How many feet in a fathom ?

The magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.

For the stated question:

By using the cosine theory of the vectors:

C² = A² + B² - 2A.B cosФ

C² = 16.0² + 7.00² - 2(16.0)(7.00).B cosФ79°

On solving:

C = 16.19 units

Thus, the magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.

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The figure for the question is attached.

The volume of the region will be 4/3 cubic unit with the help of integration.

What is integration?

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in Mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables).

Definite Integral

An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.

A definite Integral is represented as:

∫f(x)dx from a to b.

Indefinite Integral

Indefinite integrals are defined without upper and lower limits. It is represented as:

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

For volume

Integrate y=1-x^2 for x=-1 to 1.

volume=1-x^2.dx

V=x-x^3/3

=1-1/3+1-1/3

=2-2/3

Hence,

          Volume=4/3 cubic unit

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If the liquidity premium theory of the term structure of interest rates holds, 0.498% is the liquidity premium for year 2.

Any additional compensation that is necessary to attract investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. Because it is more difficult to sell than a short-term bond, a long-term bond, for instance, will have a higher interest rate. According to the principle of the liquidity premium, bond investors favour short-dated assets that are highly liquid and have a short sales cycle over those that are longer-dated. According to another tenet of the theory, fluctuations in interest rates provide investors with compensation for greater pricing and default risks.

Given that,

1 + 1R₂= {(1 + 1R₁)(1 + E(2r₁) + L₂)}1/2

or, 1.12 = (1.8)(1.14 + L₂)1/2

or, (1.12)2/1.18 = 1.14 + L₂

or, 1.898 = 1.14 + L₂

or, L₂ = 0.498%

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9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.

The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.

When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.

Finding the location of the lawn is the first stage.

Area: 110 feet by 260 feet.

28600 square feet.

Calculating how many bags of fertilizer to purchase is the next step.

Bags = Area x 3,000 feet

Bags: 28600 feet / 3000 feet

9.53 bags total are in the bag.

Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.

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Team A needs to sell 255 bags of popcorn to reach their goal of $100.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Team A will sell the bags of popcorn for $0.50 each.

Team B will sell the cotton candy for $0.75 per stick.

Let the number of bags of popcorn sold by Team A be "x".

So, the total cost for the popcorn machine rental and supplies is

= $15 + 0.05x.

To reach their goal of $100

$100 = 0.5x - ($15 + 0.05x)

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45

x = 255 bags of popcorn

Thus, Team A needs to sell 255 bags of popcorn.

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Answer:

25

Step-by-step explanation:

$50

Cost=$6

Selling price=$8

Profit=$8-$6=$2

50/2=25

A person with a Z-score of -0.42 would have a raw score of 992.4 on the SAT taken in 2018.

The standard deviation is a measure of how much the data varies from the mean. A Z-score is a standardized value that represents the number of standard deviations a raw score is from the mean.

To find the raw score given a Z-score, we can use the following formula:

raw score = mean + Z-score * standard deviation

For the mean composite score of 1068 and a standard deviation of 180, we can plug in the values for the Z-score of -0.42:

raw score = 1068 + (-0.42) * 180

raw score = 1068 - 75.6

raw score = 992.4

Note: The Z-score of -0.42 indicates that the raw score is 0.42 standard deviations below the mean.

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Answer:

Midpoint=(−12,−2)

As a decimal:

Midpoint=(−0.5,−2)

Step-by-step explanation:

M=(xM,yM)

M=(x1+x22,y1+y22)

M=(3+−42,3+−72)

M=(−12,−42)

M=(−12,−2)

As a decimal:

M=(−0.5,−2)

Distance Solution: Between Endpoints

d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

d=(−4−3)2+(−7−3)2−−−−−−−−−−−−−−−−−−√

d=(−7)2+(−10)2−−−−−−−−−−−−√

d=49+100−−−−−−−√

d=149−−−√

d=12.206556

When 80 kg is converted to lbs it will be equal to 176.36980975 pounds (lb).

        Here in this case,

        80kg x 2.20462

         = 176.36980975 pounds.

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The number of cords in 1 m^3 are four.

Here , volume of a cuboid is involved. If l, b, h are respectively the length, breadth and the height of the cuboid , then its volume is given by

V = l x b x h cubic units.

Now, here we know that 1 m =3.28 ft.

So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.

So, we have to find the number of cords in 35.288 cubic feet.

Now, volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.

So, no. of cord = 128/35.288 = 3.66.

Since, the number of cords is always a whole number , so 3.66 can treated as 4 by rounding it off to unit's place.

Hence, The number of cords in 1 m^3 are four.

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The number of cords in 1 m^3 is four.

Here, the volume of a cuboid is involved. If l, b, h are respectively the length, breadth and height of the cuboid, then its volume is given by

V = l x b x h cubic units.

Now, here we know that 1 m =3.28 ft.

So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.

So, we have to find the number of cords in 35.288 cubic feet.

Now, the volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.

So, no. of cord = 128/35.288 = 3.66.

Since the number of cords is always a whole number, 3.66 can be treated as 4 by rounding it off to the unit's place.

Hence, The number of cords in 1 m^3 is four.

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the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2

a) Average rate of change of the function over [6,8] = (f(8) - f(6))/(8-6) = (11(83) - 11(63))/2 = 882/2 = 441

b) Average rate of change of the function over [-1,1] = (f(1) - f(−1))/(1-(−1)) = (11(13) - 11(-13))/2 = 244/2 = 122

a) To find the average rate of change of the function f(x)=11x3 over the interval [6,8], first calculate the value of the function at x=6 and x=8. This gives us f(6) = 11(63) = 729 and f(8) = 11(83) = 1728. Then, the average rate of change = (f(8) - f(6))/(8-6). Substituting in the values of f(6) and f(8), we get (1728 - 729)/2 = 882/2 = 441.

b) To find the average rate of change of the function f(x)=11x3 over the interval [-1,1], first calculate the value of the function at x=-1 and x=1. This gives us f(-1) = 11(-13) = -143 and f(1) = 11(13) = 143. Then, the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2

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The correct option is "will be centered around p, the true population proportion."

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

Given that, the students select their random samples and plot the results on a dot plot, the dots, represent the sample proportions obtained by the students,

Since, the dots are representing the sample proportions, we know,

The population proportion is equal to the mean of the sampling distribution of the sample proportion.

Hence, the correct option is "will be centered around p, the true population proportion."

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Representing fractional values, if a typing examination found that Susan's typing accuracy was 93%, the decimal number representing Susan's typing accuracy is 0.93.

The decimal number of Susan's typing accuracy is a direct conversion from percentage to decimal since both are fractional values.

We know that the percentage sign represents over 100.  When 93 is divided by 100, the decimal value is 0.93.

93% = 93/100 = 0.93

Thus, as a fractional value, Susan's typing accuracy of 93% is the same as 0.93.

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Answer:2.12

Step-by-step explanation:

The height of the tree is obtained as  27.7 m

We have to note that in the solution of the problem that the tangent of the angle is going to come in to play. The tangent if one of the trigonometric ratios and the other ratios are the cos and the sine.

We know that the tangent of the angle is;

tan 36 = opposite/adjacent

Opposite of the angle = x + 5

(Where x is the height of the tree)

Adjacent of the angle = 45 m

We would then have that;

tan 36 = x + 5/45

45 tan 36 = x + 5

x = (45 tan 36) - 5

x = 27.7 m

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The probability of a taco containing only non-meat items is 56/220 = 1/4.

To find the probability of a taco containing only non-meat items, we need to find the number of possible combinations of 3 non-meat items out of the 8 non-meat items available and divide that by the total number of possible combinations of 3 items (either meat or non-meat) out of the 12 total items available.

The number of combinations of 3 non-meat items out of the 8 available is: C(8, 3) = 56

The number of combinations of 3 items out of the 12 total items available is: C(12, 3) = 220

The probability of a taco containing only non-meat items is 56/220 = 1/4.

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Answer:

-16 - 5x = -16

-5X=-16+16

-5X=0

X=5

Step-by-step explanation:

As the sides of the parallelogram are equal, the values of x and y that ensure each quadrilateral is a parallelogram are 2 and -3.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a sort of quadrilateral with opposing pairs of sides that are parallel and equal. A parallelogram is a form of quadrilateral in geometry. It has four sides and is two-dimensional. A parallelogram's most significant qualities are that its opposite sides are parallel and congruent, and its opposite angles are equal.

Here,

3x-4y=18

5x+y=7

multiply 2nd equation by 4 and solve,

3x-4y=18

20x+4y=28

23x=46

x=2

5*10+y=7

y=-3

The values of x and y that ensure each quadrilateral is a parallelogram is 2 and -3 as the side of parallelogram are equal.

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The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.

here, we have,

The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.

Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.

The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).

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The average value is the intersection point between the function and the line, which is at (0,1+C).

The average value of a function on an interval can be calculated using the following formula: Average Value = (1/b-a)∫a b f(x)dx. In this case, the function is f(x) and the interval is [0,1]. To calculate the average value, we must first calculate the integral of the function on the given interval. The integral of f(x) is nx^n-1 + C, where C is a constant. Using the fundamental theorem of calculus, we can evaluate the integral from 0 to 1 to be 1 + C.

The average value of the function on the given interval is then (1/1-0)∫0 1 (1+C)dx, which simplifies to 1+C. Therefore, the average value of the function on the given interval is 1 + C.

Graphically, the average value of the function on the given interval can be seen by plotting the graph of the function, which is a parabola with a vertex at (0,0), and a line at y=1+C. The average value is the intersection point between the function and the line, which is at (0,1+C).

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Answer: 3 - 4i

Step-by-step explanation:

For the given polynomial p(x) , if 3 +4i is a root then, 3 - 4i is also the root of p(x).

Consider the given polynomial equation p(x) = 0 It is given that the polynomial P(x) has one root 3 + 4i .

According to complex conjugate theorem,  if V is a polynomial and x + iy is a root of given polynomial then  its conjugate x - iy is also the root of the polynomial.

Thus, for the given polynomial p(x)  if 3 +4i is a root then, 3 - 4i is also the root of p(x).

If a polynomial equation P(x) = 0 has (3 + 4i) as a solution, the other solution it must have (3 - 4i).

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Conjugate complex numbers are those that only differ in the imaginary part's sign.

a + bi and a - bi, where a and b are real numbers, are generally conjugate, as are, for instance, 2 + 3i and 2 - 3i, -5 - 7i and -5 + 7i, and so on.

Due to the fact that their output is always a genuine number.

The general case is -

= (a + bi)(a - bi)

= a² - abi + abi - (b²)(i²)

= a² + b²

The real example is -

= (2 + 3i)(2 - 3i)

= 2² + 3²

= 4 + 9

= 13

Complex roots for a polynomial equation P(x) = 0 with real coefficients are always represented as conjugate pairs.

So, the following equation must contain (3 - 4i) as a second root if the coefficients are real.

Therefore, P(x) has second root (3 - 4i).

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For given expression, solution will be y=(t-1)/(1+t).

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is t^2dy/dt-t=1+y+ty

After differentiation : As (d/dx) (x^n ) = nx^{n-1}

2t-t=1+y+ty

t-1=y(1+t)

y=(t-1)/(1+t)

for y(1)=2

2+2t=1-t

3t=-1

t=-1/3

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Answer: The cheapest option is Website B.

Step-by-step explanation:

The cost of 6 rechargeable batteries and a charger from each website is:

   Website A: 6 batteries * $52/battery = $312

   Website B: 6 batteries * $2.30/battery + $35/charger = $16.80 + $35 = $51.80

   Website C: 6 batteries * $49.60/battery = $297.60

   Website D: 6 batteries * $3.5 x + $28 = $63 + $28 = $91

The cheapest option is Website B with a cost of $51.80.

The other polygon has a 108 [tex]ft^2[/tex] area.

We are given the area overall (27 [tex]ft^2[/tex]) and the length of one side (3 ft) for the polygon on the left. With this knowledge, we can calculate the other side's length, which is 9 feet. I calculated this by multiplying 27 [tex]ft^2[/tex] by 3 ft, which gave me the answer of 9 ft.

We now need to locate the opposite side of the polygon on the right in order to calculate its area. Given that 3 * 2 = 6, it appears as though there is a scale factor of 2 between the two polygons. Knowing that the bottom side of the polygon on the left is nine, we may calculate the bottom side of the polygon on the right by multiplying nine by two. 9 × 2 = 18.

Now that we know the dimensions of the polygon on the right, we can calculate its area.

The other polygon's area is 107 [tex]ft^2[/tex] since 6*18 = 107.

The complete question is;-

The polygons are similar. The area of one polygon is given find the area of the other.

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Answer:

456.9 inches

Step-by-step explanation:

We can use the law of sines to find c:

c = (a / sin C) = (270 inches / sin 164°)

To find the sine of an angle in degrees, we can use a scientific calculator or a trigonometry table. Rounding to the nearest 10th of an inch, c = approximately 456.9 inches.

Answer: It's 534.7

Step-by-step explanation:

I sacrificed my chance of getting it right to see the answer. It's right That I guarantee. btw brainiest, please?

A scale of 1:900,000 is 36 times smaller than a scale of 1:24,000.

This can be expressed mathematically as a ratio: 1:900,000 = 1:24,000 / 36. To calculate the scale factor between two maps, divide the denominator of the larger scale by the denominator of the smaller scale. In this example, the scale factor is 36.

A scale of 1:900,000 means that one unit on the map represents 900,000 units of the same type in the real world. For example, one centimeter on the map could represent 900,000 centimeters in real life, or 9 kilometers. A scale of 1:24,000 would mean that one unit on the map represents 24,000 units of the same type in the real world. For example, one centimeter on the map could represent 24,000 centimeters in real life, or 0.24 kilometers.

The scale factor is the number that is used to compare the size of one map to another. In this example, a map with a scale of 1:900,000 is 36 times smaller than a map with a scale of 1:24,000. This means that the features on the 1:900,000 map are 36 times smaller than the same features on the 1:24,000 map. Therefore, the 1:900,000 map is not as detailed as the 1:24,000 map.

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When smoothing time series data, it's important to ensure that the curve is not over-flattened, as this can lead to important information being lost.

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The magnitude of f3 is 6.403N and the coordinate direction angle is 247.9°

We can calculate the magnitude and coordinate direction angle of f3 using the vector triangle method.

We assume that the coordinate direction angle of f1 is 0° and the coordinate direction angle of f2 is 90°.

Using the law of cosines, we can determine the magnitude of f3, which is 6.403N:

f3^2 = f1^2 + f2^2 -2f1f2cos180°

f3^2 = 5^2 + 8^2 -2(5)(8)cos180°

f3^2 = 25 + 64 -80

f3^2 = 49

f3 = 6.403N

We can then use the law of sines to determine the coordinate direction angle of f3, which is 247.9°:

sinθ3 = f2sin180°/f3

sinθ3 = (8)(180°)/6.403

sinθ3 = 147.6°

θ3 = 247.9°

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If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

Given that,

If x and y each represent a single digit

The number 8.3xy round to 8.3

Then, the nearest tenth value is,

Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.

To round to the nearest tenth using a number line, look at the tenth place value closest to the number you are rounding. Round 2.12, 2.28 and 2.44 to the nearest tenth.

We can write,

If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,

We have the radius, 8.3, so we have all necessary information to solve this problem.

8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

Therefore,

If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

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If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

Given that,

If x and y each represent a single digit

The number 8.3xy round to 8.3

Then, the nearest tenth value is,

Round to the nearest tenth means to write the given decimal number up to one decimal place. This is done in such a way that after rounding off, there is one digit after the decimal point.

To round to the nearest tenth using a number line, look at the tenth-place value closest to the number you are rounding. Round 2.12, 2.28, and 2.44 to the nearest tenth.

We can write,

If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth,

We have a radius, of 8.3, so we have all the necessary information to solve this problem.

8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

Therefore,

If x and y each represent a single digit, then the 8.3xy rounded to the nearest tenth will be 8.3 when x>=5.

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The algebraic expression representing the length of the desk as a function of the width is given as follows:

L = W + 6.

The two variables in the context of this problem are given as follows:

The length is 6 inches greater than the width of the desk, hence the algebraic expression representing the length of the desk as a function of the width is given as follows:L = W + 6.

The problem asks for the algebraic expression representing the length of the desk as a function of the width.

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