The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 5% in 10 years. What will be the population in 20 years

Answer:

5

Step-by-step explanation:

when c = 7,

substitute 7, into 35÷c

35 ÷ 7 = 5

Answer:

C. Robbie's glider

Step-by-step explanation:

P.S -The exact question is -

Given - Melissa and Robbie are flying remote control gliders.

The altitude of Melissa's glider, h(s), in feet, is modeled by this function, where sis time, in seconds, after launch.

m(s) = 0.4(s³ - 11s² + 31s – 1)

The altitude of Robbie's glider is modeled by function r, where sis time, in seconds, after launch.

To find - Which glider reaches the greater maximum altitude in the first 6 seconds after launch?

A. Neither glider reaches a maximum altitude on the given interval.

В. Melissa's glider

C. Robbie's glider

D. Both gliders reach the same altitude on the given interval.

Proof -

At t = 6 sec,

Melisa glider is

h(6) = 0.4((0.6)³ - 11(0.6)² + 31(0.6) – 1)

      = 0.4( 0.216 - 3.96 + 18.6 - 1 )

      = 0.4(13.856) = 5.5424

⇒h(6) = 5.5424

∴ we get

At t = 6 seconds, Melissa glider is at the altitude of 5.54 feet

Now,

From the figure, we can see that,

At t = 6 seconds, Robbie's glider is approximately at an altitude of 13 feet

Now,

As 13 > 5.5

So,

Robbie's glider is at maximum height in 6 seconds after the launch.

So,

The correct option is - C. Robbie's glider

Path A-B-C-E represents the distance traveled, which is 18 meters.

Path A-G-C-E represents the displacement, which is 17 meters.

From the given figure, we can identify the paths and calculate the distance and displacement.

Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.

Let's calculate the lengths of both paths:

Distance traveled (Path A-B-C-E):

Length of AB = 9m

Length of BC = 3m

Length of CE = 6m

Total distance traveled = Length of AB + Length of BC + Length of CE

= 9m + 3m + 6m

= 18m

Therefore, the distance traveled along path A-B-C-E is 18 meters.

Displacement (Path A-G-C-E):

Length of AG = 5m

Length of GC = 6m

Length of CE = 6m

Total displacement = Length of AG + Length of GC + Length of CE

= 5m + 6m + 6m

= 17m

Therefore, the displacement along path A-G-C-E is 17 meters.

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Answer:

Apparently, i dont know but I will try.

Step-by-step explanation:

I believe its true because I'm a mathematician.

Answer:

These figures are not the same because the Slope of DE is not the same as the slope of JK.

Step-by-step explanation:

Slope of DE = -2/1

Slope of JK = -1

If they were similar, the slope would be the same, but the size would not.

-Chetan K

Using the compound interest formula, the time it takes the investment to double is 0.68 years

To find the time it takes the investment to double, we use the compound interest formula.

A = P(1 + r)ⁿ where

So, making n subject of the formula, we have that

n = ㏑(A/P)/(1 + r)

Since we want to find the time it takes the investment to double, we have that

So, substituting the values of the variables into the equation, we have that

n = ㏑(A/P)/(1 + r)

n = ㏑(2P/P)/(1 + 0.0133)

n = ㏑(2)/(1.0133)

n = 0.693/1.0133

n = 0.68 years

So, the time is 0.68 years

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Answer:

2. \(\displaystyle 64\:feet\)

1. \(\displaystyle 5\:seconds\)

Step-by-step explanation:

2. Sinse we do not have a y-intercept [C-value in this case], we have to use a part of the quadratic formula to solve for x, and rewrite this equation in Vertex Form, with \(\displaystyle [h, k]\) as the vertex point. Observe:

\(\displaystyle -\frac{b}{2a} = x \\ \\ -\frac{64}{2[-16]} = \frac{-64}{-32} = 2\)

Now, keep in mind that \(\displaystyle -h\) in the vertex formula, \(\displaystyle y = a[x - h]^2 + k,\) gives you the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so in this case, sinse 2 is already positive, you do not need to alter its operation sign. With this being stated, you should already have this:

\(\displaystyle y = -16[x - 2]^2\)

Now, to find k, all you have to do is plug 2 into the TOP equation to get your maximum height:

\(\displaystyle -16[2]^2 + 64[2] = -16[4] + 128 = -64 + 128 = 64 \\ \\ \\ y = -16[x - 2]^2 + 64\)

Therefore, sinse 64 is your k-value, 64 feet is indeed your maximum height.

1. Simply factour the quadratic equation:

\(\displaystyle y = -18x^2 + 90x \\ 0 = -18x[x - 5] \\ \\ 5, 0 = x\)

In this case, from a height of sixty-four feet, it is IMPOSSIBLE for the football to hit the ground in zero seconds, therefore the ball will reach the ground in 5 seconds, which makes alot more sence.

I am joyous to assist you at any time.

** Minimum Height → \(\displaystyle A\)

** Maximum Height → \(\displaystyle -A\)

Answer:

4 +(r/5)

Step-by-step explanation:

Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin

Answer:

The equation of the elipse is

\(\frac{x^2}{169} + \frac{y^2}{25} = 1\)

Step-by-step explanation:

Equation of an elipse:

The equation of a elipse with centre \((x_c,y_c)\) has the following format:

\(\frac{(x - x_c)^2}{a^2} + \frac{(y - y_c)^2}{b^2} = 1\)

Centre at (0,0):

Means that \((x_c,y_c) = (0,0)\).

So

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

Vertex at (13,0):

Vertex at 13 means that \(a = 13, a^2 = 13^2 = 169\)

Focus at (-12,0):

Means that \(c = 12, c^2 = 12^2 = 144\)

We have that:

\(a^2 = b^2 + c^2\)

So

\(169 = b^2 + 144\)

\(b^2 = 25\)

So, the equation of the elipse is

\(\frac{x^2}{169} + \frac{y^2}{25} = 1\)

Answer:

1. 22 - 8 = 14

2. 14 + 2 = 16

3. 16 - 5 = 11

4. 11 + 2 = 13

Answer:  13 and steps above

Step-by-step explanation:

Answer:

5

Step-by-step explanation: Use PEMDAS, you do addition and then subtraction first because A is before S.  When you solve it you have to go from left to right.

22 - 8 + 2 - 5 + 2 =

8 + 2 = 10

22 - 10 - 5 + 2 =

5 + 2 = 7

22 - 10 - 7 =

22 - 10 = 12

12 - 7 = 5

I hopr this helps! Have a great day!

Answer:

Triangle SUT...

You can thank me in the commrent

1. The probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond is 1/2.

3. The probability of selecting a number smaller than 9 is 9/13.

1. The probability of selecting a 3 of Diamonds:

There is only one 3 of Diamonds in the deck, and the total number of cards in the deck is 52. Therefore, the probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond:

There are 13 Clubs and 13 Diamonds in the deck, making a total of 26 cards. The probability of selecting a Club or Diamond is the ratio of the number of favorable outcomes (Club or Diamond) to the total number of possible outcomes (52 cards). Therefore, the probability is 26/52, which simplifies to 1/2.

3. The probability of selecting a number smaller than 9:

There are four suits in the deck (Clubs, Diamonds, Hearts, and Spades), and each suit has cards numbered 2 to 10. So, there are 4 suits * 9 cards per suit = 36 cards that are numbered smaller than 9.

The probability of selecting a number smaller than 9 is the ratio of the number of favorable outcomes (36 cards) to the total number of possible outcomes (52 cards). Therefore, the probability is 36/52, which simplifies to 9/13.

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Option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1.

The number expression is:

= (70 + 12.8 + 30) + 6.1

As we know from the commutative property

a +  b = b + a

Applying commutative property in the number expression:

= (70 + 30+ 12.8) + 6.1

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1.

Thus, option (D) She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1 is correct.

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer: 2%

Step-by-step explanation:

Exponential growth functions are of the form \(P(1+r)^t\), where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.

Answer:

209

Step-by-step explanation:

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Answer:

8 quarters and 4 dimes

Step-by-step explanation:

4 quarters = 1 dollars

4 quarters = 1 dollars

4 dimes = 40 cents

2.40$

============================================

Work Shown:

d = number of dimes

q = number of quarters

1 dime = 10 cents

d dimes = 10d cents

1 quarter = 25 cents

q quarters = 25q cents

d+q = 12 since we have 12 coins total

q = -d+12 after solving for q

10d+25q = total value in cents

10d+25q = 240

10d+25(-d+12) = 240 ... plug in q = -d+12

10d-25d+300 = 240

-15d+300 = 240

-15d = 240-300

-15d = -60

d = -60/(-15)

d = 4

q = -d+12

q = -4+12

q = 8

Since d = 4 and q = 8, this means we have 4 dimes and 8 quarters

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

Check:

4 dimes = 4*10 = 40 cents

8 quarters = 8*25 = 200 cents

(4 dimes) + (8 quarters) = (40 cents) + (200 cents) = 240 cents

240 cents = 240/100 = $2.40

We have 4+8 = 12 coins total

The answers are confirmed

Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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The center of mass for the system (x, y) is \(\left(\frac{a m+b M}{m+M}, 0\right)\).

What is center of mass?

The unique location where the weighted relative position of the scattered mass adds to zero is known as the center of mass in physics. Here is where a force may be applied to produce a linear acceleration without also producing an angular acceleration.

The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses.

Centre of mass is

\(x=\frac{m a+M b}{m+M}\)

and y=0

\((x, y)=\left(\frac{a m+b M}{m+M}, 0\right)\)

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Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

After multiplying the polynomials (7k - 5) and (\(7k^2 + 5k - 1\)), we can have the product as \(49k^3 - 32k - 5\).

To multiply the polynomials (7k - 5) and (\(7k^2 + 5k - 1\)), we will use the distributive property.

First, distribute the first term of the first polynomial, which is 7k, to each term in the second polynomial:

7k * \(7k^2\) + 7k * 5k + 7k * (-1)

This simplifies to:

\(49k^3 + 35k^2 - 7k\)

Next, distribute the second term of the first polynomial, which is -5, to each term in the second polynomial:

\(-5 * 7k^2 - 5 * 5k - 5 * (-1)\)

This simplifies to:

\(-35k^2 - 25k + 5\)

Finally, combine the like terms to get the final result:

\(49k^3 + 35k^2 - 7k - 35k^2 - 25k + 5\)

Combining like terms gives:

\(49k^3 - 32k - 5\)

Thus, this is the product of the polynomials (7k - 5) and (\(7k^2 + 5k - 1\)).

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The value of x in this figure is equal to: D. 5.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

112 + 7x + 5 + 6x + 2 + 10x - 8 + 4x + 24 = 540°.

27x = 135

x = 135/27

x = 5.

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