Find the length of AC.

Answer:

1,840 units²

Step-by-step explanation:

AD = BC = 16

If  FE = 23  and  FD ≅ DE  then

⇒ FD = DE = 23 ÷ 2 = 11.5

If DE = 1/10 DC then

⇒ DC = 10 × DE = 10 × 11.5 = 115

Area of rectangle ABCD = AD × DC

                                         = 16 × 115

                                         = 1,840 units²

The solution accurate to equation within \(10^{-2}\) for \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) lies in [0,2].  

Given the equation  \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) and range is  \(10^{-2}\).

We are required to find the interval in which the solution lies.

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the mid point of the interval is found. The sign of its relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than \(10^{-2}\).

Interval:[0,2], signs [+,-],mid point:1, sign at midpoint +.

[1,2]                                                       3/2

[1,3/2]                                                    5/4

The rest is in the attachment. The listed table values are the successive interval mid points.

The final midpoint is 181/128=1.411406.

This solution is within 0.0002 of the actual root.      

Hence the solution accurate to equation within \(10^{-2}\) for \(x^{4}-2x^{3} -4x^{2} +4x+4=0\) lies in [0,2].

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Answer:

2516

Step-by-step explanation:

Answer:

171.9 pages

Step-by-step explanation:

45%         x

------   =  -------

100        382

45 x 382 = 17190      100 · x = 100x

17190 ÷ 100x = 171.9 = x

Answer:

a) Sinusoidal functions are y = a sin [b(x-h)] + k    (or)                                        

y = a cos [b(x-h)] + k

Where a is amplitude a= (max-min)/2=(16-2)/2=7

period p= 2π/b

            b=2π/30

            Horizontal transformation to 10 units right h=10

            k= (max+min)/2=(16+2)/2=9

h = 7 cos [π/15(t-10)]+ 9

b) t=10min=600 sec

substitue in the above equation

h=5.5m

Answer

Second option is correct.

Option G is correct.

Area of the figure = (6.8/2) + (10.8)

Explanation

We can see that the figure is a combination of a triangle and a rectangle

Area of a rectangle = Length × Width

For the rectangular part,

Length = 10

Width = 8

Area of the rectangle = 10 × 8 = (10.8)

Area of a triangle = ½ × Base × Height

For this triangle,

Base = 16 - 10 = 6

Height = 8

Area of the triangle = ½ × Base × Height

Area of the triangle = ½ × 6 × 8 = (6.8/2)

Area of the figure = Area of the triangle + Area of the rectangle

Area of the figure = (6.8/2) + (10.8)

Hope this Helps!!!

The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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Answer:

78.5

Step-by-step explanation:

to rind area of a circle you do ..

pi×r^2

pi being 3.14

r being 5^2= 25

3.14×25 = 78.5

hope this helps

Answer:

8

Step-by-step explanation:

You can solve this a few different ways.

Firstly I did 102 - 97 = 5

Then I took 5 and added 3 to it

5 + 3 ---> which gets us 8 as our final answer.

Hope I helped!

Have a great day!

Answer: 10 wreaths

Step-by-step explanation:

First identify the terms.

She has a booth that cost $200. This price will not change thus making it a Fixed cost.

Making a wreath would cost her $10 each time so this is a Variable cost.

She sells the wreath for $30 so this is the selling price.

Breakeven = Fixed Cost / Contribution margin

Contribution margin = Selling price - Variable cost

= 30 - 10

= $20

Breakeven point = 200/20

= 10 wreaths

(a) Without more information, we cannot determine the initial number of insects. (b) The differential equation satisfied by P(t) is: dP/dt = kP, where k is the growth rate of the insect population.

(c) To find the time it takes for the population to double, we can use the formula:

2P(0) = P(0)e^(kt)

where P(0) is the initial population size. Solving for t, we get:

t = ln(2)/k

(d) Without more information, we cannot determine the time at which the population will equal a certain value.
Hi! To answer your question, I need the specific function P(t). However, I can provide you with a general framework to answer each part of your question once you have the function.

(a) To find the initial number of insects, evaluate P(t) at t=0:
P(0) = [Insert the function with t=0]

(b) To find the differential equation satisfied by P(t), differentiate P(t) with respect to t:
dP(t)/dt = [Insert the derivative of the function]

(c) To find the time at which the population doubles, first determine the initial population, P(0), then solve for t when P(t) is twice that value:
2*P(0) = P(t)
Solve for t: [Insert the solution for t]

(d) To find the time at which the population equals a specific value (let's call it N), set P(t) equal to N and solve for t:
N = P(t)
Solve for t: [Insert the solution for t]

Once you have the specific function P(t), you can follow these steps to find the answers to each part of your question.

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Answer:

D

Step-by-step explanation:

The volume of a single coin is indeed:

Volume of a single coin = π × (radius)² × height

= 3.14 × (1.4 in)² × 0.0625 in

= 0.38465 in³ (rounded to the nearest hundredth)

Therefore, the total volume of 230 coins can be found by multiplying the volume of a single coin by the number of coins:

Total volume of 230 coins = 0.38465 in³/coin × 230 coins

= 88.47 in³ (rounded to the nearest hundredth, unrounded its 88.4695)

Hence, the answer is (D) 88.47 in³.

Answer:

x = 10

Step-by-step explanation:

50 + 4x = 90

4x = 40

x=10

No, These both expressions are not equal to each other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expressions are,

⇒ 12(8y - 16k) and 16(2y - 4k)

Now, We can check both expressions as;

⇒ 12 (8y - 16k)

⇒ 12 × 8 (y - 2k)

⇒ 96 (y - 2k)

⇒ 16 (2y - 4k)

⇒ 16 × 2 (y - 2k)

⇒ 32 (y - 2k)

Thus, We get;

⇒ 96 (y - 2k) ≠ 32 (y - 2k)

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Answer:

Whole

Step-by-step explanation:

1,2,3 are all whole numbers

Answer:

10 feet long

Step-by-step explanation:

im good with that triangle theroy

Answer:

Step-by-step explanation:

Answer:

(3 ÷ 8) + (-7 ÷ 8)

0.375 + -0.875  

        -0.5

Hope this helps !

Answer:

Step-by-step explanation:

gradient = 5 = [k-(-1)]/[6-2]

[k+1]/4 = 5

k+1=20

k=19

The value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5 is found to be 19 by using the formula for gradient and solving the resulting equation for k.

To find the value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5, we'll use the formula for gradient, which is (y2 - y1) / (x2 - x1).

The given points can be substituted into the formula as follows: The gradient (m) is 5. The point A(2, -1) will be x1 and y1, and point B(6, k) will be x2 and y2. Now, we set up the formula as follows: 5 = (k - (-1)) / (6 - 2).

By simplifying, the equation becomes 5 = (k + 1) / 4. To find the value of k, we just need to solve this equation for k, which is done by multiplying both sides of the equation by 4 (to get rid of the denominator on the right side) and then subtracting 1 from both sides to isolate k. So, the equation becomes: k = 5 * 4 - 1. After carrying out the multiplication and subtraction, we find that k = 20 - 1 = 19.

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The height of the right triangle is 8.66 units.

The side of a right angle triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, let's find the base of the bigger triangle.

Therefore, let's find the height using the ratios as follows:

15 / x = x / 5

cross multiply

x² = 75

square root both sides

x = √75

x = 8.66025403784

x = 8.66 units

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Answer:

Step-by-step explanation:

Ok:

First Problem with coin!

1. A coin has 2 sides and one of them is going to land up or down which means it has a chance of 1 out of 2.

1 out of 2=

1/2= 50%

Second Problem with spinner

2. There are 12 spaces on the spinner and three of those spaces are blue.

SO: 3 out of 12=

3/12=

1/4=

25%

Answers: 50% and 25%

IN FRACTION FORM: 1/2 and 1/4

The value of the unique real number between 0 and 2π that satisfies the given composition sin(x) is π/2.

When we evaluate the sine function at π/2, the result is equal to 1. The sine function oscillates between -1 and 1 as x varies from 0 to 2π. Therefore, there is only one real number between 0 and 2π for which sin(x) equals 1, and that number is π/2.

In trigonometry, π/2 represents the angle measure of 90 degrees or a quarter of a complete circle. At this angle, the sine function reaches its maximum value of 1. So, the unique real number between 0 and 2π that satisfies the composition sin(x) is π/2.

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Answer: Therefore, the plastic for the prototypes will cost $1,452,150.

Step-by-step explanation:

The volume of the cube can be calculated as:

Volume of the cube = (side length)^3 = (14 mm)^3 = 2,744 mm^3

The volume of the hole can be calculated as:

Volume of the hole = (1/4) x π x (diameter)^2 x thickness = (1/4) x π x (12 mm)^2 x 14 mm = 5,049 mm^3

The volume of plastic used to create one prototype can be calculated as:

Volume of plastic = Volume of cube - Volume of hole = 2,744 mm^3 - 5,049 mm^3 = -2,305 mm^3

Note that the result is negative because the hole takes up more space than the cube.

However, we can still use the absolute value of this result to calculate the cost of the plastic:

Cost of plastic per prototype = |Volume of plastic| x Cost per cubic millimeter = 2,305 mm^3 x $0.07/mm^3 = $161.35/prototype

To find the cost of the plastic for 9,000 prototypes, we can multiply the cost per prototype by the number of prototypes:

Cost of plastic for 9,000 prototypes = 9,000 x $161.35/prototype = $1,452,150

The plastic for the prototypes will cost $1,452,150.

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The ogive is a line graph that plots the cumulative relative frequency distribution.

An ogive, also known as a cumulative frequency polygon, is a line graph that shows the cumulative frequency distribution of a data set. The cumulative frequency is calculated by adding up the frequencies of each value up to a certain point in the data set.

The cumulative relative frequency is calculated by dividing the cumulative frequency by the total number of observations in the data set. The ogive plots these cumulative relative frequencies against the corresponding values in the data set, usually on the x-axis.

By plotting the cumulative relative frequencies, the ogive shows how the data is distributed over the entire range of values. It can be used to identify patterns in the data, such as whether it is skewed or symmetrical. It is also useful for determining percentiles, as the percentile for a given value can be read directly from the ogive.

Overall, the ogive is a helpful tool for summarizing and visualizing the distribution of a data set, particularly when dealing with large data sets or complex distributions.

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The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

Answer:

\(\boxed {x = -\frac{1}{7}}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(6(4x + 5) = 3(x + 8) + 3\)

-Use Distributive Property:

\(6(4x + 5) = 3(x + 8) + 3\)

\(24x + 30 = 3x + 24 + 3\)

-Combine like terms:

\(24x + 30 = 3x + 24 + 3\)

\(24x + 30 = 3x + 27\)

-Take \(3x\) and subtract it from \(24x\):

\(24x + 30 -3x = 3x - 3x + 27\)

\(21x + 30 = 27\)

-Subtract both sides by \(30\):

\(21x + 30 - 30 = 27 - 30\)

\(21x = -3\)

-Divide both sides by \(21\):

\(\frac{21x}{21} = \frac{-3}{21}\)

\(x = \frac{-3}{21}\)

-Reduce the fraction to the lowest term by extracting and canceling out \(3\):

\(x = \frac{-3\div3}{21 \div 3}\)

\(\boxed {x = -\frac{1}{7}}\)

Therefore, the value of \(x\) is \(-\frac{1}{7}\).

An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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If in circle A, diameter EC is perpendicular to chord BD, and arc EB measures 62 degrees, the measure of arc ED is 208 degrees.

To solve the problem, we need to use the relationship between arcs, angles, and chords in a circle.

Since diameter EC is perpendicular to chord BD, we know that angle EBD is a right angle.

Arc EB measures 62 degrees, and we know that angle EBD is 90 degrees. Therefore, arc ED must measure:

360 degrees - arc EB - angle EBD

= 360 degrees - 62 degrees - 90 degrees

= 208 degrees

So, the measure of arc ED is 208 degrees.

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