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22 A shop sells pens, pencils and rulers.
Pens
cost 30p and pencils cost 18p.
The ratio of the cost of a pencil to the cost of a ruler is 2:5
The ratio of the cost of a pen to the cost of a ruler is 1:k
Find the value of k. I

To divide the polynomials (15x + 14x^2 - 40) by (-2x - 5), we can use long division.

The steps are:

    -----------

-2x - 5 | 14x^2 + 15x - 40

    -14x^2 - 35x

    ---------------

             -20x - 40

             -20x - 50

             ---------

                     10

Therefore, (15x + 14x^2 - 40) divided by (-2x - 5) equals (14x - 20) with a remainder of 10. So the complete expression is:

(15x + 14x^2 - 40) / (-2x - 5) = 14x - 20 + 10/(-2x - 5)

or

(15x + 14x^2 - 40) / (-2x - 5) = 14x - 20 - 2/(2x + 5)

Answer:

To find the value of a4, we need to use the recursive formula for the sequence. The formula gives us the nth term in the sequence in terms of the (n-1)th term.

We are given that a1 = -7, so we can use the recursive formula to find a2, a3, and a4:

a2 = a1 - 4 = -7 - 4 = -11

a3 = a2 - 4 = -11 - 4 = -15

a4 = a3 - 4 = -15 - 4 = -19

Therefore, the value of a4 is -19.

Answer:

It should be 25.

Step-by-step explanation:

one Triangle is 5 times the size of the other triangle

length of 5 x 5 = 25

width of 3 x 5 = 15

Answer:

16r2 + 24

Step-by-step explanation:

See the attached picture

The solution is Option C.

The equation of line is given by y = -2x + 58

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 ( 2 , 54 )

Let the second point be Q ( 5 , 48 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 48 ) / ( 2 - 5 )

On simplifying the equation , we get

Slope m = 6 / -3

Slope m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 54 = -2 ( x - 2 )

On simplifying the equation , we get

y - 54 = 2x + 4

Adding 54 on both sides of the equation , we get

y = -2x + 58

Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )

Hence , the equation of line is y = -2x + 58

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The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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C. True, because to use the Law of Sines, at least two sides must be known.

The Law of Sines is a trigonometric rule that relates the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

To use the Law of Sines, at least two sides and the angle opposite one of them (or two angles and one side) must be known.

Therefore, the statement "The Law of Sines can be used to solve triangles where three sides are known" is false, as it is not necessary to use the Law of Sines to solve a triangle where all three sides are known.

In summary, the correct answer is C. True, because to use the Law of Sines, at least two sides must be known.

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a).  2^38 bytes of memory

b). 12 bits

c). The maximum number of entries in the single-level page table would be 2^38.

d). The size would be 2^38 * 4KB, which equals 2^20 pages.

e). The maximum number of entries it can have depends on the remaining bits of the logical address.

f). The amount of bits required to denote an index into the inner page table is obtained by subtracting the offset and outer page index bits from the logical address.

a. To address a physical memory size of 128GB (2^37 bytes), a 64-bit architecture would require 38 bits for the logical address, allowing access to a maximum of 2^38 bytes of memory.

b. Given that the page size is 4KB (2^12 bytes), 12 bits would be needed to specify the displacement into a page. This means that the lower 12 bits of the logical address would be used for page offset or displacement.

c. With a single-level page table, the maximum number of entries would be equal to the number of possible logical addresses. In this case, since the logical address requires 38 bits, the maximum number of entries in the single-level page table would be 2^38.

d. The size of the single-level page table is determined by the number of entries it contains. Since each entry maps to a page of size 4KB, the size of the single-level page table can be calculated by multiplying the number of entries by the size of each entry. In this case, the size would be 2^38 * 4KB, which equals 2^20 pages.

e. For a two-level page table, the size of the outer page table is determined by the number of entries it can contain. Since the outer page table uses 4KB pages, the maximum number of entries it can have depends on the remaining bits of the logical address. The number of bits used for the index into the outer page table is determined by subtracting the bits used for the inner page index and the offset from the total number of bits in the logical address.

f. The number of bits used to specify an index into the inner page table can be determined by subtracting the bits used for the offset and the bits used for the outer page index from the total number of bits in the logical address. The remaining bits are then used to specify the index into the inner page table.

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for a uniform probability density function, the height of the function is determined by the constant value that the function takes over the interval of definition, and it is determined by the requirement that the integral of the function over the interval of definition must be equal to

1. The height of a uniform probability density function over an interval [a,b] is given by:

f(x) = 1/(b-a) for a <= x <= b

where b-a is the length of the interval.

A uniform distribution is a continuous probability distribution and connected to the events which are likely to occur equally. A uniform distribution is explained by two parameters, a and b, where a is the minimum value and b is the maximum value.

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The volume of the cylinder with radius(r) 7 inches and height(h) 9 inches

is 1384.74 cubic inches.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, a cylindrical shape of radius(r) 7 inches and height(h) 9 inches.

We know the volume of a cylinder is πr²h.

∴ The volume of this cylinder is

= π×(7)²×9 cubic inches.

= 441π cubic inches.

= 1384.74 cubic inches.

For the volume of a sphere, it is (4/3)πr³.

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Answer: g = w² - 14w + 49

\(w=7-\sqrt{g}\\\\=> \sqrt{g} =7-w \\\\<=>g=(7-w)^{2}=49-14w+w^{2}\)

Step-by-step explanation:

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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Answer:

Step-by-step explanation:

y + 5 = 8(x - 0)

y + 5 = 8x - 0

y = 8x - 5

The required diameter of the given circle is PR, radius of the given circle is PQ, chord of the given circle are ST and PR, the tangent of the given circle is FG, point of tangency of the given circle is F and secant of the given circle is AB.

Given the diagram of circle, which is marked with different line segments.

Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment  points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.

Hence, the required diameter of the given circle is PR, radius of the given circle is PQ, chord of the given circle are ST and PR, the tangent of the given circle is FG, point of tangency of the given circle is F and secant of the given circle is AB.

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The present value of an investment that will pay you $15,000 in 9 years, with an appropriate discount rate of 8 percent compounded daily, is $7,638.61.

This is calculated using the following formula:

\(\begin{equation}PV = \frac{FV}{(1 + r)^n}\end{equation}\)

\(\begin{equation}PV = \frac{15000}{(1 + 0.08)^{3285}} = 0.00001059\end{equation}\)

Present Value = $7,638.61

The number of years is 9 years multiplied by 365 days per year, which is 3285 days. The interest rate is 8 percent divided by 365 days per year, which is 0.0002191780822.

In other words, if you invest $7,638.61 today at 8 percent compounded daily, you will have $15,000 in 9 years.

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The triple integral using these bounds ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.

To evaluate the triple integral ∭E (x + y + z) dV in cylindrical coordinates, we first need to express the bounds of the integral and the differential volume element in cylindrical form.

The paraboloid z = 9 - x^2 - y^2 can be rewritten as z = 9 - r^2, where r is the radial distance from the z-axis. In cylindrical coordinates, the solid E in the first octant is defined by the conditions 0 ≤ r ≤ √(9 - z) and 0 ≤ θ ≤ π/2, where θ is the angle measured from the positive x-axis.

Now, let's express the differential volume element dV in cylindrical form. In Cartesian coordinates, dV = dx dy dz, but in cylindrical coordinates, we have dV = r dr dθ dz.

Now we can rewrite the triple integral using cylindrical coordinates:

∭E (x + y + z) dV = ∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz.

The bounds of integration are as follows:

For z: 0 ≤ z ≤ 9 - r^2 (from the equation of the paraboloid)

For r: 0 ≤ r ≤ √(9 - z) (within the first octant)

For θ: 0 ≤ θ ≤ π/2 (within the first octant)

We can now evaluate the triple integral using these bounds:

∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz

= ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.

Performing the integration in the specified order, we can find the numerical value of the triple integral.

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Given that:2.7 × 103, 5.481 × 105To find: How many times smaller is 2.7 × 103 than 5.481 × 105?To compare the numbers using scientific notation, we should express them with the same base number and exponent, such as:2.7 × 103 = 0.0027 × 1055.481 × 105 = 5.481 × 105So, now we can compare the numbers:0.0027 × 105 is how many times smaller than 5.481 × 105?5.481 × 105/0.0027 × 105=2033 dp=2.03 (rounded off)Therefore, 2.7 × 103 is 203 times smaller than 5.481 × 105. The correct option is D. 2.03.

The relative wind speed will the person sense is -5.2mph.

Speed can be explained as the  distance traveled per unit of time which is how the object is moving, and it is a  scalar quantity  having magnitude of the velocity vector.

Speed of man  =2.95 mph

Speed of wind  =-2.25 mph

Relative wind speed V_R is mathematically given directly as

Vr= Vw-Vm

=-2.25 mph -2.95 mph

= -5.2mph

Therefore, relative wind speed will the person sense is -5.2mph.

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Answer:

16$ liam you can get a shout at

The solution to the initial value problem y'-4y=f(x), y(0)=0 for 0<=x<4 is given by:

y(x) = F(-4)e^(-4x)

The Laplace transform of the differential equation y'-4y=f(x) is given by:

sY(s) - y(0) - 4Y(s) = F(s)

where Y(s) and F(s) are the Laplace transforms of y(x) and f(x), respectively.

Substituting the initial condition y(0)=0 and rearranging, we get:

Y(s) = F(s)/(s+4)

Now we need to find the inverse Laplace transform of Y(s) to obtain the solution y(x). Using the partial fraction decomposition method, we can write:

Y(s) = A/(s+4) + B

where A and B are constants to be determined.

Multiplying both sides by (s+4), we get:

F(s) = A + B(s+4)

Setting s=-4, we get:

A = F(-4)

Setting s=0, we get:

B = Y(0) = y(0) = 0

Therefore, the partial fraction decomposition of Y(s) is given by:

Y(s) = F(-4)/(s+4)

Taking the inverse Laplace transform of Y(s), we get:

y(x) = L^-1{F(-4)/(s+4)} = F(-4)L^-1{1/(s+4)}

Using the table of Laplace transforms, we find that the inverse Laplace transform of 1/(s+4) is e^(-4x). Therefore, the solution to the initial value problem is given by:

y(x) = F(-4)e^(-4x)

where F(-4) is the value of the Laplace transform of f(x) evaluated at s=-4.

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Step-by-step explanation:

In the first part, he was travelling with twice the speed, or Vs, for distance

48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part :

48 - d = 2V * 2

⇒d + 4V = 48  

Second part:

d = V * 2

⇒d = 2V  

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48

s = 8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) = 16

I hope this helps

Answer:

a and d

Step-by-step explanation:

pls mark brainliest

The given statement "Qualitative data contribute to analysis and should aid the explanation of a process that may otherwise be unclear if explained by quantitative data only." is true.

Qualitative data is non-numeric information that provides insight into attitudes, behaviors, motivations, and perceptions. It is typically collected through open-ended questions, observation, and interviews. Qualitative data can provide a rich and nuanced understanding of a process or phenomenon that may not be possible to obtain through quantitative data alone. This is because qualitative data can help to uncover the underlying reasons behind a process, how people experience it, and how it is perceived by different groups. As a result, qualitative data can provide valuable context and insight into a process that may otherwise be unclear if explained by quantitative data alone.

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Answer:

Arithmetic sequence

Step-by-step explanation:

An list of numbers whereby the difference between each consecutive number is constant is called an arithmetic sequence. Given thelistvif numbers:

–8, –4, 0, 4, 8, 12 ;

We can see that each consecutive number in the list has a constant difference of 4. Hence x this is called an arithmetic sequence.

Answer:

554

Step-by-step explanation:

The largest number (5) should go in the hundreds place, the second-largest number (also 5) should go in the tens place and the smallest number (4) should go in the units place so the answer is 554.

Answer:

Option 3 \(f(x) = 1,000 x (1.12)^{x}\)

Step-by-step explanation:

Answer:

16 = 7 * d or 16 = 7d

Step-by-step explanation:

16 is equivalent to the product of 7 and a number d

Substitute mathematical signs for the words-

is equivalent means =

product means to multiply *

16 is equivalent to the product of 7 and a number d

16 = 7 * d     Could also be written as    16 = 7d