graph the relation. find the domain and range.

Answer:  Timo is correct; the hypotenuse rounds to 11

Work Shown:

[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{6^2+9^2}\\\\c = \sqrt{36+81}\\\\c = \sqrt{117}\\\\c \approx 10.81665\\\\c \approx 11\\\\[/tex]

This confirms Timo is correct.

It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.

Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got [tex]\sqrt{117}[/tex] earlier in the steps shown above.

If Annie said [tex]\text{The hypotenuse is } \sqrt{117} \text{ units long}[/tex], then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.

The man's journey took 43 minutes.

The distance traveled divided by the motion's duration gives the average speed, or vavg. Time is calculated as distance divided by average speed. Time is calculated as distance divided by average speed. distance = v avg 150 kilometers in time 3.2 h = 47 km/h.

Take the start time and subtract the end time.

The man was supposed to arrive at 12:25, but he was 15 minutes late, thus his actual arrival time was 12:40 (12:25 plus 15).

The man's journey began at 11:57, therefore we can calculate how long it took by deducting the start time from the end time.

End time - Start time = Journey time

12:40 - 11:57 = 43 minutes

So, The man's journey took 43 minutes.

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The value of x and y in the equation are 1 and 4 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 , 4x − 4y = 4.

7x-3y=-5 equation 1

3x+2y=11 equation 2

using elimination method, we multiply the coefficient of x by both equations

21x- 9y = -15 equation 3

21x +14y = 77 equation 4

subtract equation 3 from 4

23y = 92

y = 92/23

y = 4

substitute 4 for y in equation 1

7x -3(4) = -5

7x -12 = -5

7x = -5+12

7x = 7

x= 7/7= 1

therefore the value of x and y are 1 and 4 respectively

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The number of copies that have been sold to date approximately is equal to 361,538 copies.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of copies that have been sold to date, we would develop an expression to multiply the total number of copies (T) by the percentage of the number of copies sold in its first month of release as follows;

9.1/100 × T = 32,900

0.091T = 32,900

Dividing both sides of the equation by 0.091, we have the following:

Total number of copies (T) = 32,900/0.091

Total number of copies (T) = 361,538 copies.

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The equation in slope-intercept form as required is; y = 240x + 500

This is when the value of the dependent variable depends partly on the value of the independent variable and partly on an initial value that is not 0

According to the statements in the task content;

One employee sells 5 cars and makes $1,700 that week.

A second employee sells 6 cars and makes $1,940 that week.

Hence, it follows from partial variation that;

1700 = 5a + b

1940 = 6a + b

Hence, by solving simultaneously, it follows that;

a = 240

b = 500

Hence, the equation in slope-intercept form as required is; y = 240x + 500

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The perimeter of the rectangle with area 174.8m² and side-length 3.8m is equal to 99.6 meters.

Area of the rectangle is equal to 174.8 m².

Length of the rectangle is equal to 3.8 m

let us consider 'w' be the width of the rectangle.

area of the rectangle = length × width

⇒ 174.8 = 3.8 × w

⇒ w = 174.8 / 3.8

⇒ w = 46 m

Perimeter of the rectangle = 2 ( length + width )

⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )

⇒ Perimeter of the rectangle = 2 ( 49.8 )

⇒Perimeter of the rectangle = 99.6 meter.

Therefore, the perimeter of the rectangle with length 3.8m and width 46m is equal to 99.6m.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-4 +8}{6 +3} \implies \cfrac{ 4 }{ 9 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{ 4 }{ 9 }}(x-\stackrel{x_1}{(-3)}) \implies y +8 = \cfrac{ 4 }{ 9 } ( x +3)[/tex]

Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

[tex]a^{2}+b^{2} =c^{2}[/tex]

[tex]x^{2} + 12^{2} =c^{2}[/tex]

Equilateral --> c = 2x

[tex]x^{2} +144 = (2x)^{2} \\x^{2} +144 = 4x^{2} \\3x^{2} =144\\x^{2} =48\\x=4\sqrt{3}[/tex]

The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Answer is 43.19 cm

The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Using the formula c2 = a2 + b2—where "c" stands for the hypotenuse and "a" and "b" are the two legs—it is possible to determine the third side of a right-angled triangle if the two other sides are provided as 4 and 6 units, respectively.

The sum of the squares on the shorter two sides of a right triangle equals the length of its longest side.

A2 + B2 = C2 is a formula that illustrates this.

Use the phytagorean theorem for this problem:

C= √a²+b²

C = hypotenuse = distance between the centers of the two gears

A = one side of the chain attaching the gears

= 43cm

B = the difference of the radii = (8 - 4) = 4

√43² +(8 - 4) ²

= 43.1856

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Liam started with $12 amount in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.

Total: $16

Liam has $4 amount left in his wallet.

1. Start by adding up the amount that Liam spent:

Ice Cream: $5

Movie Ticket: $8

Candy: $3

Total Spent: $16

2. Subtract the total amount spent from the amount Liam started with:

Initial Amount: $12

Total Spent: $16

Remaining Amount = Initial Amount - Total Spent

Remaining Amount = $12 - $16

Remaining Amount = -$4

Since the result is negative, this means that Liam has spent more than he started with and now has $4 left in his wallet.

Liam started with $12 in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.

The complete question is:

Liam started with $12 in his wallet. He kept track of the amount he gained and pent throughout the day, as shown in The table below.

Expense | Amount

Ice Cream | $5

Movie Ticket | $8

Candy | $3

What is the amount of money Liam has left in his wallet?

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Answer: A decline of 10% per year means that the number of landlines will be multiplied by 0.9 (100% - 10%) every year.

So, in 12 years the number of landlines will be multiplied by 0.9^12 = 0.531441

So, in 12 years there will be 86,652 * 0.531441 = 46,115.69 landlines.

Rounded to the nearest whole number there will be 46,116 landlines in 12 years.

Step-by-step explanation:

Answer: 24,473

Step-by-step explanation: This is the formula for exponential decay:

y=a(1–r)t

In this formula, a is the initial amount, r is the rate of decrease expressed as a decimal, t is the elapsed time, and y is the final amount.

solve

Plug in 86,652 landlines for the initial amount, 0.1 for the rate of decrease, and 12 years for the time elapsed.

y

= a(1–r)t

y

= 86,652(1–0.1)12 Plug in values

y

= 86,652(0.9)12 Subtract

y

= 86,652(0.28242…) Simplify

y

= 24,473.08419… Multiply

Round to the nearest whole number.

24,473.08419… → 24,473

To the nearest whole number, there will be 24,473 landlines.

Answer: 83000

Step-by-step explanation:

The exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

What is Exponential equation ?

Exponential equation can be defined as the equation in which it contains the exponent.

The exponential equation in the 'y' form to represent the reduce rate of the insects 14% as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

As given in the question,

Initial population scientist starts with is given by P₀ = 2500 insects

Rate by which number of insects reduce each week = 14%

                                                                                       = 0.14

Let time be 'n'

Final population of the insects represented by y(t)

Exponential equation to represents the reduce rate each week is given by :

y(n) = P₀( 1 - r ) ⁿ

⇒ y(n) = 2500 ( 1 - 0.14 ) ⁿ

Therefore, the exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.

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There will be a bias in the data samples in favor of the opinions of a limited subset of the research community.

To find patterns and trends in the broader data set being reviewed, data sampling is a statistical analysis approach that is used to choose, modify, and analyze a representative selection of data points.

a. Under coverage happens when some members of the population are less likely to be selected for the sample or are not eligible for selection. Bias results from under coverage when the "under covered" individuals' differences from the general population have an impact on their responses.

Undercover prejudice may lead to bias in the voluntary response. This suggests you run the risk of obtaining information from a small number of people who are enthusiastic about the research issue. Your data samples will be biased toward the opinions of a tiny subset of your research population as a result.

b. People who don't have a phone number listed in the phone book are probably more worried about privacy issues than the ordinary person. The results would have probably revealed a higher percentage of people who were concerned about privacy if they had been included in the sample.

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Answer:

1.26 meters

Step-by-step explanation:

Answer:

real

Step-by-step explanation:

-5 is real. It is not complex because it is not in the form a+bi. It also has no imaginary part so it is neither of the other two.

Hope that helps, let me know if you have any other questions!

Answer:

$709.58

Step-by-step explanation:

The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%

To find the cost of the camera with the sales tax included, we take

$653.99 divided by 100, then times 108.5 = $709.58

So, the cost of the camera with sales tax is $709.58

The Probability Distribution of X is P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k) and there is no evidence to suggest that the manager's claim is false.

a. The probability distribution for X can be found using the binomial distribution, since the number of customers who get their meal in less than 7 minutes is a count of the number of successes in a fixed number of independent trials, each with the same probability of success. The probability distribution for X is given by:

P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k)

where k = 0, 1, 2, 3, or 4, and (4 choose k) is the number of combinations of 4 items taken k at a time.

b. The probability of observing exactly 0 customers getting their meal in less than 7 minutes is P(X = 0) = (0.25)^4 = 0.390625. This is a low probability, but it is still possible to observe 0 customers getting their meal in less than 7 minutes, even if the manager's claim is true. Therefore, observing 0 customers getting their meal in less than 7 minutes does not provide any evidence to suggest that the manager's claim is false.

The complete question is:

The Cornbread Cafe in Eugene, Oregon, recently installed a new computer system that allows customers to order their meals electronically from their tables. The manager of the restaurant claims that this new system will decrease the waiting time, and that the probability of getting a meal in less than 7 minutes (with this system in place) is 0.75. Suppose four customers are selected at random. Let the random variable X be the number of customers who get their meal in less than 7 minutes. (a) Find the probability distribution for X. (b) Suppose none of the four customers gets the meal in less than 7 minutes. Is there any evidence to suggest that the manager's claim is false? Justify your answer.

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If Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high , then amount of wrapping paper that she need to use is 804 cm² .

Katy is wrapping a gift ,

the dimensions of the box that needs to be wrapped is ⇒

length(l) is = 15cm , width(w) is = 18cm and height(h) is = 4cm .

the present is in shape of cuboid ,

we know that Total Surface Area of cuboid is = 2(lw + wh + hl) ;

substituting values of length , width and height ,

we get ;

Area is = 2(15×18 + 18×4 + 4×15)

= 2( 270 + 72 + 60)

= 2( 402 )

= 804 cm² .

Therefore , Katy will need 804 cm² of wrapping paper to wrap the gift .

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An equivalent expression to 9 1/2k - (7 + 31/4k) is 51k/4 +7

The given expression is 9 1/2k - (7 + 31/4k)

This involves the the simplification of the fraction above following the rule of BOADMAS

⇒19k/2 - 7/1 + 13k/4

Simplifying the right hand side of the fraction with parenthesis,

18k/2 - [(28+13k)/4

This fraction gives

*38k - 28+ 13k)/4

Collecting the like terms

= 25k + 28

Therefore the equivalent expression is 25k/1 + 7

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Using the digits 7,8 and 9, the positive seven-digit integers can be made that are palindromes are 729.

When constructing a seven-digit palindrome out of the digits 7, 8, and 9, the first three digits must be the same as the last three digits in reverse order.

This means that each of the first three digits can be either a 7, 8, or 9. Therefore, the total number of combinations for the first three digits is 3 x 3 x 3 = 27.

Since the last three digits must match the first three, the total number of possible combinations of integers is 27 x 27 = 729.

Thus, the total number of positive seven-digit palindromes that can be created using the digits 7, 8 and 9 is 729.

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Below is the answer

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In the exponential function the initial amount a = 14 and the growth fact b = 2.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.

The simplest kinds of dynamical systems have solutions in the form of exponential functions.

Growth or decay can both be described by an exponential function.

g(x)=14x2^x

It is an exponential function.

g(x)=axb^x

where, a is initial amount and b is growth/decay factor.

Now we will compare the  function with this one.

a = 14

b = 2

Hence, The initial amount a=14 and factor b=2

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Note that the answer to the expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) Is: one (1). This problem is solved using PEMDAS.

PEMDAS is the acronym for parenthesis, exponents, multiplication, division, addition, and subtraction. These operators must be solved exactly in the order given above. Thus:

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1)

⇒ {96 ÷ [36÷3-(6)]} ÷ (31-16+1)

⇒ {96 ÷ [12-6]} ÷ (31-16+1)

⇒ {96 ÷ 6} ÷ (31-16+1)

⇒ 16 ÷ 16

⇒ 1

Thus, it is correct to state that the answer to the mathematical expression  {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) is 1 or

{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) = 1

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The probabilities of the events are

a. 0.43

b. 0.27

c. 0.1161

d. 0.2444.

According to the question,

Statistics classes require a statistical calculator = 43% = 0.43

Statistics classes require a computer that has statistical software = 27% = 0.27

Of the classes that require a statistical calculator, classes also require the use of a computer = 17% = 0.17

a. P(Statistical Calculator)

= 0.43

b. P(Statistical Software)

= 0.27

c. P(Require a Statistical Calculator and Statistical Software)

⇒ (0.43)(0.27)

= 0.1161

d. P(Require a Statistical Calculator GIVEN Require Statistical Software)

⇒ 0.066/0.27

⇒ 0.2444

Hence we can conclude that the probabilities of the events are

a. 0.43

b. 0.27

c. 0.1161

d. 0.2444

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If her average rate was 20 miles per hour faster on the trip home, Amy live 480 miles far from the mountains

Suppose Amy lives x miles from the mountains.

Fill in x as both distances and the times

going and coming 12 hours and 8 hours.  

Distance         |  speed | time

To mountains |    x        |   8

Coming home  |    x      |   5

Use: speed =distance/ time

to fill in the two rate boxes:

                         Distance | Speed | time

To mountains |          x     |  x/12  |  8

Coming home  |    x         |  x/8  |  5

The equation comes from this sentence:

Her average rate was 20 miles per hour faster on the trip home

Her speed coming home late = Her speed going to the mountains + 20 miles per hour

x/8 = x/12+20

20 = x/8-x/12

20 = x/24

x = 24×20

x = 480

So Amy lives 480 miles from the mountains.

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Answer: Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (3,−4)

Focus:  (3,−15/4)

Axis of Symmetry: x = 3

Directrix:  y = − 17/4

X   Y    

1    0

2   -3  

3   -4

4   -3

5    0

Step-by-step explanation:

The points for the inequality are plotted on the graph attached below.

What is inequality?

A linear inequality is one that, if the equals relation were used in place of the inequality, would provide a linear equation. When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed when the problem is solved. The solution set for an inequality is the set of all solutions.

We are given an inequality as y ≤ 6x/5 - 6

Now, in order to plot the points, we need to find x and y

So, let y be 0, then

⇒0 ≤ 6x/5 - 6

⇒6 ≤ 6x/5

⇒6 ≤ 6x/5

⇒5 ≤ x

So, we get first point as (5,0).

Now, let x=0, then

⇒y ≤ 6(0)/5 - 6

⇒y ≤ -6

So, we get second point as (-6,0).

From these two points, the graph is plotted which is shown below.

Hence, the graph for the inequality is plotted.

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The grams of potatoes that still need to be peeled is equal to 301 grams.

In this exercise, we would determine the total weight of the bag of potatoes in grams:

Note: 1,000 grams is equal to 1 kilogram.

Total weight of the bag of potatoes = 4 kilograms + 500 grams

Total weight of the bag of potatoes = 4,000 grams + 500 grams

Total weight of the bag of potatoes = 4,500 grams.

For the total weight of peeled potatoes, we have the following:

Total weight of peeled potatoes = 1,841 grams + 2,358 grams

Total weight of peeled potatoes = 1,841 + 2,358

Total weight of peeled potatoes = 4,199 grams.

Now, we can determine the weight of the unpeeled potatoes:

Weight of the unpeeled potatoes = 4,500 grams - 4,199 grams.

Weight of the unpeeled potatoes = 301 grams.

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Answer: h(x) = 3x

Step-by-step explanation:

The height of a toy bunny, h(x), is directly proportional to the length of the carrot, x. The given information is that the height of the bunny is three times the length of the carrot. Therefore, the equation for the function h(x) would be the answer above.

Answer:

h(x) = 3x

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