How would you get the variable alone in the equation s ÷ 10 = 12? A. Multiply both sides of the equation by 10. B. Multiply both sides of the equation by 12. C. Divide both sides of the equation by 10. D. Divide both sides of the equation by 12.

angle A = 30

(2x-9) = (2x+21)
     +9          +9
 2x=2x+30

-2x  -2x

=30

Answer:

$63.00

Step-by-step explanation:

$200.00× 0.045=9

9×7=63

So the probability that Joe will not receive a text in the next 10 minutes is approximately 0.865. So the probability that the next text arrives between 9:07 and 9:10 p.m. is approximately 0.149. So the probability that a text arrives before 9:03 p.m. is approximately 0.393. So the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, is approximately 0.394.

(a) To find the probability that Joe will not receive a text in the next 10 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the time until the next text is less than or equal to a given time t. The CDF of an exponential distribution with mean 5 minutes is:

\(F(t) = 1 - e^{(-t/5)}\)

To find the probability that Joe will not receive a text in the next 10 minutes, we need to find F(10):

\(F(10) = 1 - e^{(-10/5)}\)

\(= 1 - e^{(-2)}\)

≈ 0.865

(b) To find the probability that the next text arrives between 9:07 and 9:10 p.m., we need to find the probability that the time until the next text is between 7 and 10 minutes. We can use the CDF again to find this probability:

P(7 < X < 10) = F(10) - F(7)

\(= (1 - e^{(-10/5)}) - (1 - e^{(-7/5)})\)

\(= e^{(-7/5)} - e^{(-2)}\)

≈ 0.149

(c) To find the probability that a text arrives before 9:03 p.m., we need to find the probability that the time until the next text is less than 3 minutes. We can use the CDF again to find this probability:

P(X < 3) = F(3)

\(= 1 - e^{(-3/5)}\)

≈ 0.393

(d) To find the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, we can use the memoryless property of the exponential distribution. The memoryless property states that the conditional distribution of the time until the next text, given that no text has arrived in the first 5 minutes, is the same as the original distribution. In other words, the fact that no text has arrived in the first 5 minutes does not affect the probability of a text arriving in the next 7 minutes.

Therefore, the probability that no text will arrive for 7 minutes, given that no text has arrived for 5 minutes, is the same as the probability that no text will arrive for 7 minutes starting from scratch. This is the probability that the time until the next text is greater than 7 minutes. Using the CDF of the exponential distribution, we can calculate:

P(X > 7) = 1 - F(7)

\(= 1 - (1 - e^{(-7/5)})\)

= \(e^{(-7/5)}\)

≈ 0.394

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The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:

Now, find g(k(1)), it means, g(-7):

(g°k)(1)=573.

The surface area of the cylinder is 314.6 square inches.

The surface area of a cylinder is given by the formula:

S.A. = 2πrh + 2πr²

Where r is the radius of the circular base of the cylinder and h is the height of the cylinder.

If we know the radius and height of a cylinder, we can easily calculate its surface area.

To solve for the surface area of the cylinder whose radius is 5 inches, we use the formula and substitute the values. The net of a cylinder whose radius of the base is labeled 5 inches and a rectangle with a height labeled 4 inches is given below:

Given the radius, r = 5 inches, height of cylinder, h = 4 inches.

Substituting the values in the formula:

S.A. = 2πrh + 2πr²

= 2 × 3.14 × 5 × 4 + 2 × 3.14 × 5²

= 157.6 + 157

= 314.6 square inches

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The value of v using the equation ( 2v/3 ) + 6 = ( v/3 ) - 2 is v = - 24.

Two-thirds of anything is an amount that is two out of three equal parts of it. Similarly, one-third of something is an amount that is one out of three equal parts of it.

Now, we have

Two-thirds times v plus 6 equals one-third times v minus 2.

Hence, when the above statement is expressed as an equation we get:

Two third of v + 6 = one third of v - 2

2/3 × v + 6  = 1/3 × v - 2

( 2v/3 ) + 6 = ( v/3 ) - 2

Adding 2 on both sides of the equation,

( 2v/3 ) + 6 + 2 = ( v/3 ) - 2 + 2

( 2v/3 ) + 8 = ( v/3 )

Subtracting 2v/3 from both sides of the equation,

2v/3 + 8 - 2v/3 = v/3 - 2v/3

8 = ( v - 2v )/3

- v/3 = 8/1

By cross multiplication,

- v × 1 = 8 × 3

- v = 24

Multiplying each side by - 1,

v = - 24

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65% of the number is 1300.

To find 65% of a number, we can use the concept of proportionality.

Given that 30% of a number is 600, we can set up a proportion to find the whole number:

30% = 600

65% = ?

Let's solve for the whole number:

(30/100) * x = 600

Dividing both sides by 30/100 (or multiplying by the reciprocal):

x = 600 / (30/100)

x = 600 * (100/30)

x = 2000

So, the whole number is 2000.

Now, to find 65% of the number, we multiply the whole number by 65/100:

65% of 2000 = (65/100) * 2000

Calculating the result:

65/100 * 2000 = 0.65 * 2000 = 1300

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Answer:

0.1s + 125 < 180

Answer: 13.6 grams per egg.

Step-by-step explanation:

The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".

A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.

First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.

The word more will be represented for the add symbol (+). Thus,

the algebraic expression is 6+7x.

The expression 3*(n+8) can be represented for the sentence:

The triple of the sum between the numbers n and 8.

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Answer:

In the expression 250(1/2)^t/4, the following meanings can be attributed to the numbers:

250: This is the initial amount of caffeine in milligrams present in the coffee when it was brewed.

(1/2): This is the decay factor or the rate at which the caffeine content decreases over time. In other words, it represents the fraction of caffeine that remains after each hour. Here, the expression (1/2)^t means that the caffeine content will decrease by a factor of 1/2 after each hour.

t: This represents the time elapsed in hours since the coffee was brewed.

4: This is a scaling factor or a unit conversion factor used to convert the expression into milligrams. The expression 250(1/2)^t/4 represents the amount of caffeine remaining in milligrams after t hours.

To summarize, the expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams.

Among the answer choices provided, the second one is the most accurate:

250 represents the amount of caffeine in a body. 1/2 represents the decay rate of the caffeine. 4 represents the amount of hours it takes for the caffeine to reach its half-life.

The given expression 250(1/2)^t/4 models the amount of caffeine remaining in a coffee after t hours, where 250 is the initial amount of caffeine in milligrams, (1/2) is the decay factor or the fraction of caffeine that remains after each hour, t is the time elapsed in hours, and 4 is the scaling factor used to convert the expression into milligrams. Therefore, the answer choices that mention coffee consumption or growth factor of coffee are not correct in this context.

In this expression, the fraction 1/2 represents the decay rate or the fraction of caffeine that remains after each hour. The number 4 is used to scale the expression into milligrams and does not represent the half-life of caffeine. The half-life of caffeine is the amount of time it takes for half of the initial caffeine amount to decay, and it can be calculated using the formula t1/2 = ln(2) / k, where k is the decay constant.

Answer:

The value of sin 270 degrees is -1.

Step-by-step explanation:

Using trigonometric identities, we know, sin(270°) = cos(90° - 270°) = cos(-180°).

Answer:

C. 250-60w

Step-by-step explanation:

The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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The distribution of the number of cars on the highway during two hours follows a binomial distribution with parameters n=2 and p=0.86, and the expected number of cars that will pass the highway before the first truck is approximately 1.16 cars.

(a) The distribution of the number of cars on the highway during two hours follows a Poisson distribution with a rate of 300 cars per hour. Since each vehicle is a car with a probability of 86%, we can use the binomial distribution to determine the probability of a specific number of cars in the two hours. The probability mass function of the number of cars, denoted by X, can be calculated as \(P(X = k) = (2Ck) * (0.86)^k * (0.14)^2^-^k\), where k ranges from 0 to 2. This gives us the probability distribution of the number of cars in the two hours.

(b) To determine the expected number of cars that will pass the highway before the first truck, we can utilize the geometric distribution. The probability of a car passing the highway before the first truck is 86%. Therefore, the expected number of cars, denoted by Y, can be calculated as \(E(Y) = 1 / 0.86 = 1.16\) cars. This means that on average, approximately 1.16 cars will pass the highway before the first truck.

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Is this your question?

In training for a swim meet, Logan swam 750 meters in 1/3 of an hour. His swimming partner, Mila, swam 2/3 of Logan's distance in 1/4 of an hour. (the question is What is Mila's average swimming speed?)

Answer:

Mila's average swimming speed is 34.44 m/min.

Logan's average speed is 2.25 kilometers per hour.  

Step-by-step explanation:

Given:

In training for a swim meet, Logan swam 750 meters in 1/3 of an hour.

His swimming partner, Mila, swam 2/3 of Logan's

To Find:

What is Logan's average swimming Speed?

Solution:

The relationship between speed, distance, and time is easily remembered when you consider that speed is written in terms of units of distance per units of time. (miles per hour, or kilometers per hour, for example) "per" means "divided by".

\(\left[Speed=\frac{Distance}{Time} \right]\)

\(\left[speed = (750 m)/(1/3 h) = 2250 m/h = 2.25 km/h\right]\)

Logan's average speed is 2.25 kilometers per hour.

-------------------------------------------------------------------------------------------------------------

Given:

In training for a swim meet, Logan swam 750 meters in 1/3 of an hour.

His swimming partner, Mila, swam 2/3 of Logan's distance in 1/4 of an hour

To find:

What is Mila's average swimming speed?

Solution:

The distance swam by Logan = 750 m

The distance swam by Mila =  2/3 of Logan's distance = 2/3 x 750 = 2 x 250 = 500

The time taken by Mila to swim 500 m = 1/4 of an hour = 1/4 x 60 = 15 Minutes [since 1 hr = 60 mins]

We know the formula as:

\(\left[Speed=\frac{Distance}{Time} \right]\)

Now, substituting the values in the formula above to find the speed of swimming of Mila,

The average swimming speed of Mila = \(\frac{500m}{15mintues}\)\(=33.34m/min\)

Therefore, Mila's average swimming speed is → 34.44 m/min.

Answer:

The measurement for x is 80°

Step-by-step explanation:

In the picture, we see two parallel lines cut by a transversal line. Since the lines are cut by a transversal, then there are a few things we should know that can help us find the value of x.

Now that we know these things, we can use this information to find the measurement of ∠CBA. We do this by subtracting 100 from 180 because ∠CBA and ∠CBD are a linear pair. Once we know the measurement of this angle, then it will be much easier to find the value of x.

180 - 100 = 80

So, the measurement of ∠CBA is 80°. Now, ∠CBA and ∠x are corresponding angles so this means that they have the same measurements. If the measurement of ∠CBA is 80°, then the measurement of ∠x is also 80°

x = 80°

The slope of a regression line provides valuable insights into the relationship between two variables in a linear regression analysis. It represents the rate of change in the dependent variable for a one-unit increase in the independent variable.

Specifically, a positive slope indicates that as the independent variable increases, the dependent variable also tends to increase. Conversely, a negative slope suggests an inverse relationship where an increase in the independent variable corresponds to a decrease in the dependent variable.

The magnitude of the slope is crucial as it quantifies the strength of the relationship. A larger slope signifies a steeper incline or decline, indicating a stronger association between the variables. Additionally, the slope can be interpreted as the predicted change in the dependent variable when the independent variable increases by one unit, assuming all other variables remain constant.

Overall, the slope of the regression line serves as a crucial indicator of the direction, strength, and magnitude of the relationship between variables in a linear regression model.

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The area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.

The shaded region is the segment area in the circle, so it is derived by subtracting the area of the segment from the area of the circle as follows:

area of the circle = 22/7 × 5 cm × 5 cm

area of the circle = 78.57 cm²

area of sector = 80/360 × 22/7 × 5 cm × 5 cm

area of sector = 17.46 cm²

area of triangle = 5 cm × sin40° × 5 cm × cos40°

area of triangle = 12.31 cm²

area of the segment = 17.46 cm² - 12.31 cm²

area of the segment = 5.15 cm²

area of the shaded region = 78.57 cm² - 5.15 cm²

area of the shaded region = 73.42 cm²

Therefore, the area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.

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Answer:

B

Step-by-step explanation

Multiplying by 0.97 will decrease $200,000 to $194,000.

^c is x years after the purchase, so having (0.97)^c will make the $200,000 value decrease more and more.

Answer:

c+a=2,200

1.50c+4c=5,050

Step-by-step explanation:

We know that on one day, 2,200 people entered the fair.

So, using the variables, c/a, we know that c+a=2,200

This gives us our first equation in this system of equations.

We are also given that a total of $5,050 was made.  $1.50 is a children ticket/admission fee and $4 per adult.

So:

1.50c+4c=5,050

Thus our system of equations looks like:

c+a=2,200

1.50c+4c=5,050

Hope this helps! :)

1. An example of a surjective NFA (Non-deterministic Finite Automaton) is one where every state has at least one outgoing transition for every input symbol.

2. An example of a bijective NFA is one where every state has exactly one outgoing transition for every input symbol.

3. An example of an injective NFA is one where no two states have the same outgoing transition for any input symbol.

An NFA is a computational model used in theoretical computer science and automata theory to describe the behavior of finite state machines. In the context of surjective, bijective, and injective NFAs, we consider the properties of the transitions between states.

A surjective NFA is one in which every state has at least one outgoing transition for every input symbol. This means that for any input symbol, there is a valid transition from every state to some other state or states. An example of a surjective NFA could be a state machine representing a regular expression that matches any sequence of characters.

A bijective NFA is one in which every state has exactly one outgoing transition for every input symbol. In other words, for each input symbol, there is a unique and deterministic transition from every state to another state. An example of a bijective NFA could be a state machine representing a simple calculator that performs addition or subtraction.

An injective NFA is one in which no two states have the same outgoing transition for any input symbol. This means that for any input symbol, there is a unique transition from each state to another state. An example of an injective NFA could be a state machine representing a binary counter, where each state corresponds to a unique binary number.

These examples illustrate the different properties of surjectivity, bijectivity, and injectivity in NFAs and how they affect the transitions between states.

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We know that the transformation matrix Q transforms the 3-coordinates into 3'-coordinates, which is the inverse of the change of coordinate matrix that we obtained earlier.

The matrix of T with respect to the basis {(1, 1), (−1, 1)} for the domain and the basis {(1, 0), (0, 1)} for the codomain is [T]beta= [0 0 1 0], which is the change of coordinate matrix that changes 3'-coordinates into 3-coordinates.

Let T be the linear operator on R² defined by T(x, y) = (y, 0) and let {(1, 1), (−1, 1)} and {(1, 0), (0, 1)} be the ordered bases in Example 1.

The reader should verify that {T(1,1), T(−1,1)} = {(1,0), (0,0)} and {T(1,0), T(0,1)} = {(0,1), (0,0)}.

Hence, the matrix of T with respect to the basis {(1, 1), (−1, 1)} for the domain and the basis {(1, 0), (0, 1)} for the codomain is [T]beta= [0 0 1 0], which is the change of coordinate matrix that changes 3'-coordinates into 3-coordinates.

Thus, from the above explanation, we can get Q from [T]beta as follows:

Let Q be the transformation matrix that transforms the 3-coordinates into 3'-coordinates, which is nothing but the inverse of the change of coordinate matrix that we have obtained earlier.

So, Q = ([T]beta)^-1 = [(0, 0), (0, 0), (1, 0), (0, 1)].

Therefore, Q can be obtained from [T]beta as follows:

Q = ([T]beta)^-1 = [(0, 0), (0, 0), (1, 0), (0, 1)].

Thus, we get Q from [T]beta.

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Hubble's original determination of galactic distances was a factor of 10 too small. Assuming that all of your galaxies were 10 times closer than they are, but that their radial velocities were unchanged, then the age of the universe under these assumptions is one-tenth of the previously calculated age.

To calculate the age of the universe using the given assumptions, we can make use of the Hubble's law, which relates the recessional velocity of galaxies to their distance:

v = H0 * d,

where:

- v is the recessional velocity of a galaxy,

- H0 is the Hubble constant (representing the present-day rate of expansion of the universe), and

- d is the distance to the galaxy.

If we assume that the galaxies were 10 times closer, we can rewrite the distance as d' = d/10.

Since the radial velocities are unchanged, we have v' = v.

Now, let's consider the inverse of the Hubble's law to calculate the time it took for galaxies to reach their current distances:

t = d/v.

Using the new values, we have:

t' = d'/v' = (d/10)/(v) = d/(10v).

However, we know that v = H0 * d, so substituting it in the equation:

t' = d/(10 * H0 * d).

The distance cancels out:

t' = 1/(10 * H0).

Therefore, if the galaxies were 10 times closer but had unchanged radial velocities, the age of the universe, denoted as t', is simply 1/10th of the original age of the universe, denoted as t:

t' = 1/10 * t.

Hence, the age of the universe under these assumptions is one-tenth of the previously calculated age.

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The Cartesian equation for the curve is y = 2x/(1+x^2), which is the equation of a limacon.'

The cartesian form of equation of a plane is ax + by + cz = d, where a, b, c are the direction ratios, and d is the distance of the plane from the origin.

To find the Cartesian equation for the curve, we need to use the relationships between polar and Cartesian coordinates:

x = r cos(theta) and y = r sin(theta)

Substituting r = 2 tan(theta) sec(theta), we get:

x = 2 tan(theta) sec(theta) cos(theta) = 2 sin(theta)

y = 2 tan(theta) sec(theta) sin(theta) = 2 tan(theta)

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EXPLANATION

In order to get coordinates of D such that △ABC ≅ △ADC, the distance between the point A and the point D should be the same that the distance from the point A to the point B. Therefore, we just need to reflect the point B over the point A.

Reflecting the point B over the point A give us a point that is located 4 units right and 8 units down from the point B.

Thus, the coordinates of the point D are: (1,-3)

Answer:

(2,3)

Step-by-step explanation: