Determine the length of a chord whose central angle is 80° in a circle with a radius of 4 centimeters. Question 9 options: 3.94 cm 2.57 cm 5.14 cm 7.88 cm

Answer:

Simplifying

2xy + -4xy = 0

Combine like terms: 2xy + -4xy = -2xy

-2xy = 0

Solving

-2xy = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '-2'.

xy = 0

Simplifying

xy = 0

The solution to this equation could not be determined.

Step-by-step explanation:

i only got the first 1 sry

a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Answer:

101

Step-by-step explanation:

We are given that

r(t)=\(<t^2,1-t,4t>\)

We have to find the derivative of r(t).a(t) at t=2

a(2)=<7,-3,7> and a'(2)=<3,2,4>

We know that

\(\frac{d(uv)}{dx}=u'v+v'u\)

Using the formula

\(\frac{d(r(t)\cdot at(t))}{dt}=r'(t)\cdot a(t)+r(t)\cdot a'(t)\)

\(\frac{d(r(t)\cdot at(t))}{dt}=<2t,-1,4>\cdot a(t)+<t^2,1-t,4t>\cdot a'(t)\)

Substitute t=2

\(\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot a(2)+<4,-1,8>\cdot a'(2)\)

\(\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot <7,-3,7>+<4,-1,8>\cdot <3,2,4>\)

\(\frac{d(r(t)\cdot at(t))}{dt}_|t=2=28+3+28+12-2+32=101\)

The derivation of the equation will be "101".

Given expression is:

r(t) = 〈t², 1 - t, 4t〉

Let,

a(2) = <7, -3, 7>

a'(2) = <3, 2, 4>

As we know,

→ \(\frac{d(uv)}{dx}\) = u'v + v'u

By using the formula, the derivation will be:

→ \(\frac{d(r(t).at(t))}{dt}\) = r'(t).a(t) + r(t).a'(t)

                  = <2t, -1, 4>.a(t) + <t², 1 - t, 4t>.a'(t)

By substituting "t = 2", we get

                  =  <4, -1, 4>.a(2) + <4, -1, 8>. a'(2)

                  = <4, -1, 4>.<7, -3, 7> + <4, -1, 8>.<3, 2, 4>

                  = 28 + 3 + 28 + 12 - 2 + 32

                  = 101

Thus the response above is appropriate.

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The solution of the given expression is 9*\(x^{4}\)/100.

GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27\(x^{12}\)/300\(x^{8}\).

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27\(x^{4}\)/300

Now divide numerator an denominator by 3.

=9\(x^{4}\)/300

Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.

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Answer:

\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)

\(O \frac{9}{100}x^{4}\)

✔ \(\frac{3}{10} x^{2}\)

\(O \frac{27}{300} x^{4}\)

\(O\frac{9}{10} x^{2}\)

Answer:

  3³ = 27

Step-by-step explanation:

The applicable rules of exponents are ...

  a^b = 1/a^-b

  (a^b)(a^c) = a^(b+c)

__

  \(\dfrac{3^{-9}}{3^{-12}}=(3^{-9})(3^{12})=3^{-9+12}=\boxed{3^3=27}\)

Answer:

First, you find the volume of each box

Volume = Length * Width * Height

Box A

V = 13 * 40 * 5

V = 2600 cm^3

Box B

V = 8 * 10 * 25

V = 2000 cm ^3

Box C

V = 11 * 20 * 30

V = 6600 cm ^3

Since 7400, the cubes trying to be packed, is bigger than any of the volumes of the boxes, 2 boxes must be used

The boxes with volumes that add up to a number greater than 7400 are Box C with Box A or B (either works, as long as C is one of them)

The total volume of the boxes together can be found with simple addition

2600 + 2000 + 6600 = 11200 cm ^3

The price of 12 inch bun purchased by Elinor is $5.32.

For the given question;

Elinor wanted to have a bun.

The cost of 18 inch hoagie bun is $7.99.

As there is only 12 inch bun present, the price of 12 inch bun is calculated by unitary method.

The price can be written as;

18  inch -------> $7.99

For 1 inch bun, divide both side by 18.

18/18  inch -------> $7.99/18

1  inch -------> $7.99/18

For 12 inch, multiply each side by 12.

12  inch -------> $7.99×12/18

12  inch -------> $5.32

Thus, the price of 12 inch bun is $5.32.

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The answer is in the picture. Click on it.

The inequality in interval notation is  [ -1, ∞ ) from the given equation x ≥ - 3

Given data :

x ≥ - 3

x is greater than or equal to - 3, so - 3 is our smallest value of the interval so it goes on the left. Since there is no upper endpoint (it is ALL values greater than or equal to 3),

we put the infinity symbol on the right side. The boxed end on 3 indicates a closed interval.

In interval notation it is [ -1, ∞ )

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Answer:

Step-by-step explanation:

-4x-3=y

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

"The set of all functions from X to Y" refers to the collection of all possible functions that can be defined from a set X to a set Y. This set is denoted as Y^X or X→Y.

Each element of the set Y^X is a function that maps each element of set X to a unique element of set Y. The notation for such a function f is f: X → Y.

Given,

f is a function from X to Y .

Note:

The cardinality (size) of the set Y^X is given by |Y^X| = |Y|^|X|. In other words, if the set X has m elements and the set Y has n elements, then the set of all functions from X to Y has n^m elements.

It is often used to describe the space of all possible solutions to a given problem or equation.

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Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The value of rate does he need to invest at in order to earn the $400 in interest is,

⇒ R = 4%

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Mr. Smith needs to earn $400 in interest on a $5000 investment.

And,  He can invest the money for two years.

Since, We know that;

Interest = PRT / 100

Substitute the given values, we get;

400 = 5000 × R × 2/100

⇒ 40,000 = 10,000R

⇒ R = 4

Thus, The value of rate does he need to invest at in order to earn the $400 in interest is,

⇒ R = 4%

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The area and perimeter of the dimensions are:

Object a) Area = 1,401.75 m² and Perimeter = 195.2 m

Object b) Area = 93.15 m² and Perimeter =  40.8 m

The area refers to the product of the length and width of a two-dimensional object.

On the other hand, the perimeter is the total distance of a two-dimensional object.

Dimensions of Object a):

Length = 80.1 m

Width = 17.5 m

Area = Length x Width

= 1,401.75 m² (80.1 x 17.5)

Perimeter = 2(Length + Width)

= 2(80.1 + 17.5)

= 195.2 m

Dimensions of Object b):

Length = 13.5 m

Width = 6.9 m

Area = Length x Width

= 93.15 m² (13.5 x 6.9)

Perimeter = 2(Length + Width)

= 2(13.5 + 6.9)

= 40.8 m

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Find the area and perimeter of object a) 80.1 m and 17.5 m and object b) 6.9m and 13.5 m.

For the linear function built from the scatter plot, it is found that:

The slope-intercept representation of a linear function is the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:

b = 500.

When the input increases by 200, the output increases by 1000, hence the slope is:

m = 1000/2 = 5.

Thus the equation is:

y = 5x + 500.

The graph is given by the image at the end of the answer.

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the red square shows that this is a right angle, so we can just subtract 52 to find z

90-52=z

38=z

Answer: (3, -1)

Step-by-step explanation:

y = |x-3|-1

When y=|x|, vertex is (0, 0).

Now, let's translate the graph so it becomes y = |x-3|-1.

|x| ==> |x-3|         Translate the graph 3 units to the right

Vertex: (0+3, 0) ==> (3, 0)

|x-3| ==> |x-3|-1     Translate the graph 1 unit down

Vertex: (3, 0-1) ==> (3, -1)

Vertex: (3, -1)

10. 2/10 = 0.2 or 0.20

11.  8/10 = 0.8 or 0.80

12. 5/10 = 0.5 or 0.50

13. 17/100 = 0.17

14. 89/100 = 0.89

15. 68/100 = 0.68

Answer:

(a) x=5

(b) x= -1 1/3

(c) x= 1

Step-by-step explanation:

(a)                       (b)                        (c)

2(x-3)=4           −3(2x+1)=5          a(bx+c)=d

x−3=4/2           2x+1= −  5/3          d^1−1

x−3=2               2x= -5/3-3/3        d^0

x=2+3                 2x= -5-3/3           x=1

x=5                    2x= -8/3*2

                          x= -8/6

                          x= -4/3

Answer: The player expects to lose 184.21 dollars.

=========================================================

Explanation:

X = net winnings in dollars

Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.

If the player wins, then they walk away with 7+245 = 252 dollars

If the player loses, then their "winnings" is -7

So either X = 252 or X = -7 are the only two options.

Let's form a table showing those options with their corresponding probabilities.

\(\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}\)

Now multiply each X value and P(X) value across the rows.

252*(1/38) = 6.631579

-7*(37/38) = -6.815789

These values are approximate.

\(\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}\)

Add up the results of the third column

6.631579 + (-6.815789) = -0.18421

This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.

Do this 1000 times and the player should expect to lose about

1000*(0.18421) = 184.21 dollars

Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.

Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21

Answer:

64 miles per hour.

Step-by-step explanation:

we are asked to look for the velocity of this car. to find it, we use the equation \(velocity = \frac{distance}{time}\). we substitute the given to the equation:

\(velocity = \frac{224 m}{3.5 hr}\)

velocity = 64 miles per hour

Answer:

x = 7

Step-by-step explanation:

x + 3 < 10

x < 10 - 3

x < 7 ( this supposed to be the answer not x = 7 so please check the options again )

Answer:

-24

Step-by-step explanation:

4(3)(-2) = -24

Answer:

8:35

Step-by-step explanation:

if u see every hour has 60 mins in it, so if u see 7:45 can be said as 7 hours and 49 mins

what u have to do is first add the mins, so add 45 and 50

45+50=95

every hour has 60 mins, so convert the mins to secs

95 mins=1hr35mins

and the 1hr35mins to 7:00

1hr35mins+7hr=8hr35mins or 8:35

A tv program begins at 7:45 and ends 50 minutes later the TV program ends at 8:35.

In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.

We know that every hour has 60 minutes in it.

In 7:45 it has 7 hours and 45 minutes

The TV program duration is 50 minutes

So, 45+50=95

Now, 95 minutes has 1 hour 35 minutes

Add 1 hour 35 minutes to 7:00

That is, 7 hours + 1 hour 35 minutes

= 8 hours 35 minutes

Therefore, the TV program ends at 8:35.

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Answer:

100 cg

Step-by-step explanation:

Answer:

100 centigrams

Step-by-step explanation:

Answer:

Answer. c

Step-by-step explanation:

Answer: its c

Step-by-step explanation:

The incorrect statement regarding the dilation is given as follows:

3. The original figure was reduced to create the image.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, we have that the original triangle was dilated by a scale factor of two, hence the original figure was enlarged to create the image.

(a figure is reduced when the scale factor is less than 1).

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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