Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x
years?

Answer: [tex]24\pi\text{ units}^2[/tex]

Step-by-step explanation:

We know that the total surface area of a cylinder is given by :-

[tex]TSA= 2\pi r(r+h)[/tex] , where r = radius  and h= height of cylinder.

Given : Height : h= 4 units

Radius = 2 units

Then, the total surface area of the cylinder is given by :-

[tex]TSA= 2\pi 2(2+4)[/tex]

[tex]\Rightarrow\ TSA= 2\pi (12)=24\pi\text{ units}^2[/tex]

Hence, the total area for the cylinder = [tex]24\pi\text{ units}^2[/tex]

No, she is not correct.

The volume of cubes with side 2/5 inches is : [tex](\frac{2}{5}) ^{3}[/tex] = 8/125 [tex]in^{3}[/tex]

and the volume of cubes with side 1/5 inches is : [tex](\frac{1}{5} )^{3}[/tex] = 1/125 [tex]in^{3}[/tex]

The cubes with sides 1/5 inches have 8 times lesser volume than that of the cubes with sides 2/5 inches.

So, to fill up the same volume, we would require 8 times more cubes of side 1/5 inches than cubes of side 2/5 inches.

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The possible vertices of the right triangle are (-3, -2) and (-1, -2).

Option C and D are the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The points (-3, 2) and (1, 2) have the same y-coordinate, which means that they lie on a horizontal line.

The distance between these two points is 4 units, which is the length of the leg of the right triangle that they form.

The only way to form a right triangle using these points is to choose a third point on a vertical line passing through one of these two points.

Option B)

(-1, 4) does not lie on a vertical line passing through either of the given points.

Option C)

(-3, -2) lies on a vertical line passing through the point (-3, 2), so it could be a vertex of the right triangle.

Option D)

(-1, -2) lies on a vertical line passing through the point (1, 2), so it could be a vertex of the right triangle.

Therefore,

The possible vertices of the right triangle are (-3, -2) and (-1, -2).

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You have to formulate equations for this problem.

Let S = Science score

      M = Math score

       C = Chemistry score

To illustrate the given:

0.9S = 0.75M

0.9S = 0.8C

You are given that Karen’s Math score is 96 marks. You have to substitute the Math score to the first equation.

0.9S = 0.75(96)

0.9S = 72

S = 80

Therefore, Karen’s Science score is 80. Now, you have to substitute the Science score to the second equation.

0.9(80) = 0.8C

0.8C = 72

C = 90

So, Karen’s Chemistry score is 90.

Therefore, the total score of the 3 subjects is 266 (96 + 80 + 90).

Answer:

C 90

Step-by-step explanation:

Final answer:

Slope of function for Salesman A: 65

Slope of function for Salesman B: 40

Slope of function for Salesman C: 0

Explanation:

Slope of function for Salesman A: The slope of the function representing Salesman A's weekly paycheck is $65 per sale, as he earns $65 per sale. Since the commission is a constant rate per sale, the slope remains constant.

Slope of function for Salesman B: The slope of the function representing Salesman B's weekly paycheck is $40 per sale. This is because he earns $40 per sale, which makes the slope $40.

Slope of function for Salesman C: The slope of the function representing Salesman C's weekly paycheck is 0. Salesman C does not earn any commission, so his weekly salary remains constant at $900, regardless of the number of sales made.

9514 1404 393

Answer:

  Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5

Step-by-step explanation:

Nothing indicates any triangle sides are congruent, a necessary condition for the triangles to be congruent.

In triangles ABC and EDC, angles 1 and 5 are corresponding. They are "alternate interior angles" with respect to the transversal AE, so are congruent. Angles 2 and 6 are congruent for a similar reason. The vertical angles at C are congruent, so the triangles are similar.

Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5.

The points for the swimming event are calculated as :one point for each second the swimmer stayed under water and two points for each meter that the swimmer traveled.

Charles de Vendeville stayed under water for 68.4 seconds.

Points earned for staying under water = 68.4 (1)= 68.4

Vendeville from France travelled 60.2 meters

Points earned for traveling 60.2 meters = 60.2(2)= 120.4

Total points earned = 68.4+120.4=188.8

Answer:

10 times greater is the value of 5 in 3,590 than the value of 5 in 359.

Step-by-step explanation:

To find : How many times greater is the value of 5 in 3,590 than the value of 5 in 359 ?

Solution :

The place value stem is

Thousand     Hundred     Tens    Ones

  1000               100            10         1

The value of 5 in 3,590 is at hundred place

So, [tex]5\times 100=500[/tex]

The value of 5 in 359 is at tens place

So, [tex]5\times 10=50[/tex]

Number of time greater is the value of 5 in 3,590 than the value of 5 in 359 is given by,

[tex]n=\frac{500}{50}[/tex]

[tex]n=10[/tex]

Therefore, 10 times greater is the value of 5 in 3,590 than the value of 5 in 359.

Final answer:

The value of 5 in 3,590 is 10 times greater than the value of 5 in 359 because the 5 in 3,590 represents 500 while in 359 it represents 50.

Explanation:

The question asks how many times greater the value of 5 in 3,590 is compared to the value of 5 in 359. In the number 3,590, the 5 is in the hundred's place, meaning it has a value of 500 (5 x [tex]10^2[/tex]). In the number 359, the 5 is in the ten's place, meaning it has a value of 50 (5 x [tex]10^1[/tex]). To find out how many times greater one value is than the other, we divide the larger by the smaller

So, 500 divided by 50 equals 10. This means the value of 5 in 3,590 is 10 times greater than the value of 5 in 359.

If there are 5 boys and 10 girls in the glee club then the ratio which represents the number of boys to the total number of students in the club will be 1/3 which is option a.

Ratio is basically a relationship between two quantities which are expressed in times of another.

Number of boys in the glee club=5

Number of girls in the glee club=10

Total number of students=10+5=15

Ratio=number of boys/total number of students

=5/15

=1/3

Hence the ratio between the boys to total number of students is 1/3.

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Final answer:

To find out how many hours Suzette ran, we used a system of equations with the total distance and total time for running and biking. Solving the system, we determined that Suzette ran for 1.5 hours.

Explanation:

To determine how many hours Suzette ran, we can use the total distance and the total time given for running and biking activities, alongside her average speeds for each activity. We will then set up a system of equations that account for the distances and times and solve for the time Suzette spent running.

Let r be the time spent running and b be the time spent biking. We are given:

Total time: r + b = 3.5 hours

Total distance: 6r + 12.5b = 34 miles (6 mph is the running speed, 12.5 mph is the biking speed)

Now we'll solve this system of equations:

Substitute b from the first equation into the second equation: 6r + 12.5(3.5 - r) = 34.

Simplify and solve for r: 6r + 43.75 - 12.5r = 34.

This simplifies further to -6.5r = -9.75, hence r = 1.5.

Suzette ran for 1.5 hours.

4(x - 2) + 6 = 2(5x - 6)     use distributive property

(4)(x) + (4)(-2) + 6 = (2)(5x) + (2)(-6)

4x - 8 + 6 = 10x - 12

4x - 2 = 10x - 12       add 2 to both sides

4x = 10x - 10       subtract 10 from both sides

-6x = -10      divide both sides by (-6)

x = 10/6

In systematic sampling, a higher n-value (every nth number) means fewer members are selected, thus smaller sample size. Therefore, surveying every 25,000th number results in the smallest sample size.

In systematic sampling, every nth member of a population is chosen for sampling. The smaller the value of n, the larger the sample size will be, because you're selecting a member more frequently. When we compare the options given: A. 25,000, B. 250, C. 25, and D. 2500, we see that option A (the 25,000th member), will result in the smallest sample size. In this scenario, for a total user base of 1,000,000, selecting every 25,000th member would produce approximately 40 samples (1,000,000 / 25,000 = 40), which is less than what you'd get with the other options.

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