5. An article priced at £15 in London cost R183 in 2012. How much would it have costed in rand to buy an item that was priced at £37, using the same exchange rate?​

Step-by-step explanation:

a. To create a quadratic equation that models the arrow's height, we need to find the coefficients of the equation that best fit the data. One common method is to use a least squares regression to fit the data to a quadratic equation in the form y = ax^2 + bx + c. There are several ways to perform this regression, but one common method is to use a spreadsheet program or a graphing calculator with regression capabilities.

b. Based on the quadratic equation that models the arrow's height, we can predict the height of the arrow at any distance from the archer. If Coach Deline is 500 feet away from the archer, we can plug 500 into the equation as x and find the corresponding y value. If the y value is greater than 0, then the arrow is still in the air and has not hit the ground. If the y value is equal to 0, then the arrow has hit the ground. If the y value is less than 0, then the arrow has hit the ground and passed it. Based on this information, we can determine if the arrow will hit Coach Deline or not.

The height of the statue of Abraham Lincoln memorial in Washington, DC, being 5.7912m is written as a single digit times an integer power of 10 as: 6 × 10^{-3} (approx)

The number is written in the form a*b^10 ,where we have 1<a<10

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

here, we have,

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

We're given that:

The height of the statue of Abraham Lincoln memorial in Washington, DC  is 5.7912 m.

We can rewrite it as:

5.7912 ≈ 6

Since we need to write it as a single digit times an integer power of 10, therefore, we get:

6 × 10^{-3} (approx)

Hence,The height of the statue of Abraham Lincoln memorial in Washington, DC, being 5.7912m is written as a single digit times an integer power of 10 as: 6 × 10^{-3} (approx)

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the probability that there is at least one person who wins no games.

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

Number of players = 3

number of times game is repeated = 4

P( any person wins a game ) = 1/3

P ( any person does not win a game ) = 1 - 1/3 = 2/3

P ( any person wins no game in 4 attempts ) = ( 2/3 )^4 = 16/81

Note : each player has equal chance of winning

Find the probability that there is at least one person who wins no games

lets represent the probability of each player not wining a game with alphabet A

A1 = player 1 wins no game

A2 = player 2 wins no game

A3 = players 3 wins no game

Applying the inclusion-exclusion formula

P( A1 ∪ A2 U A3 ) = P(A1 ) + P(A2) + P(A3) - P( A1 ∩ A2 ) - P( A2 ∩ A3 ) - P( A1            ∩ A3 )  + P( A1 ∩ A2 ∩ A3 )

where

P( A1 ∩ A2 ) = P( A1 wins all games )

P ( A1 wins all games in 4 attempts ) = ( 1/3 )^4 = 1/81

P( A1 ∩ A2 ∩ A3 ) = P ( no players wins any game in 4 attempts ) = 0

Hence

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

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When the opposite sides of a parallelogram ABCD are equal, the values of x and y are 17 and 10, respectively.

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. Parallelograms are classified into four categories, three of which are exceptional. Parallelograms, squares, rectangles, and rhombuses are the four kinds. A parallelogram is a quadrilateral with opposing sides that are parallel and equal. It has equal interior opposite angles.

Here,

in parallelogram ABCD, opposite sides is equal.

4y-3=37

4y=40

y=10

3x-9=42

3x=51

x=17

The values of x and y is 17 and 10 in parallelogram ABCD when opposite sides is equal.

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Pua will use 13, 1/4 cups of oatmeal.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Pua needs 3[tex]\frac{1}{4}[/tex] cups of oatmeal.

The number of 1/4 cups of oatmeal,

she will use,

= 13/4 ÷ 1/4

= 13

Therefore, she will use 13 cups.

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The correct answer is option (D). The answer is 100 on weekdays, 80 on weekends

Given that,

Ms. Liu wants to concentrate on growing her clientele and is looking for recurring business. She is less intrigued by visitors who are new to the site. The percentage of first-time users is 20%, according to analytics.

To find : What percentage of clients return on weekdays and weekends?

Number of repeat customer on weekdays = 125 * (1 - 20%) = 100

Number of repeat customer on weekend = 100 * (1 - 20%) = 80

Therefore, option is the appropriate response (D).The answer is 80 on weekends and 100 throughout the week.

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As a result, the new length and breadth are 20% greater than the original specifications.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. To calculate the percentage, divide the amount by the total value and multiply the result by 100. While many % numbers are between 0 and 100, there is no mathematical constraint that prevents percentages from taking on other values. Percentages are extensively utilized in a variety of contexts. Discounts in stores, bank interest rates, inflation rates, and numerous data in the media, for example, are all expressed as percentages. Percentages are essential for comprehending the financial elements of daily living.

Here,

If the original length and width of the living room floor are L and W, respectively, the new dimensions after increasing by 20% would be:

New Length = L + (0.20 * L) = L * 1.20

New Width = W + (0.20 * W) = W * 1.20

So the new length and width would be 20% larger than the original dimensions.

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One other pair of coordinates that could be the missing ordered pair is (4, 0).

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

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

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (-2, -3), a linear equation of this line can be calculated in slope-intercept form as follows:

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

y = 1/2(x + 2) - 3

y = 1/2x - 2

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the missing ordered pair (4, 0).

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The length of the other side of the garden is, 5 m.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The length of one side of the garden is 3m.

And, The area of the garden Is 15 m².

Now, We know that;

Area of rectangle = Length × Width

Substitute all the values, we get;

⇒ 15 = 3 × x

⇒ x = 15 / 3

⇒ x = 5 m

Thus, The length of the other side of the garden is, 5 m.

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The answer choice that best describes the function x+ - 3 is D. The degree of the function is even, 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 graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Given the function x+ - 3, the degre is even when plotted on a graph anf the left side of the graph continues down the coordinate plane and the right side continues upward.

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The surface area of the triangular prism is 270 ft².

The surface area of a triangular prism is the sum of the areas of all 5 faces. To find the area of the triangle, you can use the formula:

A = (B × h) ÷ 2, where B is the base and h is the height.

To find surface area of triangular prism we can calculate each area of all faces :

A1 = 13 × 7 = 91 ft²

A2 = 12 × 7 = 84 ft²

A3 = 5 × 7 = 35 ft²

A4 = (12 × 5) ÷ 2 = 30 ft²

A4 = (12 × 5) ÷ 2 = 30 ft²

Surface Area = A1 + A2 + A3 + A4 + A5

Surface Area = 91 + 84 + 35 + 30 + 30

Surface Area = 270 ft²

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The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

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Answer: 12%

12% is the right answer trust me

The monthly payment to the nearest cent is $1381.51,

The total of all monthly payments over the 30 years is $497,343.6,

and her total interest for the 30 years is $284,343.6.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given amount borrowed = $213,000

time period = 30 years

interest rate = 6.75% = 0.0675

to find the monthly payment,

so M = [tex]\frac{p(\frac{r}{n} )(1 + \frac{r}{n} )^{nt}}{(1 + \frac{r}{n} )^{nt} - 1}[/tex]

here n = 12 for the monthly payment

M = monthly payment

p = principal

t = time =  30 years

r = trate = 0.0675

p = $213000

so 1 + r/n = 1 + 0.0675/12

1 + r/n =  1.005625

M = [213000(0.005625)(1.00625)³⁶⁰] ÷ [(1.00625)³⁶⁰ - 1]

M = $1381.51

B:  What's the total of all monthly payments over the 30 years,

there will be 360 payments in 30 years,

a total amount of 360 payments = $1381.51*360

a total amount of 360 payments = $497,343.6

C: What's her total interest for the 30 years

total interest in 30 years = $497,343.6 - $213000

total interest in 30 years = $284,343.6.

Hence monthly payment is  $1381.51,

total of all monthly payments is $497,343.6,

and total interest for the 30 years is $284,343.6.

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Vertex of parabola = (-8 , -6)

Focus of parabola = (-8 , -23/4)

Directrix of parabola is y = -25/4

Axis of symmetry of parabola is x = -8

Direction of opening of parabola is vertically upwards.

y - intercept = 58 unit

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given equation of parabola

y = x² + 16x + 58

It can be written as

y = x² + 16x + 64 - 6

y = (x + 8)² - 6

Comparing with standard vertex form

y = a(x - h)² + k

Vertex (h, k) = (-8 , -6), a = 1

a = 1/4(f - k)

1 = 1/4(f - -6)

4f + 24 = 1

f = -23/4

Focus (h , f) = (-8 , -23/4)

Directrix is y = d

Distance from the focus to the vertex is the same as the distance from the vertex to the directrix.

-6 - (-23/4) = d - (-6)

d = -6 -6 + 23/4

d = -12 + 23/4

d = -25/4

Directrix is y = -25/4

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus:

x = -8

Direction of opening will be vertically upwards

For y-intercept, x = 0

y = (0 + 8)² - 6

y = 64 - 6

y = 58

Hence, (-8 , -6) is Vertex of parabola

(-8 , -23/4) is Focus of parabola

y = -25/4 is Directrix of parabola

x = -8 is Axis of symmetry of parabola

Direction of opening of parabola is vertically upwards.

58 unit is y - intercept

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The required final answer is option a) Incentre

The point of concurrency of the angle bisectors of a triangle is known as the "Incentre".

It is the center of the circle inscribed within the triangle, which is equidistant from all three sides of the triangle.

The incentre is the point where the angle bisectors of a triangle intersect, forming the incircle, which is the largest circle that can be inscribed inside the triangle.

The incentre is always within the triangle and is equidistant from all three sides of the triangle, making

it a useful tool in construction and design applications. In summary, the incentre is the center of the incircle of a triangle, and it is the point where the angle bisectors of the triangle intersect.

Thus, required answer is "Incentre".

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The area of this house in square meters is 152.24.

To convert square feet to square meters, you can use the conversion factor of 1 square foot = 0.092903 square meters.

A house is advertised as having 1640 square feet under the roof.

So, the area of the house in square meters is:

1640 square feet * 0.092903 square meters/square foot = 152.24 square meters.

Unit Conversion: It is defined as the changing from one quantity unit to another quantity unit followed by the method of division, and multiplication by a conversion factor.

Thus, the area of this house in square meters is 152.24 if the house is advertised as having 1640 square feet under the roof.

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There is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

In the posed query,

We must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

Option A is the proper response, so.

The complete question is:-

What is the probability that a standard normal random variable will be between .3 and 3.2?

A. .3814

B. .3808

C. .9993

D. .6179

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Answer:5/5x-15/x

Step-by-step explanation:

Answer: your answer should be 3x^2 + 10x -75 / 5x.

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4.  Multiply the numbers

5. Re-order terms so constants are on the left

6. Combine exponents

7. Multiply the numbers

8. Rearrange terms

therefore hopefully giving you the answer of 3x^2 + 10x -75 / 5x.

Answer:

y=4x-7

Step-by-step explanation:

i hope it helped

Answer:The product of a number t and eight is twelve: t * 8 = 12

Twice the sum of a number m and five is the difference of nine and n: 2(m + 5) = 9 - n

Twenty-one is the quotient of a number y and 4: y / 4 = 21

Thrice the difference of number b and one is the product of a number c and ten: 3(b - 1) = c * 10

Step-by-step explanation:

Answer:

1. b-7= 10

2. T-(8)=12 or T X 8 =12

3. 2 (X+5)

4. 21= 4/y

5. 3 (b-1)= C (10)

The complex number in trigonometric form is given as follows:

8.49 with an angle of 45º.

A complex number has a real part and an imaginary part, and is defined as follows:

z = a + bi.

In which:

Considering that the x-axis gives the real part, and the y-axis gives the imaginary part, the number in this problem is given as follows:

z = -6 - 6i.

For the trigonometric form, we have that:

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The dilation of the triangle JKL is with a scale factor of d = 1/2

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ΔJKL

Now , the coordinates of J = J ( 8 , 12 )

The coordinates of K = K ( 4 , 8 )

The coordinates of L = L ( 12 , 6 )

Now , let the dilated triangle be represented as ΔJ'K'L'

Now , the coordinates of J' = J' ( 4 , 6 )

The coordinates of K' = K' ( 2 , 4 )

The coordinates of L' = L' ( 6 , 3 )

So , the scale factor is given by d = y₂/y₁

Scale factor d = 1/2

Hence , the scale factor of the dilation is 1/2

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The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is [tex]$\sqrt{301}$[/tex].

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are [tex]$\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$[/tex] and [tex]$\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$[/tex]. Taking the cross product of the two vectors gives us the normal vector to the plane, [tex]$\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$[/tex]. Therefore, the vector orthogonal to the plane is [tex]$\vec{n} = (8, -8, 12)$.[/tex]

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

[tex]$A = \sqrt{s(s-a)(s-b)(s-c)}$[/tex]

where [tex]$s = \frac{a+b+c}{2}$[/tex] . In this case, the sides are [tex]$a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$[/tex], and[tex]$c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$[/tex]. Plugging these values into the formula, we get

[tex]= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$[/tex]Therefore, the area of triangle PQR is [tex]$\sqrt{301}$[/tex]

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is [tex]$\sqrt{301}$[/tex].

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Mr. Smith walked a greater Distance, but Mrs. Smith walked faster.

It should be noted that speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In the table given, if can be seen that Mr and Mrs. Smith started walking home from different locations at the same time. In this case, the greater distance was by Mr Smith.

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Mr. and Mrs. Smith started walking home from different locations at the same time. They each walked at a constant speed.

Mr. Smith's distance (in kilometers) from home as a function of time (in minutes) is given by the following table of values:

Time Distance

14 3.6

21 2.9

28 2.2

The graph of Mrs. Smith's distance (in kilometers) from home as a function of time (in minutes) is shown below.

Who walked a greater distance to get home?

Choose 1 answer:

(Choice A) Mr. Smith

(Choice B) Mrs. Smith

(Choice C) They both walked the same distance

Who walked faster?

Choose 1 answer:

(Choice A) Mr. Smith

(Choice B) Mrs. Smith

(Choice C) They both walked at the same speed

The volume of the pyramid is given by the equation V = 400 cm³

The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.

Volume of Pyramid = ( 1/3 )a²H

Given data ,

Let the volume of the pyramid be represented as V

Now , the equation will be

The height of the pyramid H = 12 cm

The base side length of the pyramid a = 10 cm

So , Volume of Pyramid = ( 1/3 )a²H

Substituting the values in the equation , we get

Volume of Pyramid V = ( 1/3 ) x 10² x 12

Volume of Pyramid V = 4 x 100

Volume of Pyramid V = 400 cm³

Hence , the volume of the pyramid is 400 cm³

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The exponential equation in the standard form will be written as y = 250 (1.06)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

When he first received it, he looked online and found that the value of the book was listed at $250. He checked again one year later and saw that the value has increased to $265.

Then the equations are given as,

250 = ab⁰

a = 250

265 = ab¹

265 = 250 b

b = 1.06

Then the exponential equation in the standard form will be written as,

y = 250 (1.06)ˣ

The exponential equation in the standard form will be written as y = 250 (1.06)ˣ.

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Answer:

Step-by-step explanation:

m

a. The number of passengers for each cruise line in thousands:

4,133,000 passengers ÷ 1,000 = 4,133 passengers

2,369,000 passengers ÷ 1,000 = 2,369 passengers

1,295,000 passengers ÷ 1,000 = 1,295 passengers

928,000 passengers ÷ 1,000 = 928 passengers

679,000 passengers ÷ 1,000 = 679 passengers

So, the answer is 4,133; 2,369; 1,295; 928; 679.

b. The mean number of passengers can be found by adding the number of passengers for each cruise line and then dividing the total by the number of cruise lines, which is 5.

(4,133 + 2,369 + 1,295 + 928 + 679) ÷ 5 = 10,514 ÷ 5 = 2,102.8 passengers

So, the mean number of passengers is 2,102.8 passengers.

c. The range is the difference between the highest and lowest number of passengers, which is:

4,133 - 679 = 3,454 passengers

So, the range is 3,454 passengers.

d. The standard deviation can be calculated using the formula for the standard deviation of a sample. However, this calculation is quite complex and requires a significant amount of mathematical knowledge and computational resources. Without access to those resources, the standard deviation cannot be calculated

The standard deviation is a measure of the amount of variation or dispersion from the mean. It shows how spread out the values in a set of data are. To calculate the standard deviation, the difference of each value from the mean is squared and then divided by the number of items in the set. The standard deviation provides a way to quantify the degree of variation of the values around the mean. It is a useful tool for understanding how much each value in a set deviates from the average.

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Jack will have $332 after 5 years

The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the future value of the investment, including interest

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested/borrowed for

r = 2% = 0.02, P =  $300, n = 12 (12 times in a year), t = 5 years

A = P (1 + r/n)^(nt)

A = 300 (1 + 0.02/12)^(12*5)

A = 300 (1 + 0.02/12)^(60)

A = $332

Thus, Jack will have $331.52 after 5 years

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The surface area and volume of a sphere can be calculated using the following formulas:

Surface area: 4 * π * r^2

Volume: (4/3) * π * r^3

Where r is the radius of the sphere.

For the spheres given, the surface areas and volumes are:

(i) radius = 7 cm

Surface area: 4 * π * 7^2 = 4 * π * 49 = 196π cm^2

Volume: (4/3) * π * 7^3 = (4/3) * π * 343 = 588π cm^3

(ii) radius = 6.3 cm

Surface area: 4 * π * 6.3^2 = 4 * π * 39.69 = 158.48π cm^2

Volume: (4/3) * π * 6.3^3 = (4/3) * π * 251.187 = 447.938π cm^3

(iii) radius = 42 cm

Surface area: 4 * π * 42^2 = 4 * π * 1764 = 7056π cm^2

Volume: (4/3) * π * 42^3 = (4/3) * π * 74088 = 42672π cm^3

Learn more about radius here: brainly.com/question/27696929

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