A large manufacturing firm is interested in estimating the average distance traveled to work by its employees. Past studies of this type indicate that the standard deviation of these distances should be in the neighborhood of 2 miles. How many employees should be sampled if the estimate is to be within 0.1 mile of the true average, with 95% confidence?

The rate at which calories are burned was gotten by finding the slope of the graph which gives; 4 calories per minute

To get the slope of a linear graph, we will take two coordinates and make use of the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

The two coordinates we will pick for this slope are;

(10, 40) and (20, 80)

Thus;

Slope = (80 - 40)/(20 - 10)

Slope = 40/10

Slope = 4

Since the y-axis represents calories burned and the x-axis represents minutes of exercise, then we can say that;

Rate at which  calories get burned by bike riding = 4 calories per minute

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Answer: +6=2−62 its =68

Answer:

\(m = 12\)

Step-by-step explanation:

\(m + 6 = 2m - 6 \\ 2m - m = 6 + 6 \\ m = 12 \\ \\ hope \: it \: helps... \\ pls \: mark \: as \: brainliest\)

To find the minimum score of the top 2.5% of students, we need to calculate the z-score corresponding to the 97.5th percentile and then convert it back to the original SAT score scale.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean (1175), and σ is the standard deviation (120).

To find the z-score corresponding to the 97.5th percentile, we need to find the z-score value that leaves 2.5% in the tail of the distribution (to the right).

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can solve for x (the SAT score) in the z-score formula:

1.96 = (x - 1175) / 120

Multiply both sides by 120:

1.96 * 120 = x - 1175

235.2 = x - 1175

Add 1175 to both sides:

235.2 + 1175 = x

1410.2 = x

Therefore, the minimum score of the top 2.5% of students is approximately 1410.

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A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

We have the parabola with equation y = 4x².

We have to determine the shape and direction of it.

If we compare it to the standard equation y = ax² + bx + c, we can see that a = 4, b = 0 and c = 0.

As the value of a is positive, the parabola will open upward.

The parameter has an absolute value greater than 1. This means that y increases "faster" relative to x that a parabola with a = 1.

This means that the parabola will be narrow about its line of symmetry which we call vertical strecth.

Answer:

Because a is positive the parabola opens upward.

Because a has an absolute value larger than 1 the parabola is narrow about its line of symmetry which we call vertical stretch.

We employ a two-tailed test when determining if a sample mean would be either significantly higher and otherwise significantly lower than what the population mean.

A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution.

Thus, we employ a two-tailed test when determining if a sample mean would be either significantly higher and otherwise significantly lower than what the population mean.

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It is reasonable to estimate that about 40 students are in band.

To determine if it's reasonable to estimate that about 40 students are in band, we need to first find out how many students are on the debate team and how many participate in various sports.

We know that 2/5 of the students are on the debate team. So, the number of students on the debate team is:

2/5 x 260 = 104

We also know that 45% of the students participate in various sports. So, the number of students in sports is:

45% x 260 = 117

To find out how many students are in band, we can subtract the number of students on the debate team and the number of students in sports from the total number of seventh graders:

260 - 104 - 117 = 39

Thus, this number of students in band is reasonable.

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Yes, it is reasonable to estimate that about 40 students are in the band.

it is reasonable to estimate that about 40 students are in the band

To see why, let's break down the number of students in each activity based on the given information:

Debate team: 2/5 of 260 students = 104 students

Sports: 45% of 260 students = 117 students

Band: the remaining students after subtracting the debate team and sports participants = 260 - 104 - 117 = 39 students

So, according to this breakdown, there are 39 students in the band. Since the question asks if it's reasonable to estimate that about 40 students are in the band, the answer is yes.

However, it's important to note that this estimate is based on rounding and assuming that the given percentages are exact.

In reality, the actual number of students in the band could be slightly different.

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This contract is made on [DATE] between [TOM], owner of [AUTOMOTIVE PARTS STORE] located at [ADDRESS] (hereinafter referred to as "Seller"), and [PETE], residing at [ADDRESS] (hereinafter referred to as "Buyer"). Tom should bear the risk of loss because he is the seller and has not yet delivered the muffler to Pete. According to the UCC, the risk of loss typically transfers to the buyer upon physical delivery of the goods, which has not occurred in this case. Additionally, Tom's expertise in the specialty vehicle parts industry suggests that he should be responsible for any potential risks associated with the muffler until it is delivered.

1. Sale of Muffler

Seller agrees to sell and Buyer agrees to purchase a muffler for a 1969 Cadillac Eldorado, silver in color, for the price of $600 (hereinafter referred to as "the Muffler").

2. Delivery

Seller shall deliver the Muffler to Buyer's address in Newark, Delaware by May 1, 2015.

3. Payment

Buyer shall pay Seller the purchase price of the Muffler in full upon delivery.

4. Warranties

Seller warrants that the Muffler is free from defects in materials and workmanship. Seller further warrants that the Muffler will be fit for its intended purpose.

5. Governing Law

This contract shall be governed by and construed in accordance with the laws of the State of New York.

6. Entire Agreement

This contract constitutes the entire agreement between the parties with respect to the subject matter hereof and supersedes all prior or contemporaneous communications, representations, or agreements, whether oral or written.

7. Severability

If any provision of this contract is held to be invalid or unenforceable, such provision shall be struck from this contract and the remaining provisions shall remain in full force and effect.

8. Waiver

No waiver of any provision of this contract shall be effective unless in writing and signed by both parties.

9. Notices

All notices and other communications hereunder shall be in writing and shall be deemed to have been duly given when delivered in person, upon the first business day following deposit in the United States mail, postage prepaid, certified or registered, return receipt requested, addressed as follows:

10. Headings

The headings in this contract are for convenience only and shall not affect its interpretation.

11. Counterparts

This contract may be executed in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

IN WITNESS WHEREOF, the parties have executed this contract as of the date first written above.

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The distance between the two planes after 4 hours is approximately 150 km.

to find out how far apart the planes are after 4 hours, we can use the concept of vectors.

Let's start by finding the positions of the two planes after 4 hours.

The first plane flies at a speed of 110 km/h in a direction of 280°. To find its position after 4 hours, we can use the formula: distance = speed × time. So, the distance traveled by the first plane is 110 km/h × 4 hours = 440 km.

To determine the position of the first plane, we need to convert the direction (280°) into components. The x-component is given by: cos(280°) × distance = cos(280°) × 440 km. The y-component is given by: sin(280°) × distance = sin(280°) × 440 km.

Similarly, for the second plane, which flies at a speed of 250 km/h in a direction of 200°, the distance traveled after 4 hours is 250 km/h × 4 hours = 1000 km. To determine its position, we need to convert the direction (200°) into components. The x-component is given by: cos(200°) × distance = cos(200°) × 1000 km. The y-component is given by: sin(200°) × distance = sin(200°) × 1000 km.

Now, let's calculate the x and y components for both planes:

For the first plane:
x-component = cos(280°) × 440 km
y-component = sin(280°) × 440 km

For the second plane:
x-component = cos(200°) × 1000 km
y-component = sin(200°) × 1000 km

the distance between the two planes, we can use the distance formula, which is given by: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the positions of the first and second planes respectively.

Now, substitute the values we calculated into the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((cos(200°) × 1000 km - cos(280°) × 440 km)^2 + (sin(200°) × 1000 km - sin(280°) × 440 km)^2)

After evaluating the above expression, the distance between the two planes after 4 hours is approximately 150 km.

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Answer:

564

Step-by-step explanation:

56

Answer:

A is equal to 3 and B is equal to 2

The derivative of -3e⁴u with respect to x is -3e⁴u * du/dx.

To find the derivative of the given function, we can apply the chain rule. The derivative of a function of the form f(g(x)) is given by the product of the derivative of the outer function f'(g(x)) and the derivative of the inner function g'(x).

In this case, we have: f(u) = -3e⁴u

Applying the chain rule, we have: f'(u) = -3 * d/dx(e⁴u)

Now, the derivative of e⁴u with respect to u can be found using the chain rule again: d/dx(e⁴u) = d/du(e⁴u) * du/dx

The derivative of e⁴u with respect to u is simply e⁴u, and du/dx is the derivative of u with respect to x.

Putting it all together, we have: f'(u) = -3 * e⁴u * du/dx

So, the derivative of -3e⁴u with respect to x is -3e⁴u * du/dx.

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Answer:

Statement (b) is equivalent to statement (c), but neither is equivalent to statement (a).

Step-by-step explanation:

Let \(F\) denote that "Fido is our fish's name" and let \(R\) denote that "Rex is our dog's name". The statements listed in this question would then become:

Apply de Morgan's Law \(\lnot (P \land Q) \iff (\lnot P) \lor (\lnot Q)\) to rewrite statement (b). Let \(P = (\lnot F)\) and \(Q = (\lnot R)\). By de Morgan's Law:

\(\begin{aligned} & \lnot ((\lnot F) \land (\lnot R)) \\ \iff \; & \lnot (P \land Q)\\ \iff \; & (\lnot P) \lor (\lnot Q) && (\text{by de Morgan's Law}) \\ \iff \; & (\lnot (\lnot F)) \lor (\lnot (\lnot R)) \\ \iff \; & F \lor R\end{aligned}\).

In other words, statement (b) \(\lnot ((\lnot F) \land (\lnot R))\) is equivalent to statement (c) \(F \lor R\).

Statement (a) \(F \implies R\) isn't equivalent to \(F \lor R\).

For example, when \(F = \texttt{True}\) and \(R = \texttt{False}\), \(F \implies R\) would be false since \(\texttt{True}\) does not imply \(\texttt{False}\). However, for the same \(F\) and \(R\), \(F \lor R\) would be true since \(F = \texttt{True}\!\).

Answer:

420 students stayed for history.

Step-by-step explanation:

35% of 1200 is 420

Area of fabric needed to cover the lampshade is 768 \(cm^2\)

What is Fabric?

Fabric can be either a cloth made by weaving or knitting, or it can be the framework of a construction. Some individuals use twisting, felting, or braiding to create fabrics. When I remark that termites are "gradually eating away at the fabric of the building," I'm referring to either the floor or the walls.

The phrase may also be used to refer to the fundamental framework or organization of society. For instance, "the fabric of society" refers to its fundamental structure, which includes all of its practices and beliefs.

I'm referring to the body of the car when I remark, "I heard clanking noises in the fabric of the car." This phrase can also be used to describe the body of an aircraft.

Length= 16 cm

Breath= 12 cm

Area= 4(16*12)  \(cm^2\)

Area=768 \(cm^2\)

Hence, Fabric needed is 768 \(cm^2\)

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The solution to the differential equation with the given initial conditions is: y = 2 e^(4t) - (1/2) t e^(4t)

To solve this differential equation, we first find the characteristic equation by assuming a solution of the form y = e^(rt). Plugging this into the differential equation, we get:

r^2 e^(rt) - 8re^(rt) + 16e^(rt) = 0

Factoring out the e^(rt) term, we get:

e^(rt) (r^2 - 8r + 16) = 0

The quadratic equation r^2 - 8r + 16 = 0 has a double root of r = 4. Therefore, the general solution to the differential equation is:

y = c1 e^(4t) + c2 t e^(4t)

To solve for the constants, we use the initial conditions. First, we have y(0) = 2, which gives us:

c1 = 2

Next, we have y'(0) = 0, which gives us:

c1 (4) + c2 (0) = 0

Solving for c2, we get:

c2 = -c1/4 = -1/2

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Answer:

The answer should be 12

Step-by-step explanation

he has 60 in his account already so add 35 and 15 (60+35+15=110) then add 48+24+50 which equals 122. Now subtract 110-122 and you'll get 12. so the answer is 12.

Step-by-step explanation:

a probability is always

desired cases / total possible cases.

there is the theoretical probability in such cases, where we simply assume that all sides of such a die (or solid) truly have the same probability.

and then we have experimental probability, where we use only the actual data we got in the experiments to calculate the probability of that particular die (with all its actual internal imperfections) to roll certain results.

so, in our experiments how many total cases do we have ?

200.

how many desired cases (a number greater than 10, that means 11 or 12 as result) do we have ?

well, the sum of all appearances of 11s and 12s :

16 + 18 = 34

that means our experimental probability to get a number greater than 10 is

34/200 = 17/100 = 0.17

FYI

while the theoretical probability with an ideal die is

total cases : 12 (1 .. 12)

desired cases : 2 (11, 12)

the probability is

2/12 = 1/6 = 0.166666666...

it is actually a tiny little bit lower than what we observed in the experiments.

Answer:

B

Step-by-step explanation:

Move it down 3 units, then rotate it.

Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.

The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.

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The correlation coefficient between age and hourly wage for the given data set is approximately 0.355, rounded to three decimal places.

To calculate the correlation coefficient, we can use statistical software or tools like Excel, Python, or R. Using technology, we input the values of age and hourly wage into the software or tool. By performing the correlation calculation, we obtain the correlation coefficient, which measures the strength and direction of the relationship between the two variables.

For the given data set, the age values are 35, 47, 62, 19, 26, 22, 45, 53, 49, and 33, while the corresponding hourly wage values are $16.30, $17.95, $26.80, $11.95, $10.10, $13.40, $21.30, $45.00, $35.00, and $14.50. After performing the correlation calculation using technology, we find that the correlation coefficient between age and hourly wage is approximately 0.355. This value indicates a positive but weak correlation between age and hourly wage.

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C is the answer

Step-by-step explanation:

but I think is C

The value of u in the special triangle is 2√3

The complete question is added as an attachment

From the attached figure, the value of u can be calculated using the following sine trigonometry ratio

sin(x) = Opposite/Hypotenuse

Where

x = 30

Opposite = u

Hypotenuse = 4√3

Substitute the known values in the above equation

sin(30) = u/4√3

Multiply both sides of the equation by 4√3

u = 4√3 * sin(30)

Evaluate the trigonometry expression sin(30)

u = 4√3 * 1/2

Evaluate the product

u = 2√3

Hence, the value of u in the special triangle is 2√3

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We can use proportions to estimate the number of homes in Claiborne County that can access the Internet based on the survey results.

If 135 out of 300 homes surveyed can access the Internet, then the proportion of homes in Claiborne County that can access the Internet can be estimated as:

135/300 = x/45000

where x is the number of homes in Claiborne County that can access the Internet.

Solving for x, we get:

x = (135/300) * 45000 = 20,250

Therefore, we would expect approximately 20,250 homes in Claiborne County to be able to access the Internet based on the survey results. Note that this is just an estimate, and the actual number of homes in Claiborne County that can access the Internet may be different.

The United States has a population of about 320 million, so if homicides were proportional to Honduras' rate of homicide, we would expect about 12,800 deaths due to homicides in the United States.

This is calculated by taking the population of the United States (320 million) and multiplying it by the Honduras' homicide rate of 40 per 100,000 people.


To calculate this, we first need to find Honduras' homicide rate. The World Bank has this information, which states that the rate is 40 per 100,000 people. We then need to take the population of the United States (320 million) and multiply it by the rate.

This equals 128 million homicides per 100,000 people in the United States. This comes out to 12,800 deaths due to homicides in the United States. Round this to the nearest person, and you get 12,800.

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Answer:

f(-3) = -9

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

We are given a graph of a quadratic function f(x).

Step 2: Evaluate

f(-3) is x = -3 for the function f(x). According to the graph, when x = -3, y = -9.

∴ f(-3) would equal -9.

The value of f(-3) from the graph of the quadratic function is -9

A polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables. Polynomials are classified based on degree as linear, quadratic, cubic etc.

A quadratic equation is a polynomial of degree 2.

The value of f(-3) can be obtained from the graph. From the graph, the value of f(-3) is -9

The value of f(-3) from the graph of the quadratic function is -9

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Answer:

There are 12, 3-point problems & 16, 4-point problems

Step-by-step explanation:

3-point problem = x

4-point problem = y

Total points = 100

Total problems = 28

According to given statement; x+y=28  

The calculated volume of the model space is 1657.92 cubic inches

From the question, we have the following parameters that can be used in our computation:

The model space made from:

The volume of the model space is calculated as

Volume = Cone + Cylinder + Hemisphere

Using the volume formulas, we have

Volume = 1/3πr²h + πr²h + 2/3πr³

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3 * 3.14 * 6² * 8 + 3.14 * 6² * 8 + 2/3 * 3.14 * 6³

Evaluate

Volume = 1657.92

Hence, the volume of the model space is 1657.92 cubic inches

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The measure of each angle is:

Smallest angle: 50/11

Second smallest angle: 200/11

Largest angle: 860/11

Let's denote the measures of the three angles as follows:

Let x be the measure of the second smallest angle.

Then, the measure of the smallest angle is (1/4)x.

The measure of the largest angle is 5x - 20.

According to the given information, the sum of the measures of the angles of a triangle is 180°. Therefore, we can write the equation:

(1/4)x + x + (5x - 20) = 180

To solve this equation, we can combine like terms and simplify:

(1/4)x + x + 5x - 20 = 180

(20/4)x + 6x - 20 = 180

5x + 6x - 20 = 180

11x - 20 = 180

11x = 200

x = 200/11

Now that we have found the value of x, we can substitute it back into the expressions for the angles:

The measure of the smallest angle = (1/4)(200/11) = 50/11

The measure of the second smallest angle = 200/11

The measure of the largest angle = 5(200/11) - 20 = 980/11 - 20 = 860/11

Therefore, the measure of each angle is:

Smallest angle: 50/11

Second smallest angle: 200/11

Largest angle: 860/11

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Answer: 1) 4 1/12

2) 3 11/15

Step-by-step explanation: