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Our school flag is a rectangle. We are changing to a new rectangular flag design. The length of the new flag is 20% greater than the length of the old flag, and the width of the new flag is 10% less than the width of the old flag, The old school flag is 25 square feet. What is the area of the new flag?

Answer:

y=3x-2

Step-by-step explanation:

y is for how many miles she wants to walk which is 6. she walks 3 miles per hour which is 3x (x is for hours) and -2 because she already walked 2 miles

The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³ thus option (C) will be correct.

Density or mass density is the mass of any object per volume.

For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.

Density can be uniform or non-uniform.

Density is the division of mass and volume and the mass must be for the quantity of the volume only.

Given that,

Mass = 10 g

Volume = 2.5 cm³

Density = 10/2.5 = 4 g/cm³

Hence "The density is the ratio of mass to volume of an object thus the density of the given test sample is 4 g/cm³".

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The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.

Equation of the Axis of Symmetry of a Parabola:

The equation for the axis of symmetry of a parabola can be expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.

The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.

Calculating the Axis of Symmetry of a Parabola:

Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.

It is expressed as:

[tex]x=\frac{-b}{2a}[/tex]

Or x = -2 after you substitute in the values for a and b.

Finding the Vertex of a Parabola:

To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.

When we continue with the previous example, we know that x = -2.

We substitute that value for x in the original quadratic function.

[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]

Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.

How To Find Axis of Symmetry?

Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.

[tex]x=\frac{-b}{2a}[/tex]

Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,

[tex]y = ax^{2}+bx+c[/tex].

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The rate of change of the exponential function f(x) = 2(2)ˣ is 2

An equation shows the relationship between two or more numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the rate of change.

Given the function:

f(x) = 2(2)ˣ

Hence rate of change = 2

The rate of change is 2

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The expected total prize money is $2p/q.

Given that,

You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.

Let,

The probability of correctly answering a question is = p

The probability of incorrectly answering a question is = q

The number of failures after which you are eliminated is = 2

Let r = 2 =  No. of failures and

Let q = The probability of failure in a single question

Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.

The expected value of a negative binomial distribution is given by

E[X] = r/q

So, the expected number of questions that you will attempt is = r/q = 2/q

Out of 2/q questions, the expected number of correct questions is = 2p/q

So, the expected total prize money is $2p/q.

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Plot these points on a graph and draw a line connecting them beginning at (0, 4) and ending at (18, 31). The graph is plotted below.

Given:

Starting cart denotes that the number of nested carts is zero.

So, let the x axis represent the number of nested carts and the y axis represent the height of the nested carts.

As per question,

When x = 0 , the height is y = 4 ft

When x = 13, the height is  y = 2.5 ft

When x = 18, the height is  y = 31 ft

So, the points on the graph are (0,4), (13, 23.5) and (18, 31).

Plot these points on a graph and draw a line passing through all these points starting at (0, 4) and ending at (18, 31).

The graph is shown below.

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The total charge for the month is £625.36.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given:

Fixed monthly plan - 616

free minutes - 150

Used minutes - 170

Free text - 150

Used text - 182

Charging amount over the free limit - 18p

Number of minutes over the limit -  170 - 150 = 20

Number of text over the limit - 182 - 150 = 32

So the extra amount that will be added to the monthly charge would be -

(20 x 0.18) +(32 x 0.18)

The total charge of the month would be -

C= 616+(20*0.18) +(32*0.18)

C= 616+3.60+5.76

C= 625.36

Therefore, the total charge for the month is £625.36.

The correct question is given below,

Here are the monthly charges for Jo's mobile phone

Monthly charge 616

150 free minutes, then 18p per minute

150 free texts, then 18p per text

During one month, Jo makes 170 minutes of calls and sends 182 texts,

Work out the total charge for the month

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Answer:

decimal form> -4.87577494

Exact form> -In(212)/In(3)

We can conclude that the table in option (D) represents a linear function.

So, the linear function will be:

Then,

So, option (D) is correct.

Therefore, we can conclude that the table in option (D) represents a linear function.

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The possible number of license plates is 6084000 .

We have to make a 6 word license plate in which first two are letters and remaining four are digits.

conditions are :

1. letters and digits can repeat themselves

2. 1st digit can't be 0.

taking into account these conditions

we know total letters are 26 and total digits are 10 ( 0,1,2,3,4,5,6,7,8,9)

Now if we divide number plate in 6 columns where first two are filler by letters and rest four by digits so

1st column can be filled in ways = 26

2nd column can be filled in ways = 26

3rd column can be filled in ways = 9 ( as zero is not allowed )

4th column can be filled in ways = 10

5th column can be filled in ways = 10

6th column can be filled in ways = 10

therefore, total number of ways = 26x26x9x10x10x10

                                                      = 6084000 ways

The possible number of license plates is 6084000 .              

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The length of the rectangular area is 800 yards and width is 800 yards

The perimeter of the rectangular area = 3200 yards

The perimeter of the rectangle = 2 (l + w)

Then the equation will be

2(l + w) = 3200

l + w = 3200 / 2

l + w = 1600 yards

w = 1600 - l

The area of the rectangular area = l × w

= l(1600 - l)

Since the area is maximizing the the rate of change of area will be zero

l × w = 0

1600 - 2l = 0

2l = 1600

l = 1600/2

l = 800 yards

Then

w = 1600 - l

Substitute the value of l in the equation

w = 1600 - 800

w = 800 yards

Hence, the length of the rectangular area is 800 yards and width is 800 yards

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Answer:

[tex]\frac{11}{4}[/tex] or 2 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Here is one way to solve this problem

2x - [tex]\frac{7}{4}[/tex] = x + 1  (3/3 is another way to write one)  Multiply all the way through by 4

4(2x - [tex]\frac{7}{4}[/tex]) = 4(x + 1)  Distributive property

8x -7 = 4x +4  Subtract 4x from both sides

4x - 7 = 4  Add 11 to both sides

4x = 11  Divide both sides by 4

x = [tex]\frac{11}{4}[/tex]

The population in 208 years based on the information is 10193600.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Since the city doubles its size every 52 years. The number of times that it'll double in 208 years will be:

= 208 / 52

= 4 times

The population in 208 years will be:

= 637100 × 2⁴

= 637100 × 16

= 10193600

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The information about the graph of the relationship that is given is: E. y-intercept and a point that is not an intercept.

In Mathematics, the y-intercept of any graph such as a linear, quadratic, trigonometric function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a straight line is generally modeled or represented by this mathematical expression;

y = mx + c

Where:

In this context, we can reasonably infer and logically deduce that the total number of pages (y-intercept) which is equal to 180 is an information that was provided, as well as the number of hours (666 hours), which represents a data point on the x-coordinate of the graph.

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(7) 55 is 181.81% of 100

(8) 22% of 110 is 24.2

(9) 19 is 50% of 38

(10) 25 is 32% of 78.125

(11)  40% of 70 is 28.

(12) 30 is 200% of 60.

What is percent?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

(7) Suppose 55 is x%  of 100.

So,

55x/100 = 100

x/100 = 100/55

x = 1.8181 x 100

x = 181.81%

Therefore, 55 is 181.81% of 100.

(8) Suppose 22% of x is 24.2

So,

x(22)/100 = 24.2

x = 24.2 x 100/22

x = 110

Therefore, 22% of 110 is 24.2

(9) Suppose 19 is 50% of x.

So,

19 = 50(x)/100

x = 19 x 100/50

x = 38

Therefore, 19 is 50% of 38.

(10) Suppose 25 is 32% of x.

So,

25 = 32(x)/100

x = 25 x 100/32

x = 78.125

Therefore, 25 is 32% of 78.125

(11) Suppose 40% of x is 28

So,

40(x)/100 = 28

x = 28 x 100/40

x = 70

Therefore, 40% of 70 is 28.

(12) Suppose 30 is x% of 60

So,

30(x)/100 = 60

x = 60 x 100/30

x = 200

Therefore, 30 is 200% of 60.

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The mason should order 250 cubic yards of grit to use all the cement.

It is given that the mixture has 20 cubic yards of grit for 4 cubic yards of cement.

So the unit rate for the number of cubic yards of grit for per unit of cement is given by : 20 ÷ 4 = 5 cubic yards.

Now amount of grit required for 50 cubic yards of cement

= 50 × 5 = 250 cubic yards.

By utilising 1 as the denominator, a unit rate compares two quantities while using the second quantity as the unit of measurement. If someone runs three kilometers in 30 minutes, they have ran one mile.

Miles per minute is a unit of measurement for how far something is moving in a certain amount of time. For unit rate, the quantity value 1 is always used.

Hence he should order about 250 cubic yards in order to use all the cement.

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Answer:

x = 5

Step-by-step explanation:

3x + 5 = 2x + 10

subtract 5 from both sides:

3x + 5 - 5 = 2x + 10 - 5

3x = 2x + 5

subtract 2x from both sides:

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

x = 5

The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.

What is a sequence?

A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.

We are given a sequence 8, 5,2, -1,.....

Now the first term of the sequence is 8 and common difference is -3.

As the difference between 2 consecutive terms is same, the given sequence is arithmetic.

now substituting this in the standard equation

we get,

t(n) = a+ (n-1)d

t(n)= 8+(n-1)(-3)

t(n) = 8-3n+3

t(n) = 11-3n                           (1)

Now we have to find the 5th, 6th, 7th term of the sequence

We substitute n=5, n=6, n=6 in equation 1

We get

t(5) = 11-3(5)

t(5) = 11-15

t(5) = -4

And,

t(6) = 11-3(6)

t(6) = 11-18

t(6) = -7

And,

t(7) = 11-3(7)

t(7) = 11-21

t(7) = -10

Hence the next three terms are -4, -7, -10.

The equation is t(n) = 11-3n

The 100th term would be given as

t(100)  = 11-3(100)

t(100)  = 11-300

t(100) = -289

Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289

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Answer:

14

Step-by-step explanation:

[tex]\frac{4 \text{ miles}}{1 \text{ hour}} \times 3.5 \text{ hours}=14 \text{ miles}[/tex]

Equation of parallel line is y = x + 5

What in math is a coordinate?

a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

Step-by-step explanation:
If there is a constant distance between each point and the two lines never cross, they are considered to be parallel. If two lines have the same slope, they are said to be parallel.
By above statement we concluded that y = x should be same as its but we can change its intercept part
Hence Equation parallel to y = x + 6 is y = x + 5

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Answer:

58

Step-by-step explanation:

PEMDAS!

1) 20/2 = 10

2) 10*5+8

3) 10*5 = 50
4) 50 + 8 = 58

Answer is 58, hope this helps ;)

Radius of Earth's moon is [tex]1.737*10^{8}[/tex]

Very big or very small numbers can be presented in a simpler way using scientific notation. Although whole numbers can be stretched to infinity, humans are unable to write such enormous numbers on paper. Additionally, it was necessary to represent the numbers that appear at the millions place after the decimal in a more straightforward manner. The extended form of a few numbers is therefore difficult to represent. So, we employ scientific notations.

Given, radius of Earth's moon is 173,700,000.

As we know, in scientific notation there is only one number to the left.

So, we need to move the decimal to 8 places.

Therefore, radius of Earth's moon is [tex]1.737*10^{8}[/tex].

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The probability that shooting stars are there in the fall is 0.5904.

The probability of not seeing any falling star in that time period of 15 minutes is 1 - 0.2 = 0.8.

In this way, the combined probability of not seeing any of the falling stars in the four-time period is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096

= 1 - 0.4096 = 0.5904

=P(X = x) = μˣ * e^-μ / x!

Here, the span is of 15 minutes. In this way, the typical number of events in the span is 15λ. The probability of witnessing 0 occasions (i.e X = 0) is:

P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)

(1) is equal to 80% as the probability of at least one event happening is 20%.

So, 1 / e^(15λ) = 0.8

or, e^(15λ) = 1.25

or, 15λ = ln(1.25) = 0.2231

= λ = 0.0149 / min

In this way, the typical number of occasions (falling stars) is 0.0149 per minute.

Presently, the typical number of occasions in an hour is:

0.0149 * 60 = 0.8926 / hour

So, the Poisson distribution expression becomes:

P(X = x) = 0.8926ˣ * e^-0.8926 / x! — — (2)

Here, the time span is 60 minutes.

Presently, we should find the probability of not having even a solitary occasion in 60 minutes:

P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096

So, the probability of having at least one event is the complement of the above probability.

So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904

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Solving the system of equations we can see that:

We can define the variables:

x = price of a Douglas Fir trees

y = price of a Noble Fir trees.

By using the given information we can write:

6x + 16y = 986

6x + 24y = 1368

That is our system of equations

If we take the second equation and we subtract the first one we get.

(6x + 24y) - (6x + 16y) = 1368 - 986

8y = 382

y = 382/8 = 47.75

now that we know the value of y, we can find the value of x using the first equation.

6x + 16y = 986

6x = 965 - 16y

x = (965 - 16y)/6

x = (965 - 16*47.75)/6 = 33.5

So:

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There would be 1024 possible outcomes on a 5 question test with each question having 4 possible answers.

Based on the given information, there are 4 possible ways for each of the 5 questions.

4 possible ways to answer Question # 1

4 possible ways to answer Question # 2

4 possible ways to answer Question # 3

4 possible ways to answer Question # 4

4 possible ways to answer Question # 5

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible outcomes is

4 x 4 x 4 x 4 x 4 = 1024

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If the soccer team is going to purchase only warm-up pants, then the greatest number of warm-up pants the team can purchase is 42, but if instead the soccer team is going to purchase only duffel bags, then the greatest number of duffel bags the team can purchase is 54.

Inequality, a relationship between two values/expressions that aren't equal to each other, is involved in solving this problem.

The soccer team's got $1,512 to purchase either all warm-up pants or all duffel bags. The cost of the warm-up pants is $36 each and the cost of the duffel bags is $28 each. Since you're asked to find the greatest numbers of each purchase, you'll need to write inequalities to figure out the answer.

The keyword here is "greatest number", so you can use the symbol ≤ for the inequalities. Therefore, 36x ≤ 1,512 is the inequality for finding the greatest number of warm-up pants and 28x ≤ 1,512 is the inequality for finding the greatest number of duffel bags.

The solutions to the first and second inequalities are, consecutively, x ≤ 42 and x ≤ 54, meaning the team can buy at most 42 warm-up pants or 54 duffel bags.

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Total fenced need to replaced is 60 feet

The Perimeter of rectangle is two times the sum length and width.

i.e., Perimeter of rectangle= 2( l+ w)

Given:

Rabbit Pen: Length= 3.5, width= 4.5

Garden: length= 12, width = 10

So, Perimeter of Rabbit Pen = 2( 3.5 + 4.5)

                                               = 2( 8)

                                              = 16 feet

Now, Perimeter of Garden = 2 (12 + 10)

                                              = 2( 22)

                                              = 44 feet.

Total fenced need to replaces= 16 +44 = 60 feet

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Answer:

Step-by-step explanation:

76