need help due today……..

The percentage change in the number of websites from 1991 to 1992 is 900%.

Given that,

In 1991 there was 1 website.

In 1992 there were 10 websites.

The formula to find the percentage change is,

Percent change = (New value - old value) / old value

Here,

New number of websites = 10

Old number of websites = 1

Percentage change = (10 - 1) / 1 = 9 = 900%

Hence the percentage change in the number of websites is 900%.

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The area of enclosed region is 18 square units by equation of curve y= 5x²  and y =x² +9 with application of integration.

Dr.Jones  decides to build a fence as represented by the given two equations,

y =5x² ___(1)

and y= x² + 9 ___(2)

To find the point of intersection of the two equations we equate (1) and (2) as,

5x² = y = x² -9

⇒ 5x² = x² -9

⇒ 9 -4x²  = 0 ___(3)

⇒ 4x² = 9

⇒ x² = 9/4

Taking square roots on both the sides we get,

⇒ x = ± 3/2

Thus the interval in which value of x ( as length of fence) lies is (-3/2 , 3/2).

Therefore, we can calculate the area enclosed region by  equation (1) and (2) with the formula of integration,

Area= integration of equation (3) in interval (-3/2,3/2) = [tex]\int\limits^a_b {9-4x^2} \, dx[/tex]  

where, a =3/2 and b =-3/2

=[ 9*(3/2) - (4/3)*(3/2)³] - [ 9*(-3/2) - (4/3)(-3/2)³ ] sqaure units

= 18 square units

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The given question is incomplete, the complete question is

"Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y=5x^2 and y=x^2+9. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?"

Answer: 344

Step-by-step explanation:

Well I dont know

Answer:

7% of cars traveled east.

Answer: 536.6 cm²

Step-by-step explanation:

Area for 3 rectangles = bh*3

=(10)(15)(3) = 450

Area for 2 triangles = 1/2 bh *2

= 1/2 10*8.66*2

=86.6

Total area = 86.6+450=536.6

The circumference of a circle is 14π cm. Then, the area of the circle is 49π square centimeters.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter or the boundary of the circle. It is calculated by multiplying the diameter or radius of the circle by the mathematical constant pi (π), which is approximately equal to 3.14159.

The formula for the circumference of circle will be C = 2πr, where C is circumference and r is radius. We are given that the circumference of the circle is 14π cm, so we can write;

14π = 2πr

Dividing both sides by 2π, we get;

r = 7

Now we can use the formula for the area of a circle, A = πr², to find the area of the circle;

A = π(7)²

A = 49π

Therefore, the area of the circle will be 49π square centimeters.

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--The given question is incomplete, the complete question is

"The circumference of a circle is 14π cm. What is the area, in square centimeters? Express your answer in terms of π."--

The quadratic function g(x) = - 3 · (x + 5)² + 12 is the result of the following rigid transformations:

In this problem we find a quadratic equation that must be modified by means of rigid transformations. The most known rigid transformations are listed below:

If we know that f(x) = x², then the resulting functions are found by using the following steps:

1) Write the entire function:

f(x) = x²

2) Horizontal translation:

f'(x) = (x + 5)²

3) Vertical dilation:

f''(x) = 3 · (x + 5)²

4) Reflection about x-axis:

f'''(x) = - 3 · (x + 5)²

5) Vertical translation:

g(x) = - 3 · (x + 5)² + 12

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Gabe spent approximately $81.82 at the mall if he bought 2 items.

The expression given to us is 18.91x + 21, where x represents the number of items Gabe bought at one store. We can interpret this expression as follows: For each item Gabe buys, he spends $18.91, and he also spends an additional $21 regardless of the number of items he buys. Therefore, if he buys n items at this store, he would spend 18.91n + 21 dollars.

Now, we are told that Gabe spent $23 at another store. To find the expression that represents the total amount he spent at the mall, we add the amount he spent at both stores. Therefore, the expression we are looking for is:

Total amount = 18.91x + 21 + 23

Simplifying this expression, we get:

Total amount = 18.91x + 44

This expression represents the total amount Gabe spent at the mall based on the number of items he bought at the first store.

To estimate how much money Gabe spent if he bought 2 items, we can substitute x = 2 into the expression we just derived:

Total amount = 18.91(2) + 44

Total amount = 37.82 + 44

Total amount = 81.82

Therefore, if Gabe bought 2 items, he would have spent approximately $81.82 at the mall.

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It would take 28 minutes to evacuate 21,000 people from the Wild Wind Stadium using only 15 exits

The time to evacuate the stadium varies directly with the number of people and inversely with the number of exits used. This means that the time it takes to evacuate the stadium is proportional to the number of people and inversely proportional to the number of exits used.

Let t be the time it takes to evacuate 21,000 people if only 15 exits are used. Let k be a constant of proportionality. Then we have

t = k × (number of people) / (number of exits)

We know that it takes 20 minutes to evacuate the stadium with all 25 exits in use. This gives us another equation

20 = k × 25000 / 25

Simplifying this equation, we get

20 = 1000k

k = 0.02

Now we can use this value of k to find the time it takes to evacuate 21,000 people with only 15 exits

t = 0.02 × 21000 / 15

t = 28 minutes

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The correct point on the graph would be (1, 14). This point represents the population of stingrays in the enclosure after 1 year.

In the given inequality, the population of stingrays in the enclosure is expected to at least double every year, which means the population grows exponentially.

The graph of an exponential function appears as an upward curve, and the point that represents the initial population of 7 stingrays would be the one located closest to the y-axis, which is point (0, 7).

Since the population of stingrays is expected to double every year, after one year it would be 7 x 2 = 14.

Thus, the point (2, 28) would represent the population of stingrays after 2 years, and so on.

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Based on the concepts of simple interest and compound interest, the TRUE statement about these two accounts after 5 years is b) Account Y would earn Monica $62.70 more interest than Account X.

Under the simple interest system, interest is computed on only the principal for each period.

Under the compound interest system, interest is computed on both the principal and accumulated interest for each period.

Principal = $3,000

Interest Rate = 2.1%

Period = 5 years

Simple Interest = $315.00 ($3,000 x 2.1% x 5)

N (# of periods) = 5 years

I/Y (Interest per year) = 2.4%

PV (Present Value) = $3,000

PMT (Periodic Payment) = $0

Results:

FV = $3,377.70

Total Compound Interest =$377.70

Difference in Interest = $62.70 ($377.70 - $315.00)

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Monica wants to open a savings account with a deposit of $3,000.  Monica will not make any further withdrawals or deposits after she opens the account.  Her bank offers two different savings accounts.

Which statement about these two accounts after 5 years is true?

Options:

a) Account X would earn Monica $62.70 more interest than Account Y.

b) Account Y would earn Monica $62.70 more interest than Account X.

c) Account X would earn Monica $45.00 more interest than Account Y.

b) Account Y would earn Monica $45.00 more interest than Account X.

Step-by-step explanation:

Maximum area enclosed will be a square enclosure

  since the river is one side , the other three sides of the square will be

       1440 / 3 = 480 ft long

Square with sides 480 ft

area =480 x 480 = 230 400 ft^2

To determine if the point (5,1) is part of the line y = 7-2x, we need to substitute x=5 and y=1 into the equation of the line and check if it is a true statement:

y = 7 - 2x

1 = 7 - 2(5)

1 = 7 - 10

1 = -3

Since -3 is not equal to 1, the point (5,1) is not part of the line y = 7-2x.

The time of the day when two vehicles will leave park at same time is 11:20 a.m.

Traffic can be controlled by adjust the departure times, use a reservation system, limit the number of vehicles , and promote carpooling.

To create the departure timetable,

Start by listing the times at which the first bus and minibus will leave the park.

From there, add 40 and 50 minutes respectively to each departure time to find the next departure time for each vehicle.

Here is the timetable,

Departure time                Bus interval         Minibus interval

8.00 a.m.                               40min               50min

8.40 a.m.                               40min               50min

9.20 a.m.                               40min               50min

10.00 a.m.                               40min               50min

10.40 a.m.                               40min               50min

11.20 a.m.                               40min               50min

12.00 p.m.                               40min               50min

12.40 p.m.                               40min               50min

1.20 p.m.                               40min               50min

2.00 p.m.                               40min               50min

2.40 p.m.                               40min               50min

3.20 p.m.                               40min               50min

4.00 p.m.                               40min               50min

4.40 p.m.                               40min               50min

To identify any time of the day when the two vehicles will leave the park at the same time.

When the time of the intervals of the two vehicles overlap.

The least common multiple LCM of 40 and 50 is 200.

The two vehicles will leave the park at the same time every 200 minutes, or 3 hours and 20 minutes.

The first time this happens is at,

8:00am + 200 mins = 11:20am

So, at 11:20am both vehicles will leave the park at the same time.

To control traffic jam the park manager can consider the following strategies,

Adjust the departure times,

If the departure times are causing congestion,

The manager can adjust the intervals or the departure times to spread out the flow of vehicles.

Use a reservation system,

The manager can use a reservation system to stagger the departure times of the vehicles.

Ensuring that there are no backlogs at the loading area.

Limit the number of vehicles,

The manager can limit the number of vehicles that are allowed in the park at any given time.

To reduce the number of vehicles on the road and prevent congestion.

Promote carpooling,

The manager can encourage visitors to carpool to the park to reduce the number of vehicles on the road.

This can be done through promotional campaigns or by offering incentives for carpooling.

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Answer:

13

Step-by-step explanation:

5^2+8^2= c^2

25+64=c^2

89=c^2

c=9.4

9.4^2+9^2=c^2

c=170

c=13

Answer:

B

Step-by-step explanation:

• a line sloping upwards from left to right is positive

• a line sloping downwards from left to right is negative

• a horizontal line parallel to the x- axis has a slope of zero

the line here is sloping upwards from left to right, thus has a positive slope.

Answer:

Step-by-step explanation:

B

if the line makes an angle less than or equal to 90 with the horizontal has a positive slope

An equation using x as the number of pages in the book that has 6 chapters with the same number of pages and an introduction with 8 pages is 6x + 8 = 194.

An equation is a mathematical statement that defines that two or more mathematical or algebraic expressions are equal or equivalent.

Equations use the equal symbol (=) while mathematical expressions just combine variables with numbers, constants, and values using mathematical operands.

The number of chapters in the book = 6

The number of pages of the introduction = 8 pages

The total number of pages of the whole book = 194

Let the number of pages in each chapter = x

6x + 8 = 194

6x = 186 (194 - 8)

x = 31

Thus, we can evaluate the equation to show that x is 31.

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Write an equation using x to show the number of pages in each chapter of the book.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=2 \end{cases}\implies 192\pi =\cfrac{\pi 2^2 h}{3} \\\\\\ 192\pi =\cfrac{4\pi h}{3}\implies \cfrac{ 3}{4\pi }\cdot 192\pi=h\implies 144=h \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=3 \end{cases}\implies 192\pi =\cfrac{\pi 3^2 h}{3} \\\\\\ 192\pi =3\pi h\implies \cfrac{192\pi }{3\pi }=h\implies 64=h \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=4 \end{cases}\implies 192\pi =\cfrac{\pi 4^2 h}{3} \\\\\\ 192\pi =\cfrac{16\pi h}{3}\implies \cfrac{ 3}{16\pi }\cdot 192\pi=h\implies 36=h[/tex]

The measure of the angle N is 17 degrees

From the information given in the parallelogram, we have the angles written as;

m<N = 3y + 8

m<M = 6y - 1

m< P = 6x

m< L = 5x + 9

Then, we can say that;

m< M = m<N

Substitute the values, we get;

6y - 1 = 3y + 8

collect the like terms

6y - 3y = 8 + 1

add the values

3y =9

Divide both sides by the coefficient of the variable, y , we have;

y = 9/3

Divide the values

y = 3

Then, m<N = 3y + 8 = 3(3) + 8 = 17 degrees

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The difference between the two high altitudes is therefore 300 feet.

Let 't' denote the time in minutes when both birds are at the same height. If both of these fowls are traveling, one descending and the latter ascending, then we obtain a formulaic value for t using the equations below.

Therefore, if we solve: 75t - 25t = 400, it follows that 50t = 400 and t = 8 minutes.

Given this information, after 8 minutes, the two birds reach the same height.

Consequently, before the 8-minute interval, bird A is situated at a higher level than bird B since the prior's rate of descent is less than the current bird's ascent.

Once they have reached the shared altitude, bird B is above bird A given its continuous upward elevation, contrasting against bird A's descending course.

Their heights after only 1 minute has elapsed; the Height of bird A after 1 minute is calculated to be 425 feet - (500 - 75(1)) and for bird B it is 125 feet - (100 + 25(1)).

The difference between the two high altitudes is therefore 300 feet.

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Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1). Then the correct option is B.

Given that:

P(Player 1) = 4/7 = 0.57

P(Player 2) = 5/8 = 0.625

P(Player 3) = 3/6 = 0.50

The probabilities are arranged in ascending order as,

P(Player 3) < P(Player 1) < P(Player 2)

Player 2 is more likely to hit the ball than Player 1 and Player 1 is more likely to hit the ball than Player 3.

Thus, the correct option is B.

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Answer:

If Sarah received 10 points for each of the four targets she hit, her total point gain from hitting targets would be:

4 targets x 10 points = 40 points

If Sarah loses 105 points for taking too long, her total loss is -105 points (due to the negative change in her score).

As a result, the total change in Sarah's score may be determined by adding her point gain from hitting targets to her point loss from taking too long:

Total difference = 40 points minus 105 points

-65 points total change

As a result, Sarah's score dropped by 65 points after completing the following level of her video game.

An equivalent decimal, fraction and percent is C) 0.45, 4/5, 45%.

To understand why this is the correct choice, we need to look at how decimals, fractions, and percentages are related. Decimals are just another way of representing fractions, where the denominator is a power of 10. For example, 0.45 is the same as 45/100 or 9/20.

Percentages, on the other hand, are just a way of representing fractions with a denominator of 100. So, 45% is the same as 45/100 or 9/20.

The other options do not have equivalent representations of decimals, fractions, and percentages.

In conclusion, understanding the relationships between decimals, fractions, and percentages is essential to solving problems like these. The key is to remember that they are just different ways of representing the same value, and with a bit of practice, it becomes second nature to recognize equivalent representations.

Therefore, option C shows an equivalent decimal (0.45), fraction (4/5), and percent (45%).

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Answer: the answer is 24

The fraction that represents the point M is 2 3/10

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

The number line

Such that

M is between 2 1/5 and 2 1/2

This means that

M is between 2.2 and 2.5

By the positiining of the points, we have

M = 2.2 + 0.1

Evaluate

M = 2.3

As a fraction, we have

M = 2 3/10

Hence, the fraction is 2 3/10

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Answer:

x = 14, y = 7√3, z = 7√2

Step-by-step explanation:

In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. So x = 14, y = 7√3, and

z = 7√2.

The area of the tile shown is 42.5 [tex]cm^2[/tex]. So, the correct option is (c) 42.5 [tex]cm^2[/tex].

What is area of triangle?

The area of a triangle can be calculated using the formula:

A = (1/2)bh

where A is the area of the triangle, b is the length of the base of the triangle, and h is the height of the triangle.

To find the area of the quadrilateral, we need to split it into two triangles and a rectangle.

First, we find the area of the rectangle: 5 cm × 6 cm = 30 [tex]cm^2[/tex].

Next, we find the area of the left triangle: (1/2) × 5 cm × 3 cm = 7.5 [tex]cm^2[/tex].

Finally, we find the area of the right triangle: (1/2) × 5 cm × 2 cm = 5 [tex]cm^2[/tex].

Adding up the areas of the two triangles and the rectangle, we get:

30 [tex]cm^2[/tex] + 7.5 [tex]cm^2[/tex] + 5 [tex]cm^2[/tex] = 42.5 [tex]cm^2[/tex]

Therefore, the area of the tile shown is 42.5 [tex]cm^2[/tex].

So, the correct option is (c) 42.5 [tex]cm^2[/tex].

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