Jennifer has run many marathons and keeps track of all of her finishing times. At a marathon last month, she finished in 350 minutes. The other day, she ran another marathon and finished with a time of 406 minutes. What is the percent of increase in Jennifer's marathon time?

The probability that exactly 50 people will order a drink is approximately 0.153.

Given: There are 90 people in the restaurant. The probability of someone ordering a drink with the food is 60%. We need to find the probability that exactly 50 people will order a drink.

The given problem is related to Binomial distribution, and we can solve this problem by using Normal approximation.

Let the random variable X be the number of people who will order the drink with the food. Since the probability of success is 0.6 and the probability of failure is 0.4.Assume this is a binomial distribution. Since the sample size n = 90 is large, n * p = 90 * 0.6 = 54 and n * q = 90 * 0.4 = 36.Both n * p and n * q are greater than 10.We need to find P(X = 50), which means we need to find the probability of exactly 50 people who will order the drink with the food. Now, we can use Normal approximation as below:

Mean = μ = n * p = 90 * 0.6 = 54Variance = σ2 = n * p * q = 90 * 0.6 * 0.4 = 21.6

Standard deviation = σ = √σ2 = √21.6 = 4.64.

By using Normal approximation, the required probability is: P(49.5 < X < 50.5) = P[(49.5 - 54)/4.64 < Z < (50.5 - 54)/4.64] = P[-1.077 < Z < -0.543] = Φ(-0.543) - Φ(-1.077) = 0.293 - 0.140 = 0.153

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The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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The property that is illustrated by the given statement is called: A. Transitive property of equality.

The transitive property of equality states that, if two quantities, a and b, are equal to each other, and the second quantity, b, is equal to a thrid quantity, c, then, the first quantity equals the third quantity (a = c).

Using the same logic, ΔABC ≅ ΔXYZ.

Therefore, the property that is illustrated by the given statement is called: A. Transitive property of equality.

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Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

If he spins the four-part spinner 100 times, he can expect to win each prize approximately 25 times. This can be determined by using the concept of probability.

Let's say Gustavo spins the spinner 100 times to demonstrate the likelihood of winning each prize. Since the spinner has four equal parts representing the four prizes, each prize has a 1/4 (or 25%) chance of being won on any given spin.

After spinning the spinner 100 times, we can expect Gustavo to win each prize approximately 25 times. However, it's important to note that these are expected values based on probability, and the actual results may vary due to chance.

Here's a breakdown of the expected number of times Gustavo might win each prize:

1. Video game system: Gustavo can expect to win the video game system around 25 times out of the 100 spins.

2. Bicycle: Similarly, Gustavo can expect to win the bicycle approximately 25 times out of the 100 spins.

3. Watch: Gustavo can also expect to win the watch around 25 times out of the 100 spins.

4. Gift card: Lastly, Gustavo can expect to win the gift card approximately 25 times out of the 100 spins.

Keep in mind that these are average values based on the assumption that each prize has an equal chance of being won. In reality, due to random chance, the actual results might deviate slightly from these expected values.

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Answer:

1,251 miles

Step-by-step explanation:

if 1/3 inch is 417 miles then one inch would be 3/3 so

417 x 3= 1,251 miles.

I hope this helps!

Answer:

The inequalities have the same solutions.

Step-by-step explanation:

hope this helps

To solve the equation \begin{equation}-\log{\left(x^2 - 15\right)} = \log{\left(2x\right)}\end{equation}, the following steps can be taken:

Apply the logarithmic identity log(a) = log(b) if and only if a = b to obtain the equation x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero, to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

Therefore, the steps to solve the equation log(x^2 - 15) = log(2x) from 1 to 5 are:

Apply the logarithmic identity to get x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

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The linear function that models the data is S = 3.8x - 14.506 and  the circumference of a finger with a ring size of 6 is 5.4 cm.

a. To find a linear function S that models the data, we need to find the slope and y-intercept of the line that best fits the data. The slope can be found by using the formula:

m = (y2 - y1) / (x2 - x1)

Using the first two data points, we can find the slope:

m = (7 - 4) / (5.66 - 4.87)

m = 3 / 0.79

m = 3.8

To find the y-intercept, we can use the formula:

y = mx + b

Substituting one of the data points and the slope into the formula and solving for b:

4 = (3.8)(4.87) + b

b = 4 - (3.8)(4.87)

b = -14.506

So the linear function that models the data is:

S = 3.8x - 14.506

b. To find the circumference of a finger with a ring size of 6, we can substitute S = 6 into the linear function and solve for x:

6 = 3.8x - 14.506

3.8x = 20.506

x = 5.4 cm

So the circumference of a finger with a ring size of 6 is 5.4 cm.

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The area of the parallelogram with vertices P(1,3,3), Q(2,5,5), R(5,9,14), and S(4,7,12) is 14 square units.

To find the area of the parallelogram, we can use the cross product of two vectors formed by the given vertices. Let's consider the vectors PQ and PR.

Vector PQ = Q - P = (2-1, 5-3, 5-3) = (1, 2, 2)

Vector PR = R - P = (5-1, 9-3, 14-3) = (4, 6, 11)

Next, we calculate the cross product of vectors PQ and PR:

Cross product = (211 - 62, -(111 - 42), 16 - 41)

= (22 - 12, -(11 - 8), 6 - 4)

= (10, -3, 2)

The magnitude of the cross product gives us the area of the parallelogram:

Area = ||Cross product|| = √(10^2 + (-3)^2 + 2^2) = √(100 + 9 + 4) = √113

Hence, the area of the parallelogram is √113 square units, which is approximately 10.63 square units.

The area of the parallelogram with vertices P(1,3,3), Q(2,5,5), R(5,9,14), and S(4,7,12) is approximately 10.63 square units.

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The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).

The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05

Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.

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Answer:

  D.  less than: 4 < 4.52

Step-by-step explanation:

The area of the circle is found using the given formula:

  A = π(1.2 in)^2 = 1.44π in^2 ≈ 4.52 in^2

The table tells you the area of a 2-inch square is 4 in^2.

Comparing the two areas, we see that ...

  4 < 4.52

The area of the square is less than the area of the circle.

Answer

La letra D es la respuesta. Menos que.

Step-by-step explanation:

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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We return "Yes"; otherwise, we return "No".

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

To solve this problem, we can work backward from (c,d) to (a,b) and check if each step is valid. Specifically, we can use the following observations:

If c < a or d < b, it is impossible to reach (c,d) from (a,b) using the given operations.

If c - a = d - b, we can reach (c,d) from (a,b) using only the second operation. Specifically, we can perform the operation (a, a+b) repeatedly until we reach (c,d).

If c - a != d - b, we can reach (c,d) from (a,b) using a combination of the two operations. Specifically, we can perform the first operation (a,b) -> (a+b,b) repeatedly until we get to a point where c - a = d - b, and then use the second operation to get to (c,d).

Here, we first check if it is impossible to reach (c,d) from (a,b) using the observations above. If not, we perform the second operation as many times as possible to reduce the difference between c and a, and d and b. Once this is done, we check if we have arrived at (a,b).

Therefore, we return "Yes"; otherwise, we return "No".

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Answer:

33

Step-by-step explanation:

6 * 3 = 18

8-3 = h

h = 5

A = 5 * 3 = 15

Combined:

15 + 18

33

Answer:

92 percent

Step-by-step explanation:

Answer:

92% of balloons filled did not pop.

Step-by-step explanation:

2 / 25 balloons is the fraction of balloons that do pop, and we want the percentage that don't pop.

To start off with, we will get the fraction of balloons that don't pop - 23 / 25.

We will then convert this fraction to a decimal by dividing the fraction:

23 divided by 25 = 0.92

Now, to convert this to a percentage, we just multiply by 100.

0.92 x 100 = 92%

Therefore the answer is 92% of balloons filled did not pop.

Step-by-step explanation:

step 1. AD is parallel to BC

step 2. <y = 90° (definition of right trapezoid)

step 3. x + y + 90 + 140 = 360 (a quadrilateral has 360° of internal angles)

step 4. x + 90 + 90 + 140 = 360

step 5. x = 40°.

Answer:

C is your answer for this question

Answer:

3/4

Step-by-step explanation:

tan A =opposite/adjacent = 6/8 =3/4

Hope this helps

Have a good day

Answer:

yeah just do that it's just side times side

Answer:

Yes pretty much.

Step-by-step explanation:

The formula for a square

A=s^2

When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it

The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.

These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.

Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.

For this reason, the correct choice is get closer and closer to the x-axis but never touches it.

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Answer:

yes they are

Step-by-step explanation:

If you distribute the minus then the 4 becomes positive.

Have a great day!

If it helped mark me brainliest!

Answer:

yes

Step-by-step explanation:

x - (-4)

Apply rule - (-a) = a:

⇒ x + 4

Answer:

\(y=-\frac{4}{3} x+4\)

Step-by-step explanation:

Slope-intercept form is written in \(y=mx+b\)

So, to solve, we must separate y onto one side and make its coefficient one.

\(4x+3y=12\)

Subtract 4x on both sides.

\(3y=12-4x\)

Divide both sides by the coefficient of \(y\), which is 3.

\(\frac{3y}{3} =\frac{12-4x}{3}\)

Simplify.

\(y=4-\frac{4}{3} x\)

Rewrite this equation into standard form by changing the order of \(mx\) and \(b\)

\(y=-\frac{4}{3} x+4\)

Answer

y=4/5 times 2/3

Step-by-step explanation:

The total electric charge inside the cube is -2.52×10^-9 C in the x-direction and 5.72×10^-9 C in the z-direction.

We can calculate the total electric charge inside the cube by using Gauss's law, which relates the electric flux through a closed surface to the total charge enclosed within that surface.

Since the electric field is not uniform, we need to choose a closed surface over which the electric flux is easy to calculate. We can choose a cube with sides of length L centered at the origin, since the electric field is given at all points in space.

Using the symmetry of the problem, we can choose the cube so that it is aligned with the x, y, and z-axes. Each face of the cube has an area of L^2, so the total surface area of the cube is 6L^2.

The electric flux through each face of the cube is given by the dot product of the electric field with the normal vector to that face. For the x-faces, the normal vector is i, and for the z-face, the normal vector is k. The electric field does not have a component in the y-direction, so the flux through the y-faces is zero.

The electric flux through each x-face is

Φx = E•A = (-5.65 N/C)(L^2)i

The electric flux through the z-face is:

Φz = E•A = (3.23 N/C)(L^2)k

Since the electric field is constant over each face, we can add the flux through each face to get the total electric flux through the cube:

Φtotal = 2Φx + 2Φy + 2Φz = (-5.65 N/C)(2L^2)i + (3.23 N/C)(2L^2)k

By Gauss's law, the total electric flux through a closed surface is equal to the total charge enclosed within that surface divided by the permittivity of free space (ε0):

Φtotal = Qenc/ε0

Solving for the total charge enclosed within the cube:

Qenc = Φtotal ε0 = [(-5.65 N/C)(2L^2)i + (3.23 N/C)(2L^2)k] ε0

Using the value of the permittivity of free space ε0 = 8.85×10^-12 C^2/(N m^2), we get:

Qenc = [-2.52×10^-9 C i + 5.72×10^-9 C k]

The total electric charge inside the cube is -2.52×10^-9 C in the x-direction and 5.72×10^-9 C in the z-direction.

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The given question is incomplete, the complete question is:

A cube has sides of length L = 0.370 m . It is placed with one corner at the origin as shown in the figure . The electric field is not uniform but is given by E =( -5.65 N/(C) )xi^+( 3.23 N/(C) )zk Find the total electric charge inside the cube.

Answer:

100π

Step-by-step explanation:

The main purpose of business sustainability is to achieve long-term success by balancing economic, social, and environmental concerns. It involves integrating sustainable practices into business strategies to create positive impacts on the environment, society, and stakeholders while ensuring profitability and resilience.

Environmental management plays a crucial role in sustainable business development. It involves identifying and managing environmental risks, implementing eco-friendly practices, reducing resource consumption, minimizing waste generation, and promoting environmental stewardship. By incorporating environmental management into their operations, businesses can enhance their sustainability performance, comply with regulations, improve brand reputation, and contribute to a healthier planet.

Stakeholder analysis plays a vital role in sustainable development, particularly in the context of specific industries or sectors. In the case of rubber cultivation in Southwest China, stakeholder analysis helps identify and understand the diverse stakeholders involved, such as rubber farmers, local communities, government agencies, environmental organizations, and consumers. By analyzing stakeholders' interests, concerns, and power dynamics, sustainable development initiatives can be tailored to address their needs effectively. Stakeholder engagement and collaboration are crucial for promoting sustainable practices, ensuring social acceptance, mitigating conflicts, and achieving sustainable outcomes in rubber cultivation and other industries.

Environmental management plays a vital role in sustainable business development. It involves assessing and managing environmental risks, implementing eco-friendly practices, complying with environmental regulations, and monitoring environmental performance. By adopting sustainable production processes, minimizing resource consumption, reducing emissions and waste generation, and promoting environmental stewardship, businesses can enhance their environmental performance. Effective environmental management not only benefits the environment but also leads to cost savings, improved efficiency, enhanced brand reputation, and reduced regulatory risks.

The pillars of sustainable development provide a framework for addressing the interconnectedness of economic, social, and environmental aspects. The economic pillar emphasizes the need for sustainable economic growth, productivity, and innovation while ensuring equitable distribution of resources. The social pillar highlights the importance of social well-being, equality, human rights, and inclusivity. The environmental pillar recognizes the significance of environmental conservation, resource efficiency, pollution prevention, and climate change mitigation. These pillars are interdependent, and progress in one pillar can influence the others. Sustainable development requires a balanced and integrated approach that considers all three dimensions.

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Answer:

\(\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}\)

Step-by-step explanation:

Given equation:

\(y=\log_2x-1\)

To fill out the given x-y chart, substitute each given value of x into the given log equation.

The argument of a log function can only take positive arguments, so when x = -2, x = -1 and x = 0, the y-values are undefined.

The values of y for x = 1 and x = 2 are:

\(\begin{aligned}x=1 \implies y&=\log_21-1\\&=0-1\\&=-1\end{aligned}\)

\(\begin{aligned}x=2 \implies y&=\log_22-1\\&=1-1\\&=0\end{aligned}\)

Therefore, the completed x-y chart for the equation y = log₂x - 1 is:

\(\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}\)

Note: I have used DNE for does not exist.