amy drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 12 hours. when amy drove home, there was no traffic and the trip only took 8 hours. if her average rate was 20 miles per hour faster on the trip home, how far away does amy live from the mountains?

It is recommended to model the data in the tables using a ilnear or exponential function.

The exponential function will be the best model for tigers.

The optimal model for narwhals will be a linear function.

Test for vertical lines:

A vertical line test can be used to determine whether an expression is a function or not. In this test, we look for a single image of x and determine whether we receive one or many images.

It won't be a function if we receive more photographs.

For illustration, use y2 = 4ax.

y = ±√4ax

We receive two values of y for a single value of x.

Consequently, it won't be a function.

Due to that,

There are two data sets for the numbers of tigers and narwhals.

first gather tiger info,

Let's see if it satisfies the requirement for a linear function or not.

y = mx + c

x = 0, y = 1204

1204 = m0 + c

c = 1204

y = mx + 12-04

when y = 1050 and x = 3

1050 = 3m + 1205

m = -155/3

If a linear relationship exists,

Therefore, y should be 902 for x = 6.

However, is not the same as 902.

So, for this dataset exponential function will be best.

Similarly, we can check for the second dataset.

And it will satisfy the all the conditions of linear function.

So, for the Narwhals linear function is best model.

Complete question:

The populations of Siberian tigers and narwhals since 1990 are represented by the following tables:

Determine whether the data described in the tables is best modeled by a linear function or an exponential function.

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The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric function is given below.

sin(x) + 1 = cos(x)

Simplify the equation, then we have

sin(x) + 1 = cos(x)

(sin(x) + 1)² = cos² (x)

(sin(x) + 1)² = 1 - sin² (x)

sin² (x) + 2sin x + 1 = 1 - sin² (x)

2sin² (x) = 0

sin (x) = sin 0

x = 0

The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

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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!

The speed of the cheetah based on the information provided is 12.85 feet per second.

The speed of a body in movement can be expressed using different units such as:

Based on this, it is necessary to find how much distance the cheetah covers every second by dividing the distance given by the time given as it follows:

Therefore, the speed of the cheetah is 12.85 feet per second

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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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Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.

Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.

Ratio scales are interval scales where lengths are expressed in relation to a rational zero.

Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.

Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.

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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]

Answer: There would be 345 students because 85+200+60=345

Step-by-step explanation: it equal 245

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:

Step-by-step explanation:

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

I'm so cool w/ my fashionista lipstick! :D

The simplified form of expression -2.6f +0.7f - 14 - 9 is -1.9f - 23

We know that an expression is nothing but a mathematical statement that consists of at least two terms( variables or constants) along with one algebraic operation.

As we know simplifying an expression means rewriting the same expression in a compact manner with no like terms.

To simplify expressions, we combine all the like terms ; solve all the given brackets, if any.

In the simplified expression, we left with unlike terms which cannot be reduced further.

Consider an expression:

-2.6f +0.7f - 14 - 9

We simplify above expression.

-2.6f +0.7f - 14 - 9

= (-2.6 + 0.7)f - (14 + 9)              .........(combine like terms)

= -1.9f - 23

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Answer: t=2

Step-by-step explanation:

-4t+14= -9t+24

+9t     =+9t

5t+14=24

    -14=-14

5t=10

5t/5       10/5

t=2

As per the given half life the approximate mass of the sample after 20 hours is 0.03125

The term half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

Here we have know that Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours.

And here we also know that he begins with a sample of the isotope with a mass of 92 grams and then measures the mass of the object every hour.

Then the approximate mass of the sample after 20 hours is calculated as,

=> 20/4 = 5

Then the value after 5 hours of time is calculated as,

=> 1/2⁵

=> 0.03125

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So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.

To obtain 25 liters of a 42% solution, you would need to mix a certain amount of an 80% solution with a certain amount of a 54% solution. To determine the specific amounts, you would need to set up and solve a system of equations.

x + y = 25

(0.8x) + (0.54y) = 0.42(x + y)

x = (0.42*25) / (0.8 + 0.54) = 14.58 liters

y = 25 - x = 10.42 liters

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The plant's growth over 6 weeks is described as the increasing of plant volume and/or mass with or without formation of new structures such as organs, tissues, cells or cell organelles.

The term volume in math is called as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Here we need to describe the plant's growth over 6 weeks.

As we know that the stages that plants go through are from seed to sprout, then through vegetative, budding, flowering, and ripening stages.

On the other hand the nutritional needs of people and plants change as they grow.

Then the main stages in the life cycle of a plant are seed germination, seedling formation, growth, development and differentiation leading to a mature plant, pollination and fertilizations and the formation of fruit and seeds.

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The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.

To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.

We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.

To summarize, the formula used to calculate the number of pieces Lucy needs is:

(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.

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Answer

1: 3x-y=0
2: 5x+y= -4
3: y=-x+4

Step-by-step explanation:

There are 32.1 pounds of meat.

Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.

Add up the pounds of meat.

7.75 + 17.85 + 6.5 = 32.1 pounds

Thus, there are 32.1 pounds of meat.

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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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After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(6, -3) →M'(-3, -6)

N(4, 3) →N'(3, -4)

Therefore, option D is the correct answer.

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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:

1.26 meters

Step-by-step explanation:

Nareh should give his brother $80. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

Subtract the amount of money that Urch has from the amount of money that Nareh has:

300 - 220 = 80

Nareh should give his brother $80 so that both of them will have the same amount of money.

Nareh currently has $300 and Urch currently has $220, so Nareh should give Urch $80 in order to make them have the same amount of money. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

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Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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The mass of the liquid in the container is 18.17 g, correct to 3 significant figures

Calculate the volume of the container:

Volume = πr2h

Volume = π x (5 cm)2 x 20 cm

Volume = 3,142 cm3

Calculate the total volume of liquid A and B:

Total volume of A and B = 4:11

Total volume of A and B = 4 + 11 = 15 cm3

Calculate the volume of liquid A:

Volume of A = 4/15 x 15 cm3

Volume of A = 4 cm3

Calculate the volume of liquid B:

Volume of B = 11/15 x 15 cm3

Volume of B = 11 cm3

Calculate the mass of liquid A:

Mass of A = Volume of A x Density of A

Mass of A = 4 cm3 x 1.05 g/cm3

Mass of A = 4.2 g

Calculate the mass of liquid B:

Mass of B = Volume of B x Density of B

Mass of B = 11 cm3 x 1.27 g/cm3

Mass of B = 13.97 g

Calculate the total mass of liquid C:

Total mass of C = Mass of A + Mass of B

Total mass of C = 4.2 g + 13.97 g

Total mass of C = 18.17 g

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.

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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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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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The value of α2ββ2α2 is -20. a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation.

Given,

p(x) = 4x2 − 5x − 1

α and β are the zeroes of the quadratic polynomial p(x).

Therefore,

α + β = -5/4

and

αβ = 1/4

Therefore,

α2ββ2α2 = (α+β)2αβ = (-5/4)2(1/4) = (-5/4)(-5/4)(1/4) = 25/16 = -20

Given a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation. To find the value of α2ββ2α2, we first need to find the sum and product of the two zeroes, which can be done by solving the equation. The sum of the zeroes is -5/4 and their product is 1/4. We can then use these values to calculate the value of α2ββ2α2, which is equal to (-5/4)2(1/4) = 25/16 = -20. Thus, the value of α2ββ2α2 is -20.

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