there are 36 students in a class. 1/3 of the class brings lunch and 1/2 of them order lunch. How many of them eat lunch each day​

Rounding to the nearest tenth, the length of side k is approximately 23.3 feet. The answer is 23.3 ft.

To solve for the length of side k using the Law of Sines, we can use the formula:

sin(K) / k = sin(J) / j

Given that ∠J measures 40°, ∠K measures 90°, and side j is 15 feet, we can substitute these values into the equation:

sin(90°) / k = sin(40°) / 15

Since sin(90°) = 1, the equation simplifies to:

1 / k = sin(40°) / 15

To find k, we need to isolate it on one side of the equation. We can achieve this by taking the reciprocal of both sides:

k = 15 / sin(40°)

Using a calculator, we can evaluate sin(40°) ≈ 0.6428:

k ≈ 15 / 0.6428 ≈ 23.328.

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Answer:

D

Step-by-step explanation:

An equation that describes the relationship shown in the table is y = 2x + 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (11 - 7)/(5 - 3)

Slope (m) = 4/2

Slope (m) = 2.

At data point (3, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = 2(x - 3)

y = 2x - 6 + 7

y = 2x + 1

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Complete Question:

The table snows a linear relationship between x and y.

x     y

3     7

5     11

10    21

Create an equation that describes the relationship shown in the table.

Move the correct answer to each box. Not all answer will be used.

The number of bales purchased for the farm is n = 7 bales

Given data ,

Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week

Now , Dan buys new hay for the farm every week

To find the total amount of hay needed for the week, we multiply the amount consumed by each horse by the number of horses:

Total hay needed = 10 horses x 140 pounds/horse = 1400 pounds

To determine the number of bales needed, we divide the total hay needed by the weight of each bale:

Number of bales needed = Total hay needed / Weight of each bale

On simplifying the equation , we get

Number of bales needed for agri supply = 1400 / 75 = 18.667

Number of bales needed for farm supply = 1400 / 150 = 9.33

Number of bales needed for tractor supply = 1400 / 200 = 7 bales

Number of bales needed ≈ 7 bales when there is not leftover

Hence , there is no leftover at the end of the week if he purchases 7 bales from the tractor supply

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The complete question is attached below :

Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week. Dan buys new hay for the farm every week. Where should Dan purchase hay from if he does not want any hay leftover at the end of the week? How many bales should he purchase?

Acceleration rate of change of velocity can be written as

a = (v₁ - v₀)/t.

The given keyword is,

Acceleration

Since we know that,

Acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.

Now let,

a =  is the acceleration

v₁ is the final velocity

v₀ is the initial velocity

t is the time interval

Δv is the small change in the velocity

Therefore,

The acceleration = ( final velocity - initial velocity)/time

Thus,

The acceleration be,

⇒ a = (v₁ - v₀)/t

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The sum of magnitude of vectors is 17.4 and direction is 88 degree.

Hence, option 3 is correct.

Given that,

Vector A: magnitude = 12 and direction = 60 degree

Vector B: magnitude = 10 and direction = 150 degree

Find the x and y components using the following formulas,

Ax = AcosΘ and Ay = AsinΘ

Substitute the values,

Ax = 12cos(60) and Ax = 6

Ay = 12sin(60) and Ay = 10.39

For vector B,

By using the same formulas,

Bx = 10cos(150) and  Bx = -5

By = 10sin(150)  and By = 7.66

We have the x and y components of both vectors,

Add them,

Rx = Ax + Bx

⇒ Rx = 6 + (-5)

⇒ Rx = 1

⇒ Ry = Ay + By

⇒ Ry = 10.39 + 7.66

⇒ Ry = 18.05

Finally, we can find the magnitude and direction of the resulting vector,

Magnitude = √(R²x + R²y)

Therefore, after putting values we get,

Magnitude = 17.4

Direction = [tex]tan^{-1}[/tex](Ry/Rx)

                = [tex]tan^{-1}[/tex](18.05/1)

                = 88 degrees

Therefore, the sum of the two vectors is a vector with magnitude 17.4 and direction 88 degrees.

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The probability that a data value is between 48 and 52 is 31.1 %

Given data ,

To find the probability that a data value is between 48 and 52 in a normal distribution with a mean of 50 and a standard deviation of 5, we can use the Z-score and the standard normal distribution.

First, we need to standardize the values of 48 and 52 by calculating their respective Z-scores.

Z-score formula: Z = (X - μ) / σ

X is the data value,

μ is the mean, and

σ is the standard deviation.

For 48:

Z1 = (48 - 50) / 5 = -0.4

For 52:

Z2 = (52 - 50) / 5 = 0.4

The probability of a Z-score between -0.4 and 0.4 can be found by subtracting the cumulative probability associated with -0.4 from the cumulative probability associated with 0.4.

Using a standard normal distribution table or calculator, we find that the cumulative probability for Z = -0.4 is approximately 0.3446, and the cumulative probability for Z = 0.4 is approximately 0.6554.

Hence , the probability of a data value being between 48 and 52 given by

P(48 ≤ X ≤ 52) ≈ 0.6554 - 0.3446 ≈ 0.3108 or 31.1%

Hence , the probability is 31.1 %

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Answer:

1. $6,076

2. $55076

Step-by-step explanation:

price increase: 49,000x12.4%

12.4%=0.124

49,000x0.124=6,076

price of next model:49000x0.124=6076

6076+49000=55076

Answer:

Step-by-step explanation:

To find MDG, we need to calculate the length of line segment DG.

Using the distance formula, the length of a line segment between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the length of line segment DG:

DG = √((-4 - 2)^2 + (9 - 5)^2)

= √((-6)^2 + (4)^2)

= √(36 + 16)

= √52

= 2√13

Therefore, MDG is equal to 2√13.

Now, let's analyze the line segments DE and DG:

Line segment DE: The coordinates of D are (2, 5) and the coordinates of E are (-4, -4). By calculating the length of DE using the distance formula, we can determine the length of DE.

DE = √((-4 - 2)^2 + (-4 - 5)^2)

= √((-6)^2 + (-9)^2)

= √(36 + 81)

= √117

= √(9 * 13)

= 3√13

Therefore, the length of line segment DE is 3√13.

Line segment DG: We have already calculated the length of DG as 2√13.

From the calculations, we can conclude that DE and DG have different lengths. DE is 3√13 while DG is 2√13.

In summary, line segments DE and DG have different lengths.

Possible numbers: 345, 354, 435, 453, 534, 543.

345+354+435+453+534+543=2664

if the terminal point determined by t is in quadrant I, then tan(t) = sin(t)/sqrt(1 - sin^2(t)).

If the terminal point determined by t is in quadrant I, then both sine and tangent are positive. We can use the identity:

tan(t) = sin(t)/cos(t)

to express tangent in terms of sine. Since the terminal point is in quadrant I, cosine is positive, so we can use the Pythagorean identity:

sin^2(t) + cos^2(t) = 1

to solve for cosine:

cos(t) = sqrt(1 - sin^2(t))

Substituting this expression for cosine in the formula for tangent, we get:

tan(t) = sin(t)/cos(t) = sin(t)/sqrt(1 - sin^2(t))

what is quadrant?

A quadrant is one of the four regions that a coordinate plane is divided into by the x-axis and the y-axis. The x-axis is a horizontal line that runs left and right through the plane, and the y-axis is a vertical line that runs up and down through the plane. The point where the x-axis and the y-axis intersect is called the origin.

Each quadrant is labeled with a Roman numeral (I, II, III, or IV) to distinguish it from the others. Quadrant I is the region in the upper-right corner of the plane, where both the x and y coordinates are positive. Quadrant II is the region in the upper-left corner of the plane, where the x-coordinate is negative and the y-coordinate is positive.

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To find out how much Jeff is paid per hour of work, we need to divide his total earnings by the number of hours he worked.

Total earnings: $243.75

Number of hours worked: 25

Hourly pay rate: Total earnings / Number of hours worked

Hourly pay rate: $243.75 / 25 = $9.75

Therefore, Jeff is paid $9.75 per hour of work

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Answer:

-------------------

Use the formula:

Plugging in the given values, solve for h:

The height of the prism is 6 cm.

The linear equation be 2lw + 2lh + 2wh + lb and total area is 2200 square feet.

Assume that,

l is the length of the pool (40 feet),

w is the width of the pool (30 feet),

h is the height of the pool (5 feet),

And b is the depth of the pool (also 5 feet).

To determine the total area of the pool liner needed to line the rectangular pool on all sides and the bottom, Mr. Vern can use the following equation:

Total area = 2lw + 2lh + 2wh + lb,

Plugging in the values, we get:

Total area = 2(40)(5) + 2(30)(5) + 2(30)(5) + (40)(30) Total area = 400 + 300 + 300 + 1200 Total area = 2200

Therefore, Mr. Vern would need to cover a total area of 2200 square feet with pool liner to line his rectangular pool on all sides and the bottom.

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The probability of rolling an even number on a fair 666-sided die is 1/2. Therefore, the probability of rolling an even number twice in a row is (1/2) * (1/2) = 1/4. Rounded to 222 decimal places, the answer is 0.25.

To calculate the probability of rolling an even number with a fair 666-sided die, follow these steps:

1. Identify the total number of outcomes: There are 666 sides on the die, so there are 666 possible outcomes.
2. Identify the number of favorable outcomes: Half of the numbers on the die will be even (2, 4, 6, ...). Therefore, there are 333 even numbers.
3. Calculate the probability: Divide the number of favorable outcomes (even numbers) by the total number of outcomes (all possible rolls).

Probability = (number of even numbers) / (total number of possible rolls) = 333 / 666 = 0.5

So, the probability of rolling an even number on a fair 666-sided die is 0.5 or 50%. There's no need to round the answer to 222 decimal places as the probability is already exact.

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The standard error of the difference in sample proportions is 0.0161.

Given that an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country.

Similarly, 170 out of 1250 Americans reported being foreign born,

P₁ = 192/960 = 0.2

P₂ = 170/1250 = 0.136

The standard error of the difference in sample proportions =

[tex]\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}[/tex]

[tex]\sqrt{\frac{0.2(1-0.2)}{960} + \frac{0.136(1-0.136)}{1250}[/tex] [tex]\approx 0.0161[/tex]

Hence the standard error of the difference in sample proportions is 0.0161.

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a. The probability will be less than $400 is approximately 4.78%. b. The probability will be $800 or more is approximately 34.13%. c. The probability will be between $500 and $1000 is approximately 68.27%. d. The most expensive travel plans are approximately $1,170 or more.

a. To find the probability that family expenses for the weekend will be less than $400, we need to standardize the value using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = $400, μ = $749, and σ = $225. So, z = (400 - 749) / 225 = -1.56. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.56 is approximately 0.0594. Therefore, the probability that family expenses for the weekend will be less than $400 is about 0.0594 or 5.94%.

b. To find the probability that family expenses for the weekend will be $800 or more, we again need to standardize the value. In this case, x = $800, μ = $749, and σ = $225. So, z = (800 - 749) / 225 = 0.227. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being greater than 0.227 is approximately 0.409. Therefore, the probability that family expenses for the weekend will be $800 or more is about 0.409 or 40.9%.

c. To find the probability that family expenses for the weekend will be between $500 and $1000, we need to standardize both values and then find the area between them. For $500, z = (500 - 749) / 225 = -1.11, and for $1000, z = (1000 - 749) / 225 = 1.11. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.11 is approximately 0.1335 and the probability of a standard normal variable being less than 1.11 is approximately 0.8664. Therefore, the probability that family expenses for the weekend will be between $500 and $1000 is about 0.8664 - 0.1335 = 0.7329 or 73.29%.

d. To find the Labor Day weekend expenses for 5% of the families with the most expensive travel plans, we need to find the z-score corresponding to the 95th percentile of the normal distribution. This can be done using a standard normal distribution table or calculator, and we find that the z-score is approximately 1.645. Then, we can use the formula x = μ + zσ, where x is the value we want to find, μ is the mean, σ is the standard deviation, and z is the z-score we just found. Plugging in the values, we get x = 749 + 1.645(225) = $1,100.13. Therefore, the Labor Day weekend expenses for 5% of the families with the most expensive travel plans is about $1,100.13 or higher.
According to the American Automobile Association (AAA), families planning to travel over the Labor Day weekend are expected to spend an average of $749, with a standard deviation of $225. Assuming the amount spent is normally distributed:

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The rate of discount on the music system during the sale is 13.58%.

The rate of discount is the percentage reduction in the original price of a product during a sale.

The regular cost of the music system is $80,999 and it was sold during the sale for $69,999.

The rate of discount, we first need to find the amount of discount.

We can do this by subtracting the sale price from the regular price:

Discount = Regular price - Sale price

Discount = $80,999 - $69,999

Discount = $11,000

So the discount on the music system during the sale is $11,000.

Next, we can calculate the rate of discount as a percentage of the regular price.

We can use the formula:

Discount rate = (Discount / Regular price) x 100%

Plugging in the values we have:

Discount rate = ($11,000 / $80,999) x 100%

Discount rate = 0.1358 x 100%

Discount rate = 13.58%

The music system was discounted by 13.58% during the sale, resulting in a sale price of $69,999.

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To find the limit of F(x) as x approaches -1, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.

For x < -1, F(x) = sin(x + 1) * e^(x - 1). Since we are interested in the limit as x approaches -1, we consider values of x that are approaching -1 from the left side.Let's evaluate the left-hand limit:

lim(x→-1-) F(x) = lim(x→-1-) sin(x + 1) * e^(x - 1)

As x approaches -1 from the left side, sin(x + 1) approaches sin(0) = 0, and e^(x - 1) approaches e^(-2).

Therefore, lim(x→-1-) F(x) = 0 * e^(-2) = 0.

Now, let's evaluate the right-hand limit:

lim(x→-1+) F(x) = lim(x→-1+) F(x)

For x greater than or equal to -1, F(x) is not defined.

Since the left-hand limit and the right-hand limit are not equal, the limit of F(x) as x approaches -1 does not exist.

Therefore, lim(x→-1+) F(x) is undefined.

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The bounds for the length of the rectangular playing field are 5.9 meters ≤ length ≤ 44.1 meters. This answer is more than 100 words.

To solve this problem, we first need to know the formula for the perimeter of a rectangular field, which is 2(length + width). Since the perimeter of the field is given as 100 meters, we can write the equation as 2(length + width) = 100.
We also know that the area of a rectangular field is given by the formula length x width. We are given that the field must have an area of at least 500 square meters, so we can write the inequality length x width ≥ 500.
Now we need to find the bounds for the length. We can use the equation for the perimeter to solve for the width in terms of the length: width = (100 - 2length)/2. Substituting this expression for width into the inequality for the area, we get length x (100 - 2length)/2 ≥ 500.
Multiplying both sides by 2 and simplifying, we get length(100 - 2length) ≥ 1000. Expanding the left side, we get 100length - 2length^2 ≥ 1000. Rearranging and factoring, we get -2(length^2 - 50length + 500) ≥ 0.
Dividing both sides by -2 and flipping the inequality, we get length^2 - 50length + 500 ≤ 0. This quadratic inequality can be solved by finding the roots of the quadratic equation length^2 - 50length + 500 = 0. The roots are approximately 5.9 and 44.1.
Since the length of a field cannot be negative, the lower bound for the length is 5.9 meters. To satisfy the inequality for the area, the upper bound for the length is 44.1 meters. Therefore, the length of the rectangular playing field must be between 5.9 and 44.1 meters to have a perimeter of 100 meters and an area of at least 500 square meters.
In summary, the bounds for the length of the rectangular playing field are 5.9 meters ≤ length ≤ 44.1 meters.

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The total surface area of the cone is 67T cm².

Surface Area of the cone = πre + B

Given: radius, r = 5 cm

slant height, e = 12 cm

The base of the cone is a circle with radius r, so B = πr²

B = π(5 cm)² = 25π cm²

Now, let's find πre:

πre = π(5 cm)(12 cm) = 60π cm²

So, the total surface area of the cone is:

SA = πre + B = 60π cm² + 25π cm² = 85π cm²

Finally, substituting π with T/3:

SA = 85π cm² = 85(T/3) cm² = 67T cm² (rounded to the nearest whole number)

A cone is a three-dimensional shape that has a circular base and a curved surface that tapers to a point called the apex. The surface area of a cone is the sum of the areas of its base and its curved surface.

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The number of ceiling boards in the room is 5000

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

Measurement = 5 cm by 10 cm

Room = square of 5 m dimension

The area of the room is calculated as

Area = (5 m)²

When evaluated, we have

Area = 25 m²

The area of the board is

Area = 5 cm * 10 cm

So, we have

Area = 50 cm²

So, we have

Boards = (25 m²)/(50 cm²)

Evaluate the quotient

Boards = 5000

Hence, the number of boards is 5000

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The length of the major arc for the given circle, in terms of pi, is:

L = π*2.16 yards.

We know that an arc defined by an angle x on a circle of radius R has a length:

L = (x/360°)*2*π*R

where π = 3.14

Here we know that the angle DCE is 100°, and the total angle of a circle is 360°, then the angle of the arc DFE is 360° - 100° = 260°

And the radius of the circle is R = 3yd, then the length in terms of pi is:

L = (260°/360)*2*π*3yd

L = π*2.16 yards.

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The rate of a molecule's migration through an electric field during electrophoresis is determined by factors such as the molecule's size, shape, and charge, as well as the properties of the electric field and the medium through which the molecule is moving.

The rate of a molecule's migration through an electric field during electrophoresis is determined by several factors. The size and shape of the molecule play a significant role. Larger molecules will migrate more slowly than smaller molecules, and molecules with more complex shapes will also migrate more slowly due to increased resistance to movement through the gel or solution. Secondly, the charge of the molecule is also a determining factor. Molecules with a higher charge will migrate more quickly than those with a lower charge.

The strength of the electric field and the properties of the gel or solution used for electrophoresis can also affect the rate of migration. The rate of a molecule's migration through an electric field during electrophoresis is a complex process with multiple factors influencing the final outcome.

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The upper limit of the 90% confidence interval for the population mean is 104.11.

Using the formula for a 90% confidence interval for the population mean, we have:
Upper limit = mean + (z-value)*(standard deviation/square root of sample size)
where the z-value for a 90% confidence interval is 1.645.
Plugging in the values from the given information, we get:
Upper limit = 100 + (1.645)*(10/square root of 16)
Upper limit = 100 + 4.1125
Upper limit = 104.11 (rounded to two decimal places)


A 90% confidence interval is an interval that, with a 90% probability, contains the true value of the population mean. To find the upper limit of the interval, we need to use the formula that takes into account the sample mean, sample standard deviation, sample size, and the z-value corresponding to the desired confidence level.

Given a sample size of 16 with a mean and standard deviation of 100 and 10 respectively, the upper limit of the 90% confidence interval is calculated to be 104.11.

This means that we are 90% confident that the true value of the population mean lies between 100 and 104.11.


The upper limit of the 90% confidence interval for the population mean, given a random sample of 16 values with a mean and standard deviation of 100 and 10 respectively, is 104.11.

This means that we can be 90% confident that the true value of the population mean lies between 100 and 104.11.

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Answer:

B. 0.344

Step-by-step explanation:

The question asks about the probability that the person is at at least 175 centimeters. The first column has a total of 86 people under the category of at least 175 centimeters tall. To find the probability, divide the given number of people at least 175 cm (86) by the total number surveyed (250). This gives you the answer of 0.344.

The value of E(x- μ) for the population for any given data is always equal to option b. 0.

Sum of squared deviations,

ss = 100

variance, σ² = 4

The value of E(x - μ) for the population can be determined .

Using the relationship between the sum of squared deviations (ss) and the variance (σ²).

ss = n × σ²

where ss is the sum of squared deviations,

σ² is the variance,

and n is the population size.

Substituting these values into the equation, solve for n,

⇒ 100 = n × 4

⇒ n = 100 / 4

⇒ n = 25

The expected value (E) of (x - μ) for the population is zero.

This means that on average, the difference between each data point (x) and the population mean (μ) is zero.

Therefore, the value of the expected operator E(x- μ) for the population is equal to option b. 0

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The above question is incomplete, the complete question is:

A population has sum of squared deviations, ss = 100 and variance, σ² = 4. What is the value of E(x- μ) for the population?

a. 400

b. 0

c. 10

d. 25

APA format was developed to create a uniform standard of writing.

APA format, which stands for the American Psychological Association format, was established to provide a standardized structure and style for writing scientific papers in the social sciences. It ensures consistency and uniformity in the presentation of research papers, allowing researchers to communicate their work effectively and facilitate the dissemination of knowledge. APA format includes guidelines for organizing the content, citing sources, formatting references, and presenting data. By following these guidelines, researchers can promote clarity, accuracy, and professionalism in their written work. The adoption of APA format helps maintain a common writing style across various disciplines, enhancing readability, facilitating comprehension, and ensuring that scholarly work adheres to established conventions.

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Answer:

∠ T = 126°

Step-by-step explanation:

in an isosceles trapezoid

• lower base angles are congruent

• any lower base angle is supplementary to any upper base angle

then

∠ U = ∠ W = 54° , so

∠ T + ∠ U = 180°

∠ T + 54° = 180° ( subtract 54° from both sides )

∠ T = 126°

Answer:

Step-by-step explanation:

the answer is 3 first do 1+1=2 -1=1+2=3