At the beginning of an environmental study, a forest covered an area of 1500 km2 . Since then, this area has decreased by 9.8% each year.Let t be the number of years since the start of the study. Let y be the area that the forest covers in km2.
Write an exponential function showing the relationship between y and t.

Answer:

0.18401015

Step-by-step explanation:

You should use an online calculator

Answer:

cx

Step-by-step explanation:

Answer:

the answer is C 282

Step-by-step explanation:

Answer:

X= 1 + 7/12

x = 1 - 7/12

Step-by-step explanation:

Answer:

[tex]x=\frac{19}{12}\\ or\\x=\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]6x^2-x-2=0[/tex]

a=6

b=-1

c=-2

[tex]x=-b\frac{+}{}\frac{\sqrt[]{b^2-4ac} }{2a}[/tex]

[tex]x=-(-1)\frac{+}{}\frac{\sqrt[]{(-1)^2-4(6)(-2)} }{2(6)}[/tex]

[tex]x=1\frac{+}{}\frac{\sqrt[]{1+48} }{12}[/tex]

[tex]x=1\frac{+}{}\frac{\sqrt[]{49} }{12}[/tex]

[tex]x=1\frac{+}{}\frac{7}{12}[/tex]

------------------------------

[tex]x=1+\frac{7}{12}[/tex]

[tex]x=1-\frac{7}{12}[/tex]

------------------------------

[tex]1+\frac{7}{12}=\frac{(1*12)+(7*1)}{12} =\frac{12+7}{12} =\frac{19}{12}[/tex]

------------------------------

[tex]1-\frac{7}{12}=\frac{(1*12)-(7*1)}{12} =\frac{12-7}{12} =\frac{5}{12}[/tex]

Answer:

49pi or about 153.94 square meters.

Step-by-step explanation:

Because the two semicircles together take up the 28m long edge of the rectangle, they each half that diameter and a quarter of that radius. This means that both semicircles have a radius of 28/4=7.  Since two semicircle with the same radius form a full circle, we can just calculate the area of a full circle of radius 7. [tex]\pi \cdot 7^2=49\pi\approx 153.94[/tex]. Hope this helps!

Answer:

The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2

Step-by-step explanation:

If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.

Therefore, we prove with negative values.

Therefore, -2 is a root. We can find the other knowing that

p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)

The independent term is 11*2*(-r₂) = -22r₂ = -10

thus, r₂ = -10/-22 = 5/11.

Therefore, p(x) = 11*(x+2)*(x-5/11)

To write 11x2+17x−10 in factored form we find two numbers whose sum is 17 and product is -110. The correct pair is 2 and -55 which leads to the factored form (11x - 55)(x + 2).

The question involves factoring a quadratic expression, 11x2+17x−10. To re-write this expression in factored form, one needs to find two numbers, such that their sum equals to the coefficient of x, 17, and their product equals to the product of the coefficient of x² and the constant term (11*(-10)=-110). Diego started by listing all pairs of factors of the constant term, -10. The correct pair here, considering the product and the sum, are 2 and -55, because 2*(-55)=-110 and 2+(-55)=17. Therefore, our factored form will be: (11x - 55)(x + 2).

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Answer:

a) no

Step-by-step explanation:

-The diagrams can be said to be mathematically similar if the dimensions of their corresponding sides enlarge or reduce by the same factor.

-We therefore determine the enlargement factor for both the radius and height as below:

-Let k be the scale factor

[tex]k_r=\frac{R}{r}\\\\=\frac{3.64}{2.6}\\\\=1.4\\\\k_h=\frac{H}{h}\\\\=\frac{10.192}{8.32}\\\\=1.225\\\\k_r\neq k_h[/tex]

Hence, the cylinders are not mathematically similar since the enlargment factors for the radius and height are not equal.

Answer:

Surface Area and Volume Unit Test

1. 14

2. hexagon

3. 224 m2

4. 896 pi in.2

5. 405 in.2

6. 49,009 m2

7. 4,910.4 yd3

8. 3.6 in

9. 4,608 cm3

10. 1,296 cm3

11. 1,442.0 yd3

12. 2,158 m2

13. no

14. 7 : 10

15. 100 m2

16. one-point perspective

17. 18.3 cm

Answer:

18

Step-by-step explanation:

Normally, when you multiply two numbers, their product equal to the product of their greatest common factor and their least common multiple

Let the number be y

The product of 12 and y is 12 y

Also, the product of their greatest common factor and their least common multiple is 6*36=216

Now

12y=216

Divide both sides by 12 to obtain y as

Y=216/12=18

Therefore, the other number is 18.

To prove

Factors of

12=2*2*3

18=2*3*3

Common factors for both are 2*3=6 equal to given GCD

The multiplies are 2*2*3*3=36

Answer:

1944 Inches Squared

Step-by-step explanation:

Surface area Formula for a Cube:

[tex]A = 6a^2[/tex]

The "edge", which is also the side, is 18 inches.

[tex]a = 18[/tex]

Solve the formula.

[tex]A= 6a^2 = 6(18)^2 = 6 * 18^2\\18^2 = 324\\324 * 6 = 1944\\A=1944[/tex]

The cube's surface area should be 1944 square inches.

Answer:

Step-by-step explanation:

1944 Inches Squared

Step-by-step explanation:

Surface area Formula for a Cube:

The "edge", which is also the side, is 18 inches.

Solve the formula.

Answer:

6,802

Step-by-step explanation:

Our first step is to change 76% into a decimal:

76% -> [tex]\frac{76}{100}[/tex] -> 0.76

Next, lets multiply and solve for x:

[tex]x=8,950(0.76)[/tex]

[tex]x = 6,802[/tex]

There were 6,802 public libraries that offered free access electronic books in 2012.

Answer:

6802 Libraries offered free electronic books.

Step-by-step explanation:

Answer:378

Step-by-step explanation:32 times 4=178 +250=378

Alice Jones's gross pay for the week is the sum of her hourly earnings ($128 from working 32 hours at $4.00 per hour) and her tips ($250), totalling $378.

To calculate Alice Jones's gross pay, we need to consider both her hourly wage and her tips. Alice worked 32 hours this week and was paid $4.00 per hour. This means her earnings from her hourly wage are:

32 hours times $4.00/hour = $128

Alice also earned $250 in tips. To find her gross pay for the week, we add her hourly earnings to her tips:

$128 + $250 = $378

Therefore, Alice's gross pay for the week is $378.

Answer:

175 cents

Step-by-step explanation:

1 quarter is equal to 25 cents.

Since there are 7 of them,

7 times 25 cents = 175 cents

Answer:

532

Step-by-step explanation:

divide 5,320 by 10

Answer:Since each type of drink (lemonade, water, and juice) is equally likely to be chosen, the probability of choosing a type of drink is 1 in 3 picks. Thus, in order to get all three types of drinks, one must pick 3

Step-by-step explanation:

Answer:[tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]

Step-by-step explanation:

Given

length of three sides are

[tex]3x, 7\ and\ 12[/tex]

according to Euclidean geometry

[tex]7+12>3x[/tex]

[tex]19>3x[/tex]

[tex]\frac{19}{3}>x[/tex]

also

[tex]3x+7>12[/tex]

[tex]3x>5[/tex]

[tex]x>\frac{5}{3}[/tex]

therefore value of [tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]

If x is an integer then x can be [tex]2,3,4,5,6[/tex]

Answer:

I think the answer is 38.

Answer:

[tex]I=7000C[/tex]

Step-by-step explanation:

Let C represent number of dairy cows.  

We have been given that each dairy cow produces 3500 gallons of milk per year. So amount of milk produced by C cows in 1 year would be [tex]3500C[/tex] gallons.

We are also told that the dairy sells milk for 2.00 per gallon. So yearly income I, in dollars for the dairy milk production would be 2.00 times the yearly milk production.

Since yearly milk production from C cows is [tex]3500C[/tex], so Income would be:

[tex]I=2.00(3500C)[/tex]

[tex]I=7000C[/tex]

Therefore, the formula [tex]I=7000C[/tex] represents yearly income (I) as a linear function of C.

Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.

Let's denote the total number of gold medals obtained by Russia as [tex]\( x \)[/tex]. Since we know Russia got 3 gold medals, we have [tex]\( x = 3 \)[/tex].

Now, let's denote the total number of gold medals obtained by the top 8 countries (including Russia) as T. We're told that the total number of gold medals obtained by all top 8 countries combined is 60. Since Russia got 3 gold medals, the gold medals obtained by the other top 7 countries is [tex]\( T - 3 \)[/tex].

So, the percentage of gold medals obtained by Russia can be calculated as:

Percentage of gold medals obtained by Russia = [tex]\frac{\text{Number of gold medals obtained by Russia}}{\text{Total number of gold medals obtained by the top 8 countries}} \times 100\%\][/tex]

Substituting the known values:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{T} \times 100\%\][/tex]

We know that the total number of gold medals obtained by the top 8 countries is 60, so [tex]\( T = 60 \).[/tex] Substituting this into the equation:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{60} \times 100\%\][/tex]

Solving this equation:

[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{1}{20} \times 100\% = 5\%\][/tex]

So, Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.

Answer:

2 yards

Step-by-step explanation:

[tex]\frac{218.16}{10.8\cdot 10.1}=2[/tex] yards. Hope this helps!

Answer:

get the brainliest duck

Step-by-step explanation:

Answer:

Jackson's kitten gained 21 ounces that moth, or 1.3125 pounds.

Step-by-step explanation:

56-35=21

Answer:

21 ounces

Step-by-step explanation:

2 pounds is equal to 32 ounces, plus the 3 ounces, so the kitten was originally 35 ounces. You subtract 56-35, and get 21 ounces.

Answer:

The correct answer is 25.

Step-by-step explanation:

A cooking magazine shows a photo of a main dish on the front cover of 5 out of the 12 issues it publishes each year.

Number of publications by the magazine every year = 12.

Number of publications in 5 years = 12 × 5 = 60.

Out of these 12 magazines in a year, the photo of a main dish is on 5 magazines.

Therefore in 60 magazines, the photo of a main dish would be 5 × 5 = 25 magazines.

Thus in five years there would be 25 publications in which the front page will have a poster of a main dish.

Based on the number of times the photo appears per year, in 5 years it will appear 25 times.

Every year, the photo in question appears 5 out of 12 times.

If there were 5 years therefore, it would appear:

= Number of times per year x Number of years

= 5 x 5

= 25 times

In conclusion, the photo of a main dish will appear 25 times in 5 years.

Find out more about such multiplication at https://brainly.com/question/98253.

Answer:

(3n + 4) (n-2)

Step-by-step explanation:

Are you asking to factor this 3n^2 - 2n -8 ?

If so the best way to do this problem  is with the X method.

                                     top:    3*(-8)

    left:  factor of 3*-8                             right:  factor of 3*-8

                                   bottom:  -2

try the factors  4 and -6  because   4*-6 =  3 *-8 = -24

Because   notice that  4 + -6 = -2

so:

    3n^2 -2n - 8  can be rewritten as    3n^2  -6n + 4n  - 8

We should first use Distributive property to factor:  3n^2  -6n + 4n  - 8

3n^2  -6n + 4n  - 8  =   3n (n - 2)  +  4(n - 2)

Now we factor by grouping here :   (3n + 4) (n-2)  

I factored out the group  (n-2)

Therefore:  (3n + 4) (n-2) = 3n^2 -2n - 8

Answer:

(-12, 9)

Step-by-step explanation:

Answer:I can't really tell what B says could you do another pic

Step-by-step explanation:

Answer:

Across the x axis.

Step-by-step explanation:

The question is incomplete! Complete question along with answer and explanation is provided below.  

Question:  

Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.

The Probability is (2/12)(4/12) = 8/144

Answer:

P = (2/12)(4/11) = 2/33

Step-by-step explanation:

There are total 3 + 2 + 4 + 3 = 12 marbles

The probability of drawing a yellow marble is given by

P(yellow) = number of yellow marbles/total number of marbles

There are 2 yellow marbles and total 12 marbles

P(yellow) = 2/12

Then Francisco draws a red marble without replacing the first one so that means there are total 11 marbles left.

P(red) = number of red marbles/total number of marbles

There are 4 red marbles and total 11 marbles

P(red) = 4/11

Therefore, the overall probability is

P = (2/12)(4/11) = 2/33

Francisco made the error of calculating the probability with replacement whereas, in reality he did not replaced the marble after drawing the yellow marble, so he should have used total 11 marbles for the calculation of drawing red marble,

Answer:

a. (√3)/2

b. 60 degrees.

Step-by-step explanation:

Please kindly check the attached files for explanation.

The sine of the angle is √3 / 2, and the measure of the angle is 60°.

Finding the Angle Between a Cable and the Ground

To determine the sine of the angle ( heta) between the cable and the ground, we need to use the horizontal and vertical forces exerted by the cable. We have a horizontal pull of 800 Newtons and a vertical pull of 800√3 Newtons.

First, we calculate the sine of the angle using the formula:

Sine ( heta) = Opposite / Hypotenuse

Here,
Opposite = Vertical Pull = 800√3 N
Hypotenuse = Resultant Force = √[(Horizontal Pull)^2 + (Vertical Pull)^2] = √[(800)^2 + (800√3)^2] = 1600 N

Thus,

Sine ( heta) = 800√3 / 1600 = √3 / 2

We know that the angle  heta with a sine value of √3 / 2 is 60 degrees (or  heta = 60°).

In conclusion, sine of the angle is √3 / 2, and the measure of the angle is 60°.

The volume of the new building is 11,726,069,760 cubic inches, and its surface area is 51,555,840 square inches.

To find the volume and surface area of the new building, we first need to calculate the dimensions of the new building by scaling up the dimensions of the model by a factor of 144.

1. Dimensions of the new building:

  -[tex]Width: \(10 \times 144 = 1440\) inches[/tex]

  - [tex]Length: \(18 \times 144 = 2592\) inches[/tex]

  - [tex]Height: \(28 \times 144 = 4032\) inches[/tex]

2. Volume of the new building:

  The volume of a rectangular prism (building) is calculated by multiplying its length, width, and height.

[tex]\[Volume = \text{Length} \times \text{Width} \times \text{Height}\][/tex]

  Substituting the given dimensions:

 [tex]\[Volume = 2592 \times 1440 \times 4032\][/tex]

 [tex]\[Volume = 11,726,069,760 \text{ cubic inches}\][/tex]

3. Surface area of the new building:

  The surface area of a rectangular prism (building) is calculated by adding the areas of all six sides.

[tex]\[Surface\,Area = 2(\text{Length} \times \text{Width} + \text{Length} \times \text{Height} + \text{Width} \times \text{Height})\][/tex]

  Substituting the given dimensions:

[tex]\[Surface\,Area = 2(2592 \times 1440 + 2592 \times 4032 + 1440 \times 4032)\][/tex]

 [tex]\[Surface\,Area = 51,555,840 \text{ square inches}\][/tex]

So, when the new building is completed:

- The volume will be [tex]\(11,726,069,760 \text{ cubic inches}\).[/tex]

- The surface area will be [tex]\(51,555,840 \text{ square inches}\).[/tex]

Answer:

d

Step-by-step explanation:

hope this helps

Answer:

49998 pennies left

Step-by-step explanation:

50000 - 2 = 49998

Answer:

50000-2=49998

Step-by-step explanation:

Answer:

solution is (-2, -4)

Step-by-step explanation:

I assume you want the solution?

so we want to find the intersection.

3x -  2y  = 2

5x = 5y + 10

simplify the last equation

x = y + 2  by dividing out the 5

substitute

3*(y + 2) - 2y = 2

3y + 6 - 2y = 2

y  + 6 = 2

y = -4

x  = -4 + 2 = -2

solution is (-2, -4)

Answer:

P(A∪B) = 0.92

Step-by-step explanation:

Let's call A the event that the sandwich was made with raspberry Jelly and B the event that the sandwich was made with creamy peanut butter.

So, the probability P(A∪B) that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is calculated as:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where P(A) is the probability that a sandwich was made with raspberry jelly, P(B) is the probability that it was made with creamy peanut butter and P(A∩B) is the probability that it was made with raspberry jelly and creamy peanut butter.

So, replacing P(A) by 0.84, P(B) by 0.27 and P(A∩B) by 0.19, we get that P(A∪B) is equal to:

P(A∪B) = 0.84 + 0.27 - 0.19

P(A∪B) = 0.92

The probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%, computed using the formula for the probability of A or B happening in probability theory.

In probability, when we want to find the probability of event A or event B happening, we use the formula P(A U B) = P(A) + P(B) - P(A ∩ B). Here, event A is the event that a sandwich was made with raspberry jelly, and event B is the event that it was made with creamy peanut butter. Given P(A) = 0.84, P(B) = 0.27, and P(A ∩ B) = 0.19, we can substitute these values into the formula.

So, P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.84 + 0.27 - 0.19 = 0.92.

This means that the probability that a randomly chosen sandwich was made with raspberry jelly or creamy peanut butter is 0.92, or 92%.

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