You and a friend of your choice are driving to Nashville in two different
cars. You are traveling 65 miles per hour and your friend is traveling 51
miles per hour. Your friend has a 35 mile head start. Nashville is about 200
miles from Memphis (just so you'll know). When will you catch up with
your friend?

Answer:

Step-by-step explanation:

Eratosthenes then measured the angle of a shadow cast by a stick at noon on the summer solstice in Alexandria, and found it made an angle of about 7.2 degrees, or about 1/50 of a complete circle. ... Eratosthenes then used this to calculate the circumference of the Earth to be about 250,000 stadia.

Answer:

There is no linear relationship in this problem.

Step-by-step explanation:

When plotting the coordinates on the graph, the line curves and slopes upwards. It is not a straight line.

Answer:

unknown numbers

Step-by-step explanation:

letters are used for unknown numbers

Answer:

Step-by-step explanation:

2 [ x + ( x + 2y )] = 28

2x  + 2y = 14

x + y = 7

x = 7 - y

x ∈ ( 0 , 7 )

y ∈ ( 0 , 7 )

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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The function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

A relation is a function if it has only One y-value for each x-value.

The given function is g(x)= 10x² - 8x

we need to find the value when x is -2

Replace x with -2

g(-2)=10(-2)²-8(-2)

=10×4+16

=40+16=56

Now when x =0

g(0)= 10(0)² - 8(0)=0

Now when x =2

Replace x with 2

g(2)=10(2)²-8(2)

=40-16

=24

Hence, the function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x

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The values of the given trigonometric ratios are:

sin (2x) = 24/25

cos (2x) = -16/25

tan (2x) =  -3/2

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given that:

cot (x) = 3/4

We know that cot(x) = 1/tan x

Thus:

tan x = 4/3

Thus, using the knowledge of Pythagoras theorem:

sin x = 4/5

cos x = 3/5

Thus:

sin (2x) = 2 sin x cos x

= 2 * (4/5) * (3/5) = 24/25

Similarly:

cos (2x) = cos²x - sin²x

= (3/5)² - (4/5)²

= -16/25

tan (2x) = sin (2x)/cos (2x)

= (24/25) ÷ (-16/25)

= -24/16

= -3/2

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Answer:

158 in.

Step-by-step explanation:

Surface area of a prism = Area of all the faces added together

So, Face 1 & 2 = 5 x 80 = 40 x 2 = 80

Face 3 & 4 = 8 x 3 = 24 x 2 = 48

Face 5 & 6 = 5 x 3 = 15 x 2 = 30

Therefore, adding them together makes:

80 + 48 + 30 = 158 in.

Answer:

1.05

Step-by-step explanation:

Answer:

u;t5g3ji/lfvjk.dvnjfvjk.f

Step-by-step explanation:

When the point (-1/2, y) lies on the line with the equation 2x - 3y = 6, the value of y is -7/3.

To find the value of y when the point (-1/2, y) lies on the line with the equation 2x - 3y = 6, we can substitute the x-coordinate of the point into the equation and solve for y.

Let's substitute x = -1/2 into the equation:

2(-1/2) - 3y = 6

Simplifying:

-1 - 3y = 6

Next, we can isolate the term with y:

-3y = 6 + 1

-3y = 7

Finally, we can solve for y by dividing both sides by -3:

y = 7 / -3

This simplifies to:

y = -7/3

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The probability that you win a prize is 0.00003797372

Here, we have,

From the question, we have the following parameters:

Sample Space = 1 to 22

This means that

Sample size, n = 22 i.e. the count of numbers from 1 to 22

The count of numbers to be drawn is 5

So, the individual probabilities are

P(1) = 5/22

P(2) = 4/21

P(3) = 3/20

P(4) = 2/19

P(5) = 1/18

The probability of winning is the product of the above

So, we have

p = 5/22 * 4/21 * 3/20 * 2/19 * 1/18

Evaluate

p = 0.00003797372

Hence, the probability is 0.00003797372

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complete question:

In a certain state's lottery, 22 balls numbered 1 through 22 are placed in a machine and 5 of them are drawn at random. If the 5 numbers drawn match the numbers that a player had chosen, the player wins $30,000. In this lottery, THE ORDER THE NUMBERS ARE DRAWN DOES MATTER. Compute the probability that you win the prize if you purchase a single lottery ticket.

The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.

a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?a)Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45We know that the proportion of teenagers aged 12-17 who own smartphones is 0.38. Now, we need to find the probability that the proportion of sampled teenagers who own smartphones is between 0.35 and 0.45.The sample size is 120.Let P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z scores for both sides, i.e. for 0.35 and 0.45.z1 = (0.35 - 0.38) /0.048 = -0.625z2 = (0.45 - 0.38) /0.048 = 1.458Hence, P(0.35 < p < 0.45) is equal to P(-0.625 < z < 1.458).The probability can be calculated using standard normal tables, which gives 0.5763. Therefore, the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is 0.5763.b) Find the probability that less than 45% of sampled teenagers own smartphonesLet P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z score as follows:z = (0.45 - 0.38) /0.048 = 1.458We must find the probability that a randomly selected teenager from the sample has less than 0.45 probability of owning a smartphone. This probability can be calculated using a standard normal table. P(z < 1.458) = 0.9265, thus, the probability that less than 45% of sampled teenagers own smartphones is 0.9265.c) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?For this, we need to find the Z-score of 0.30.z = (0.30 - 0.38) /0.048 = -1.667The probability is obtained using a standard normal table. The probability is 0.0475. The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.

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The value of w in the inequality six times a number w is at least - 24 is w ≥ -4.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

In this case, six times a number w is at least - 24. This will be expressed as:

(6 × w) ≥ -24

6w ≥ -24

Divide

w ≥ -24/6

w ≥ -4

The inequality is w ≥ -4.

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Answer:

sorry but I can understand

The function that would necessitate the use of variation of parameters is g(x) = x (cos2x + e^(-2x)).  Therefore, the correct option is option 4.

In calculus, variation of parameters is a technique used to determine a particular solution to an inhomogeneous linear ordinary differential equation.The technique of variation of parameters is used when the forcing is not of the form used for undetermined coefficients. In order words, variation of parameters is used when the nonhomogeneous term (the forcing term) is not a polynomial or exponential function with finite terms.

Hence, to determine the function that would necessitate the use of variation of parameters follow these steps:

Step 1: Identify the functions that cannot be solved using undetermined coefficients.

- Undetermined coefficients work for functions that are polynomials, exponentials, sines, and cosines, or any linear combination of them.

Step 2: Analyze each given function.

- g(x) = arcsin x + cos x + 6 contains an inverse trigonometric function (arcsin x) but can still be solved using undetermined coefficients.

- g(x) = tan x + cot x contains trigonometric functions but can also be solved using undetermined coefficients.

- g(x) = 5x^3 sin (2x) contains polynomial and trigonometric functions and can be solved using undetermined coefficients.

- g(x) = x (cos2x + e^(-2x)) contains both trigonometric and exponential functions multiplied by a polynomial, which is not solvable using undetermined coefficients, and thus requires variation of parameters.

Hence, option 4 is correct.

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Answer:

no

Step-by-step explanation:

x + 15 = 42

Subtract 15 from each side

x + 15-15 = 42-15

x = 27

x = 17 is not 27 so it is not a solution

Answer:

No.

Step-by-step explanation:

If you substitute 17 in for x in the equation you get 17+15=42.  Simplify to get 32=42.  This is not a true statement, so x=17 is not the answer.

Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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The isosceles trapezoid symmetry about the line b indicates that the transformation that maps the trapezoid onto itself is the option

An isosceles trapezoid is a trapezoid in which the the length of the slant side are congruent.

The transformations that maps the isosceles trapezoid onto itself are a reflection across the line of symmetry, or a rotation of 360° about the center of the isosceles trapezoid, which is about point P

Therefore, the option that indicates the transformation that must map the isosceles trapezoid exactly onto itself is the option

The line b that bisects each side and passes through the point P, where P is the center, is a line of symmetry such that the shape of the isosceles trapezoid is symmetrical about the line b

The image of the isosceles trapezoid is the same on both sides of the line b, such that a reflection across the line b maps the isosceles trapezoid exactly unto itself.

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Answer:

So frist thing is frist, since we are using the BODMAS. We should start with the numbers in the brackets, simplify the small bracket frist.

3p + [ 5 - (2p + 7q)]

= 3p + (5 - 2p - 7q)

= 3p - 2p - 7q + 5

= p - 7q + 5

Answer:

a relation and a function

= A

Step-by-step explanation:

Thus, the right choice is A.

Answer:

Since in option B, the bacteria are growing exponentially, B would be the correct answer to this question.

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

i literally just took the test

A clue that would help to find the speed of the current is that the rate of Chan's rowing in still water is 8 mph.

This concept comprises of 4 terminologies:

Given:

Speed of Chan's boat in still water = 8 mph

Time taken by Chan to row upstream from his house to the park = 3 h

Time taken by Chan to row downstream from the park to his house = 2 h

we have to find the speed of the current.

Let the speed of the current be v.

We know, Speed = Distance / Time

⇒ Distance = Speed × Time

Now, the distance between the house and the park is constant, hence the distance travelled upstream and downstream will be constant.

For upstream, speed of the boat is calculated as:

⇒ Speed = (speed of the boat in still water) - (speed of the current)

⇒ Speed = (8 - v)

Hence, distance is:

⇒ Distance = (8 - v) × 3              …(1)

Similarly for downstream, speed of the boat is:

⇒ Speed = (speed of the boat in still water) + (speed of the current)

⇒ Speed = (8 + v)

Distance will be:                          

⇒ Distance = (8 + v) × 2             …(2)

Now since the distance is equal we can equate the equation (1) and (2).

⇒ (8 - v) × 3 = (8 + v) × 2

⇒ 24 - 3v = 16 + 2v

⇒ 5v = 8

⇒ v = 1.6 mph

Hence, the speed of the current is 1.6 mph.

Here, we can observe that to solve this problem we need the time taken to cross along each stream and the speed of the boat in the still water.

The option: Chan rows from house to the park on Wednesday, gives information about the the distance travelled by the boat and it is  constant and cannot be used to deduce the speed of the current.

The option: The entire trip takes five hours, is not used anywhere to solve the problem, instead the separate times to cross each stream was required. Hence this option was also not sufficient.

Therefore, the rate of Chan's rowing in still water is 8 mph, is the clue that helps to solve this word problem.

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The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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Answer:

Cost of a kit is $20

cost of a microscope is $80

Step-by-step explanation:

Here, we want to write a set of equations and solve

Let the cost of a microscope be $m while the cost of a kit be $k

Total cost of 38 microscopes will be 38 * m = $38m

Total cost of 47 kits = 47 * k = $47k

The sum of these is $3980

That will be;

47k + 38m = 3980 ••••••(i)

A microscope cost 4 times a kit

Mathematically;

m = 4k •••••••••(ii)

Substitute ii into i

47k + 38(4k) = 3980

47k + 152k = 3980

199k = 3980

k = 3980/199

k = $20

Recall;

m = 4k

m = 4 * 20 = $80

Answer:

b.

Step-by-step explanation:

100x2−20x+1

= (10x - 1)(10x - 1)

= (10x - 1)^2.

Answer:

B

Step-by-step explanation:

I did math

The rate law for the reaction can be expressed as: \(\[Rate = k[A][B]^0\]\) or simply: \(\[Rate = k[A]\]\)

In this reaction, the rate is only dependent on the concentration of species A and is independent of the concentration of species B. The exponent for B in the rate law is zero, indicating that changes in the concentration of B do not affect the rate of the reaction. This suggests that B is not involved in the rate-determining step of the reaction and does not participate in the reaction's rate equation.

The rate law is determined experimentally by measuring the initial rates of the reaction at different concentrations of A and B. Since the reaction is first order with respect to A, the rate of the reaction is directly proportional to the concentration of A. The rate constant, denoted as k, is a proportionality constant that incorporates factors such as temperature, catalysts, and reaction mechanism. By observing the reaction rate as a function of the concentration of A, it can be concluded that the rate law for this reaction is \(\(Rate = k[A]\)\), where the concentration of B does not affect the reaction rate.

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If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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Step-by-step explanation:

6000

your answer is 6000

Answer:

6000

Step-by-step explanation:

Use the following formula

a/b × c

(a×c) ÷b

2/3 × 9000

(2×9000) ÷ 3

= 6000

Answer:

6:

\( {x}^{2} - 2x - 3 \\ = (x - 3)(x + 1) \\ when \: y = 2 \\ x = 1 \\ vertex \: is \: (1, \: 2)\)

7:

\( {x}^{2} = - 625 \\ x = \sqrt{ - 625} \\ x = \sqrt{625} \times \sqrt{ - 1} \\ x = 25 \times \sqrt{ {i}^{2} } \\ x = 25 \times i \\ x = 25i\)