A spring with a 8-kg mass and a damping constant 18 can be held stretched 2 meters beyond its natural length by a force of 8 newtons. Suppose the spring is stretched 4 meters beyond its natural length and then released with zero velocity.
Find the position of the mass after t seconds.

Answer:

Step-by-step explanation:

To find the percentage of Tara's monthly income spent on her car payment, we need to divide her car payment by her monthly income and then multiply by 100 to get the percentage:

$219 / $3,200 = 0.0684375

0.0684375 * 100 = 6.84375

So, Tara spends approximately 6.8% of her monthly income on her car payment.

The closest answer choice is C. 6.8%.

Answer:

C

Step-by-step explanation:

I got just did it and got it right

I'm sorry, but I cannot determine the values of the line segment lengths

and angle measures without further information or context about the

geometry problem. Please provide me with more details or the specific

problem in question.

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The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

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The central angle is approximately 51.6 degrees.

To solve this problem, we can use the formula for arc length of a circle:

arc length = θ × r

where θ is the central angle in radians, and r is the radius of the circle.

We know that the arc length is 4.5 feet and the radius is 5 feet. So we can rearrange the formula to solve for θ:

θ = arc length / r

θ = 4.5 / 5

θ = 0.9 radians

To find the central angle in degrees, we can convert radians to degrees by multiplying by 180/π:

θ = 0.9 × (180/π)

θ ≈ 51.6 degrees

Therefore, the central angle is approximately 51.6 degrees.

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The exponential function that models the total population p after t years is p = 3,500 x 1.025^t.

To write an exponential function that models the total population of the town after t years, we need to use the formula:

p = p0 x  (1 + r)^t

where p0 is the initial population, r is the annual growth rate as a decimal (so in this case, 2.5% = 0.025), and t is the number of years.

In this case, we know that the initial population is 3,500, and the annual growth rate is 2.5%, or 0.025. So we can substitute these values into the formula to get:

p = 3,500 x (1 + 0.025)^t

Simplifying this expression gives:

p = 3,500 x 1.025^t

So the exponential function that models the total population p after t years is:

p(t) = 3,500 x 1.025^t

Note that the function is exponential because the population grows at a constant percentage rate each year, which means that the growth itself is increasing over time.

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The ratio of a : b : c : d is 3 : 7 : 2 : 7.

The ratios are determined as follows from the data given.

The given data is:

7a = 2b

b = (7/2)a.

a and b have no common factors, thus a must be even and b must be odd.

c : d is 2 : 7

For an integer x, c = 2x and d = 7x

a : d is 3 : 1

So for an integer y, a = 3y and d = y

Substituting into 7a = 2b:

7(3y) = 2(7/2)y a

21y = 7y * b

b = 3a

Substituting these expressions for a and b into c : d = 2:7, we get:

2x : 7x = 3 : 1

2x = 3y and 7x = y

y = 14x/3

a : b : c : d = 3y : 7y : 2x : 7x

a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)

a : b : c : d = 9y : 21y : 6x : 21x

a : b : c : d = 3 : 7 : 2 : 7

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The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.

Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion

(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP

Plugging in the given values and simplifying, we get

(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)

15.4/(3x + 2.4) = (x + 17.3)/(x + 5)

Cross-multiplying and solving for x, we get

x = 2.8

To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths

(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4

Therefore, the scale factor of GKNM to RPTV is 1.4.

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Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth

To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:

1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.

Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.

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Using the chain rule, we have: f'(x) = 2ln(x^4 + 5) * 2(x^4 + 5)^1 * 4x^3
f'(x) = 16x^3 * ln(x^4 + 5) * (x^4 + 5)

To find f'(-2), we plug in -2 for x:

f'(-2) = 16(-2)^3 * ln((-2)^4 + 5) * ((-2)^4 + 5)
f'(-2) = -128 * ln(21) * 21
f'(-2) ≈ -599.92 (rounded to 2 decimal places)

Therefore, f'(-2) is approximately -599.92.
To find f'(-2) for the function f(x) = ln((x^4 + 5)^2), we will first find the derivative of the function, and then evaluate it at x = -2.

1. Differentiate the function using the chain rule:
f'(x) = (d/dx) ln((x^4 + 5)^2) = (1/((x^4 + 5)^2)) * (d/dx) ((x^4 + 5)^2)

2. Differentiate the inner function:
(d/dx) ((x^4 + 5)^2) = 2(x^4 + 5) * (d/dx) (x^4 + 5) = 2(x^4 + 5) * (4x^3)

3. Combine the derivatives:
f'(x) = (1/((x^4 + 5)^2)) * (2(x^4 + 5) * (4x^3)) = (8x^3(x^4 + 5))/((x^4 + 5)^2)

4. Evaluate the derivative at x = -2:
f'(-2) = (8(-2)^3((-2)^4 + 5))/((-2)^4 + 5)^2 = (-128(21))/(21^2) = -128/21

So, f'(-2) is -128/21 as an exact fraction.

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Answer: B

Step-by-step explanation: I did the quiz :p

Hope this helps

The correct answer is B. 12. There are 12 numbers in the table, which represents the number of observations Beckett recorded.

The table shows the number of days each of Beckett's classmates floss their teeth in a typical week. The number of observations recorded is simply the number of classmates, or the number of entries in the table. In this case, there are 12 entries, so the answer is 12.

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Answer:

A BOB, C TOT

Step-by-step explanation:

If we draw a vertical line throgh the word the left side is the mirror image of the right.

Note that where the above function is given, the equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold. See the graph attached.

To change the given equation to slope-intercept form, we need to solve for y.

2x + 3y = 1470

3y = -2x + 1470

y = (-2/3)x + 490

Therefore, the slope of the line is -2/3 and the y-intercept is 490.

To graph this line using the slope-intercept method, we can plot the y-intercept first, which is (0, 490). Then, using the slope of -2/3, we can find another point by moving 2 units to the right and 3 units down from the first point. We can continue this pattern to plot additional points and then draw a straight line through them.

The equation in function notation is f(x) = (-2/3)x + 490. This function represents the profit Sal makes from lunch specials based on the number of sandwich and wrap lunch specials sold.

To graph the function, we can plot the intercepts (0, 490) and (735, 0), where 735 is the x-intercept. Then, using the slope of -2/3, we can find other points and draw a straight line through them.

If Sal's total profit on lunch specials for the next month is $1,593, then the equation would be 2x + 3y = 1593. The graphs of the functions for both months would have the same slope of -2/3, indicating that the profit per lunch special sold remains constant.

However, the y-intercept would be different, indicating a different starting profit for the month. The graphs would have different intercepts and intersect the y-axis at different points, reflecting the difference in starting profits.

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Answer:

D.5

Step-by-step explanation:

8x – 6 > 12 + 2x

= 8x−2x>12+6= 6x>18

= x>38x−2x>12+6

= 6x>18

= x>3

From the given options the only value which is greater than 3 is Option (D) 5

Answer:

x=50

Step-by-step explanation:

1. multiply the numbers

48x25=24x

1200=24x

2. Divide both sides by the same factor

1200/24 = 24/24x

simplify the expression

x=50

The height of the replica souvenir is approximately 7.55 inches.

To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:

151 ft / 20 ft/in = 7.55 inches

The height of the replica souvenir is approximately 7.55 inches.

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Pair C of adjacent angles is supplementary because both the angles make the sum of 180°.

Adjacent angles are those angles which have a common vertex and supplementary angles are those which on adding make sum of 180°. In the given question, only the adjacent angles of Pair C make the sum of 180°.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.

Complementary angles, on the other hand, add up to 90 degrees. When the two additional angles are brought together, they form a straight line and an angle.

It should be emphasized, however, that the two supplementary angles do not have to be adjacent to each other. As a result, any two angles can be supplementary if their sum is equal to 180°.

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Correct question:

Which pair of adjacent angles is complementary?

A. Pair A

B. Pair B

C. Pair C

D. Pair D

Image is attached below.

The angular velocity of the point on the rim of the wheel is 25 radians per second.

The linear velocity of a point on a wheel's rim is determined by:

v = rω

v = linear velocity

r = radius of the wheel

ω = angular velocity.

In this case, the diameter of the wheel is 8 feet, so the radius is 4 feet. The linear velocity is given as 100 feet per second, so we have:

100 = 4ω

Solving for ω, we get:

ω = 25 radians per second

Therefore, the angular velocity of the point on the rim of the wheel is 25 radians per second.

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Answer:

B) <FBG

Step-by-step explanation:

An adjacent angle is an angle that is right next to the given angle.

In this case, the given angle is <EBF.

We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.

Looking at the options, we can only see that <FBG is an option, making B the correct option.

Hope this helps :)

To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

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The resultant component of the vector addition, 1/3a - 2b is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

The solutions of the equation algebraically are x = 5 and x = -7

From the information given, we have the quadratic equation;

|x| = x2 + x − 35

The sign , '| |' represents the modulus sign and says that the value must be a positive value.

Then, we have;

x² + x + x - 35

add the like terms

x² + 2x - 35

Find the pair factors of -35 that add up to 2, we have;

x² + 7x - 5x - 35

Group the expression in pairs

(x² + 7x) - (5x - 35)

factorize the expression

x(x + 7) - 5(x + 7)

Then, we have that;

x - 5 = 0

x = 5

x + 7 = 0

x = -7

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There were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

In 1980, there were 1.2 million elephants in Africa. With a decrease of 6.8% per year, we need to calculate the population in 1987, which is 7 years later.

To find the population in 1987, we use the formula:

Final population = Initial population * (1 - decrease rate) ^ number of years

Final population = 1,200,000 * (1 - 0.068) ^ 7

Final population ≈ 1,200,000 * 0.489

Final population ≈ 586,800

In 1987, there were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

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The doctor would prescribe 8 milliliters of acetaminophen for Jocelyn, who weighs 40 pounds.

According to the given information, pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child's weight. So, if a child weighs 50 pounds, the doctor would prescribe 10 ml of acetaminophen.

Now, let's apply this formula to Jocelyn's weight. As Jocelyn weighs 40 pounds, we need to calculate how many 25-pound increments her weight contains. To do this, we can divide her weight by 25:

40 pounds ÷ 25 pounds = 1.6 increments

This means that Jocelyn's weight is equivalent to 1.6 times the 25-pound increment used in the prescription. To determine the amount of acetaminophen she needs, we can multiply 5 ml (the prescribed dose for 25 pounds) by 1.6:

5 ml × 1.6 = 8 ml

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Answer:

Answer:17

Explanation: 5-0.75=4.25 4.25÷0.25=17

Hope this helps

The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

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Answer:

SSA

Step-by-step explanation:

It would be SSA (Side-Side-Angle).  They are congruent where they intersect at B (opposite angles).  Since CF is congruent to GH, and CB is congruent to HB, you have an angle and two sides congruent, in the order SSA.

A. Approximately 9.85% of New York City commutes are less than 30 minutes

B. Approximately 16.91% of New York City commutes are between 30 and 35 minutes.

A. To find the percent of New York City commutes that are less than 30 minutes, we need to calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we are interested in (30 minutes), μ is the mean commute time (39.7 minutes), and σ is the standard deviation (7.5 minutes).

z = (30 - 39.7) / 7.5 = -1.29

We can use a standard normal distribution table or calculator to find the area to the left of z = -1.29, which gives us:

P(z < -1.29) = 0.0985

Therefore, approximately 9.85% of New York City commutes are less than 30 minutes.

B. To find the percent of New York City commutes that are between 30 and 35 minutes, we need to calculate the z-scores for both values using the same formula:

z1 = (30 - 39.7) / 7.5 = -1.29

z2 = (35 - 39.7) / 7.5 = -0.62

We can then find the area between these two z-scores using a standard normal distribution table or calculator, which gives us:

P(-1.29 < z < -0.62) = P(z < -0.62) - P(z < -1.29) = 0.2676 - 0.0985 = 0.1691

Therefore, approximately 16.91% of New York City commutes are between 30 and 35 minutes.

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The volume of the solid generated when the right triangle below is rotated about side IK is: 37.7 units²

The three-dimensional figure that is formed by rotating a triangle about it's height is called a Cone.

Where:

The triangle base length will be seen to become the radius of the cone

The triangle height will be seen to become the height of the cone

The formula for the volume of a cone is expressed as:

V = ¹/₃πr²h

Where:

r refers to the radius

h refers to the height

Therefore, we can say that the volume will be expressed as:

V = ¹/₃ * π * 2² * 9

V = 37.7 units²

Thus, that is the  volume of the solid generated when the right triangle below is rotated about side IK.

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The power rule for derivatives is  -26/5.

The derivative is a fundamental concept that measures how much a function changes as its input changes. It is a mathematical tool used to find the instantaneous rate of change of a function at a specific point. The derivative of a function f(x) at a point x=a, denoted by f'(a), is the slope of the tangent line to the graph of f(x) at the point (a, f(a)).

a. f(x) = 2x³

Using the power rule for derivatives, we have:

f'(x) = 6x²

So, f'(2) = 6(2)² = 24.

b. g(x) = 13x^(1/2)

Using the power rule for derivatives, we have:

g'(x) = (1/2) * 13x^(-1/2) = (13/2√x)

So, g'(3) = (13/2√3).

c. h(x) = hx

Using the power rule for derivatives, we have:

h'(x) = h

So, h'(4) = h.

d. j(x) = 130x^(-1)

Using the power rule for derivatives, we have:

j'(x) = -130x^(-2)

So, j'(5) = -130(5)^(-2) = -130/25 = -26/5.

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