A linear relationhip i hown in the table. Time (hour) 2 4 6 8 Ditance (mile) 4 8 12 16 I the linear relationhip alo proportional? Explain

Let u and v be a vectors. Then u can be broken up into two components, r and s such that r is parallel to v and s is perpendicular to v.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

In particular, u (v w) makes no sense if u, v, and w are vectors because v w is a scalar. Before confirming that the dot product has the desired geometric characteristics, we'll mention.

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When given vector u = (1, 2) and v = (1, -4), Then the value of 4u + 3v = ⟨7, -4⟩, graph in attachment.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

Given u = (1, 2) and v = (1, -4),

4u + 3v = 4(1, 2) + 3(1, -4)

= (4, 8) + (3, -12)

= ⟨4 + 3, 8 + (-12)⟩

= ⟨7, -4⟩

Thus, 4u + 3v = ⟨7, -4⟩

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For the roots to be real and equal, the value of k should be 9, -9.

The complete question is:

For what values of k are the roots of the quadratic equation 3x2 + 2kx + 27 = 0 real and equal?      

For the roots of the equation to be real and equal, we first compare the given quadratic equation with standard form of quadratic equations, which is: [tex]ax^2+ bx+ c=0[/tex]

Thus, a = 3; b= 2k and c = 27

We know, for real and equal roots, Discriminant (D) = [tex]b^2 - 4ac[/tex] = 0

Therefore, we now substitute the values of a, b, and c in the above formula, we get

(2k)^2 - 4(3)(27) = 0

4k^2 - 324 = 0

4k^2 = 324

k^2 = 81

k= 9 or -9

Thus, the value of k is 9 or -9.

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The measure of the arc NST will be the largest one. Then the correct option is C.

Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

If the central angle of the arc is maximum, then the measure of the arc will be maximum.

The measure of the angle ∠NST is maximum. Then the measure of the arc NST will be the largest one.

Thus, the correct option is C.

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The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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Answer:

$77.5

Step-by-step explanation:

Has risen in price BY 310% To mean its price has added 310% from the old price:

Price new = Price old + (Price old × 310%).

To calculate the difference, we just need to calculate 310% of the old price (a percentage is a hundredth):

$25 × 310% = $25 × 3.1 = $77.5

The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

The annual percentage rate, or APR, is the interest rate that is charged on a loan balance that is still outstanding. The expected cost of the annual fees connected with a certain sort of borrowing is what the APR conceptually reflects.

APR is a commonly used formula by lenders that enables borrowers to compare various loan choices. The stated interest rate on a loan is typically insufficient on its own to help borrowers choose the best loan option.

A loan with a low stated interest rate could also have significant costs attached that should not be disregarded. The best alternative might be a loan with a smaller fee structure and a higher advertised interest rate. APR is calculated as (Periodic Interest Rate x 365 Days) x 100 i.e.

[tex]$\mathrm{APR=\left(\left(\frac{\frac{Fees+Interest}{Principal}}{n} \right) \times 365 \right) \times 100}[/tex]

​where:

Interest = Total interest paid over life of the loan

Principal = Loan amount

n = Number of days in loan term

Fees = 0

​Interest = 2​Interest = $519.48

Principal = $624.00

n = 52 × 7 = 364 days

Plug the data in the formula:-

[tex]$\mathrm{APR=\left(\left(\frac{\frac{0+519.48}{624}}{364} \right) \times 365 \right) \times 100}[/tex]

APR = 83.48%

Thus, The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

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Answer:

Quadrilateral

Step-by-step explanation:

I remember learning this in math class. A parallelogram has two dimensions. Each of its four sides has two parallel pairs. The parallel sides have the same length.

The mass of sugar in 1 bottle is 1.65kg.

The equation that represents the information in the question is:

Total kg of sugar bought = total kg of the bottes + sugar left over

Total kg of sugar bought = (number of bottles x mass of sugar in one bottles + sugar leftover

8.6 = (5 x s) + 0.35

8.6 = 5s + 0.35

In order to determine the value of s, take the following steps:

Combine and add similar terms together:

8.6 - 0.35 = 5s

8.25 = 5s

Divide both sides of the equation by 5

s = 8.25 / 5

s = 1.65 kg

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Answer:

15.87% (2 d.p.)

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the weights of adult male rhesus monkeys are normally distributed:

[tex]\boxed{X \sim\text{N}(17, 3^2)}[/tex]

where X is the weight of an adult male rhesus monkey.

To calculate the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds, we need to find P(X < 14).

Calculator input for "normal cumulative distribution function (cdf)":

⇒ P (X < 14) = 0.158655253...

⇒ P (X < 14) = 15.8655253...%

⇒ P (X < 14) = 15.87%

Therefore, the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds is approximately 15.87% (2 d.p.).

A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.

Mathematically, the point-slope form of any straight line can be calculated by using this expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on this line:

At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(2 - 0)(x - 0)

y - 3 = -3/2(x)

y = -3x/2 + 3

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Answer:

Step-by-step explanation:

A graph which has a slope of negative three halves and a y-intercept of 3 include the following: C. graph of a line passing through the points 0 comma 3 and 2 comma 0.

What is the point-slope form?

Mathematically, the point-slope form of any straight line can be calculated by using this expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.

x and y represents the data points.

From the information provided above, we have the following slope and data points on this line:

Points on x-axis = (0, 2).

Points on y-axis = (3, 0).

At data point (0, 3), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 3 = (0 - 3)/(2 - 0)(x - 0)

y - 3 = -3/2(x)

y = -3x/2 + 3

The solution of the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).

In the given question, we have to solve the solution to the system of equations

y = 2x - 3.5..................(1)

x - 2y = -14...............(2)

Now putting the value of y from the equation 1 in the equation 2.

x - 2(2x - 3.5) = -14

Now simplifying the expression using the distributive property

x - 4x + 7 = -14

-3x + 7 = -14

Subtract 7 on both side, we get

-3x = -21

Divide by -3 on both side, we get

x = 7

Now putting the value of x in the equation 1,

y = 2(7) - 3.5

y = 14 - 3.5

y = 10.5

Hence, the solution to the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).

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The complete question is:

What is the solution to the system of equations y = 2x - 3.5 and x - 2y = -14?

Answer:

of course it would be 45

Step-by-step explanation:

it right trusss

Ratio of sine of angle of incidence to the sine of angle of refraction is constant by Snell’s law.

According to Snell's Law, the refractive index, or n, is a constant that represents the ratio of a wave's angle of incidence to angle of refraction as it passes through a boundary between two mediums.

₁n₂=n₂/n₁=sin θ₁/sin θ₂= v₁/v₂,

where n is the refractive index,

v is the speed in different medium and θ is the angle between the normal and the ray at the surface of boundary.

If we do an experiment and measure the angles of incidence and refraction, we will discover that a straight line passing through the origin results from plotting the sine of the angles of incidence and refraction.

This shows that the sine of the angle of incidence and the sine of the angle of refraction are directly related, and that the ratio of the two will result in a constant value that we refer to as the refractive index. The ratio of the sines of the angles corresponds to the proportion of the wave speeds through the medium.

Thus, we can say that refractive index is constant for a given pair of media.

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The leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

What is function ?

function can be defined in such a way that it relates an input to the output.

Given function y = x-3

The degree of the function means the highest power of the variable

Here, the degree is 1, it is odd.

The leading coefficient is 1, which is positive.

By taking sample values of x, we get values of y with the graph as shown

From the graph, we can say that the degree of the function is odd, so the ends of the graph continue in opposite directions

Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

The following describes the function x-3  that the degree of the function is odd, so the ends of the graph continue in opposite directions.

Hence,  the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

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Answer:

x > -1

10 ≤ d

k ≤ -24

Step-by-step explanation:

a)

13 + 4x > 9

4x > -4

x > -1

b)

99 - 5d ≤ 4d

99 ≤ 9d

10 ≤ d

c)

3k - 9 ≤ -6k - 225

3k + 6k ≤ 9 - 225

9k ≤ -216

k ≤ -24

Two matrices are row equivalent if they can be transformed into each other using elementary row operations.

Elementary row operations are operations such as the addition or subtraction of two rows, the multiplication or division of a row by a non-zero constant, or the interchange of two rows. Row equivalent matrices are equal in terms of row space, meaning any linear combination of the rows of one matrix will yield the same linear combination of the rows of the other matrix. An example of two row equivalent matrices is given below:

Matrix A =

[tex]\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}[/tex]

Matrix B =

[tex]\begin{bmatrix} 1 & 2 & 3 \\2 & 3 & 4 \end{bmatrix}[/tex]

These matrices are row equivalent because adding the first row of Matrix A to the second row of Matrix B yields Matrix A. To show this mathematically, let row 1 of Matrix A be represented as r1, and row 2 of Matrix B be represented as r2. We can then say that r2 + r1 =

[tex]\begin{bmatrix} 1 & 2 & 3 \\6 & 8 & 10 \end{bmatrix}[/tex]

which is equal to Matrix A.

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The domain is the set of all x-values (or inputs) used by the function.  In a graph like this, you want to see how the graph lines up with the x-axis.  

As an interval, the domain is [-4,-1], as shown on the domain graph.
(Remember to write intervals from lesser-to-greater.)

The range is the set of all y-values (or outputs) used by the function.  In a graph like this, you want to see how the graph lines up with the y-axis.  

As an interval, the range is [-4,-2].  
(Again, remember to write intervals from lesser-to-greater.)

Expanding, which entails multiplying out the factors, allows an equation in factored form to be rewritten in standard quadratic form.

The steps we employ in doing so are as follows:

Opposite of expanding is factoring an expression. Parenthesis or grouping symbols are removed from an expression when it is expanded. The Greatest Common Factor (GCF) from each phrase allows each extended statement to be factored.

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If a = the measure of the smaller angle, we have:

[tex]\it a+2a+9^o=180^o\bigg|_{-9^o} \Rightarrow 3a=171^o\bigg|_{:3} \Rightarrow a=57^o[/tex]

To graph a linear inequality in slope intercept form:

The solutions that make both inequalities true are all shown on the graph of an inequality system. When you are graphing inequalities, keep the following in mind: Form your inequality as y=mx+b, the slope intercept. Either the equal sign or the provided inequality symbol may be used.

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Answer:

14.0cm

Step-by-step explanation:

if 13.8 = 12.0

then 16.1 = ?

[tex] \frac{16.1}{13.8} \times 12.0cm = 14.0cm [/tex]

Answer:

14 cm

Step-by-step explanation:

1st plant:

13.8 - 12.0 = 1.8

1.8/12 = .15

.15 x 100 = 15% growth

2nd plant:

let x =  original height

x + x(.15) = 16.1

1.15x = 16.1

x = 16.1 / 1.15 = 14.0 cm

Answer:

f = 53.13 degrees

Step-by-step explanation:

An isosceles triangle has two equal sides, so in this case the sides of length 60cm are equal. The base angle (f) is opposite the base of the triangle, which is the side of length 100cm.

To find the base angle, we can use the law of cosines.

c^2 = a^2 + b^2 - 2ab*cos(f)

where c is the hypotenuse (the side of length 100cm), a and b are the legs (the sides of length 60cm), and f is the base angle we are trying to find.

Substituting in the given values, we get:

100^2 = 60^2 + 60^2 - 2(60)(60)cos(f)

Simplifying this equation, we get:

10000 = 3600 - 3600cos(f)

so

cos(f) = (10000-3600)/3600 = 6400/3600 = (8/3)^2

then

f = cos^-1((8/3)^2)

Therefore, f = 53.13 degrees

Answer:

see explanation

Step-by-step explanation:

using the identity

• tan A = [tex]\frac{sinA}{cosA}[/tex]

consider left side

cos A × [tex]\frac{1}{tanA}[/tex]

= cos A × [tex]\frac{1}{\frac{sinA}{cosA} }[/tex]

= cos A × [tex]\frac{cosA}{sinA}[/tex]

= [tex]\frac{cos^2A}{sinA}[/tex]

= right side

A right angle is defined as an angle that measures exactly 90 degrees.

To prove this:

This definition of a right angle has been established by mathematical convention, and it is widely accepted and used in mathematics and geometry. The reason for this is that a right angle is the most convenient and natural angle to use as a standard unit of measure for angles.

One reason is that a right angle is easy to construct and measure. A right angle can be created by using a square or a set square, which are simple and inexpensive tools. Also, right angles are found in many natural and man-made objects, such as corners of walls and buildings, which makes them easy to recognize.

Another reason is that a right angle is a fundamental building block in Euclidean geometry, and it is used to define other geometric concepts such as parallel lines and perpendicular lines. The properties of a right angle make it a useful tool for solving geometric problems and for understanding the relationships between angles and shapes.

In summary, the 90 degrees definition of a right angle is a mathematical convention that is widely accepted due to its convenience, natural appearance in many objects, and its importance in Euclidean geometry.

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Answer:

when x = 12, a = 360 and b = 16.8.

Step-by-step explanation:

A given linear model shows negative correlation.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

Given that, a researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29.

Here, a linear model shows negative, or inverse, correlation.

Therefore, a given linear model shows negative correlation.

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Answer:4

Step-by-step explanation:12/3=4

The given expressions are the results of applying the function f to a value that is being multiplied by -3 or 3.

f(-3x) means that the function is applied to -3x, in this case the output is -3f(x)

f(3x) means that the function is applied to 3x, in this case the output is 3f(x)

It should be noted that the function f(x) could be any type of function and the output depends on the function's definition.

Answer: 3x^2

Step-by-step explanation:

e2023

The translation and rotation of 180° about the origin. Then the correct option is A.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

From the graph, the trapezoid W'X'Y'Z' is derived by the translation and rotation of 180° about the origin. Then the correct option is A.

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