PLEASE HELP!!

Which of the following is statements is TRUE about the figure.

A. △ABC~ △DFE by AA Similarity Theorem
B. △ABC~ △DFE by ASA Similarity Theorem
C. △ABC~ △DFE by SSS Similarity Theorem
D. △ABC~ △DFE by SAS Similarity Theorem
E. There is not enough information provided

In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.

The 4 independent variables are represented by the four numbers in the experimental design

(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).

The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.

A factorial experiment includes multiple factors simultaneously, each consisting of two or more

levels. Many factors simultaneously influence what is studied in a factorial experiment, and

experimenters consider the main effects and interactions between factors.

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The x-component of the force acting on the third charge is -0.041 N and the y-component of the force acting on the third charge is -0.058 N. The magnitude of the force acting on the third charge is 0.071 N.

Given Data :Charge of the first charge, q₁ = -3.4nC

Charge of the second charge, q₂ = 260nC

Charge of the third charge, q₃ = 5.00L

Cordinates of the third charge, x₃ = 2.95 cm and y₃ = 4.25 cm

Now, we need to find the magnitude of the force acting on the third charge due to the first and second charges and also find the x and y components of the total force acting on it.

Electric force is a vector quantity that is a combination of the magnitude of the charge and the direction in which it is acting.

Electric force is expressed in terms of Coulombs, which is a measure of the electric charge. The Coulombs are defined as the number of electrons that are present in one unit of charge.

Coulombs are expressed in terms of their magnitudes, with positive charges indicating that the charge is repelling, and negative charges indicating that the charge is attracting.

The electric force is a vector quantity, which means that it has both a magnitude and a direction. In order to find the magnitude of the force, we need to calculate the sum of the electric forces acting on the third charge due to the first and second charges.

Now, we need to find the magnitude of the force acting on the third charge due to the first and second charges and also find the x and y components of the total force acting on it.

From the diagram above, we can see that the distance between the first charge and the third charge is r₁ = x and the distance between the second charge and the third charge is r₂ = y - 4.25 cm.

Therefore, the magnitude of the electric force acting on the third charge due to the first charge is given by

F₁₃ = k * q₁ * q₃ / r₁² where k is Coulomb's constant which is equal to 9.0 × 10⁹ N · m²/C² and q₁, q₃ are the charges of the first and third charges respectively.

Thus, the magnitude of the force acting on the third charge due to the first charge is given by:

F₁₃ = (9.0 × 10⁹ N · m²/C²) * (-3.4 × 10⁻⁹ C) * (5.00 C) / (2.95 × 10⁻² m)²

F₁₃ = -0.071 N

Now, we can find the x and y components of the total force acting on the third charge as:

Fx = F₁₃ * cosθ where θ is the angle between the force F and the x-axis.

Thus,θ = tan⁻¹(y / x)

θ = tan⁻¹(4.25 cm / 2.95 cm)

θ = 53.5°

Therefore, the x-component of the force acting on the third charge is given by:

Fx = (-0.071 N) * cos(53.5°)

Fx = -0.041 N

Similarly, we can find the y-component of the force acting on the third charge as:

Fy = F₁₃ * sinθ where θ is the angle between the force F and the x-axis.

Therefore, the y-component of the force acting on the third charge is given by:

Fy = (-0.071 N) * sin(53.5°)

Fy = -0.058 N

Thus, the x and y components of the total force acting on the third charge are -0.041 N and -0.058 N respectively. Therefore, the magnitude of the force is given by:

F = sqrt(Fx² + Fy²)F = sqrt((-0.041 N)² + (-0.058 N)²)

F = 0.071 N

The x-component of the force acting on the third charge is -0.041 N and the y-component of the force acting on the third charge is -0.058 N. The magnitude of the force acting on the third charge is 0.071 N.

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The relationship between the number of buses, number of cars and the students is an illustration of a linear equation.

The number of bus on the trip is 7

Let:

\(b \to bus\)

\(c \to car\)

\(c = 13\) --- students that traveled by car

\(Total = 328\) --- the total number of students

So, the equation is:

\(45b + c = Total\)

Substitute values for c and Total

\(45b + 13 = 328\)

Collect like terms

\(45b = 328 - 13\)

\(45b = 315\)

Divide both sides by 45

\(b = 7\)

Hence, the number of buses on the trip is 7

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To test the effect of living environment on cholesterol levels using samples from rural and urban areas, the best statistical test to utilize would be the two-sample t-test.

The two-sample t-test is appropriate in this case because it compares the means of two independent groups (rural and urban residents) to determine if there is a significant difference between their cholesterol levels.

This test will help researchers determine if living environment has an impact on cholesterol levels.

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The normal component of the acceleration vector (a_n) is a_n = √(|a(t)|^2 - a_t^2).

To find the tangential and normal components of the acceleration vector for the given position vector r(t) = 7e^t*i + 7√2^t*j + 7e^(-t)*k, follow these steps:

1. Differentiate the position vector r(t) to find the velocity vector v(t):

v(t) = dr(t)/dt = (7e^t)*i + (7√2^t * ln(√2))*j - (7e^(-t))*k

2. Differentiate the velocity vector v(t) to find the acceleration vector a(t):

a(t) = dv(t)/dt = (7e^t)*i + (7√2^t * ln^2(√2))*j + (7e^(-t))*k

3. Calculate the magnitude of the velocity vector |v(t)|:

|v(t)| = √((7e^t)^2 + (7√2^t * ln(√2))^2 + (7e^(-t))^2)

4. Find the tangential component of the acceleration vector (a_t):

a_t = (a(t) • v(t)) / |v(t)|

Here, '•' denotes the dot product.

5. Find the normal component of the acceleration vector (a_n):

a_n = √(|a(t)|^2 - a_t^2)

By following these steps, you can find the tangential and normal components of the acceleration vector for the given position vector r(t).

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Irrational numbers are real numbers that can't be expressed as a fraction, p/q, where p and q are integers.

Thus, √13 is irrational number.

Thus, 4 1/3 and 8 are rational number.

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The scenario that illustrates an appreciation of the dollar against the euro is option D. Last week, 1 dollar was equal to 0.88 euros, but this week, 1 dollar is equal to 0.78 euros.

In this scenario, the exchange rate between the dollar and the euro has decreased from 0.88 to 0.78 euros per dollar. This means that the value of the dollar has increased relative to the euro. With fewer euros required to purchase one dollar, it implies that the dollar has appreciated in value.

Appreciation of a currency indicates that it can buy more of another currency. In this case, the dollar can buy more euros, which demonstrates an appreciation of the dollar against the euro. This would be beneficial for individuals or entities holding dollars who want to exchange them for euros, as they can now obtain more euros for the same amount of dollars compared to the previous week.

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Answer:

Option 2

Step-by-step explanation:

Let's say that Phalicia opens her savings account one year (12 months) before she goes to college.

With Option 1, she would have saved 300 + 50 * 11 = $850. We do 50 * 11 and not 50 * 12 because she deposits $50 for 11 months, not 12.

With Option 2, she would have saved 5 * 3¹¹ = $885735. Note that we do 3¹¹ and not 3¹² because 5 is being tripled 11 times.

Obviously, she should choose Option 2 because she saves A LOT more money.

Additionally, we can notice that Option 1 is an example of an arithmetic sequence whereas Option 2 is an example of a geometric sequence. Their explicit formulas would be aₙ = 50n + 250 and aₙ = 5 * 3⁽ⁿ⁻¹⁾ respectively.

The variance of the binomial probability distribution with n = 3 and π = 0.52 is 0.749. The correct answer is option d. 0.749.

The variance of a binomial distribution can be calculated using the formula Var(X) = nπ(1 - π), where X is the random variable, n is the number of trials, and π is the probability of success.

In this case, we are given n = 3 and π = 0.52. Plugging these values into the formula, we get Var(X) = 3 * 0.52 * (1 - 0.52) = 0.749.

Therefore, the variance of the distribution is 0.749.

In the given multiple-choice options:

a. 1.500 - Not the correct variance value.

b. 1.440 - Not the correct variance value.

c. 1.650 - Not the correct variance value.

d. 0.749 - This is the correct variance value.

Hence, the correct answer is option d. 0.749.

In summary, the variance of the binomial probability distribution with n = 3 and π = 0.52 is 0.749.

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Reason:

The green dashed boundary line goes through (0,5) and (5,0)

Use the slope formula to find the slope is m = -1

Use the point-slope equation to find the equation of the boundary line is y = -x+5

Since we're below this boundary line, we change the equal sign to a less than sign.

Therefore, the green shaded region is represented by y < -x+5

If the boundary was solid, then you use "or equal to" as part of the inequality sign. But in this case, points on the boundary are not part of the solution set.

Through similar steps you should find that the purple region is represented by the inequality y > 6x-4

Note that the purple shaded region is above its corresponding boundary line. So we use "greater than" instead of "less than".

Answer:y < -x+5    and     y > 6x-4

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

50 is half of 100

27x2=54

The required slope-intercept form of the line is y = x /2 - 4.

Given that,
A line has a slope of 1/2 and passes through the point (10, 1). What is its equation in slope-intercept form is to be determined.

The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.

y - y₁ = m (x - x₁)

Substitute the value in the above equation,
y -1 = 1/2(x - 10)
y = x /2 -5 + 1
y = x/2 -4

Thus, the required slope-intercept form of the line is y = x /2 - 4.

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The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

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As per the normal distribution, the probability that x is less than or equal to 38 is 0.9861.

Probability:

In math, probability denotes a  branch of mathematics concerning numerical descriptions of how likely an event is to occur.

Given,

Here let x be a normally distributed random variable with mean 5 and standard deviation 15. please express your answer as a number between 0 and 100. if you want to write 52%, please enter 52.

Here we need to find the probability that x is less than or equal to 28.

According to a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

Here first, we have to solve for the z-score using the formula below.

=> z-score = (x – μ) / σ

Here x refers the individual data value = 38

μ refers mean = 5

σ refers standard deviation = 15

Then when we apply the values on it, then we get,

=> z-score = (38 - 5) / 15

=> z-score = 33 / 15

=> z-score = 2.2

Then the probability that corresponds to the z-score in the z-table.

=> probability = 0.9861

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Approximately 19.9919 pounds of bananas are removed from the display table during the first 2 hours the store is open.

The function has a constant term 10, which represents the minimum rate of banana removal even if no customers are present.

The second function is g(t), which models the rate at which bananas are added to the display table.

Now, to answer the question, we need to find out how many pounds of bananas are removed from the display table during the first 2 hours. We can do this by integrating the function f(t) from 0 to 2, which gives us the total amount of bananas removed during this time interval. Using the integral notation, we have:

Total amount of bananas removed = ∫₀² f(t) dt

Using the formula for f(t), we can evaluate this integral as follows:

∫₀² [10 + (0.81)sin(100t)] dt = [10t - (0.81/100)cos(100t)] from 0 to 2

Plugging in the limits of integration, we get:

[10(2) - (0.81/100)cos(200)] - [10(0) - (0.81/100)cos(0)] = 20 - 0.0081 ≈ 19.9919 pounds

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Complete Question:

When a certain grocery store opens, it has 50 pounds of bananas on a display table. Customers remove bananas from the display table at a rate modeled by

f(t) = 10 + (0.81)sin 100 for 0

where f(t) is measured in pounds per hour and is the number of hours after the store opened. After the store has been open for three hours, store employees add bananas to the display table at a rate modeled by

8(t) = 3 + 2.4 In (12 + 2+) for 3

where g(t) is measured in pounds per hour and is the number of hours after the store opened.

(a) How many pounds of bananas are removed from the display table during the first 2 hours the store is open?

Answer: Mike stops running at 12:18 PM

Step-by-step explanation: We know he runs 1 mile each 12 minutes and we also knows he ran 4 miles so the equation is 12*4 or (12 times 4) which is equal to 48. We then add 38 minutes to 11:30 AM and end up at 12:18 PM.  

Answer:

12:18 P.M

Step-by-step explanation:

So the first thing I did was find out the amount of time it takes Mike to run 4 miles by multiplying 12 x 4 = 48

So Mike spends 48 minutes running the 4 miles.

Now we add 48 minutes to 11:30. So since there is no such thing as 11:78 I first subtracted the 30 minutes from the 48 minutes and added that to 11:30 which gave me 12:00 pm and then I just added the reamaining18 minutes.

which in conclusion means,

Mike will finish his 4 miles at 12:18 P.M

Solution:

Given a table of data;

Where the total hours in 50 hours

The hours spent for jogging is 20 hours.

The sum of angles about a point or in a circle is, 360°

The portion for jogging in degrees is

Substitute into the formula above

Hence, the portion for jogging is 144°

Answer:

13 pounds

Step-by-step explanation:

0.35x = 4.55

x = 13

Answer:

13

Step-by-step explanation:

Divide $4.55/$0.35

Option (B) is correct. The first group will have a commuting time of 0-15 minutes, as it covers the desired range and includes the shortest commuting time of 5 minutes.

The first group will have a commuting time of 0-15 minutes. This range is selected because it covers the desired commuting time range of 5-120 minutes. Since the shortest commuting time is 5 minutes, a range starting from 0 minutes would include it. Additionally, the upper limit of 15 minutes ensures that employees with longer commuting times are not included in this group.

By placing employees with commuting times ranging from 0-15 minutes in the first group, the employment agency can create a statistical grouping that represents those who have relatively short commutes. This grouping allows for better analysis and understanding of the distribution of commuting times among the 125 employees and can aid in making informed decisions regarding job placements and other related factors.

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a. The correct statement regarding the classification of the functions as exponential and linear is given as follows:

The total number of views for Video 1 are exponential because they grow by equal factors over equal intervals.

b. The average rate of change of the total number of views for Video 2 between July 12 and July 14 is of: 45,000 views a day.

The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:

Hence the functions are classified as follows:

The average rate of change is given by the change in the output divided by the change in the input, hence it is of:

r = (190000 - 100000)/2 = 45,000 views a day.

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Answer:

  (d)  7.9 ft

Step-by-step explanation:

The geometry of the problem can be represented by a right triangle whose hypotenuse is the ramp, and the side opposite the given angle is 3 feet. Then the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Solving for Hypotenuse, we find ...

  Hypotenuse = Opposite/Sin

  ramp length = (3 ft)/sin(22.3°) ≈ 7.9 ft

The ramp is about 7.9 feet long.

Check the picture below.

Answer:

904.78

Step-by-step explanation:

I hope this is correct, if it isn't please feel free to let me know and I can fix it. I'm sorry in advance if it is incorrect.

Answer:

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.

The probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires is approximately 0.994 or 99.4%.

We can use the central limit theorem to find the probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires.

According to the central limit theorem, the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, we can calculate the z-score as follows:

z = (\(\bar{X}\) - μ) / (σ / √n)

where \(\bar{X}\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we want to find the probability that the sample mean would differ from the population mean by less than 170 miles, which means we need to find the probability that the z-score is between -170/ (σ / √n) and 170/ (σ / √n).

Plugging in the given values, we get:

z = (\(\bar{X}\) - μ) / (σ / √n)

z = (170) / (4693 / √211)

z ≈ 8.13

Using a calculator, we can find that the probability of getting a z-score less than 8.13 or greater than -8.13 is approximately 1.0.  Therefore, the probability is approximately 0.994 or 99.4%.

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Answer:

Radical 7 is between 2 and 3, so radical 7 is about 2.65.

Step-by-step explanation:

Since 2 squared = 4 is too low and 3 squared = 9 is too high, we know it is somewhere between 2 and 3.

Since 7 is closer to 9 than it is to 4, we also know that the estimate will be closer to 3 than it is to 4.

Since 7 is only 2 units away from 9 and 3 units away from 4, we can estimate that it isn't too much closer to 3 and would be more towards to middle.

The area bounded between g(x) and f(x) over the interval [-31,-26] is approximately equal to 1.55 x 10^23 square units.

To determine the area, in square units, of the region bounded above by g(x)=-8x^3 and below by f(x)=-7x^16 over the interval [-31,-26], we need to find the definite integral of the difference between g(x) and f(x) over the given interval.

The integral of g(x) over the interval [-31,-26] is given by:
∫[-31,-26] -8x^3 dx = [-2x^4]_[-31,-26] = (-2(-26)^4) - (-2(-31)^4) = -13,354

Similarly, the integral of f(x) over the interval [-31,-26] is given by:
∫[-31,-26] -7x^16 dx = [-x^17]_[-31,-26] = (-(-26)^17) - (-(-31)^17) = -1.39 x 10^23

Therefore, the area bounded between g(x) and f(x) over the interval [-31,-26] is:
∫[-31,-26] (g(x) - f(x)) dx = ∫[-31,-26] (-8x^3 + 7x^16) dx
= (-2x^4 + (-1/2)x^17)_[-31,-26]
= [(-2(-26)^4 + (-1/2)(-26)^17) - ((-2(-31)^4 + (-1/2)(-31)^17)]
= [35,288,148 - (-1.55 x 10^23)]
= 1.55 x 10^23 - 35,288,148

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Answer:

110

Step-by-step explanation: