Evaluate X ds, where C is the straight line segment x=t;y= from (0,0) to (20,4) the parabolic curve x =t, y =12, from (0,0) to (2,4) For the straight line segment, x ds

Answer:

....

Step-by-step explanation:

3.6 units

Draw the circle with the center at the intersection of the perpendicular bisectors and the radius equal to the distance found in step 4.

When constructing a circle circumscribed about a triangle, the following step is needed:

Identify the three vertices of the triangle.

Let's say the triangle has vertices A, B, and C.

Find the perpendicular bisectors of the triangle's sides.

For each side of the triangle, construct a line that is perpendicular to the side and passes through its midpoint.

Locate the point of intersection of the perpendicular bisectors.

The point where all three perpendicular bisectors intersect is the center of the circumscribed circle.

Measure the distance from the center to any of the triangle's vertices.

This distance is the radius of the circumscribed circle.

By following these steps, you can construct a circle that passes through all three vertices of the triangle. This circle is known as the circumscribed circle or circumcircle of the triangle. It is unique to each triangle and provides a useful geometric property that can be applied in various mathematical and geometric contexts.

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Answer:

84

Step-by-step explanation:

Pretend her first 3 quizzes were all 83 since that was the average. So the 4th was 87.

83+83+83+87 = 336

Divide by the total number of quizzes because they are equally weighted.

336/4 = 84

Her new average score is 84.

Answer:

thank you still mad

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

-3+x=7

Add 3 to both sides.

7+3=10

x=10

Answer:

x=10

Step-by-step explanation:

-3+x=7

You have to add 3 to both sides to cancel out the -3

x=10

That leaves you with x=10

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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A variety of healthful sizes are available for newborns. The average baby weighs between 5 pounds, 8 ounces (2,500 grammes) and 8 pounds, 13 ounces when they are born between 37 and 40 weeks (4,000 grams). It's usually ok for newborns who weigh more or less than the typical infant.

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Recall that for \(|x|<1\), we have the convergent geometric series

\(\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}\)

Now, for \(\left|\frac x5\right| < 1\), we have

\(\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}\)

Integrating both sides gives

\(\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx\)

\(\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}\)

If we let \(x=0\), the sum on the right side drops out and we're left with \(C=-\ln(5)\).

It follows that

\(\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}\)

or

\(\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}\)

Therefore, Cassidy's upfront cost was $11.50.

Answer:

To find Cassidy's upfront cost, we need to use the information given in the problem and the formula for the linear function that models his profit:

Cassidy purchased a total of 150 containers of popcorn to sell.

After selling 25 containers, he will make a total profit, after his upfront costs, of $5.50.

Cassidy's profit after upfront costs can be modeled by a linear function in the form y = mx + b.

We know that when Cassidy sells 25 containers of popcorn, his profit after upfront costs is $5.50. Using the linear function, we can plug in 25 for x and solve for b, which represents the upfront costs:

y = mx + b

$5.50 = m(25) + b

$5.50 = 0.68(25) + b

$5.50 = $17.00 + b

b = $5.50 - $17.00

b = -$11.50

Therefore, Cassidy's upfront cost was $11.50.

Step-by-step explanation:

1. Cassidy is selling popcorn for a fundraiser sale at the following prices: $1

per container for the first 25 containers, $0.75 per container for the next 50

containers, and $0.50 per container for the remaining containers.

2. Cassidy purchased a total of 150 containers of popcorn to sell.

3. After selling 25 containers, Cassidy will make a total profit, after upfront

costs, of $5.50.

4. Cassidy's profit can be modeled by a linear function in the form of y=mx+b.

Answer:

C. The function will be continuous because Cassidy's profit will change

smoothly as he sells more containers of popcorn.

DD. To write the function that models Cassidy's profit, we need to find the slope

(m) and y-intercept (b) values.

Slope (m) = (profit for 50 containers-profit for 25 containers) / (50-25) =

($22.50 - $5.50) / 25 = $0.68

y-intercept (b) = $5.50

Therefore, the function that models Cassidy's profit is y = 0.68x + 5.50, where x

represents the number of containers of popcorn sold after the first 25.

E. The domain of the function is the set of non-negative integers from 0 to 125,

because Cassidy can sell anywhere from 0 to 125 containers of popcorn after

the first 25.

F. Cassidy's loss if he does not sell any popcorn is $-5.50, which means he lost

money due to the upfront costs.

G. Cassidy's profit if he sells all the popcorn is $82.00, which is the profit for

selling 125 containers of popcorn after the first 25.

H. The range of the function is the set of non-negative real numbers, because

Cassidy's profit can be any non-negative amount of money.

Formula used:

Slope (m) = (profit for 50 containers-profit for 25 containers) / (50-25)

• y-intercept (b) = $5.50

• Function: y = 0.68x + 5.50 (where x represents the number of containers of

popcorn sold after the first 25)

chatgpt

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Answer:

Triangles A and C

Step-by-step explanation:

Look at the angles, they are the same, but not for B

Answer: A and C

Step-by-step explanation:

First they all have the same angle length ( 28, 90, 62) and both equal 106°. Hope this helps you and can someone please help me with my question!

Answer:

L = 5a + 2

Step-by-step explanation:

Explain how to write the exponential model, and then write the model: B. substitute the values of x and y from one of the points into the equation and solve for a. The equation is \(y = 7.39a^x\)

How can you use the exponential model to find the value of y when x = 8: D. substitute 8 for x in the model and simplify. Thus, y = 22029.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

\(f(x) = a(b)^x\)

Where:

By substituting the values of x and y from one of the points into the equation, we have:

54.61 = ae²

a = 54.61/e²

a = 7.39

Therefore, the exponential function is \(y = 7.39a^x\).

When x = 8, we have;

\(y = f(8) = 7.39a^8\)

y = f(8) = 22029.28 ≈ 22029.

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The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.

Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³

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Answer:

1.24 m

Step-by-step explanation:

F ∝ 1/d²

F = k/d²

Use values given to solve for k

0.006 = k/3²

k  = 0.054 (I multiplied both sides by 3² in the equation above)

New equation is F= 0.054/d²

Plug in your numbers so 0.035 = 0.054/d²

0.054/0.035 = d²

You can simplify if you want so d² = 54/35

Square root both sides to solve for d

√54/35 = 1.24 m

The correct answer is A. det(rA) = r^n . det A.

The formula for calculating the determinant of a matrix, when it is multiplied by a scalar constant, is det(rA) = r^n . det A. This means that when a scalar constant, r, is multiplied to an n × n matrix, A, the determinant of the result is equal to r^n multiplied by the determinant of A.

This formula is based on the fact that multiplying a matrix by a scalar constant changes the value of each element in the matrix by a factor of the scalar constant. As such, the determinant of the resulting matrix is the same scalar constant multiplied by the determinant of the original matrix.

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Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

Standard error = (standard deviation) / sqrt(sample size)

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

\(Standard\  error = \frac{10} { \sqrt{(100)}} = 1\)

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

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Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Possible number of death rays (D) and claws (C) that Archimedes can build are given by the following system of inequalities: 350D + 200C ≤ 3000. D, C ≥ 0

The first inequality represents the fact that the total amount of gold used to build the machines cannot exceed the 3000 lbs of gold given by the city. The second inequality ensures that the number of death rays and claws cannot be negative.

To explain this system, let us assume that Archimedes builds x death rays and y claws. The amount of gold required to build x death rays and y claws is given by 350x + 200y. The first inequality ensures that this value cannot exceed 3000 lbs of gold. The second inequality ensures that the number of death rays and claws cannot be negative.

Therefore, the solution to this system of inequalities gives us all the possible combinations of death rays and claws that Archimedes can build with the given amount of gold.

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The request is to download a document and complete the proof of the Triangle Sum Theorem. After finishing the proof, the completed file should be saved for upload on a webpage.

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. To complete the proof, it is necessary to provide a logical and coherent argument that supports this theorem. The document provided likely contains a partially completed proof, and the task is to finish it.

The proof of the Triangle Sum Theorem typically involves using the properties of parallel lines and alternate interior angles. By extending one side of the triangle, parallel lines can be created that intersect with the other sides. This forms interior and exterior angles that can be related to the interior angles of the triangle. Through geometric reasoning and the use of angle relationships, the proof should demonstrate that the sum of the interior angles of a triangle equals 180 degrees.

Once the proof is completed, the document should be saved for upload on the webpage specified, most likely for evaluation or further review. It is important to follow any instructions provided regarding the file format or naming conventions for the upload.

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Answer:

48 × 3 units³.

Step-by-step explanation:

V = l · w · h

8 · 3 · 6 = 144.

Answer is 144³.

Answer:

f(-8) = -512, f(8) = 2

Step-by-step explanation:

Substitute x = -8 and 8 into the function, taking into account the rules of the function.

For x = -8, x < 0 so the value is equal to the cube of -8, which is -512.

For x = 8, x > 0 so the value is equal to the cube root of 8, which is 2.

Hey there! :)

We are given the piecewise function:

\( \displaystyle \large{f(x) = \begin{cases} {x}^{3} \: \: (x < 0) \\ \sqrt[3]{x} \: \: (x > 0) \end{cases}}\)

To evaluate the value of function at x = -8 and x = 8, we know that -8 is less than 0 and 8 is greater than 0.

Therefore, if we want to evaluate the value of function at x = -8; we use the x^3 since it's given x < 0 for the function and for x = 8; we use the cube root of x since it's given x > 0.

Evaluate x = -8

From the piecewise function:

\( \displaystyle \large{f(x) = \begin{cases} {x}^{3} \: \: (x < 0) \\ \sqrt[3]{x} \: \: (x > 0) \end{cases}}\)

Since -8 is less than 0, we use x^3.

\( \displaystyle \large{f( - 8) = {( - 8)}^{3} } \\ \displaystyle \large{f( - 8) = - 512} \)

Evaluate x = 8

From the piecewise function, since 8 is greater than 0, we use the cube root of x.

\( \displaystyle \large{f(8) = \sqrt[3]{8} }\)

To evaluate the cube root, first we prime-factor the number.

\( \displaystyle \large{f(8) = \sqrt[3]{2 \cdot 2 \cdot 2} }\)

Since it's a cube root, we pull three 2's out of the cube root and write only one 2.

\( \displaystyle \large{f(8) =2}\)

Answer

Let me know if you have any questions!

The cost Marie to fill the planter with soil to fill her vegetable planter is $57.

A bag of soil has 64 quarts and is costing 9.50

And required soil is 380 quarts so,

380 → X

64 → 9.50

By using cross multiplication method,

64 × X = 380 × 9.50

X = 3610/64

X = 56.4

X ≈ $57

Cross multiplying is the process of multiplying the denominator of the second fraction by the numerator of the first fraction, which is on one side of the equals to symbol. In a similar way, the denominator of the first fraction is multiplied by the numerator of the second fraction. The butterfly method, also referred to as cross-multiplication, has another name.

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Answer:

c Calculate the product of the length and width, height and width and height and length then

multiply by 2.

Step-by-step explanation:

it will look like this 2lw+2hw+2hl

A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.

In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;

(x, y)                               →            (y, -x)

Ordered pair B' (-2, 1)   →          E (1, 2)

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The confidence interval for the proportion of orders shipped late is 2.763 and 2.523

We are to going to construct a 95% confidence interval, so here the value is x, divided by n.

That is 120 divided by 1000

120/1000= 0.12

Capital value = 1 - 0.12

                      = 0.88

So definitely we are going to right here for this confidence interval must be written as on.

Confidence interval must be written as a cap plus minus go alpha by 2 multiplied by under root of 0.12 multiplied by 0.88 and this must be divisible by n, which is 1000 points.

So if I write here for this, this is 0.12 plus minus

x = 0.12

n = 1000

s = 0.88 = 0.8

z = 95 = 99

Formula to calculate the confidence interval

CI = x ± zs/ √n

    =0.12 ± 95 × 0.88/√1000

    = 0.12 ± 2.643

     = 2.763 and 2.523

Therefore the confidence interval is 2.763 and 2.523.

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Answer:

24.25 years

Step-by-step explanation:

We know that average of a set = (sum of all terms) / (number of terms). Right now, we know two things: the average of the set (21 years) and the number of terms in the set (5). Therefore, we can rewrite the equation to solve for the sum of all terms.

We have: 21 = \(\frac{sum}{5}\)

sum = 21 · 5 = 105

Now we know the sum of ages of the 5 girls. We want to find the average age of the 4 remaining girls when we take out the girl who is 8 years old. As previously stated, to find the average of a set, we need to know two things: the sum of all terms in the set and the number of terms in the set. Right now, we only know one of those things: the number of terms in the set, which is 4. To find the sum, we can simply subtract the 8-year-old girl's age from the sum of ages of the 5 girls, which would be 105 - 8 = 97.

Therefore, the average age of the 4 remaining girls is \(\frac{97}{4} = 24.25\) years.

Hope this helps!

Answer:

24.25

Step-by-step explanation:

Since the average of 5 girls is 21, there total age is 105 (21*5)

If one of them is 8, 105-8 is 97 and 97/4 (because there is 4 girls left) is 24.25

Hope this helps you!

A; The distance between the starting point to Obstacle 2 is  13 meters

B; There are 10 meters around one lap of course.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Part A;

Starting point: (-12, 5); Obstacle 2: (0, 0)

(x₁, y₁) and (x₂, y₂)

Therefore,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

B. Starting point: (-12, 5); Obstacle 2: (0, 0);

Obstacle 1: (-12, 0)

(Starting Point + Obstacle 2)

Now,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

Therefore, (Starting Point + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - (-12))² + (0 - 5)²

d = √(0)² + (-5)²

d = √25

d = 5 meters

(Obstacle 2 + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - 0)² + (0 - 0)²

d = √(-12)² + (0)²

d = √144

d = 12 meters

Total = 12m + 5m + 13m = 30

30 ÷ 3 = 10 meters

we can conclude that 10 meters around one lap of course.

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