L Pretest Unit 3
Question 14 of 28
What is the length of leg s in the right triangle shown?
45
512
OA. 5
45°

Answer:

d ≈ 1.398 meters

Step-by-step explanation:

The circumference (C) of a cylindrical tank is related to its diameter (d) through the formula:

C = πd

Given that the circumference is 4.4 meters, we can solve for the diameter:

4.4 = πd

To find the diameter (d), divide both sides of the equation by π:

d = 4.4 / π

Using a calculator, we can approximate the value of π to be approximately 3.14159:

d ≈ 4.4 / 3.14159

Calculating this value, we find:

d ≈ 1.398 meters

Therefore, the diameter of the cylindrical tank is approximately 1.398 meters.

The sampling technique used in this scenario is Random sampling

The correct answer is an option (a)

We know that the random sampling is nothing but a method of choosing a sample of observations from a population to make assumptions about the population. It is also called as a porbability sampling.

It  allows for the randomization of sample selection.

There are four random sampling methods –

simple random sampling,

systematic sampling,

stratified sampling,

and cluster sampling.

In random sampling, the randomized selection of a small segment of individuals or members from a whole population.

Here, the soda bottle company  have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

Therefore,  the sampling technique used: Random

The correct answer is an option (a)

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The complete question is:

Select the sampling technique used:

A soda bottling company needs to test the quality of the bottles they produce. They have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

a) Random

b) Stratified

c) Cluster

d) Systematic

e) Convenience

Answer:

Step-by-step explanation:

2 .

a )

     A - 3

     B - 5

     C  - 16

    D - 3

    E - 1

b)

    i) 16

    ii) 28 / 5 = 5 . 6 ( if we round it off then the answer is 6 )

c)

    Mode of data is - A , B , C , D

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

Step-by-step explanation:

The best conclusion for her to come to: D. this could easily happen with a fair coin after only 3 flips.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly tossed.

This ultimately implies that, the best conclusion for her to come to is that this could easily happen with a fair coin after only 3 flips considering 2 of the three coins come up tails.

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Answer:

x+10=45

x+10-45=0

x-35=0

x=35

The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.

To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.

Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.

Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.

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The speed of the aeroplane per hour during the journey is (d) 1550 km/hr.

The time the aeroplane would take to reach its destination if it starts on schedule is T.The distance from the starting point to its destination is D.The speed of the plane from the starting point to its destination is S.When the plane starts 1.5 hours late, it takes T + 1.5 hours to reach its destination at the scheduled time.The distance traveled by the plane under this circumstance is still D.

When the pilot increases the speed of the plane by 800 km/h, the time it takes to travel from the starting point to the destination is reduced by 1.5 hours. So, the time taken to travel the distance D is (T - 1.5) hours.The formula to find speed is distance divided by time.Using these values we can find the speed of the aeroplane.

Solving the equation,D/S = T... equation [1]D/S+800 = T - 1.5... equation [2]Substitute the value of T from equation [1] in equation [2], we get:D/S + 800 = D/(S + 800) - 1.5Solving the equation, we get:S2 - 400S - 3,20,000 = 0S = 1550 km/hr

Therefore, the speed of the aeroplane per hour during the journey is (d) 1550 km/hr.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

It basically means to lessen or reduct the amount.

answer: 1/16

If you flip a coin 4 times, the probability of getting all heads is 1/16.

Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

Answer:

y=2/7x+9

Step-by-step explanation:

Slope-intercept form is written y=mx+b.

y= also known as f(x), and is always by itself in slope-intercept form.

m= the slope.

x= the variable written to the right of the slope.

b= the y-intercept.

We know that the slope is 2/7 and the y-intercept in the equation is 9. Therefore, we can plug these numbers into the equation. So...

y=2/7x+9

is the correct equation written in slope-intercept form.

Hope this helps!! Have an amazing day (^人^)

Answer:

f(0) = -3

x increases by 1 f(x) increase by 2

f(x) = 2x -3

Step-by-step explanation:

Looking at the graph

f(0) means when x =0 the value of y = ?

when x = 0 y = -3

f(1) means when x = 1  y = ?

When x = 1 y = -1

y increased from -3 to -1 so it increased by 2

f(x) = ax+b  where a is the increase and b is the value at x =0

f(x) = 2x -3

The remaining zeros of each function are given as follows:

3. 4 + i.

4. 4i and 2 - square root of 5.

For function 3, we must consider that when we have a complex root, it's conjugate is also a root of the function.

The complex root for this problem is given as follows:

4 - i.

For the conjugate, the real part remains constant, while the signal of the imaginary part is exchanged, hence the remaining root is given as follows:

4 + i.

The same is applied for one of the roots of function 4. Considering the complex root of -4i, the conjugate 4i is one of the remaining roots.

Additionally, as 2 + square root of 5 is a root, 2 - square root of 5 is another remaining root of the function.

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The power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

To find the power series expansion of the product f(x)g(x), we need to multiply the power series expansions of f(x) and g(x) and collect like terms.

First, let's find the power series expansion of f(x):

\(f(x) = e^56 - 2(5x)^"\)

Using the formula for the power series expansion of e^x:

\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...\)

We can write the power series expansion of f(x) as:

\(f(x) = e^56 - 2(5x)^"\)

\(= (1 + 56 + (56^2)/2! + (56^3)/3! + ...) - 2(5x)^(1)\)

= \(1 - 5x + (56 - 25x^2) +\)...

Now let's find the power series expansion of g(x):

g(x) = sin 8x

= (8x) - (8x)^3/3! + (8x)^5/5! - ...

Finally, we can multiply the power series expansions of f(x) and g(x) to get the power series expansion of f(x)g(x):

\(f(x)g(x) = (1 - 5x + (56 - 25x^2) + ...) * ((8x) - (8x)^3/3! + (8x)^5/5! - ...)\)

\(= (8x) - (40x^2) + (568x^2)/2! + ((56-8*8)/2!)x^4 + ...\)

Collecting like terms up to order 3, we get:

\(f(x)g(x) = (8x) - (40x^2) + (224x^3)/3! + ...\)

Therefore, the power series approximation of f(x)g(x) up to order 3 is:

\(e^56 sin 8x - 22(5x)sin 8x - 2e^56(5x) + 22(5x)^2 sin 8x\)

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The measure of angle A, B, C are 60°,60°,60°

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The sum of angle in a polygon is 180°. i.e

A+B + C = 180°

therefore we can say that;

2x+2x + 3x-30 = 180

7x -30 = 180

7x = 180+30

7x = 210

divide both sides by 7

x = 210/7 = 30

therefore ;

angle A = 2× 30 = 60°

angle B = 2×30 = 60°

angle C = 3×30-30 = 90-30 = 60°

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The mouse's impact speed is approximately 14 m/s, and its direction is downward.

- Initial horizontal velocity of the owl: 10 m/s

- Vertical displacement of the mouse: 10 m

- Acceleration due to gravity (g): 9.8 m/s²

```

      |

      | 10 m

      |

O--------M

```

Here, O represents the initial position of the mouse (where it was dropped) and M represents the position where the mouse lands.

For the horizontal motion:

- Initial horizontal velocity (u) = 10 m/s

- Final horizontal velocity (v) = ? (this will remain constant)

- Horizontal displacement (s) = ? (we are not given this information, but it's not necessary to solve for the impact speed)

For the vertical motion:

- Initial vertical velocity (u) = 0 m/s (since the mouse was dropped vertically)

- Final vertical velocity (v) = ? (this will be the impact speed we're looking for)

- Vertical displacement (s) = -10 m (negative because it's downward)

We can use the equation s = ut + (1/2)at² to solve for time (t), as the horizontal and vertical motions are independent.

For the vertical motion:

s = ut + (1/2)at²

-10 = 0 + (1/2)(-9.8)t²

-10 = -4.9t²

Simplifying the equation, we get:

t² = 2.04

t ≈ 1.43 s (taking the positive square root since time cannot be negative)

Now, we can find the impact speed using the equation v = u + at:

v = 0 + (-9.8)(1.43)

v ≈ -14 m/s (negative sign indicates downward direction)

The mouse's impact speed is approximately 14 m/s, and its direction is downward.

So, the mouse's impact speed is 14 m/s in the downward direction.

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Step-by-step explanation:

The total of the number of computers he sold in 2015 is 67.

The total of the number of computers he sold in 2016 is 61.

The total of the number of computers he sold in 2017 is 71.

He sold 35 computers in Quarter 1, 24 in Quarter 2, 61 in Quarter 3, and 79 in Quarter 4.

He sold the most computers in 2017 and the least in Quarter 2.

Therefore, to find the total number of computers he sold all time, we add 67, 61, and 71 together to get 199.

Hope this helped!

Answer with Step-by-step explanation:

From the given table

(a)

In quarter 1

Computer sold in 2015=12

Computer sold in 2016=15

Computer sold in 2017=8

Total computer sold in quarter 1=12+15+8=35

In quarter 2

Computer sold in 2015=9

Computer sold in 2016=10

Computer sold in 2017=5

Total computer sold in quarter 2=9+10+5=24

In quarter 3

Computer sold in 2015=21

Computer sold in 2016=17

Computer sold in 2017=23

Total computer sold in quarter 3=21+17+23=61

In quarter 4

Computer sold in 2015=25

Computer sold in 2016=19

Computer sold in 2017=35

Total computer sold in quarter 4=25+19+35=79

In 2015

Total number of computer sold=12+9+21+25=67

In 2016

Total number of computer sold=15+10+17+19=61

In 2017

Total number of computer sold=8+5+23+35=71

(b)He sold the most computers in 2017

(c) He sold the least computers in quarter 2.

Step-by-step explanation:

I assume the question really looks like

-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.

so,

3b² + 2b - 5 - (-4b² + 4b - 4) =

= 3b² + 2b - 5 + 4b² - 4b + 4 =

= 7b² - 2b - 1

Answer: 324

Step-by-step explanation:

Ratio--> 1/0.15=x/48.6

Do the butterfly method of multiplying

0.15x=48.6

Divide by 0.15 on both sides

48.6/0.15=324

This type of research aims to provide an in-depth understanding of the group's cultural context and the ways in which its members make sense of their world.

If you observe a group in order to determine its norms, values, rules, and meanings, you are engaging in qualitative research, specifically ethnographic research. Ethnographic research is a methodological approach that involves immersing oneself in a particular social group or culture to gain a deep understanding of their beliefs, behaviors, and practices.

Through participant observation, the researcher becomes an active member of the group, observing their interactions, rituals, and social dynamics. This method allows for the collection of rich, detailed data about the group's norms, values, rules, and meanings. By spending a significant amount of time with the group, the researcher can uncover the underlying cultural patterns that guide the group's behavior and decision-making processes.

Ethnographic research involves a holistic and interpretive approach, focusing on capturing the subjective experiences and perspectives of the group members. It often includes methods such as interviews, field notes, and audiovisual recordings to document and analyze the data.

Overall, this type of research aims to provide an in-depth understanding of the group's cultural context and the ways in which its members make sense of their world.

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Answer:`211

123123

Step-by-step explanation:

Answer:

76.92 percent win rate 23.08 lose rate

Step-by-step explanation:

Answer:

OPTION C: 2 < x < 6

Step-by-step explanation:

3.5x - 10 > -3

Adding 10 to both sides:

3.5x > 7

Dividing by 3.5:

x > 2

8x - 9 < 39

Adding 9 to both sides:

8x < 48

Dividing by 8:

x < 6

Therefore, the solution set of the compound inequality is:

2 < x < 6

The probability of guessing at least 4 out of 10 correctly is approximately 0.3770.

In this scenario, each question has five choices, so the probability of guessing a question correctly is 1/5, and the probability of guessing incorrectly is 4/5. Since the student is guessing on each question, we can model this as a binomial distribution problem.

To find the probability of guessing at least 4 out of 10 correctly, we need to calculate the probability of guessing 4, 5, 6, 7, 8, 9, or 10 questions correctly and sum up these probabilities.

Using the binomial probability formula, the probability of guessing exactly k questions correctly out of n questions is given by the formula P(X=k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of questions, k is the number of correct guesses, and p is the probability of guessing a question correctly.

In this case, n = 10, k ranges from 4 to 10, and p = 1/5. We can calculate the probability for each value of k and then sum them up to find the overall probability of guessing at least 4 out of 10 correctly.

Calculating these probabilities and summing them up, we find that the probability of guessing at least 4 out of 10 correctly is approximately 0.3770, or 37.70%.

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Answer:

Step-by-step explanation:

The transformation (x,y) →(0.75x,0.75y)  represents a dilation centered at the origin. which is the correct answer would be an option (D).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

On the coordinate plane, you may dilate figures. The origin is frequently utilized as the center of dilatation. If you are distorting a figure centered at the origin, you may find the points in the image by multiplying the coordinates of the points in the preimage by the scale factor.

As per the given option, we can see the scale factor i.e. 0.75 is multiplying the coordinates of the points (x, y) in option (D).

Thus, the transformation (x,y) →(0.75x,0.75y)  represents a dilation centered at the origin.

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Answer:

119,318

Step-by-step explanation:

We will see that she drinks more than 3 liters, so she meets her goal.

We know that her goal is to drink 3 liters per day.

She drinks 8 glases, each of 450ml of water.

Then the amount that she drinks is:

8*450 ml = 3,600 ml

Now we must apply a change of units.

And we know that:

1,000 ml = 1L

Then the amount that she drinks, in liters, is:

(3,600/1,000)L = 3.6 L

So yes, she meets her goal.

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