Directions: Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work

Activity: You will use the GeoGebra geometry tool to explore how a line parallel to one side of a triangle divides the other two sides of the triangle. Go to
segments parallel to sides of a triangle e, and complete each step below. If you need help, follow these instructions for using GeoGebra.

Question 1: Check the box labeled Show Segment Parallel to BC. Notice that DE intersects two sides of AABC creating a smaller triangle. AADE. How is
AADE related to AABC? How do you know?

The probability that the diameter of a selected ball bearing is between 143 and 144 millimeters, given a normal distribution with a mean diameter of 138 millimeters and a variance of 9. Therefore, the probability that the diameter of a selected ball bearing is between 143 and 144 millimeters is approximately 0.0247

To calculate the probability, we first need to standardize the values of 143 and 144 millimeters using the z-score formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, the mean (μ) is 138 millimeters and the variance (σ^2) is 9, so the standard deviation (σ) is the square root of the variance, which is √9 = 3.

For 143 millimeters:

z1 = (143 - 138) / 3 = 5 / 3 ≈ 1.6667

For 144 millimeters:

z2 = (144 - 138) / 3 = 6 / 3 = 2

Next, we need to use the standard normal distribution table or a calculator to find the probability associated with these z-scores. The probability between these two z-scores represents the probability of the diameter being between 143 and 144 millimeters.

Using the table or a calculator, we find that the cumulative probability corresponding to z1 = 1.6667 is approximately 0.9525, and the cumulative probability corresponding to z2 = 2 is approximately 0.9772.

To find the probability between 143 and 144 millimeters, we subtract the cumulative probability corresponding to z1 from the cumulative probability corresponding to z2:

P(143 < x < 144) = P(z1 < Z < z2) = P(z2) - P(z1) = 0.9772 - 0.9525 ≈ 0.0247

Therefore, the probability that the diameter of a selected ball bearing is between 143 and 144 millimeters is approximately 0.0247 (or 2.47% rounded to four decimal places).

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The vector as a linear combination of standard unit vectors i and j is,

⇒ - i + 7j

We have to given that;

The initial and terminal points of RS are given below,

⇒ R(11, -4) and S(10, 3)

Hence, We can write as;

R = 11i - 4j

S = 10i + 3j

Hence, The vector as a linear combination of standard unit vectors i and j is,

⇒ RS = S - R

         = (10i + 3j) - (11i - 4j)

         = - i + 7j

Thus, The vector as a linear combination of standard unit vectors i and j is,

⇒ - i + 7j

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Answer:

20 gallons per 10 mintues or  10 gallons per minute so c!

Step-by-step explanation:

We can see the time going up in incriments of 10 and gallons going down in incrimients of 20. This gives us the answer.

Answer:

a

Step-by-step explanation:

Answer:

1,125 km

Step-by-step explanation:

So you want to find out how far the balloon went and we already know how fast and how long it's been traveling for. So now, all you have to do is come up with an equation which looks like:

2.5 x 450

Which equals 1,125 km.

The speed 450km/hour tells us that the balloon travels 450km in one hour. To find how much it traveled in 2.5 hours, we multiply 450 by 2.5.

450 x 2.5 = 1125 km

Therefore, the balloon traveled 1125 km in 2.5 hours

keeping in mind that Mt Everest is 8000 meters, or namely 8 Kilometers, Check the picture below.

The total number of rows of tiles paved in a path 1845 total used tiles is equal to 15.

Total number of tiles used = 1845

Number of columns  = 15

Let us assume that there are 'n' rows of tiles in the path.

Since there are 15 columns of equal number of tiles.

Divide the total number of tiles used by the number of columns to get the number of tiles in each column.

⇒Number of tiles in each column = Total number of tiles / Number of columns

⇒Number of tiles in each column = 1845 / 15

⇒Number of tiles in each column = 123

So each column has 123 tiles.

The number of rows,

= Divide total number of tiles used by the number of tiles in each row same as number of tiles in each column.

⇒ Number of rows = Total number of tiles / Number of tiles in each row

⇒ Number of rows = 1845 / 123

⇒ Number of rows = 15

Therefore, there are 15 rows of tiles in the path.

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Answer:

it's formula is tn=a+(n-1)d

Step-by-step explanation:

======================================================

Explanation:

Let's find the slope of line AB

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

m = (7-(-3))/(-4-1)

m = (7+3)/(-4-1)

m = 10/(-5)

m = -2

The slope of line AB is -2

The slope of any line parallel to line AB will also have the same slope.

Parallel lines have equal slopes, but different y intercepts.

Answer:

Equivalent fraction of ⅘:

\( \frac{4}{5} = \frac{8}{10} = \frac{12}{15} = \frac{16}{20} \)

a. 1101 0001 1010 1111 --> D1AF, b. 001 1111 --> 1F, c. 1 --> 1, d. 1110 1101 1011 0010 --> EDB2.

What is the hexadecimal representation of the given binary numbers?

Converting binary numbers to hexadecimal involves grouping the binary digits into sets of four, starting from the rightmost digit. Each group is then converted to its corresponding hexadecimal digit.

In the first step, we convert the binary numbers to hexadecimal as follows:

a. 1101 0001 1010 1111 --> D1AF

b. 001 1111 --> 1F

c. 1 --> 1

d. 1110 1101 1011 0010 --> EDB2

In binary, each digit represents a power of 2, while in hexadecimal, each digit represents a power of 16.

The conversion simplifies the representation and allows for easier understanding and manipulation of binary numbers.

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Answer:i think the anwser is 6

Step-by-step explanation:

The area of the surface defined by z = xy and x2 + y2 ≤ 22 would be, Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.Evaluate the integral to get the area of the surface.

To find the area of the surface defined by z = xy and x^2 + y^2 ≤ 2, we need to use a double integral over the region bounded by the inequality x^2 + y^2 ≤ 2.

First, we should rewrite the inequality in polar coordinates: x^2 + y^2 ≤ 2 becomes r^2 ≤ 2, where r is the radial distance and θ is the angle. This means 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Next, we find the Jacobian for the polar coordinates, which is |J(r,θ)| = r.

Now, we need to compute the magnitude of the gradient of z = xy in terms of polar coordinates. The gradient of z is given by the partial derivatives:

∂z/∂x = y and ∂z/∂y = x

In polar coordinates, x = r*cos(θ) and y = r*sin(θ). So, we have:

∂z/∂r = cos(θ)*∂z/∂x + sin(θ)*∂z/∂y = r*cos^2(θ) + r*sin^2(θ) = r

Now, we use the double integral to find the surface area:

Area = ∬ sqrt(1 + (∂z/∂r)^2) * |J(r,θ)| dr dθ

Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Evaluate the integral to get the area of the surface.

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The standard deviation for the given data is c. 0.024 cm.

Let's calculate the standard deviation using the given data:

Diameters: 0.493, 0.534, 0.527, 0.511, 0.565, 0.559, 0.519, 0.562, 0.551, and 0.530.

Find the mean:

Mean = (0.493 + 0.534 + 0.527 + 0.511 + 0.565 + 0.559 + 0.519 + 0.562 + 0.551 + 0.530) / 10

Mean ≈ 0.5411 cm

Calculate the squared differences:

\((0.493 - 0.5411)^2, (0.534 - 0.5411)^2, (0.527 - 0.5411)^2, (0.511 - 0.5411)^2, (0.565 - 0.5411)^2, (0.559 - 0.5411)^2, (0.519 - 0.5411)^2, (0.562 - 0.5411)^2, (0.551 - 0.5411)^2, (0.530 - 0.5411)^2\)

Find the average of the squared differences:

Average = (sum of squared differences) / 10

Take the square root of the average to get the standard deviation.

By calculating the above steps, the standard deviation of the given data set is approximately 0.024 cm.

Therefore, the correct answer is c. 0.024 cm.

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The z statistic that is associated with the class's average is 1.25.

In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.

We have to find z statistic that is associated with the class's average.

n = 25

μ = 500

σ = 100

\(\bar X\) = 525

Then ,

z statistic = \(\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }\)

putting the value in the formula:

z statistic = (525-500)/(100/\sqrt 25)

z statistic = (25)/(100/5)

z statistic = (25)/(20)

z statistic = 1.25

Therefore,

The z statistic that is associated with the class's average is 1.25.

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Step-by-step explanation:

to graph a line always find 2 points out has to go through. that means the points' coordinates make the equation true.

I usually start with x = 0.

point 1 of equation 1 is then

y = -2×0 + 6 = 6

(0, 6)

point 1 of equation 2 is then

y = (3/2)×0 - 1 = -1

(0, -1)

then I pick a value for x that makes the handling of any fractions easier. like in our case x = 2.

point 2 of equation 1 is then

y = -2×2 + 6 = -4 + 6 = 2

(2, 2)

point 2 of equation 2 is then

y = (3/2)×2 - 1 = 3 - 1 = 2

(2, 2)

oh, so I have found the intersection point right away (point 2 of both equations).

so, let's pick a different point 2 for equation 1, like x = 4

y = -2×4 + 6 = -8 + 6 = -2

(4, -2)

with these 4 points you define the 2 lines, and you have the intersection point at (2, 2).

Answer:

327675

Step-by-step explanation:

the formula of the series is:

16

∑5*2^(n-1)

n=1

the formula for the sum of a geometric series is:

Sn=a(1-r^n)/(1-r)

plug in the values from above

n=16 a=5 and r=2 (values from the geometric function) so

Sn=5(1-2^16)/(1-2)

Sn=327675

By taking the help of the standard deviation, the answer obtained is

n = 719

What is Standard Deviation?

At first it is important to know about Variance.

Variance is the sum of the square of deviation from the mean of the data.

On taking the square root of variance, Standard deviation is obtained.

The formula used for calculating the number of samples required is

\(n=\frac{Z^{2}_{\alpha /2}\times \sigma ^{2}}{e^{2}}\), \(\sigma\) is the standard deviation , e is the error,

Here,

\(\alpha\) = 1 - \(\frac{95}{100}\)

  = 1 - 0.95

  = 0.05

Critical values of Z = \(\pm\)1.96 [ From the table]

Standard deviation (\(\sigma\)) = 9.3

error (e) = $0.68

On putting  the value,

n = \(\frac{1.96^2 \times 9.3^2}{0.68^2}\)

n = 718.5

n = 719

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

no abla espanol

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

\(s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7\)

Answer: W

Step-by-step explanation:

i took the test

Answer:

37

Step-by-step explanation:

6m+5n

plug in your given values

6(2) + 5(5)

12+25

=37

Answer:

37

Step-by-step explanation:

6m + 5n

6*2  +  5*5 = 12 + 25

= 37

Answer:

Usain Bolt runs about 37,383 meters an hour so he will not exceed the speed limit but will run at about 23 miles per hour.

Step-by-step explanation:

Usain Bolt runs about 37,383 meters an hour so he will not exceed the speed limit but will run at about 23 miles per hour. We get this from 3600 seconds in an hour, 3600÷9.63×100≈37383 meters an hour. 1609.344 meters in a mile. 37383÷1609.344≈23 mph

Answer:Sample Response: The speed limit is about 11.2 meters per second. Usain is running 10.38 meters per second. So he is running slower than the speed limit.

Step-by-step explanation:Need brainliest award

The height of the cylinder given the volume of 300 m³ is approximately 8.788 m. Therefore, the answer is c. 8.

The height of the cylinder given the surface area of 400 m² is approximately 15.954 m. Therefore, the answer is b. 18.

The height of the cylinder given the lateral area of 350 m² is approximately 12.536 m.

Let's solve each problem step by step.

Finding the height given the volume:

The formula for the volume of a right circular cylinder is V = πr²h, where V is the volume, r is the radius of the base, and h is the height.

We are given that the volume is 300 m³. We also know that the height is twice the radius, which means h = 2r.

Substituting the value of h in terms of r into the volume formula, we get:

300 = πr²(2r)

300 = 2πr³

r³ = 150/π

r = (150/π)^(1/3)

To find the height, we substitute the value of r back into h = 2r:

h = 2((150/π)^(1/3))

Now, let's calculate the approximate value for h:

h ≈ 2(4.394) ≈ 8.788

So, the height of the cylinder is approximately 8.788 m.

Finding the height given the surface area:

The formula for the surface area of a right circular cylinder is A = 2πrh + 2πr², where A is the surface area, r is the radius of the base, and h is the height.

We are given that the surface area is 400 m². We also know that the height is twice the radius, which means h = 2r.

Substituting the value of h in terms of r into the surface area formula, we get:

400 = 2πr(2r) + 2πr²

400 = 4πr² + 2πr²

400 = 6πr²

r² = 400/(6π)

r = √(400/(6π))

To find the height, we substitute the value of r back into h = 2r:

h = 2√(400/(6π))

Now, let's calculate the approximate value for h:

h ≈ 2(7.977) ≈ 15.954

So, the height of the cylinder is approximately 15.954 m.

Finding the height given the lateral area:

The lateral area of a right circular cylinder is given by A = 2πrh, where A is the lateral area, r is the radius of the base, and h is the height.

We are given that the lateral area is 350 m². We also know that the height is twice the radius, which means h = 2r.

Substituting the value of h in terms of r into the lateral area formula, we get:

350 = 2πr(2r)

350 = 4πr²

r² = 350/(4π)

r = √(350/(4π))

To find the height, we substitute the value of r back into h = 2r:

h = 2√(350/(4π))

Now, let's calculate the approximate value for h:

h ≈ 2(6.268) ≈ 12.536

So, the height of the cylinder is approximately 12.536 m.

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Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

The area of the parallelogram is 281.91 m²

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the area of the parallelogram can be found as follows:

area of the parallelogram = bh

where

Therefore, let's find the height of the parallelogram using trigonometric ratios,

sin 70° = opposite / hypotenuse

sin 70° = h / 15

h = 15 sin 70°

h = 15 × 0.9396

h = 14.0953893118

h = 14.1 metres

Therefore,

area of the parallelogram = 14.1 × 20

area of the parallelogram = 281.907786236

area of the parallelogram = 281.91 m²

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Step-by-step explanation:

the nth root of something can be expressed as 1/n as exponent.

e.g. sqrt(2) = 2^(1/2).

so, the 5th root of 3⁴ = 3^(4/5)

for f(x) = 3^x

that means that x = 4/5 = 0.8.

so, I go on the x-axis to the right to 0.8, and from there straight up to the actual curve.

that is the desired point.

Answer:

Step-by-step explanation:

It is asking for the "mode" which is the data element you see the most, therefore it is 2.