a forest of 800 trees is exposed to a disease that kills 1/4 of the trees per year. how many trees will be left after after 11 years? round your answer to the nearest whole number

The radius of the circle E is 27/5.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.

Since the radius of B is 3, AX = 4.

Assume AE = p.

Then EX and EY are radii of circle E and have length 4 + p.

AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.

Using the Law of Cosines on Δ CAE, we obtain

(6+p)² =p² + 64 - 2(8)(p) cos 60

The 2 and the cos 60 terms cancel out:

p² + 12p + 36 = p² + 64 - 8p

12p+ 36 = 64 - 8p

p = 28/20

= 7/5

The radius of circle E is 4 + (7/5)

= 27/5

Hence, the radius of the circle E is 27/5.

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Answer: 0.94

Step-by-step explanation: This is the same as saying subtract 0.954 from 1.894.

1.894 - 0.954 = 0.94

Answer:

A rotation about the origin 180 degrees means that the pre-image essentially rotates half an actual circle

The rule for 180 degrees rotation is (x,y)-->(-x, -y)

So the points of this quadrilateral are now

(1,3) = (-1, -3)

(4,1)=(-4, -1)

(4,4)=(-4, -4)

(1,4)=(-1,-4)

So it moves from 1st to 3rd quadrant

HOPE THIS HELPS

The altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

What is right angled triangle ?

A right-angled triangle is a triangle that has one angle that measures 90 degrees (a right angle). This means that the other two angles must add up to 90 degrees as well. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem, which states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse, is a fundamental concept in mathematics and has many practical applications. Right-angled triangles are used in fields such as engineering, architecture, and physics to calculate distances, heights, and angles.

a) Let's use the Pythagorean theorem to find the altitude of the plane. We have a right triangle with the slant range as the hypotenuse, the ground range as one leg, and the altitude as the other leg. So, we can use:

altitude² + ground range² = slant range²

altitude² + 10.15² = 14.5²

altitude² = 14.5² - 10.15²

altitude² = 84.9025

altitude ≈ 9.21 km or 9210 meters (rounded to the nearest meter)

b) If the plane descends at a rate of 750 meters per minute, the pilot will have:

time = altitude / descent rate

time = 9210 / 750

time ≈ 12.28 minutes (rounded to two decimal places).

Therefore, the altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

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Answer: 390

Step-by-step explanation:

m

Isabel is in a hot air balloon that has just taken off and is now floating 140 meters above

its launching point. Debbie is standing on the ground, 147 meters away from the

launching point. How many meters apart are Isabel and Debb

Answer:

Isabel and Debbie are 203m apart.

Step-by-step explanation:

Since Isabel went straight up in the balloon and Debbie is straight over presumably on flat ground, they make a right triangle with the third point being the launching spot.

It is a right triangle. See image. Use the Pythagorean Theorem.

140^2 + 147^2 = d^2

Where d is the distance between Isabel and Debbie.

see image for work shown.

Mech #1 charged 45$/hr and Mech #2 charged 75 $/hr. We can find the solution in the following manner:

Let's make,

mechanic #1's rate = x

mechanic #2's rate = y

Their rate is dollars per hour ($/hr)

Mechanic #1 worked for 20 hours (hr × $/hr = $)

20x = money earned by mechanic #1

And mechanic #2 worked for 15 hours

15y = money earned by mech#2

Together they charged a total of $2175. So the amount of money earned by both mechanics.

20x + 15y = 2175

The sum of the two rates was $120 per hour.

x + y = 120

which means

x = 120- y

Putting (120 - y) in for "x" in the other equation to get everything in terms of one variable.

20(120 - y) + 15y = 2175

Now we can solve for y and get the solution:

20(120 - y) + 15y = 2175

y=45 $/hr

Now use this to solve for x

x + y = 120

x + 45 = 120

x =75

x = 75 $/hr

Mech #1 charged 45$/hr

Mech #2 charged 75 $/hr

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Solving the inequalities for x and y, we have x > 3 and y > 1

Inequalities are mathematical expressiοns that cοmpare twο quantities οr values and indicate their relative sizes. Inequalities are represented using symbοls such as < (less than), > (greater than), ≤ (less than οr equal tο), and ≥ (greater than οr equal tο).

Here Given that the twο inequalities are:

x + 5 < 8y

And

x + 5 > 8

x > 8 - 5

x > 3

Substate the value of x in x + 5 < 8y:

x + 5 < 8y

x < 8y - 5

3 < x < 8y - 5

3 < 8y - 5

3 + 5 < 8y

8 < 8y

y > 8/8

y  > 1

Thus, Solving the inequalities for x and y, we have x > 3 and y > 1

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Complete question:

Solve the for x and y.

a. x + 5 < 8y

   x + 5 > 8

​

Answer:

5 3/4

Hope this is what you're looking for

Answer: y = 4/3x+1

Step-by-step explanation:

Answer:

y=4/3 + 1

Step-by-step explanation:

There are different ways to do this for finding slope, you can use the formula or you can do rise over run. How to find rise over run you count how many places up so our current place is (-3,-3) and we are trying to find (3,5) so if you were to start with rise, you rise 8 places then run you go either left or right in our case right, you move 6 places.  So our fraction would be 8/6 or simplified 4/3. But using the formula to make sure we got the right answer, our formula is y2-y1/x2-x1 so that would look like 5- -3/3- -3. To solve on our top side two negatives give us a positive so the top is 8 and then bottom is 6 so we get 8/6 or 4/3. But our slope intercept would be y= 4/3x +1.

The same solutions equations are  B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is,

=> 2.3p – 10.1 = 6.5p – 4 – 0.01p

To remove decimal we need to multiply by 100 on both side of the equation then,

=> (2.3p – 10.1)*100 = (6.5p – 4 – 0.01p)*100

=> 2.3*100p-10.1*100=6.5*100p-4*100-0.01*100p

=> 230p-1010=650p-400-p

And simplifying then,

=>2.3p – 10.1 = 6.5p – 4 – 0.01p

=>2.3p – 10.1 = 6.49p-4

Hence the correct options are, B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.

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Step-by-step explanation:

What we do here is divide 43 by 50

[tex] \frac{43}{50} = 0.86 = 86\%[/tex]

Cason must read for at least 22 weeks to meet his goal. The correct answer is D. x ≥ 22

Let x be the number of weeks Cason needs to read to meet his goal. In each week, he can read 2 books. Therefore, the total number of books he will read in x weeks is:

2x

Since Cason has already read one book, the total number of books he will have read after x weeks is:

2x + 1

We want Cason to read at least 45 books, so we can set up an inequality:

2x + 1 ≥ 45

Subtracting 1 from both sides, we get:

2x ≥ 44

Dividing both sides by 2, we get:

x ≥ 22

Therefore, Cason must read for at least 22 weeks to meet his goal.

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The area of the circle with a radius of 10 meters is given as follows:

314.16 m².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr².

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle, on a segment that passes through the center. Hence, the diameter’s length is twice the radius length.

Considering the above concept, the measure of the radius for the circle in this problem is given as follows:

r = 10m.

Thus the area of the circle is given as follows:

A = π x 10²

A = 314.16 m².

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Answer:

Step-by-step explanation:

1 gallon= 4 liters

2gallons=8liters

8liters answered

But exactly: 7.57082 liters

The table of the piecewise function is shown below and the point of maximum growth rate for the function is (8.96, 7.5)

Given that

g(x) = x² - 1 if x ≤ 3

g(x) = x - 5 if x > 3

For values greater than 3, we use the function g(x) = x - 5;

Otherwise, we use g(x) = x² - 1

This means that

x               Workings              g(x)

-2              g(-2) = (-2)² - 1         3

0               g(0) = (0)² - 1           -1

1                g(1) = (1)² - 1              0

3                g(3) = (3)² - 1           8

5                g(5) = 5 - 5             0

Given that

f(x) = 15/(1 + 6e⁻⁰°²ˣ)

The point of maximum growth rate for a logistics function represented as f(x) = c/(1 + ae⁻ᵇ⁺) is

t = ln(a)/b

y(t) = c/2

So, we have

t = ln(6)/0.2 = 8.96

y(t) = 15/2 = 7.5

Hence, the point is (8.96, 7.5)

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The solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

First, let's graph the line x = -2, which is a vertical line passing through -2 on the x-axis.

Next, let's graph the line x - y = 1, which can be rewritten as y = x - 1. This is a line with a slope of 1 (meaning it goes up 1 unit for every 1 unit it goes to the right) and a y-intercept of -1 (meaning it passes through -1 on the y-axis).

Now, we need to shade in the region that satisfies both inequalities. We know that x has to be greater than or equal to -2, so we shade to the right of the vertical line x = -2. We also know that x - y has to be greater than or equal to 1, so we shade above the line y = x - 1.

The shaded region is the overlapping region that satisfies both inequalities. It is the region above the line y = x - 1 and to the right of the vertical line x = -2.

Therefore, the solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

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The complete question is as follows:

What is the solution to the system of inequalities?

x ≥ -2

x - y ≥ 1

Answer:

The first question asks which variable Amari used to construct a bar graph. It is not specified which variable she used, so we cannot determine the answer.

The second question asks which graph correctly displays the data collected from the customers about their favorite topping. The data is nominal, so a bar graph would be appropriate. The correct answer is:

c) a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled chocolate chips going to a value of 17, the second bar labeled hot fudge going to a value of 12, the third bar labeled nuts going to a value of 27, and the fourth bar labeled sprinkles going to a value of 44

The third question asks which stem-and-leaf plot correctly graphs the data set of points scored by the Riverside Red Dragons during the 2021 football season. The correct answer is:

c)

2021 Riverside Red Dragon Football Season Points

0 0 4

1 1 3 3

2 0 0 6 7 7 7

3 0 0 0 0 1

Key 1|1 = 11

The fourth question asks which graphical representation would be best for a principal interested in the number of hours slept per night by 14-year-olds in a particular town. The data is quantitative, so a histogram would be appropriate. The correct answer is:

b) Histogram

The probability of a false positive test result is approximately 0.1702 or 17.02%.

The person who will suffer from a false positive are the subjects who aren't drug users.

From the given data, we can see that there are a total of 46 + 1 = 47 positive test results, out of which 8 are false positives (i.e., the subject is not a drug user).

The probability of a false positive test result is:

Probability of false positive = Number of false positives / Total number of positive test results.

Probability of false positive = 8 / 47

Probability of false positive = 0.1702

Therefore, the probability of a false positive test result is approximately 0.1702 or 17.02%.

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The number 7234 can be rounded to the nearest multiple of and it is 7235.

Check the value of the remainder:

If the remainder is less than 2.5, round down to the nearest multiple of 5

If the remainder is 2.5 or greater, round up to the nearest multiple of 5

Rounding off 7234 to the nearest 5 means we need to find the multiple of 5 that is closest to 7234.

Divide 7234 by 5 and get the quotient and remainder

= 7234 ÷ 5

= 1446 with a remainder of 4

Multiply the quotient by 5 and add the value determined.

Using this method, we can see that the nearest multiple of 5 to 7234 is 7235, since the remainder is 4 which is less than 2.5. Therefore, rounding off 7234 to the nearest 5 results in 7235.

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The complete question:

What will be the value when 7234 rounded off to the nearest 5(which will be divisible by 5)?

Given - the system of the equations as

[tex]y=-2x+1\\y=-11x-3[/tex]

To find - the solution of the set of equation

Explanation- given the set and we can see that left hand side of the equation is equal.

we get

[tex]-2x+1=-11x-3\\-2x+11x=-3-4\\9x=-7\\x=-7/9=-0.77[/tex]

we get

[tex]y=-2(0.77)+1\\y=-1.54+1\\y=-0.54[/tex]

Hence the value is x =-0.77, y=0.54

Final answer- the value of x = 0.77, y = -0.54

Answer:

2

Step-by-step explanation:

Take out 25% of 8

25/100*8= 2

Required Amount=2

Answer:

Step-by-step explanation:

If Sara is making 3 batches of chocolate chip cookies using 2 1/4 cups of flour per batch, then the total amount of flour she uses for the chocolate chip cookies is:

3 batches x 2 1/4 cups per batch = 6 3/4 cups of flour

Since she will use 12 3/4 cups of flour for all six batches, the amount of flour used for the oatmeal cookies can be found by subtracting the amount of flour used for the chocolate chip cookies from the total amount of flour:

12 3/4 cups - 6 3/4 cups = 6 cups

To determine how many cups of flour are needed for each batch of oatmeal cookies, we can divide the total amount of flour used for the oatmeal cookies by the number of batches:

6 cups ÷ 3 batches = 2 cups per batch

Therefore, the equation that can be used to determine how many cups of flour are needed for each batch of oatmeal cookies is:

Flour needed per batch of oatmeal cookies = Total flour needed for oatmeal cookies ÷ Number of oatmeal cookie batches

Or, in this case:

Flour needed per batch of oatmeal cookies = 6 cups ÷ 3 batches = 2 cups per batch.

The Area of Garden is 62/3 feet².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area. A shape's area is a two-dimensional measurement.

Given:

Length = 7 3/4 feet = 31/4 feet

Width = 2 2/3 feet = 8/3 feet

So, Area of Garden

= l w

= 31/4 x 8/3

= 62/3 feet²

and, Now, 5/6th of the Garden

= 62/3 x 5/6

= 31 / 3 x 5 / 2

= 155 / 6 feet²

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The exponential function is a decay, and it can be written as:

f(x) = 1,200*( 0.875)^x

The general exponential function can be written as:

f(x) = A*(b)^x

Where A is the initial value and b is the base.

Here we have a decay rate, so this is an exponential decay, and we can write:

b = 1 - r

Where r is the decay rate in decimal form:

b = 1 - 0.125 = 0.875

And the initial value is 1,200, so the exponential function is:

f(x) = 1,200*( 0.875)^x

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Answer:

A. 62 units

Step-by-step explanation:

To find the perimeter of the rectangle, you have to use the Pythagorean theorem.

a^2 + b^2 = c^2 - Formula

24^2 + b^2 = 25^2 - Plug in values

576 + b^2 = 625 - Simplify

b^2 = 49 - Isolate the variable

b = 7 - Solve

After finding the height, find the perimeter.

P = 2b + 2h

P = 2(24) + 2(7)

P = 48 + 14

P = 62 units

In response to the aforementioned query, we may say that The interest for the previous month, rounded to the nearest cent, is $289.84.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

The Annual Percentage Rate (APR) can first be changed to a monthly interest rate as follows:

r = APR/12 = 0.085/12 = 0.0070833

Then, we may determine how many months the loan will last:

n = 2.5 years * 12 months a year = 30 months.

We can now calculate the total amount owing at the conclusion of the loan term using the compound interest formula:

A= P(1 + r)^n

where P is the loan's principle, r is the interest rate each month, and n is the number of months.

A = $3000(1 + 0.0070833)^30\s= $3,789.64

At the conclusion of the loan period, there will be a balance of $3,789.64.

B = $3000(1 + 0.0070833)^(30-1) - [((1 + 0.0070833)^30 - 1)/(0.0070833)]

= $3,499.80

I = $3,789.64 - $3,499.80\s= $289.84

The interest for the previous month, rounded to the nearest cent, is $289.84.

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The angles on the diagram are vertical angles and the value of x is 25.

The two angles are said to be adjacent angles when they have a common vertex and side.

On the other hand, vertical angles are angles that are opposite of each other when two lines cross and they are conguent.

Therefore, the angles on the diagram are vertical angles.

Now, since vertical angles are congruent.

Angle 75 and angle (4x - 25 ) are equal.

Hence;

4x - 25 = 75

Solve for x

4x - 25 = 75

Add 25 to both sides

4x - 25 + 25 = 75 + 25

4x = 75 + 25

4x = 100

Divide both sides by 4

4x/4 = 100/4

x = 100/4

x = 25

Therefore, the value of x is 25.

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The probability that a person is 64 or over and has a loan is 0.20 × 0.28 = 0.056.

Probability is the study of the likelihood of certain outcomes or events occurring. It is the measure of how likely it is for something to happen. Probability can be expressed as a percentage, a fraction, or a number between zero and one. Probability is used to help make decisions in a variety of situations, from games of chance to business decisions and scientific research.
(b) The probability that a person has a loan is 0.20 × 0.28 + 0.80 × 0.53 = 0.464.

(c) The events that a person is 64 or over and that the person has a loan are not independent. This is because the probability of having a loan depends on whether the person is 64 or over. Therefore, the two events are not independent.

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