Help me out please !!!!!!!!

Let us begin by defining arc measure

Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc.

From the given diagram, we can determine that:

measure of arc DC = 100 degrees

Answer: 100 degrees

The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.

To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the periodic payment

r is the interest rate per period

n is the number of periods

In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.

Plugging these values into the formula, we get:

FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07

  = 1000 * [1.07^20 - 1] / 0.07

  ≈ 1000 * [2.6532976 - 1] / 0.07

  ≈ 1000 * 1.6532976 / 0.07

  ≈ 43,865.18

Therefore, the future value of this series after 20 years would be approximately $43,865.18.

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\(\frac{3x^{2} }{x^{2} +x-6}\) is the product of the rational expressions.

What are rational expressions?

Two polynomials' ratio is shown through rational expressions. It denotes a polynomial in the denominator as well as the numerator. It is an algebraic expression that contains an unknown variable and is similar to a fraction in that it is a ratio.

We are given \(\frac{3x^{2} }{x^{2} +x-6}\)

This means that the expression has to be multiplied by the number 1 for obtaining the product of the rational expression.

We know that when anything is multiplied by the number 1, we get the number itself.

Hence, \(\frac{3x^{2} }{x^{2} +x-6}\) is the product of the rational expressions.

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Answer:

The number of bacteria in 0.25 mL is 6.25 x 10^3.

Step-by-step explanation:

5 liter flask contains 1.25 x 10^8 bacteria.

So, 1liter flask contains = \(\frac{1.25 \times 10^8}{5} =2.5\times 10^7\)

Now

0.25 mL contains = \(2.5\times 10^7 \times0.25\times 10^{-3} = 6.25\times 10^3\)

To construct a 90% confidence interval for the population proportion using the given information (x = 120, n = 200), calculate the sample proportion, standard error, and margin of error.

To calculate the sample proportion (p-hat) by dividing the number of successes (x) by the sample size (n):

Sample Proportion (p-hat) = \(\frac{x}{n}\) = \(\frac{120}{200}\) = 0.6

Next, calculate the standard error, which is the measure of variability in the sample proportion:

Standard Error = \(\sqrt\frac{(p - hat) X (1 - p-hat)}{n}\)  

Standard Error  =  \(\frac{\sqrt{0.6 X (1 - 0.9)} }{200}\)     ≈ 0.0258

Referring to the table of critical values, for a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = critical value × standard error = 1.645 × 0.0258 ≈ 0.0424

Finally,  construct the confidence interval:

Lower Bound = sample proportion - margin of error

                       = 0.6 - 0.0424 ≈ 0.5576

Upper Bound = sample proportion + margin of error

                       = 0.6 + 0.0424 ≈ 0.6424

Therefore, the 90% confidence interval for the population proportion is approximately 0.558 to 0.642.

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Answer:0.0049

Step-by-step explanation: You move the decimal 3 places to the left because its negative which gives you 0.0049

See attachment for math work and answer.

The Laplace transform of f(t) for the given functions f(t) = 5t² − 4 sin(3t) and f(t) = t² + 4t − 6 were found as ℒ{f(t)} = 10/s³ − 12/(s² + 9) and ℒ{f(t)} = 2/s³ + 4/s - 6/s,

A.

We are given the function f(t) as f(t) = 5t2 − 4 sin(3t).

Theorem 7.1.1 states that if f(t) is piecewise continuous on [0,∞) and of exponential order, then the Laplace transform ℒ{f(t)} exists for all s > a, where a is a constant that depends on f(t).

We need to find the Laplace transform ℒ{f(t)}.The Laplace transform of 5t² is obtained from the formula:

ℒ{tn} = n!/s^(n+1), which gives us: ℒ{5t²} = 5ℒ{t²} = 5(2!)/s^3 = 10/s³

The Laplace transform of sin(3t) is given as: ℒ{sin(at)} = a/(s² + a²), where a is a constant.

Hence, we have: ℒ{4 sin(3t)} = 4ℒ{sin(3t)} = 4(3)/(s² + 3²) = 12/(s² + 9)

Therefore, the Laplace transform of f(t) is given by: ℒ{f(t)} = ℒ{5t² − 4 sin(3t)}= 10/s³ − 12/(s² + 9)

B.

Calculation using Theorem 7.1.1 to find ℒ{f(t)}:

We are given the function f(t) as f(t) = t² + 4t − 6.

The Laplace transform of t² can be obtained as: ℒ{tn} = n!/s^(n+1), where n = 2 gives: ℒ{t²} = 2!/s³ = 2/s³

The Laplace transform of t can be obtained as: ℒ{t} = 1/s

Therefore, the Laplace transform of 4t can be obtained as: ℒ{4t} = 4ℒ{t} = 4/s

The Laplace transform of a constant, c can be obtained as: ℒ{c} = c/s

Therefore, the Laplace transform of -6 can be obtained as: ℒ{-6} = -6/s

Therefore, the Laplace transform of f(t) is given by: ℒ{f(t)} = ℒ{t² + 4t − 6}= ℒ{t²} + ℒ{4t} - ℒ{6}= 2/s³ + 4/s - 6/s

The Laplace transform of f(t) for the given functions f(t) = 5t² − 4 sin(3t) and f(t) = t² + 4t − 6 were found as ℒ{f(t)} = 10/s³ − 12/(s² + 9) and ℒ{f(t)} = 2/s³ + 4/s - 6/s, respectively.

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Answer:

Step-by-step explanation:

Multiply each term of (x² + 2x - 1) by x  and multiply each term of            (x² + 2x - 1) by 3

Area of parallelogram = bh

  = (x² + 2x - 1)(x + 3)

  = (x² + 2x - 1)*x + (x² + 2x - 1)*3

 =x²*x + 2x*x  - 1*x + x²*3 +2x*3 - 1*3

 = x³ + 2x² - x + 3x² + 6x - 3

 = x³ + 2x² + 3x²   -x + 6x - 3

 = x³ + 5x² + 5x - 3

The scale factor of the dilation shown from ABCD to A'B'C'D' is given as follows:

k = 0.5.

Then the length of segment B'C' is given as follows:

B'C' = 7.5.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The side lengths on the dilated quadrilateral are half the side lengths of the original quadrilateral, hence the scale factor is given as follows:

k = 0.5.

Considering that BC = 15 and k = 0.5, the length of segment B'C' is given as follows:

B'C' = 0.5 x 15

B'C' = 7.5.

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To partition a line segment with a given ratio, you can follow these steps:

1. Identify the two endpoints of the line segment. Let's call them point A and point B.

2. Determine the ratio in which you want to partition the line segment. For example, let's say the ratio is 2:1.

3. Use the ratio to divide the line segment into parts. To do this, you'll need to find a point, let's call it point C, that is a certain distance from point A and a certain distance from point B. The distance from point A to point C should be twice the distance from point C to point B.

4. To find point C, calculate the total length of the line segment by finding the distance between point A and point B. Let's say the length of the line segment is d.

5. Divide d by the sum of the ratio (2+1=3) to determine the length of each part. In this case, each part would be d/3.

6. Multiply the length of each part by the corresponding ratio factor to determine the distance from point A to point C. In this case, point C would be located at a distance of (2/3) * (d/3) from point A.

7. Similarly, multiply the length of each part by the remaining ratio factor to determine the distance from point C to point B. In this case, point C would be located at a distance of (1/3) * (d/3) from point B.

8. Once you have the coordinates of point C, you have successfully partitioned the line segment with the given ratio.

For example, let's say the line segment AB has a length of 12 units and we want to partition it with a ratio of 2:1. Using the steps above:

1. Identify the endpoints: A and B.
2. Ratio: 2:1.
3. Calculate each part: d/3 = 12/3 = 4 units.
4. Distance from A to C: (2/3) * (d/3) = (2/3) * 4 = 8/3 units.
5. Distance from C to B: (1/3) * (d/3) = (1/3) * 4 = 4/3 units.
6. Point C would be located at coordinates (8/3, 4/3) on the line segment AB.

Remember, these steps can be modified based on the specific ratio you are given.

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Question- Partitioning a line segment, AB, into a ratio a/b involves dividing the line segment into a + b equal parts and finding a point that is an equal part from A and b equal parts from B. When finding a point, P, to partition a line segment, AB, into the ratio a/b, we first find a ratio c = a / (a + b)

The side of the square that is twice the area of one triangle (0.18 units²) is: 0.6 unit.

Area of a square = s², where s is the side length of the square.

1 square = 2(areas of triangles)

1 square = 2(0.18)

1 square = 0.36 units²

s² = 0.36

s = √0.36

s = 0.6 unit.

Length of the side of the square = 0.6 unit.

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X= -5 ,y=10  : Z = 1.5

X= -6 ,y=2  : Z = -2.6 (goes on forever so put the line over the 6)

X= 6 ,y=2 : Z = 2.6 (again goes on forever so put the line over the 6)

The slope of the tangent line to the graph of the function f(x) = x + 3x² + 3 at the point (2, 5/7) is -13/49. The equation of the tangent line can be written in the slope-intercept form as y = (-13/49)x + 41/49.

To find the slope of the tangent line, we need to find the derivative of the function f(x) = x + 3x² + 3 and evaluate it at x = 2. Taking the derivative, we have:
f'(x) = 1 + 6x.

Evaluating f'(x) at x = 2, we get:
f'(2) = 1 + 6(2) = 1 + 12 = 13.

Therefore, the slope of the tangent line at the point (2, 5/7) is 13.

To find the equation of the tangent line, we use the point-slope form:
y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point and m is the slope. Plugging in the values, we have:
y - 5/7 = (-13/49)(x - 2).

Simplifying, we get:
y - 5/7 = (-13/49)x + 26/49,
y = (-13/49)x + 41/49.

Therefore, the equation of the tangent line to the graph of f at the point (2, 5/7) is y = (-13/49)x + 41/49.

Moving on to the second question, we are given the function N(t) = 9400/(1 + t²), which represents the number of bacteria in the culture t minutes after the bactericide is introduced.

(a) To find the rate of change of the number of bacteria in the culture 3 minutes after the bactericide is introduced, we need to find the derivative N'(t) and evaluate it at t = 3. Taking the derivative, we have:
N'(t) = -9400(2t)/(1 + t²)².

Evaluating N'(t) at t = 3, we get:
N'(3) = -9400(2(3))/(1 + 3²)² = -9400(6)/(1 + 9)² = -9400(6)/10² = -9400(6)/100 = -5640.

Therefore, the rate of change of the number of bacteria in the culture 3 minutes after the bactericide is introduced is -5640 bacteria/min.

(b) To find the population of the bacteria in the culture 3 minutes after the bactericide is introduced, we plug in t = 3 into the function N(t):
N(3) = 9400/(1 + 3²) = 9400/(1 + 9) = 9400/10 = 940.

Therefore, the population of the bacteria in the culture 3 minutes after the bactericide is introduced is 940 bacteria.

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The population of the bacteria in the culture 3 minutes after the bactericide is introduced is 940 bacteria. The rate of change of the number of bacteria in the culture 3 minutes after the bactericide is introduced is -5640 bacteria/min.

The slope of the tangent line to the graph of the function f(x) = x + 3x² + 3 at the point (2, 5/7) is -13/49. The equation of the tangent line can be written in the slope-intercept form as y = (-13/49)x + 41/49.

To find the slope of the tangent line, we need to find the derivative of the function f(x) = x + 3x² + 3 and evaluate it at x = 2. Taking the derivative, we have:

f'(x) = 1 + 6x.

Evaluating f'(x) at x = 2, we get:

f'(2) = 1 + 6(2) = 1 + 12 = 13.

Therefore, the slope of the tangent line at the point (2, 5/7) is 13.

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point and m is the slope. Plugging in the values, we have:

y - 5/7 = (-13/49)(x - 2).

Simplifying, we get:

y - 5/7 = (-13/49)x + 26/49,

y = (-13/49)x + 41/49.

Therefore, the equation of the tangent line to the graph of f at the point (2, 5/7) is y = (-13/49)x + 41/49.

Moving on to the second question, we are given the function N(t) = 9400/(1 + t²), which represents the number of bacteria in the culture t minutes after the bactericide is introduced.

(a) To find the rate of change of the number of bacteria in the culture 3 minutes after the bactericide is introduced, we need to find the derivative N'(t) and evaluate it at t = 3. Taking the derivative, we have:

N'(t) = -9400(2t)/(1 + t²)².

Evaluating N'(t) at t = 3, we get:

N'(3) = -9400(2(3))/(1 + 3²)² = -9400(6)/(1 + 9)² = -9400(6)/10² = -9400(6)/100 = -5640.

Therefore, the rate of change of the number of bacteria in the culture 3 minutes after the bactericide is introduced is -5640 bacteria/min.

(b) To find the population of the bacteria in the culture 3 minutes after the bactericide is introduced, we plug in t = 3 into the function N(t):

N(3) = 9400/(1 + 3²) = 9400/(1 + 9) = 9400/10 = 940.

Therefore, the population of the bacteria in the culture 3 minutes after the bactericide is introduced is 940 bacteria.

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Answer:

he would be 14

Step-by-step explanation:

Answer:Bob is 8 years old

Step-by-step explanation:

Andrew is 6 years, Phil is 8 years, add those together, subtract that by 22

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:x=-0.5

Step-by-step explanation:

You would add the 2.5 on both sides of the equal sign

1.06418

The same as of sec 20 degrees in radians to obtain 20 degrees in radian multiply 20° by / 180° = 1/9

Answer:

26

Step-by-step explanation:

JKL= ABC,  jkl=abc

1.) use law of sines to find k.

\(c^{2} =a^{2} +b^{2} -2abCosC\)    

\(c=\sqrt{920^{2} +860^{2} -2(920)(860)cos(126) } = 1586.225515\)

2.) use law of cosines to find L

\(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)  

plug in for b and c:  \(\frac{860}{sinB} =\frac{1586.225515}{sin126}\)

cross multiply: \(\frac{1586.23sinB}{1586.23} =\frac{860sin126}{1586.23}\)

\(sinB= 0.4386227612\\B=sin^-1(0.4386227612)= 26.01604086\\\)

L=26

Answer:

So you just calculate the distance from.point 1 to 2 and then from 2 to 3 and then from 3 to 1. then sum them all up and you get the perimeter

The mass of the thin bar is \((\pi/2) - 1\).

To find the mass of the thin bar with the given density function, we need to integrate the density function over the length of the bar.

The length of the bar is given as L = SA - SX = \(\pi/2 - 0 = \pi/2.\)

So, the mass of the bar is given by the integral:

M = ∫(SX to SA) p(x) dx

Substituting the given density function, we get:

M = ∫(0 to \(\pi/2\)) (1 + sin x) dx

Using integration rules, we can integrate this as follows:

M = [x - cos x] from 0 to \(\pi/2\)

M = \((\pi/2) - cos(\pi/2) - 0 + cos(0)\)

\(M = (\pi/2) - 1\)

Therefore, the mass of the thin bar is \((\pi/2) - 1.\)

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Answer:

96 cm^2

Step-by-step explanation:

the diagonal bisect in the point of intersection, so their length is 12 cm and 16 cm

Area = (12 * 16)/2 = 96 cm^2

Answer:

24 cm^2

Step-by-step explanation:

rhombus -.-

Answer:

the answer is 7/13

Step-by-step explanation:

because the total number of translators is 13, therefore, the probability of picking yellow is 7/13

The equation of the line passing through the point (-1,2) with slope m is y = mx + m-2. This is a general equation of the line and we can find different equations by putting different values of m.

We know that when a point and slope of the equation are given, an equation can be written as

\(\frac{y-y_{1} }{x - x_{1} } =m\)

which is known as the slope-point form

where m is the slope of the equation

y1 is the  y coordinate of the given point

x1 is the x coordinate of the given point

In the given question, y1 = 2 and x1 = -1

Substituting the value of coordinates in the slope point equation, we get

\(\frac{y-2}{x-(-1)} = m\)

\(\frac{y-2}{x+1}=m\)

y-2 = mx + m

y = mx + m-2

Hence, the equation of the line passing through the point (-1,2) with slope m is y = mx + m-2.

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What is the equation of the line passing the point (-1, 2) with a slope m?

My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.

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The terms -x and 5x are combined to give 4x.

To simplify the expression 4k - x - 3k + 5x, we can combine like terms by grouping together the terms with the same variables.

Let's rearrange the terms:

(4k - 3k) + (-x + 5x)

Combining the k terms, we have:

k + (-x + 5x)

Now, let's simplify the x terms:

k + 4x

Therefore, the simplified form of the expression 4k - x - 3k + 5x is k + 4x.

In this simplified form, the terms 4k and -3k are combined to give a single term k. Similarly, the terms -x and 5x are combined to give 4x.

By combining like terms, we are simplifying the expression by adding or subtracting coefficients that share the same variable. This process helps us streamline and condense the expression, making it easier to work with and interpret.

It's important to note that combining like terms does not change the value or meaning of the expression; it simply presents it in a more concise form.

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Answer: the answer is $9,600

Step-by-step explanation:

option A = 40(24)   =  option B = x (.1)       where x is her gross sales

40(24) = x(.1)

40(24)/.1 = x = sales = $9600

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer: 3 tons of glass in a day.

Step-by-step explanation: If a plant processes 1/8 ton of glass every 4 hours, it processes 1 ton of glass every 8 hours because 8 x (1/8) = 1.

Since there are 24 hours in a day, the plant will process 1 ton of glass every 8 hours for a total of 24/8 = 3 times in a day.

Therefore, the plant will manufacture 3 tons of glass in a day.

Answer:

3/4 ton of glass

Step-by-step explanation:

1day = 24 hours

1/8 ton = 4 hours

? = 24 hours

We cross-multiply and get

3/4 ton of glass

So, the plant manufacturer gets 3/4 ton of glass in a day.

Answer:

Well Ima put the link, hope it works!

jkjk

The answer here is 240 in^3

Step-by-step explanation:

Well You have a triangular prism which all you need is the base. The base cna be found by finding the area of the surface triangle.

Triangle area formula: 1/2(bh)

Well base is 4 height is 10, 4*10=40. 40/2= 20

Now the heighth given or (h) is 12. TO find the volume jsut multiply the height by the base

20*12=240

Plus don’t click the links, their viruses.