The volume of a gas varies inversely as the pressure and directly as the temperature (in Kelvin). If a certain gas occupies a volume of 2.4 liters at a temperature of 340 K and a
pressure of 24 newtons per square centimeter, find the volume when the temperature is 408 K and the pressure is 12 newtons per square centimeter. Round your answer to the
nearest tenth.
O 58L
1.0 L
48.0 L
O 340L

Answers

Answer 1

Using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.

What is volume?

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

The area that any three-dimensional solid occupies is known as its volume.

These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

So, the volume can be obtained using the equation:

V = k*T/P

The value of the constant k is:

K = PV/T = 16N/cm²*2.2L/340K = 0.104N*L*K⁻¹*cm⁻²

We can now determine the volume when:

T = 408 K

P = 24 N/cm²

V = k*T/P = 0.104N*L*K⁻¹*cm⁻²*408K/21Ncm = 1.77L

Therefore, using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.

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Correct question:

The volume of a gas varies inversely to the pressure and direction of the temperature (in degrees Kelvin). If a certain gas occupies a volume of 2.2 liters at a temperature of 340 K and a pressure of 16 newtons per square centimeter, find the volume when the temperature is 408 K and the pressure is 24 newtons per square centimeter.


Related Questions

A sample of an element with a half-life of 8 years has a mass of 10 grams after 100 years. What was the mass of the original sample?

Answers

The mass of the original sample was approximately 1592.5 grams.

A sample of an element with a half-life of 8 years has a mass of 10 grams after 100 years. What was the mass of the original sample?

The half-life of an element is the time it takes for half of a given sample of that element to decay.

Let's assume that the original mass of the sample was x grams.

After the first half-life of 8 years, the mass of the sample would be x/2 grams.

After the second half-life (16 years total), the mass would be x/4 grams.

After the third half-life (24 years total), the mass would be x/8 grams.

We can continue this pattern until we get to 100 years (which is 12.5 half-lives):

Mass after 100 years = x/2^12.5

We also know from the problem that the mass after 100 years is 10 grams:

x/2^12.5 = 10

Solving for x:

x = 10 x 2^12.5

x ≈ 1592.5 grams

Therefore, the mass of the original sample was approximately 1592.5 grams.

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Tony is playing a games there is 1/8 chance the spinner will land on red and 3/8 chance that the spinner will land on yellow what is the probabilty chance the the spinner will not land on red then land on red

Answers

The probability of the spinner not landing on red and then landing on red is 7/64.

What is the probability that none is red?

The probability chance that the spinner will not land on red then land on red is calculated as follows;

The probability of the spinner not landing on red is 1 - 1/8 = 7/8.

To find the probability that the spinner will not land on red and then land on red, we multiply the probabilities:

(7/8) x (1/8) = 7/64

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Find the critical points of f(x) = x - 18x² + 96x and use the Second Derivative Test (if possible) to determine whether each corresponds to a local minimum or maximum. (Use symbolic notation and fractions when needed)

Answers

To find the critical points of f(x) = x - 18x² + 96x, we need to find the values of x where f'(x) = 0.

f'(x) = 1 - 36x + 96

Setting f'(x) = 0, we get:

-36x + 97 = 0

x = 97/36

So the critical point is (97/36, f(97/36)).

To use the Second Derivative Test, we need to find f''(x):

f''(x) = -36

At the critical point x = 97/36, f''(97/36) = -36 < 0.

Since f''(97/36) is negative, the Second Derivative Test tells us that the critical point corresponds to a local maximum.

Therefore, the critical point (97/36, f(97/36)) is a local maximum.
To find the critical points of the function f(x) = x - 18x² + 96x, we first need to find its first derivative, f'(x), and then set it to zero to find the critical points.

1. Find the first derivative, f'(x):
f'(x) = d/dx (x - 18x² + 96x) = 1 - 36x + 96

2. Set f'(x) to zero and solve for x:
0 = 1 - 36x + 96
36x = 95
x = 95/36

Now, let's use the Second Derivative Test to determine if this critical point corresponds to a local minimum or maximum.

3. Find the second derivative, f''(x):
f''(x) = d/dx (1 - 36x + 96) = -36

4. Evaluate f''(x) at the critical point x = 95/36:
f''(95/36) = -36

Since f''(95/36) is negative, the Second Derivative Test tells us that the critical point x = 95/36 corresponds to a local maximum.

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Explain the relationship between -41/2 and its opposite postiton in relation to yhe postitoon of zero on a number line

Answers

Answer:

Step-by-step explanation:

To understand the relationship between -41/2 and its opposite position in relation to zero on a number line, let's first plot them on the number line.

We start by marking the position of zero at the center of the number line, and then we can represent -41/2 and its opposite position by moving to the left and right of zero respectively.

When we move 41/2 units to the left of zero on the number line, we reach the point -41/2. This means that -41/2 is located to the left of zero on the number line.

On the other hand, the opposite position of -41/2 is obtained by moving the same distance (41/2 units) to the right of zero. This position is represented by the point 41/2 on the number line.

Therefore, we can see that -41/2 and its opposite position (41/2) are equidistant from zero on the number line, with zero located exactly halfway between them. In other words, -41/2 and 41/2 are located at equal distances from zero but in opposite directions. This relationship is often referred to as the symmetry property of the number line.

Laura is driving to Los Angeles. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.85. See the figure below. Laura has 52 miles remaining after 41 minutes of driving. How many miles were remaining after 33 minutes of driving?

Answers

The remaining distance after 33 minutes of driving = 58.8 miles.

Here, the slope of a linear function the remaining distance to drive (in miles) is -0.85

For this situation, we can write a linear equation as,

remaining distance = (slope)(drive time) + (intercept)

remaining distance = -0.85(drive time) + (intercept)      

y =  -0.85x + c        ..........(1)

where y represents the remaining distance

x is the drive time

and c is the y-intercept

Here, Laura has 52 miles remaining after 41 minutes of driving.

i.e., x = 41 and y = 52

Substitute these values in equation (1)

52 =  -0.85(41) + c    

c = 52 + 34.85

c = 86.85

So, equation (1) becomes,

y =  -0.85x + 86.85

Now, we need to find the remaining distance after 33 minutes of driving.

i.e., the value of y for x = 33

y =  -0.85(33) + 86.85

y =  -28.05 + 86.85        

y = 58.8

This is the remaining distance 58.8 miles.

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The area of a rectangle is 72x^13y^9z^16 square yards. The length of the rectangle is 3x9y4z^5 yards. Find the simplified expression of the width of the rectangle in yards.​

Answers

The expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

Given that the area of a rectangle is 72x¹³y⁹z¹⁶ sq. yds and the length of the rectangle is 3x9y4z⁵, we need to find the width,

Using these expressions, we have,

Area = length × width

72x¹³y⁹z¹⁶ / 3x9y4z⁵ = width

Width = 72x¹³/3x × y⁹/9y × z¹⁶/4z⁵

Width = 24x¹²y⁸z¹¹/36 = 2x¹²y⁸z¹¹/3

Hence the expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

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Every day, Carmen walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, with all times being equally likely (i. E. , a uniform distribution). This means that the mean wait time is 6 minutes, with a variance of 12 minutes. What is the probability that her total wait time over the course of 60 days is less than 5. 5 hours

Answers

The probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

The total wait time over 60 days will have a mean of 360 minutes (6 minutes per day x 60 days) and a variance of 720 minutes (12 minutes per day x 60 days). Since the wait times are uniformly distributed, the total wait time over 60 days will follow a normal distribution.

To find the probability that the total wait time over 60 days is less than 5.5 hours, we need to standardize the value using the z-score formula:

z = (x - μ) / σ

where x is the total wait time in minutes, μ is the mean total wait time in minutes, and σ is the standard deviation of the total wait time in minutes.

Substituting the values, we get:

z = (330 - 360) / sqrt(720) = -1.4434

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.4434 is 0.0746.

Therefore, the probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

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Jack's bill at a restaurant came to $51.31 he wants to leave a 15% tip how much will the new total be including tip

Answers

The new total bill including the tip of 15% is $59.01.

Calculating the new bill including the tip

To find the amount of the tip, we can multiply the total bill by the percentage as a decimal:

tip = 0.15 * $51.31 = $7.70

To find the new total including the tip, we can add the tip to the original bill:

new total = $51.31 + $7.70 = $59.01

So the new total, including a 15% tip, will be $59.01.

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A paving company is paving the rectangular student parking lot at hamilton high school. the length of the parking lot can be represented as (5 − 7) and the width as (3 + 4) . which expression represents the area of the parking lot?

Answers

The expression that represents the area of the parking lot is (5 - 7) * (3 + 4).

How to express the area of the parking lot?

The length of the parking lot can be represented as (5 - 7), which simplifies to -2. The width of the parking lot can be represented as (3 + 4), which simplifies to 7. To find the area of a rectangle, we multiply the length by the width.

Therefore, the expression that represents the area of the parking lot is (-2) * 7. Multiplying -2 by 7 gives us -14. So, the area of the parking lot is -14 square units.

However, it is important to note that negative areas do not have practical meaning in this context, as areas are typically positive values. Therefore, the area of the parking lot would be considered 14 square units.

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Which table shows a proportional relationship between x and y?

Answers

Find surface area and volume

Evaluate the integral ∫√5+x/5-x dx

Answers

To evaluate the integral ∫√5+x/5-x dx, we first need to simplify the integrand. We can do this by multiplying the numerator and denominator of the fraction by the conjugate of the denominator, which is 5+x. This gives us:

∫√(5+x)(5+x)/(5-x)(5+x) dx

Simplifying further, we get:

∫(5+x)/(√(5-x)(5+x)) dx

We can now make a substitution by letting u = 5-x. This gives us du = -dx, and we can substitute these values into the integral to get:

-∫(4-u)/(√u(9-u)) du

To simplify this expression, we can use partial fraction decomposition to break it up into simpler integrals. We can write:

(4-u)/(√u(9-u)) = A/√u + B/√(9-u)

Multiplying both sides by √u(9-u), we get:

4-u = A√(9-u) + B√u

Squaring both sides and simplifying, we get:

16 - 8u + u^2 = 9A^2 - 18AB + 9B^2

From this equation, we can solve for A and B to get:

A = -B/3
B = 2√2/3

Substituting these values back into the partial fraction decomposition, we get:

(4-u)/(√u(9-u)) = -√(9-u)/3√u + 2√2/3√(9-u)

We can now substitute this expression back into the integral to get:

-∫(-√(9-x)/3√x + 2√2/3√(9-x)) dx

This integral can be evaluated using standard integral formulas, and we get:

(2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C

where C is the constant of integration.

In summary, to evaluate the integral ∫√5+x/5-x dx, we simplified the integrand by multiplying the numerator and denominator by the conjugate of the denominator, made a substitution to simplify the expression further, used partial fraction decomposition to break it up into simpler integrals, and evaluated the integral using standard integral formulas. The final answer is (2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C.

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A. name 3 different angles which could have a reference angle of 20 degrees. how did you arrive at this answer?.

b. what are the characteristics of a reference angle?

c. how is it possible that angles can have different measurements, but still have the exact same reference angle?

Answers

A) The acute angles equivalent to 70 degrees, 110 degrees, and 250 degrees are all 20 degrees.

B) The characteristics of a reference angle is acute and positive.

C) Because reference angle only depends on quadrant.

A. Three different angles which could have a reference angle of 20 degrees are 70 degrees, 110 degrees, and 250 degrees. To arrive at this answer, we need to subtract 20 degrees from 90 degrees, which gives us 70 degrees. To find the other two angles, we add 180 degrees to 70 degrees, which gives us 250 degrees, and we subtract 180 degrees from 110 degrees, which gives us 290 degrees. However, since we're looking for angles with a reference angle of 20 degrees, we have to find the acute angle between 0 and 90 degrees that is equivalent to these angles. So, we subtract 90 degrees from 250 degrees, which gives us 160 degrees, and we subtract 90 degrees from 290 degrees, which gives us 200 degrees. The acute angles equivalent to 70 degrees, 110 degrees, and 250 degrees are all 20 degrees.

B. The characteristics of a reference angle are that it is always an acute angle, it is the smallest angle between the terminal side of the given angle and the x-axis, and it is always positive.

C. Angles can have different measurements but still have the exact same reference angle because the reference angle only depends on the quadrant in which the terminal side of the angle lies. For example, an angle of 50 degrees and an angle of 310 degrees are both in the fourth quadrant and therefore have the same reference angle of 40 degrees. Similarly, an angle of 100 degrees and an angle of 260 degrees are both in the third quadrant and therefore have the same reference angle of 10 degrees.

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Two radar A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B. How far apart are the two aircraft

Answers

The two aircraft are 128.535 far away.

What is the distance formula?

The d-distance between two places is calculated using the distance formula. The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.

Here, we have

Given: Two radars A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B.

Calculating the Slope of AC,  tan60° = 1.732

Calculating the Slope of BC, tan104° = -4.011

Calculating the Slope of AD, tan125° = -1.482

Calculating the Slope of BD, tan157° = -0.424

When pointing C intercepts:

y₁ = 1.732x₁....(1)

y₁ = -4.011(x₁-80)....(2)

Solving equation(1) and(2) , we get

x₁ = 55.873

y₁ = 96.772

When point D intercepts:

y₂ = -1.428x₂....(3)

y₂ = 0.424(x₂-80)....(4)

Solving equations (3) and (4), we get

x₂ = 18.315

y₂  = -26.154

Calculating distance by applying the distance formula:

D = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

D = [tex]\sqrt{(-26.154-96.772)^2+(18.315-55.873)^2}[/tex]

D = [tex]\sqrt{4986.9019+1410.6033}[/tex]

D = 128.535

Hence, the two aircraft are 128.535 far away.

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In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less
find the sample size needed to estimate that percentage. use a 0.01 margin of error and use a confidence level of 95%. assume that nothing is known about the percentage to be estimated

Answers

A sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.

To find the sample size needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, we can use the following formula:

n = [Z^2 * p * (1 - p)] / E^2

where:

Z is the z-score associated with the desired confidence level (95%), which is 1.96
p is the estimated proportion of students who earn a bachelor's degree in four years or less (since we don't have any prior knowledge, we can use 0.5 as a conservative estimate)
E is the margin of error, which is 0.01
Plugging in the values, we get:

n = [(1.96)^2 * 0.5 * (1 - 0.5)] / (0.01)^2
n = 9604

Therefore, a sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.

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Joey is 20 years younger than becky in two years becky will be twice as old as joey what are their present ages

Answers

Becky is currently 38 years old and Joey is currently 18 years old.

Let's start by assigning variables to their ages. Let Joey's age be "J" and Becky's age be "B".

From the first piece of information, we know that Joey is 20 years younger than Becky. This can be expressed as:

J = B - 20

Now, let's use the second piece of information. In two years, Becky will be twice as old as Joey. So, we can set up an equation:

B + 2 = 2(J + 2)

We add 2 to Becky's age because in two years she will be that much older. On the right side, we add 2 to Joey's age because he will also be two years older. Then we multiply Joey's age by 2 because Becky will be twice his age.

Now, we can substitute the first equation into the second equation:

B + 2 = 2((B - 20) + 2)

Simplifying the right side:

B + 2 = 2B - 36

Add 36 to both sides:

B + 38 = 2B

Subtract B from both sides:

38 = B

So, Becky is currently 38 years old. Using the first equation, we can find Joey's age:

J = B - 20
J = 38 - 20
J = 18

So, Joey is currently 18 years old.

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Mr. Lance designed a class banner shaped like a polygon shown what is the name of the polygon

Answers

Step 1: Answer

The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).

Step 2: Explanation

The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.

Find the absolute (i.e., global) maximum and absolute minimum values of the function f(x) = 8x/6х + 4 on the interval (1,5) Absolute maximum = Absolute minimum =

Answers

The absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

To find the absolute maximum and minimum values of the function f(x) = 8x/(6x + 4) on the interval (1, 5), we need to find the critical points of the function within the interval and evaluate the function at those points, as well as at the endpoints of the interval.

First, let's find the derivative of the function:

f(x) = 8x/(6x + 4)

f'(x) = [8(6x + 4) - 8x(6)] / (6x + 4)^2

f'(x) = [8(2)] / (6x + 4)^2

f'(x) = 16 / (6x + 4)^2

The critical points occur when f'(x) = 0 or is undefined. However, since f'(x) is always positive on the interval (1, 5), there are no critical points within the interval.

Next, let's evaluate the function at the endpoints of the interval:

f(1) = 8(1)/(6(1) + 4) = 8/10 = 4/5

f(5) = 8(5)/(6(5) + 4) = 40/34 = 20/17

Finally, we need to determine which of these values is the absolute maximum and which is the absolute minimum.

Since f(x) is always positive on the interval (1, 5), the function can never be less than 0. Therefore, the absolute minimum value is the smallest value of f(x) on the interval, which occurs at x = 5, where f(5) = 20/17.

To find the absolute maximum value, we compare the values of f(1), f(5), and the maximum value of f(x) as x approaches the endpoints of the interval. We can use the fact that the function is continuous on the closed interval [1, 5] to find the maximum value.

As x approaches 1, we have:

f(x) = 8x/(6x + 4) → 8/10 = 4/5

As x approaches 5, we have:

f(x) = 8x/(6x + 4) → 40/34 = 20/17

Therefore, the absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

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An electronics company has two contract manufacturers in Asia. Foxconn assembles its tablets and smart phones while Flextronics assembles its laptops. Monthly demand for tablets and smartphones is 10,000 units while that for laptops is 4,000. Tablets cost the company $100 while laptops cost $400 and the company has a holding cost of 25 percent. Currently the company has to place separate orders with Foxconn and Flextronics and receives separate shipments. The fixed cost of each shipment is $10,000

Answers

To optimize the company's inventory costs, we need to determine the optimal order quantities for both tablets and laptops.

Let's start by finding the optimal order quantity for tablets:

Total cost (TC) = ordering cost + holding cost

Ordering cost = (demand rate/order quantity) x ordering cost per shipment

Holding cost = (order quantity/2) x unit cost x holding cost rate

We can set these two costs equal to each other and solve for the optimal order quantity (Q):

(demand rate/Q) x ordering cost per shipment = (Q/2) x unit cost x holding cost rate

Solving for Q, we get:

Q = sqrt((2 x demand rate x ordering cost per shipment)/(unit cost x holding cost rate))

Plugging in the values given in the problem, we get:

Q = sqrt((2 x 10000 x 10000)/(100 x 0.25)) = 2000

Therefore, the optimal order quantity for tablets is 2000 units per shipment.

Next, let's find the optimal order quantity for laptops:

Following the same procedure as for tablets, we get:

Q = sqrt((2 x 4000 x 10000)/(400 x 0.25)) = 2000

Therefore, the optimal order quantity for laptops is also 2000 units per shipment.

In summary, the company should place orders of 2000 units each for both tablets and laptops to minimize its inventory costs.

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(1 point) Evaluate the line integral Sc 2y dx + 2x dy where is the straight line path from (4,3) to (9,6). Jc 2g dc + 2z du =

Answers

the value of the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6) is 84.

To evaluate the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6), follow these steps:
Step:1. Parametrize the straight line path: Define a vector-valued function r(t) = (1-t)(4,3) + t(9,6) = (4+5t, 3+3t), where 0 ≤ t ≤ 1. Step:2. Calculate the derivatives: dr/dt = (5,3). Step:3. Substitute the parametric equations into the line integral: 2(3+3t)(5) + 2(4+5t)(3). Step:4. Calculate the line integral: ∫(30+30t + 24+30t) dt, where the integration is from 0 to 1. Step:5. Combine the terms and integrate: ∫(54+60t) dt from 0 to 1 = [54t + 30t^2] from 0 to 1.
Step:6. Evaluate the integral at the limits: (54(1) + 30(1)^2) - (54(0) + 30(0)^2) = 54 + 30 = 84.

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The length of one diagonal in a rhombus is 26. 4 cm and the area of the rhombus is 204. 6 cm squared. How long is the second diagonal?

Answers

A rhombus with a diagonal of 26.4 cm and an area of 204.6 square cm has another diagonal of length 15.5 cm

Rhombus is a 2-Dimensional shape. It is a quadrilateral. It is a specialized form of a parallelogram. All sides of a rhombus are equal in length.

Similar to a parallelogram, it has opposite sides parallel to each other and opposite angles of equal magnitude.

The area of a rhombus is expressed as half of the product of diagonals.

A = 0.5pq

A is the area

p is the length of one diagonal

q is the length of another diagonal

A = 204.6 square cm

p = 26.4 cm

204.6 = 0.5 * 26.4 * q

q = 15.5 cm

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Your supervisor asks you to separate 4,780 castings into 25 piles. When you complete the job, how many castings will you have left over

Answers

Answer:5

Step-by-step explanation:
4780/25=191.2
You don't want an odd amount of castings in different piles.
191*25=4755
4780-4755=5









I think i read the question wrong. Sorry if i did

Final answer:

When separating 4,780 castings into 25 piles, there will be 5 castings left over.

Explanation:

A fraction is a numerical expression representing a part of a whole. It consists of a numerator (the top number) that indicates how many parts are considered, and a denominator (the bottom number) that shows the total number of equal parts in the whole. Fractions are typically expressed as a/b, where "a" is the numerator and "b" is the denominator. They are used in various mathematical operations, including addition, subtraction, multiplication, and division, and in real-life scenarios involving proportions and portions.

In order to determine the number of castings left over when separating 4,780 castings into 25 piles, we can use division. Divide 4,780 by 25 to find the number of castings in each pile.

The quotient is 191.2. Since we can't have a fraction of a casting, we round down to 191.

To find the number of castings left over, subtract the total number of castings in the piles from the original total. 4,780 - (191 x 25)

= 4,780 - 4,775

= 5

Therefore, when you complete the job, you will have 5 castings left over.

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can yall awnser this asap pls I NEED TO PASS!!

Answers

Answer: 36 inches

Step-by-step explanation:

The lateral surface area of a cube with sides of length 3 inches is given by the sum of the areas of all four side faces. Each side face is a square with an area equal to the product of the length and width, which in this case is 3 inches by 3 inches. Therefore, the lateral surface area of the cube is:

LSA = 4 x (3 inches x 3 inches) = 36 square inches

So the lateral surface area of the cube is 36 square inches

he circumference of an inflated basketball is 29.516 inches. What is the volume of the basketball? Use 3.14 for π. Round final answer to the nearest whole number.

Use 3.14 for π. PLSSSS HELPPP

Answers

the volume of the basketball is approximately 490 cubic inches. we can get this answer by using volume formula of volume

what is approximately ?

"Approximately" means almost, but not exactly. It is used to indicate that a value or quantity is very close to the true or exact value, but there may be a small difference or error. In mathematical terms, an approximate value is an estimate or a rounded value that is used

In the given question,

To find the volume of the basketball, we first need to find its radius.

Circumference of a sphere = 2πr

29.516 = 2 * 3.14 * r

r = 29.516 / (2 * 3.14) ≈ 4.7 inches (rounded to one decimal place)

Now, we can use the formula for the volume of a sphere:

Volume of sphere = (4/3) * π * r^3

Volume of basketball = (4/3) * 3.14 * (4.7)^3

Volume of basketball ≈ 490 cubic inches (rounded to the nearest whole number)

Therefore, the volume of the basketball is approximately 490 cubic inches..

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You are going to calculate what speed the kayaker 's are paddling, if they stay at a constant rate the entire trip, while kayaking in Humboldt bay.
key information:

River current: 3 miles per hour
Trip distance: 2 miles (1 mile up, 1 mile back)
Total time of the trip: 3 hours 20 minutes

1) Label variables and create a table

2) Write an quadratic equation to model the problem

3) Solve the equation. Provide supporting work and detail

4) Explain the results

Answers

1) Variables and Table:
Let's label the speed of the kayaker as "k" and the speed of the current as "c". We can use the following table to organize the information:

| Distance | Rate | Time |
|------------|--------|--------|
| 1 mile | k - c | t1 |
| 1 mile | k + c | t2 |
| 2 miles | | 3h20m |

Note that we use "t1" and "t2" to represent the time it takes to travel one mile in each direction, since the kayaker is traveling at a different rate relative to the current in each direction.

2) Quadratic Equation:
To solve for "k", we can use the formula:

distance = rate x time

For the first leg of the trip, we have:

1 = (k - c) x t1

Solving for t1, we get:

t1 = 1 / (k - c)

For the second leg of the trip, we have:

1 = (k + c) x t2

Solving for t2, we get:

t2 = 1 / (k + c)

Since the total time of the trip is 3 hours 20 minutes, or 3.33 hours, we can write:

t1 + t2 = 3.33

Substituting the expressions for t1 and t2, we get:

1/(k-c) + 1/(k+c) = 3.33

Multiplying both sides by (k-c)(k+c), we get:

(k+c) + (k-c) = 3.33(k-c)(k+c)

Simplifying, we get:

2k = 3.33(k^2 - c^2)

Multiplying out the right side, we get:

2k = 3.33k^2 - 3.33c^2

Rearranging and setting the equation equal to zero, we get:

3.33k^2 - 2k - 3.33c^2 = 0

This is a quadratic equation in "k".

3) Solving the Equation:
We can solve this quadratic equation using the quadratic formula:

k = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3.33, b = -2, and c = -3.33c^2. Substituting these values, we get:

k = (-(-2) ± sqrt((-2)^2 - 4(3.33)(-3.33c^2))) / 2(3.33)

Simplifying, we get:

k = (2 ± sqrt(4 + 44.286c^2)) / 6.66

4) Explanation of Results:
The quadratic equation has two solutions for "k", but one of them is negative and therefore not physically meaningful. The other solution gives the speed of the kayaker relative to the water:

k = (2 + sqrt(4 + 44.286c^2)) / 6.66

This equation shows that the speed of the kayaker depends on the speed of the river current. As the current gets stronger (i.e., as "c" increases), the kayaker needs to paddle faster to maintain a constant speed relative to the water. Conversely, if the current is weaker, the kayaker can paddle more slowly and still maintain the same speed.

This table represents rico's check register. a transfer of $30.00 was made on august 15 from his savings account into his checking
account
how should the august 15th transaction be recorded on his check register?

Answers

This will ensure that his check register accurately reflects his current account balance and transaction history.

This table represents Rico's check register, and on August 15th, he made a transfer of $30.00 from his savings account into his checking account.

To record this transaction on his check register, Rico should enter it as a deposit in his checking account column, and also include a note indicating that the deposit was a transfer from his savings account.

This will ensure that his check register accurately reflects his current account balance and transaction history.

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Can someone help me fast!?!?
Trying to get better at these word problems will help a lot.

Sharon is a new store manager. She can spend $750 a day for operating costs and payroll. It costs $75 each day to operate the store and $25 a day for each employee. Use the following inequality to determine, at most, how many employees Sharon can afford for the day.
A. x ≥ 27
B. x ≥ 33
C. x ≤ 33
D. x ≤ 27

Answers

Answer:

D

Step-by-step explanation:

25x+75=750

25x=675

x=27

we can't go over this amount, but we can have 27 employees, so it will be equal as well.

x<27 and x=27

In circle P with m \angle NPQ= 104m∠NPQ=104 and NP=9NP=9 units find area of sector NPQ. Round to the nearest hundredth

Answers

Area of sector NPQ ≈ 127.23 square units

To find the area of the sector NPQ, we first need to find the measure of the central angle that defines the sector. We know that the measure of the angle NPQ is 104 degrees, but we need to find the measure of the central angle that includes this arc.

Since NP is a radius of the circle, we know that triangle NQP is an isosceles triangle, with angles NQP and PNQ each measuring (180 - 104)/2 = 38 degrees. Therefore, the measure of the central angle that includes arc NPQ is 2 * 38 + 104 = 180 degrees.

The area of the sector NPQ is then a fraction of the total area of the circle, where the fraction is equal to the ratio of the central angle to the total angle around the circle. Since the total angle around a circle is 360 degrees, the fraction of the circle's area covered by the sector is:

180 degrees / 360 degrees = 1/2

Therefore, the area of the sector NPQ is equal to half the area of the circle with radius 9 units:

Area of sector NPQ = (1/2) * π * 9^2 = 40.5π

Rounding to the nearest hundredth, the area of the sector NPQ is approximately:

Area of sector NPQ ≈ 127.23 square units

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Write the product using exponents.

4⋅4⋅4⋅4⋅4

Answers

4^5 is the answer with a final product 1024 due to 4 being multiplied 5 times.

Mr.Franklin drives 37 miles each day to and from work. How many miles does he drive in 20 work days

Answers

Answer:

740

Step-by-step explanation:

37 times 20

Answer:

740 miles

Step-by-step explanation:

37 miles in 1 day

So we need to multiply 37*20 to find the number of miles for 20 days

So, he travels 740 miles

Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)

Answers

The price of one teddy bear is $7 and the price of one doll is $14.

Let's use matrices to solve this system of equations:

First, we need to define the variables:

x = price of one teddy bear

y = price of one doll

Then we can write the system of equations:

14x + 3y = 158

8x + 12y = 296

system of matix:

| 14   3 |   | x |   | 158 |

|  8  12 | * | y | = | 296 |

To solve for x and y, we can use matrix multiplication and inversion:

| x |   | 12  -3 |   | 158 |   |  99 |

| y | = | -8  14 | * | 296 | = | -14 |

So, x = $7 and y = $14. Therefore, the price of one teddy bear is $7 and the price of one doll is $14.

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