estimate the instantaneous rate of growth in 2000 by taking the average of the last two rates of change

There are 35% sixth-graders at Kendrick's school who picked the museum.

Percentage is a part of the whole number.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.

1 %= 1/100.

Given that,

Total number of sixth-graders at Kendrick's school = 56,

Also,

The number of s sixth-graders that picked the museum = 14.

The percentage of the sixth-graders that picked the museum

= (14/56) x 100

= (1/4) x 100

= 25 %

25 percent of the sixth-graders picked the museum.

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Answer:

40/3

Step-by-step explanation:

\(\frac{x}{8} =\frac{5}{3}\)

Multiply both sides by 8:

\(x=\frac{5}{3}* \frac{8}{1} =\frac{40}{3}\)

Answer:

40/3

Step-by-step explanation:

hopefully this helps

first multiply 8 x 5 from x/8 and 5/3

next after you multiply 8 x 5 you should get 40 and your is

40/3

hopefully this helps

Answer:

  (a)  $810.45

Step-by-step explanation:

You want the value of an investment of $300 earning 5% interest compounded quarterly for 20 years.

The compound interest formula tells you the value is ...

  A = P(1 +r/n)^(nt)

where P = 300, r = 0.05, n = 4, t = 20.

Using the given parameters in the given equation, you find the account value to be ...

  A = $300(1 +0.05/4)^(4·20) ≈ $810.45

__

Additional comment

The "rule of 72" tells you the account value will approximately double in a number of years equal to 72 divided by the interest rate percentage: 72/5 = 14.4 years. After 20 years, it will be worth more than that doubled amount, $600. This only leaves one reasonable answer choice.

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Answer:

x = - \(\frac{5}{6}\) , x = \(\frac{1}{2}\)

Step-by-step explanation:

To find the zeros let f(x) = 0 , that is

12x² + 4x - 5 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 12 × - 5 = - 60 and sum = + 4

The factors are - 6 and + 10

Use these factors to split the x- term

12x² - 6x + 10x - 5 = 0 ( factor first/second and third/fourth terms )

6x(2x - 1) + 5(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(6x + 5) = 0

Equate each factor to zero and solve for x

6x + 5 = 0 ⇒ 6x = - 5 ⇒ x = - \(\frac{5}{6}\)

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = \(\frac{1}{2}\)

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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Using expression 21000 cm ÷ 65 cm/pace, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that are grouped together, but not necessarily equated to anything. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple variables and operations.

Now,

To find the minimum number of full paces that Robert needs to take to walk the full length of the bridge, we need to divide the total length of the bridge by the length of each pace.

First, we need to convert the length of the bridge from meters to centimeters because the length of each pace is given in centimeters:

210 m = 21000 cm

Now, we divide the length of the bridge in centimeters by the length of each pace in centimeters:

21000 cm ÷ 65 cm/pace ≈ 323.08 paces

Since Robert cannot take a fraction of a pace, we need to round up to the nearest whole number to get the minimum number of full paces that he needs to take:

323.08 ≈ 324 full paces.

Therefore, Robert needs to take a minimum of 324 full paces to walk the full length of the bridge.

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The fact that the sum can be approximated by an integral. we can approximate the sum as the area under the curve y=√x from x=1 to x=10000. This can be written as: ∫1^10000 √x dx

Using integration rules, we can evaluate this integral to get:
(2/3) * (10000^(3/2) - 1^(3/2))
This evaluates to approximately 66663.33. Therefore, an estimate for the sum ∑ i=1 to 10000 √i is 66663.33.

In mathematics, integrals are continuous combinations of numbers used to calculate areas, volumes, and their dimensions. Integration, which is the process of calculating compounds, is one of the two main operations of computation, [a] the other being derivative. Integration was designed as a way to solve math and physics problems like finding the area under a curve or determining velocity. Today, integration is widely used in many fields of science.

To estimate the sum of ∑ from i=1 to 10000 of √i using an integral, we'll approximate the sum with the integral of the function f(x) = √x from 1 to 10000.

The integral can be written as:

∫(from 1 to 10000) √x dx

To solve this integral, we first find the antiderivative of √x:

Antiderivative of √x = (2/3)x^(3/2)

Now, we'll evaluate the antiderivative at limits 1 and 10000:

(2/3)(10000^(3/2)) - (2/3)(1^(3/2))

(2/3)(100000000) - (2/3)

= (200000000/3) - (2/3)

= 199999998/3

Thus, the integral estimate of the sum from i=1 to 10000 of √i is approximately 199999998/3.

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\( \frac{0.2x - 3.2}{5} = 1.8 \\ 0.2x - 3.2 = 1.8 \times 5 \\ 0.2x - 3.2 = 9 \\ 0.2x = 9 + 3.2 \\ 0.2x = 12.2 \\ x = \frac{12.2}{0.2} \\ \boxed{ x = 61}\)

The probability distribution used to model a random variable x that equals the number of events that occur within an interval or area of opportunity is the Poisson distribution. This is used to model a random variable representing the number of events occurring within a fixed interval or area of opportunity, given an average rate of occurrence.

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space, given the average rate at which events occur and the assumption that the events are independent of each other. It is commonly used in fields such as biology, physics, and engineering to model occurrences of rare events such as accidents, defects, or rare diseases.

The Poisson distribution has a single parameter λ, which represents the average rate of events occurring in the interval or area of opportunity. The probability of observing exactly k events in this interval is given by the Poisson probability mass function:

P(X=k) = (e^-λ * λ^k) / k!

where X is the random variable representing the number of events, e is the mathematical constant approximately equal to 2.71828, and k! is the factorial of k.

The Poisson distribution is similar to the binomial distribution but is used when the number of trials is very large and the probability of success is very small. In this case, the binomial distribution becomes impractical to use, and the Poisson distribution is a more appropriate model.

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The number of marbles Ann had at the end is 54.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total marbles = 100

The number of marbles:

Marcy:

= 25% of 100

= 1/4 x 100

= 25

Roger:

= 21

Now,

The number of marbles:

Ann = 100 - (25 + 21) = 100 - 46 = 54

Thus,

Ann has 54 marbles at the end.

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To find the height of a triangle using trigonometry, you can use the sine or cosine ratios. The specific ratio to use depends on the information you have about the triangle.

If you have the length of one side of the triangle and the measure of the angle opposite that side, you can use the sine ratio to find the height. The sine ratio is defined as the length of the side opposite the angle divided by the length of the hypotenuse.

Here are the steps to find the height using the sine ratio:

1. Identify the side of the triangle that represents the height.
2. Determine the angle opposite that side.
3. Measure the length of the side adjacent to the angle or obtain that information from the problem.
4. Use the sine ratio: height = length of adjacent side * sin(angle).

For example, let's say you have a right triangle with an angle of 30 degrees and a side adjacent to that angle measuring 6 units. To find the height, you would use the sine ratio:

height = 6 * sin(30)
height ≈ 3 units

If you have the length of two sides of a right triangle and you need to find the height, you can use the cosine ratio. The cosine ratio is defined as the length of the side adjacent to the angle divided by the length of the hypotenuse.

Here are the steps to find the height using the cosine ratio:

1. Identify the side of the triangle that represents the height.
2. Determine one of the acute angles of the triangle.
3. Measure the lengths of the two sides adjacent to that angle or obtain that information from the problem.
4. Use the cosine ratio: height = length of adjacent side * cos(angle).

For example, let's say you have a right triangle with an angle of 45 degrees and two sides adjacent to that angle measuring 4 units and 4√2 units. To find the height, you would use the cosine ratio:

height = 4 * cos(45)
height ≈ 2.828 units

In summary, to find the height of a triangle using trigonometry, you can use the sine or cosine ratios. The sine ratio applies when you have the length of one side and the angle opposite that side, while the cosine ratio applies when you have the lengths of two sides adjacent to an angle.

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Answer:

Multiplication

Step-by-step explanation:

19 (multiplied by) 2.3 = x, or 43.7

Answer:

x>−42

Step-by-step explanation:

Multiply both sides by 7.

x>−6×7

 Simplify times 6×7  to 42.

x>−42

Answer:

cost of each sub = $6, delivery fee = $2

Step-by-step explanation:

Let $x be the cost of each sub and $c be the delivery fee

3x + c = 20

4x + c = 26

x = 6, c = 2

Answer:

The equation of the axis of symmetry is x = 7

Step-by-step explanation:

Mathematically, we have the equation of the axis of symmetry as;

x = -b/2a

where a is the coefficient of x^2 = 1

b is the coefficient of x which is -14

So, the equation of the axis of symmetry will be;

x = -(-14)/2(1) = 14/2 = 7

So the equation of the axis of symmetry is x =7

Answer:

13/4

Step-by-step explanation:

\(f(x) = \frac{7x - 22}{4} \)

\(f(5) = \frac{7(5) - 22}{4} = \frac{35 - 22}{4} = \frac{13}{4} \)

Answer:

\(3(2x + 1) = 5(x -4) \\ 6x + 3 = 5x - 20 \\ 6x - 5x = - 3 - 20 \\ \boxed{x = - 23}\)

The height of an equilateral triangle with sides that are 12 cm long is approximately 10.4 cm.

An equilateral triangle is a triangle whose sides are equal in length. All the angles in an equilateral triangle measure 60 degrees. The height of an equilateral triangle is the line segment that goes from the center of the triangle to the opposite side, perpendicular to that side. In order to find the height of an equilateral triangle, we can use a special right triangle formula: 30-60-90 triangle ratio.

Let's look at the 30-60-90 triangle ratio:
In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle. The hypotenuse is twice the length of the side opposite the 30-degree angle.

Using the 30-60-90 triangle ratio, we can find the height of an equilateral triangle as follows:

Since all the sides of an equilateral triangle are equal, the height of the triangle is the length of the side multiplied by √3/2. Therefore, the height of an equilateral triangle with sides that are 12 cm long is:

height = side x √3/2
height = 12 x √3/2
height = 6√3
height ≈ 10.4 cm
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Answer

Step by step explanation

The correct option is The surface area will decrease by 672 sq. ft.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular parallelepiped or a rectangular cuboid.

The surface area of a rectangular prism can be calculated using the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism.

Given that the original rectangular prism has l = 33 ft, b = 14 ft, and h = 15 ft, we can calculate its surface area as:

SA = 2lw + 2lh + 2wh

= 2(33)(14) + 2(33)(15) + 2(14)(15)

= 924 + 990 + 420

= 2,334 sq ft

Now, if we halve the width (b), we get a new width of b/2 = 14/2 = 7 ft. The new surface area can be calculated using the same formula as:

SA = 2lw + 2lh + 2wh

= 2(33)(7) + 2(33)(15) + 2(7)(15)

= 462 + 990 + 210

= 1,662 sq ft

The decrease in surface area can be calculated as:

2,334 - 1,662 = 672 sq ft

Therefore, the correct option is:

The surface area will decrease by 672 sq. ft.

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Answer:

24

Step-by-step explanation:

Find LCM of  3 8 and 12

(calculation attached)

lcm = 3 x 2 x 2 x 2  = 24

i hope im  right!

The shortest length of the wood will be 24 meters.

The Least Common Multiple (LCM) refers to the common multiple that is the least (smallest) among all possible multiples for both numbers. Calculating this least common multiple for numbers is made easier by the LCM formula.

Given that the length of the wood is 3m, 8m, and 12 m. The shortest length will be calculated by taking the least common factor of the given lengths 3m, 8m, and 12 m.

The least common factor is calculated as:-

3 = 3 x 1

8 = 2 x 2 x 2

12 = 2 x 2 x 3

LCM = 3 x 2 x 2 x 2 = 24

Hence, the shortest length of the wood will be 24 meters.

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The equation of the line that is perpendicular to y = 5 and that passes through the point (-7, -5) is x = -7.

We have to find the equation of a line that is perpendicular to y = 5 and that passes through the point (-7, -5).

y = 5 is a line that is parallel to the x-axis hence, the line perpendicular to it will be parallel to the y-axis.

Also, the line touches (-7,-5) hence, it will touch the line y = 5 at (-7,5).

Hence, the line perpendicular  to y = 5 and that passes through the point (-7, -5)  is x = -7.

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We have the following polynomial:

Now, we can rewrite the polynomial in descending order as follows:

As we can see, the order in descending order takes into account the values for the exponents of the variable (an unknown value), x. Since the degree of a polynomial is the highest degree of any term of the polynomial, and this term is represented by:

In other words, the degree of a polynomial is the highest power we have for any term in the polynomial.

Therefore, the degree of the polynomial is 5, and we can write it, in descending order as follows:

In summary, therefore, the degree of the polynomial is 5, in this case, and if we write it in descending order, we have:

Answer:

c. 30%

Step-by-step explanation:

Answer:

Step-by-step explanation:

n=n/2 +7

The different text structures are discussed below.

Given is the excerpt from Leviathan by Scott Westerfeld.

Since the excerpt is not given, we will have a brief idea about the given text structures.

Description-Explanation

A description text structure shows mental images of the details of an event, person, place, or object. An explanation text structure shows a set of facts, which clarify the context, causes, and consequences of those facts.

Problem-Solution

A problem-solution text structure presents a problem, including why there is a problem, followed by one or more possible solutions.

Cause-Effect

A cause and effect text structure shows the connection between what has happened and its impact or result. Cause is what happened. Effect is the resulting action or consequence.

Sequence-Time

A sequence-time text structure describes or explains how things happen or work in chronological order.

Therefore, the different text structures are discussed above.

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Answer:

x = 2, y = -3 and z = 1.

Step-by-step explanation:

3x+4y-z=-7  ............. A

X-5y+2z=19 ..............B

5x+y-2z=5  ...............C

Adding equations B and C to eliminate z:

6x - 4y + 0 =  24

6x - 4y = 24.............D

Now we multiply Equation A by 2:-

6x + 8y - 2z = -14

Now adding this to equation B, ( again to eliminate z) we get equation E:

7x + 3y = 5 -----------E

Bring down equation D:

6x - 4y = 24.............D

Multiplying  E by 4 and D by 3:

28x + 12y = 20

18x - 12y = 72

Adding:

46x = 92

x = 2.

and substituting in equation D

6(2)- 4y = 24

-4y = 12

y = -3.

Finally we find z by substituting in equation A:

3(2) + 4(-3) - z = -7

-z = -7 - 6 + 12

-z = -1

z = 1.

Answer:

AB = 17 meters

Step-by-step explanation:

Given that the triangle, ∆ABC, has 2 congruent sides that are indicated with a single marking on segment AC and segment AB, both segments would be of equal measure.

Therefore, since the measure of segment C is 17 meters, the measure of segment AB = measure of segment AC = 17 meters.

Segment AB = 17 meters. It is congruent to segment AC.

Answer:

13

Step-by-step explanation: