculated using the following formula :E[D] = ΣD P(D) Where ΣD is the sum of all possible values of D and P(D) is the probability of each of those values. In this case, the possible values of D are 0, 1, 2, 3, 4, 5. The probability of each of these values is the same, since each has an equal chance of being rolled on the dice. To calculate the expected value, we must multiply each value of D with its probability, and then sum all of these products. This gives us the following equation:E[D] = 0(1/6) + 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) .E[D] = 36/6 = 6.Therefore, the expected value of the random variable D is 6.

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The algebraic representation of the expression is (m + n)

sum of m and the number after it

= m + n

Therefore, the algebraic representation of the expression is (m + n)

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A line graph is a type of chart used to show information that changes over time.

The line graph is given below.

A line graph or line plot or a line chart is a graph that uses lines to connect individual data points. It displays quantitative values over a specified time interval.

We have,

2 | x + 2 | ≤ 14

We have to substitute x = 1,2,3,4,5,..... such that it is less than or equal to 14.

      x           1     2     3     4     5        

2 | x + 2 |     6    8     10   12    14

Since we need 2 | x + 2 | to be less than or equal to 14 we can take the x values up to 5 only.

Now,

We will plot the line graph and it is given below.

Thus the line graph is given below.

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The probability that the sample mean will be greater than M = 10 pounds is 0.9525.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain. Probability is used in many fields, including mathematics, statistics, science, and finance.

To solve this problem, we need to use the central limit theorem (CLT), which states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is small (n = 4), we need to use the t-distribution instead of the normal distribution. However, since the population standard deviation is known, we can use the standard normal distribution with a z-score.

First, we need to calculate the standard error of the mean:

SE = σ / sqrt(n) = 6 / sqrt(4) = 3

Next, we can calculate the z-score:

z = (M - µ) / SE = (10 - 15) / 3 = -1.67

Finally, we can use a standard normal distribution table or calculator to find the probability of a z-score greater than -1.67:

p(M > 10) = P(z > -1.67) = 0.9525 (rounded to four decimals)

Therefore, the probability that the sample mean will be greater than M = 10 pounds is 0.9525.

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Part a

\(A(11)=224-16(11)=\boxed{\$48}\)

Part b

\(A(t)=0\\\\224-16t=0\\\\t=\frac{224}{16}\\\\t=\boxed{14 \text{ trips}}\)

a) The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48

b) The number of trips on the toll roads can he take until his account is empty is 14 trips

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A ( t ) = 224 - 16t , where t is the number of trips

a)

The amount of money does Ahmad have left in the account after 11 trips on the toll roads be P

Substituting the value of t = 11 in the equation , we get

A ( 11 ) = 224 - 16 ( 11 )

A ( 11 ) = 224 - 176

A ( 11 ) = $ 48

So , The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48

b)

The number of trips on the toll roads can he take until his account is empty be n

when A ( t ) = 0

224 - 16t = 0

Adding 16t on both sides of the equation , we get

224 = 16t

Divide by 16 on both sides , we get

t = 14 trips

Hence , the equations are solved

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Answer:

The answer is 5.20

Step-by-step explanation:

Since the tenth place is lower than 5 it stays the same

Answer:

y = 13x - 6

Step-by-step explanation:

Hope This Helps ;)

Plz Mark Brainliest!!!

The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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Answer:

it made Texas thrive because they were one of the leading cotton producers and made a lot of money off of it

The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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The transformed function can be written as:

g(x) = 6*log₆(x) - 5

We start with the function f(x), if first we apply a vertical dilation of scale factor 6 we will get:

g(x) = 6*f(x)

If now we apply a translation of 5 units down, we will get:

g(x) = 6*f(x) - 5

We know that f(x)=  log₆(x), then the transformed function is:

g(x) = 6*log₆(x) - 5

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Answer:

10 pieces

Step-by-step explanation:

Total no. of pieces of calzone = 24

No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

Total no of pieces eaten by both of them on saturday = 12.

No of pieces of calzone left = 24-12 = 12

_______________________________________________

No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone  left= 1/6 of 12 = (1/6)*12= 2 pieces

No of pieces of calzone left now after Glenn ate 2 of them = 12-2 = 10.

Thus 10 pieces  of original calzone are left  .

The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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