Which of the following relations is a function?

The direction of the sum of the two vectors is along the west direction

Assuming vector A is pointing west ward and vector B is pointing eastward

The direction of vector A to the horizontal is negative solved by

= -6 cos 30

= -5.196

Adding both vectors

= vector A + vector B

= -5.196 + 5

= -0.196

Hence the direction is to the west since it is negative

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The measure of angle 1 is given as follows:

m < 1 = 42º.

To obtain the measure of angle 1 in the kite, we must consider that the consecutive angles are complementary, that is, the sum of their measures is of 90º.

Relative to angle 1, we have that:

m < 4 + m < 1 = 90º.

For the bottom left triangle, the internal angle measures are given as follows:

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle 4 is obtained as follows:

m < 4 + 42 + 90 = 180

m < 4 = 58º.

Then the measure of angle 1 is obtained as follows:

m < 1 = 90 - 58

m < 1 = 42º.

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- 54  is the value of x in the linear equation .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(X) =  x² + 7x - 4

A) f(-2) + f(4) = - 14 + 40  = 26

B) f(-2) - f(4) =  - 14 - 40  = -54

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Answer:

Step-by-step explanation:

To find the height of the rocket, we can use the tangent function. We know the angle of elevation (75°), the height of Homer's eyes (1.8 meters), and the distance from Homer to the rocket (8 meters), so we can use the formula:

tan(angle) = height / distance

We'll solve for the height:

height = distance * tan(angle)

height = 8 * tan(75°)

However, we need to convert the angle from degrees to radians first, as the tangent function operates in radians. We can use the formula:

radians = degrees * (π / 180)

radians = 75° * (π / 180) = 1.309 radians

Now, we can substitute the value for the angle in radians back into the original equation:

height = 8 * tan(1.309)

Using a calculator, we can find that the height is approximately 15.57 meters.

So, the height of the rocket is approximately 15.57 meters.

The number of positive integers that satisfy the conditions is 4

The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,

To satisfy positive integers that will have sum of four with a 1, a 2 or a 3

The integers are

13

31

112

211

therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3

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Answer:

280 calories and 12 grams of dietary fiber

Step-by-step explanation:

because 210(2/3) = 140

= 140 ÷ 1/2 = 280

we do the same steps with grams

9(2/3) = 6

= 6 ÷ 1/2 = 12

The perimeter of the triangle is equal to 28.7 using the trigonometric ratio

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

tan60 = q/4 {opposite/adjacent}

q = 4 × tan60 {cross multiplication}

q = 6.9282

sin60 = q/r {opposite/hypotenuse}

sin60 = 6.9282/r

r = 6.9282/sin60 {cross multiplication}

r = 8

sin45 = q/s {opposite/hypotenuse}

sin45 = 6.9282/s

s = 6.9282/sin45 {cross multiplication}

s = 9.8

cos45 = p/s {adjacent/hypotenuse}

cos45 = p/9.8

p = 6.9282 {cross multiplication}

perimeter of the triangle = 4 + p + s + r

perimeter of the triangle = 4 + 6.9282 + 9.8 + 8

perimeter of the triangle = 28.7282

Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.

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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic

volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic

total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh =  18+24 = 32 in cubic

In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.

Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic

Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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Answer:258 containers

Step-by-step explanation:

Simply,

16770/65=258.

Hope this helps :]

Answer:

There are approximately 38 cows in the herd.

Step-by-step explanation:

In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.

Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).

[tex]100\%-16\% = 84\%[/tex]

We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.

[tex]32 \text{ cows} = 84\% \cdot x[/tex]

Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.

[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]

[tex]x \approx 38 \text{ cows}[/tex]

So, there are approximately 38 cows in the herd.

The given expression simplifies to sin 2x.

Option (D) is correct.

What are trigonometric ratios?

Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:

sin(A - B) = sin A cos B - cos A sin B

By comparing this formula to the given expression, we can see that:

A = 3x

B = x

Substituting these values into the formula, we get:

sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)

Hence, the given expression simplifies to sin 2x.

Option (D) is correct.

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On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.

An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.

An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.

x = first angle

Complementary angle is 14.2 degrees more than the cοmplementary angle.

First angle  = x

Second angle = x + 14.2°

Complementary angle

x+x+14.2=90

2x+14.290

2x 90 14.2

2x = 75.8 x = 37.9

First angle is 37.9°.

Second angle will be:

x+14.2°

⇒37.9°+ 14.2°

⇒52.1°

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The value of the fifth term B is 17.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

The first term of the sequence is 2.

a₁ = 2

And the explicit formula of the sequence,

aₙ = (-2)aₙ₋₁ + 3.

The value of a₂:

a₂ = (-2)a₁+ 3.

a₂ = -2(2) + 3 = -1

And a₃ = -2(-1) + 3 =5

a₄ = -2(5) + 3 = -7

Now, the value of the fifth term,

a₅ = -2(-7) + 3 = 17.

Therefore, the fifth term is 17.

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Answer:

(3) 3

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.

So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.

An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)

So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]

Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]

Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)

where:

PMT = $300 (the monthly payment)

r = 0.06/12 (the monthly interest rate)

n = 10*12 (the number of periods over 10 years, with 12 months in a year)

Plugging in the values into the formula, we get:

PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * 10.34300138

PV = $31,029.

So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.

Step-by-step explanation:

y=mx+b

m=slope

b= y-intercept

x=6

y=-5

-5= -1/3(6)+b

-5= 2+b

-2       -2

      -7    =  b

y= -1/3x-7

Answer:

y=-1/3x-3

Step-by-step explanation:

Answer:

cost of couch: $846

cost of coffee table: $282

Step-by-step explanation:

The amount of money that Amelia is expected to raise is given as follows:

£78.13.

The outcomes of a person winning, and their probabilities, as given as follows:

Hence the probabilities of winning and losing are given as follows:

Then the distribution of earnings for each person is given as follows:

Hence, considering 250 people, the expected amount raised is given as follows:

E(X) = 250/16 x (2.5 x 6 - 1 x 10)

E(X) = £78.13.

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Answer:

x=4

Step-by-step explanation:

-6x = -6-18

-6x = -24

-6x/-6 = -24/-6

x =4

The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.

Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³

The volume of this cylinder is 1.5 times that of the cone

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The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.

The correct answer choice is option D

Potential energy is a form of energy which is dependent on the relationship between different system components.

The gravitational constant, g = 9.8 m/s².

Mass, m = 1088 grams

Height, h = 62 meters

So, The amount of potential energy the car has;

PE = mgh.

PE = 1088 × 9.8 × 62

PE = 661,068.8J

Ultimately, the car has a potential energy of 661,068.8J.

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The coordinates that lie on the equation of line y = 1 - 2x are P ( -3 , 7 ) and Q ( 6, -11)

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , 7 )

Let the second point be Q ( 6 , -11 )

The equation of line is y = 1 - 2x

Substituting the values of x and y in the equation , we get

when x = -3

y = 1 - 2 ( -3 )

y = 1 + 6

y = 7

when x = 6

y = 1 - 2 ( 6 )

y = 1 - 12

y = -11

Hence , the coordinates of the equation of line are P ( -3 , 7 ) and Q ( 6, -11 )

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From  transitive property of equality, RT = SU.

Given:

RS = TU

What is Segment addition postulate  ?

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC

Since , from Segment addition postulate

ST = ST

What is addition property of equality ?

The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation. if a-b=c,then a−b+b=c+b, or a=c+b. The same goes with the subtraction property of equality.

Now , by addition property of equality

SU = ST + TU

Similarly,

RT = RS + ST

Now , Using transitive property of equality,

RT = SU

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a) The required margin of error and lower and upper limits are:-

E =0.124

Lower limit =3.026

Upper limit =  3.274

b) sample size is n = 27.

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

The margin of error will be calculated as:-

a) Margin of error (E) :

[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]

E =0.124

Margin of error = E =0.124

The lower and upper limits are calculated as:-

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

b) The following equation may be used to calculate the right number of samples, n when is already known:

Margin of error = 0.13

Sample size (n):

[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]

[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]

n = 26.21

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Answer:

To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:

b_n = b_1 + (n-1)d

where d is the common difference. In this case, d = -3.

So, we can plug in the values for b_1 and d to find b_n:

b_n = 8 + (n-1)(-3)

b_n = 8 - 3(n-1)

Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:

b_14 = 8 - 3(14-1)

b_14 = 8 - 3(13)

b_14 = 8 - 39

b_14 = -31

So, the value of b_14 is -31, and the answer is (1) 14.

Answer:

you su ck hah lol

Step-by-step explanation:

ez

Answer:

8.25 gallan=33 quart

Step-by-step explanation: