Two tugboats are towing a loaded barge and the magnitude and direction of the two forces acting on the barge are 30 pounds N10°E and 60 pounds, N60°E.
Find the magnitude, to the nearest hundredth of a pound, of the resultant force.
Find the direction, to the nearest degree, of the resultant force.

The value x may be expressed as (a - b)(ab + b) / (ab - 1)(ab + 1).

To simplify the given expression x = (a² + b²) / (a b + 1), start by multiplying both the numerator and the denominator by (a b - 1) as follows:

x = (a² + b²)(a b - 1) / (a b + 1)(a b - 1)

Expanding the numerator using the distributive property:

x = (a² b - a² + a b² - b²) / (a² b - a b + a b² - 1)

Rearranging the terms in the numerator:

x = (a² b + a b² - a² - b²) / (a² b - a b + a b² - 1)

Factoring the numerator:

x = [(a² b - a b) + (a b² - b²)] / (a²b - a b + a b² - 1)

x = [a b (a - b) + b²(a - b)] / (a b - 1)(a b + 1)

x = (a - b)(a b + b) / (a b - 1)(a b + 1)

Therefore, the simplified expression for x is (a - b)(ab + b) / (ab - 1)(ab + 1).

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Answer:

Step-by-step explanation:

First, we have to find 14% of 56

14% of 56 is = 56 x 14/100

                  = 7.84

Now we have to increase the number 56 by 14%, which means we have to add 14% of 56 (7.84) to the given number (56)  

56 + (14% of 56)

= 56 + 7.84

= £63.84

The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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Answer:

x = 24 , y = 24√3 = 41.57

Step-by-step explanation:

In the triangle,

sin 30° = x/48

1/2 = x/48

48 = 2x

24 = x ---------- (1)

Then,

tan 30° = x/y

1/√3 = 24/y [from (1)]

y = 24√3

y = 24 × 1.732

y = 41.57 [approx.]

Hope it helps ⚜

Answer:X = 13

Step-by-step explanation:

An exterior angle is equal to the sum of the two opposite interior angle

⇒95=4x+3 + 3x+ 1

95=4x + 3x + 3 + 1

95=7x + 4

95-4=7x

91=7x

91/7=x

13=x

This implies that X= 13

Answer:93

Step-by-step explanation:

Answer:

A 4-liter container holds more than a 3500-milliliter container

Step-by-step explanation:

4 liters = 4000 milliliters

4000 > 3500

Radicals expression with variables and exponents can be simplify by:

To help us understand each step better, we will take an example of a radical expression with variables and exponents of: \(\sqrt{16a^{3}b^6c^5 }\)

First, we need to separate the number and variables:

\(\sqrt{16a^3b^6c^5}=\sqrt{16} \sqrt{a^3b^6c^5}\)

Next, we will try to find variables with even exponents:

\(\sqrt{16} \sqrt{a^3b^6c^5} = \sqrt{16} \sqrt{a.a^2.b^6.c^4.c^}\)

Remember that:

(xᵃ)ᵇ = xᵃᵇ; then:

\(\sqrt{16}\sqrt{a.a^2.b^6.c^4.c} =\sqrt{16}\sqrt{a.a^2.(b^3)^2.(c^2)^2.c}\)

We try to breakdown any number into any factor that are perfect square:

\(\sqrt{16}\sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will rewrite both number and the variables into a square exponents:

\(\sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will separate the squared factors into individual radicals:

\(\sqrt{4 ^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c}\)

We take the square root of each radical into:

\(\sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c} = 4|a|.|b^3|.c^2\sqrt{ac}\)

We just need to simplify our last equation into:

\(4|a|.|b^3|.c^2\sqrt{ac} = 4|ab^3|c^2\sqrt{ac}\)

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Answer:

50

Step-by-step explanation:

Answer:

b. 50

interior angles of a triangle equal 180

Step-by-step explanation:

Answer:

200=4hrs=10 of the machines

200=4hrs

300=xhrs

Cross multiply

200×xhrs = 300×4hrs

X=1200/200

X= 6 hours

Answer:

D

Step-by-step explanation:

TS and QR Is your answer

Answer:

TS and QR

Step-by-step explanation:

edge 2021

The value that Mrs. Alvarez will pay depends on the rental value of the ski and the poles per day, for example $144.

To know the total cost of the loan of the Ski equipment, we must know the loan price per day or per hour.

For example, suppose the loan price per hour is $2, then we would have to calculate how much one day is equivalent to and then multiply it by the total number of days.

$2 x 24 = $48

$48 x 3 = $144

Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.

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Answer:

(Question 1) If a circle graph was constructed from the results, which lake activity has a central angle of 46.8°?

Kayaking

Wakeboarding

Paddleboarding

(Question 2) Which of the following circle graphs correctly represents the data in the table?

B. a circle graph titled social media usage, with four sections labeled vidtok 17 percent, headbook 48 percent, picturegram 25 percent, and tweeter 10 percent

(Question 3) A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?

26.7%

86.4%

96%

(Question 5)Which of the following circle graphs correctly represents the data in the table?

A: a circle graph with four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent

(Question 6) How many middle school students prefer the Documentaries television genre?

24

76

86.4

Step-by-step explanation:

I did some of them, You're welcome.

Answer:

The answer is x = -7 and x = -8

Step-by-step explanation:

Yes, there are diminishing returns to labor in the given production function.

There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.

When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.

Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.

The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.

The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.

Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.

Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.

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Answer:

9/4 *(x-2)

Step-by-step explanation:

Replace xa and y in the given function then solve for y

If he climbs at a constant speed, then the tension in the rope is 637 N.

The force required to pull the 65 kg gymnast upward against the gravity is the tension in the rope. When the gymnast climbs at a constant speed, it indicates that the forces acting on the gymnast are balanced.

The force acting downwards on the gymnast is its weight, which is given by the mass of the gymnast (m) times acceleration due to gravity (g). Hence, weight = mg = 65 kg x 9.8 m/s² = 637 N.

Since the forces are balanced, the upward force provided by the rope is equal in magnitude to the downward force of weight acting on the gymnast. Therefore, the tension in the rope is 637 N when the gymnast climbs at a constant speed.

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Answer:

103.8

Step-by-step explanation:

Length of diagonal of a cube is given by the formula:

\(d = side \times \sqrt{3} \\ \\ \therefore \: d = 60 \times \sqrt{3} \\ \\ \therefore \: d = 60 \times 1.73 \\ \\ \therefore \: d = 103.8 \: units\)

The length of the diagonal of the cube is 103.9 units.

What is a cube?

A cube is a three dimensional figure or object which has all the side with equal length.

The length of each side of the cube = a = 60 units.

Therefore, the length of the diagonal of the cube = d = a\(\sqrt{3}\) = 60\(\sqrt{3}\) units = 103.9 units.

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In a case whereby you can buy 5 small pizzas for the same price as 3 small pizzas and 10 one dollar drinks. price that each of the pizza cost  can be expressed as $5.

The concept that will be used here is simplification.

We were to to compute the cost of each small pizza

Let represent the cost of each small pizza = x

The we can compute the equation as:

5x = (3x + 10)

(5x - 3x) = 10

2x = 10

x= 5

Hence, the cost of each small pizza = $5

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We can expect to find approximately 68% of all adults' temperatures between 97.62 °F and 98.86 °F. We can conclude that approximately 95% of adults have temperatures between 96.38 °F and 100.1 °F.

(a) According to the Empirical Rule, for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. In this case, since the standard deviation is 0.62 °F, we can locate 68% of all adults' temperatures within a range of mean ± 1 standard deviation.

Temperature range = (98.24 - 0.62) °F to (98.24 + 0.62) °F

                   = 97.62 °F to 98.86 °F

Therefore, we can expect to find approximately 68% of all adults' temperatures between 97.62 °F and 98.86 °F.

(b) To determine the percentage of adults with temperatures between 96.38 °F and 100.1 °F, we can use the Empirical Rule again. According to the rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, we can calculate the percentage of adults within this range.

Temperature range = (98.24 - 2 * 0.62) °F to (98.24 + 2 * 0.62) °F

                   = 96.38 °F to 100.1 °F

Since 95% of the data falls within this range, we can conclude that approximately 95% of adults have temperatures between 96.38 °F and 100.1 °F.

It's important to note that the Empirical Rule provides approximate percentages based on the assumption of a normal distribution. While it can give us a rough estimate, the actual percentage of adults within a specific temperature range may vary slightly from the values predicted by the rule.

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The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

Monday, at 12:15 AM

Step-by-step explanation:

Do this question in parts. First, add 2 days to Friday to get Sunday at 5:45 PM. Then, add 6 hours to 5:45 to get 11:45 PM. Finally, add 30 minutes to 11:45 PM. That takes you to 12:15, and since you passed midnight, Sunday is now Monday. That means the bus arrives Monday, at 12:15 AM.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Inequality is the absence of an equality link between two expressions or values. So inequality emerges from an imbalance.

a) inequality represents the solution to the given inequality

such as

3b > 48

3b /3 > 48/3

b>16

b) inequality represents the solution to the given inequality

such as

M/7 > -56

7 * M/7 > 7 * -56

m>-392

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Answer:

yeah I know you are literally perfect for you to be home

By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools. We will find that the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

The expression for the radius of a circle is:

R = √(A/3)

Where A is the area of said circle.

The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:

R =  √(28 ft^2/3) = 3 ft

The full-sized pool has an area of 113 ft^2, then its radius is:

R' = √(113 ft^2/3) = 6 ft

To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:

R'/R = 6ft/3ft = 2

Meaning that the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

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Answer:

m=\(\frac{(C-12)}{a}\)

Step-by-step explanation:

C=12+am

Subtract 12 from both sides

C-12=am

Divide both sides by a

m=\(\frac{(C-12)}{a}\)

Answer:

4032

Step-by-step explanation:

1 day is 1440 min

1440 divided by 10 = 144

144 times 4 = 576

576 times 7 (because there are 7 days in a week) = 4032

*I may be wrong if so im sorry*

Answer:

B

Step-by-step explanation:

A constant rate of change refers to a pattern/slope that is unchanging. On a graph, these rate of changes are usually represented by a straight line, and B is the only graph in the question with such a line.

The system of equations does not have any solutions since the values on both sides of the final expression are different and the lines will not cross.

A system of equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.

Given the system of equations below;

x + 2y = 4............ 1

3x + 6y = 18 ........... 2

From equation 1:

x = 4 - 2y .........3

Substitute equation 3 into 2 to have:

3(4 - 2y) + 6y = 18

3(4) - 3(2y) + 6y = 18

12 - 6y + 6y = 18

12= 18

Since the values on both sides of the resulting expression is different, hence the given system of equation has NO solutions showing the lines  will not cross on the graph.

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Answer:

right 2 up 8 units

Step-by-step explanation:

the (x-2) is basically the opposite of what u think so it goes right

and +8 is normal so its up 8