Work out the percentage change when a price of £20 is decreased to £3.
.

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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Answer:

Option (c) : f' (x) = - 2 / 5x

The estimate's percent error is 4%, to the closest percentage.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Find the difference between the estimate and the actual value:

Actual value - Estimated value = 676 - 650 = 26

The absolute value of the difference is 26, indicating that the actual value exceeded the estimated value.

Next, we need to find the relative error, which is the difference divided by the estimated value:

Relative error = Difference / Estimated value = 26 / 650

Finally, we can convert the relative error to a percentage by multiplying it by 100:

Percent error = Relative error x 100 = 26 / 650 x 100 ≈ 4

Therefore, the percent error, to the nearest percent, of the estimate is 4%.

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Answer:

To determine the velocity of the roller coaster as it moves down, we use the kinematic equation which is expressed as 2gy = vf^2 - v0^2 where g is the gravitational acceleration, y is the elevation of the roller coaster, vf and vo are the final and initial velocity. We calculate as follows:

2gy = vf^2 - v0^2

Since it starts at rest, v0 is zero.

2gy = vf^2

vf = √2gy

vf = √2(9.8)(101)

vf = 44.5 m/s ----> option B

Step-by-step explanation:

Answer:

63

Step-by-step explanation: The ratio from planet A to B is 100 to 3. If an elephant weight 2100 is planet a, then we are multiplying 21 to hundred. Whatever you do on the left side you have to do it on the right side and if you multiply 21 and 3 on the right side then you get 63.

Answer:

63 pounds

Step-by-step explanation:

The ratio for Planet A to Planet B is

100 : 3

Creating a proportionality with the unknown as x

=> \(\frac{100}{3} = \frac{2100}{x}\)

Isolating x would give

x = \(\frac{2100 * 3}{100}\)

x = 21 × 3

x = 63 pounds

Answer: P(B)= 15 P(A^c)

Step-by-step explanation:

Multiply the first one then the second one multiply and then do to the 2nd power

Step-by-step explanation:

every coordinate you are going to make a point for example the first which is (-1,4) the first number goes through the x-axis left to right if the number is negative it goes to the left so the -1 on the horizontal line, then the 4 is y-axis vertical line up and down, so take that point on -1 then go up 4

The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value given will be expressed thus:

= 24 - (5 + 3)^2 + 4 × 2^3

= 24 - (8)² + 4 × 8

= 24 - 64 + 32

= -8

The value is -8.

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a) The value of x is 42.6 when k =16/3 is directly proportional to y.

b) The value of x is -56 when k is -7  is directly proportional to y.

What kind of variation is one where x and y are directly proportional?

x varies directly as y

x α y

x = ky

a) x=6 ; y = 32

x = ky

6 = k(32)

k = 16/3

if y = 8

then,

x = (16/3) * 8

= 128/3

x = 42.6

Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.

b) x= 14 and y = -2

x = ky

14 = k(-2)

k = -7

if y = 8

then,

x = ky

x= (-7) 8

x = -56

Hence, the value of x is -56 when k is -7  is directly proportional to y.

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Answer:

  (c)  $63.75

Step-by-step explanation:

The discounted price will be 100% -25% = 75% of the marked price. Mike's final price will be ...

  ($80 +5)×0.75 = $63.75

Peter is 1.68 meters tall.

What is height?

Height is a measure of the distance between the base and the top of an object, or the distance between the bottom and the top of a vertical structure. It is often used to describe the vertical dimension of an object or structure, such as the height of a building, the height of a person, or the height of a mountain. In mathematics, height can also refer to the vertical distance between two points on a coordinate plane or the vertical dimension of a three-dimensional shape. The height of a triangle, for example, is the perpendicular distance from the base to the highest point of the triangle.

Peter's height is Thandi's height plus the additional 0.45 m. Therefore:

Peter's height = Thandi's height + 0.45 m

Peter's height = 1.23 m + 0.45 m

Peter's height = 1.68 m

Therefore, Peter is 1.68 meters tall.

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The length of the ladder needed to reach a window with 50 feet above the ground is 52 ft.

The angle formed with the ground and the ladder is 75 degrees.

The window is 50 ft above the ground.

The situation forms a right triangle.

Therefore, using trigonometric,

sin 75  = opposite / hypotenuse

where

Therefore,

sin 75 = 50 / h

cross multiply

h = 50 / sin 75

h = 50 / 0.96592582628

h = 51.763809036

h = 52 ft

Therefore, the length of the ladder needed to reach a window with 50 feet above the ground is 52 ft.

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer:

Step-by-step explanation:

5=cx-ax=x(c-a)

x(c-a)/5=1

(c-a)/5=1/x

x=5/(c-a)

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

1.) V=πr2h=π·6.52·16≈  2123.71663, rounded= 2123.72

2.)V=πr2h=π·22·3≈37.69911, rounded= 37.80, or 37.8

3.) V=πr2h=π·12·3≈9.42478, rounded= 9.42

4.)70.69

5.)V=πr2h=π·3.82·3≈136.09379, rounded= 136.09

Answer:

\(\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........\)

The interval of convergence is:\((-\frac{2}{3},\frac{16}{3})\)

Step-by-step explanation:

Given

\(f(x)= \frac{9}{3x+ 2}\)

\(c = 6\)

The geometric series centered at c is of the form:

\(\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.\)

Where:

\(a \to\) first term

\(r - c \to\) common ratio

We have to write

\(f(x)= \frac{9}{3x+ 2}\)

In the following form:

\(\frac{a}{1 - r}\)

So, we have:

\(f(x)= \frac{9}{3x+ 2}\)

Rewrite as:

\(f(x) = \frac{9}{3x - 18 + 18 +2}\)

\(f(x) = \frac{9}{3x - 18 + 20}\)

Factorize

\(f(x) = \frac{1}{\frac{1}{9}(3x + 2)}\)

Open bracket

\(f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}\)

Rewrite as:

\(f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}\)

Collect like terms

\(f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}\)

Take LCM

\(f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}\)

\(f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}\)

So, we have:

\(f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}\)

By comparison with: \(\frac{a}{1 - r}\)

\(a = 1\)

\(r = -\frac{1}{3}x + \frac{7}{9}\)

\(r = -\frac{1}{3}(x - \frac{7}{3})\)

At c = 6, we have:

\(r = -\frac{1}{3}(x - \frac{7}{3}+6-6)\)

Take LCM

\(r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)\)

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n\)

Substitute 1 for a

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n\)

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n\)

Substitute the expression for r

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n\)

Expand

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]\)

Further expand:

\(\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................\)

The power series converges when:

\(\frac{1}{3}|x - \frac{7}{3}| < 1\)

Multiply both sides by 3

\(|x - \frac{7}{3}| <3\)

Expand the absolute inequality

\(-3 < x - \frac{7}{3} <3\)

Solve for x

\(\frac{7}{3} -3 < x <3+\frac{7}{3}\)

Take LCM

\(\frac{7-9}{3} < x <\frac{9+7}{3}\)

\(-\frac{2}{3} < x <\frac{16}{3}\)

The interval of convergence is:\((-\frac{2}{3},\frac{16}{3})\)

Answer:

where is F

Step-by-step explanation:

Answer:

(a)First Row, First Column =1

(b)First Row, second Column =0

(c)Second Row, First Column =0

(d)Second Row, second Column =1

Step-by-step explanation:

Given matrix \(M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\)

The Inverse of a 2X2 matrix

\(A=\left(\begin{array}{ccc}a&b\\c&d\end{array}\right)\)

can be found using the following:

\(A^{-1}=\dfrac{1}{ad-bc} \left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\)

Therefore:

\(M^{-1}=\dfrac{1}{(5*-5)-(3*-8)} \left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=-1\left(\begin{array}{ccc}5&-3\\8&-5\end{array}\right)\\=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\)

Next, we find the product \(M^{-1}M\)

\(M^{-1}M=\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\left(\begin{array}{ccc}-5&3\\-8&5\end{array}\right)\\=\left(\begin{array}{ccc}-5*-5+3*-8&-5*3+3*5\\-8*-5+5*-8&-8*3+5*5\end{array}\right)\\=\left(\begin{array}{ccc}1&0\\0&1\end{array}\right)\)

Therefore:

(a)First Row, First Column =1

(b)First Row, second Column =0

(c)Second Row, First Column =0

(d)Second Row, second Column =1

NOTE: The multiplication of a matrix and its inverse always gives the identity matrix as seen above,

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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The median would best describe the centre of the distribution for a highly skewed right histogram of US household income.  The correct option is A.

The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.

Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.

The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.

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Answer:

Below in bold.

Step-by-step explanation:

First term a1 = 13

11th term a11 =  a1 + 10d = 83

So a1 + 10d - a1 = 83 - 13

10d = 70

d = 10

The common difference d = 7.

Sum of n terms = (n/2)[2a1 + (n - 1)d]

Sum of the first 20 terms:

S20 = (20/2)[2*13 + (20-1)7]

S20 = 10 *(26 + 19*7)

S20 = 10*159 =  1590.

Answer:

y-intercept = (0, 8)

axis of symmetry= -b/2a

Step-by-step explanation:

Also when you want something to be squared use this symbol ^

Answer:

832

Step-by-step explanation:

align the numbers for standard multiplication and multiply the numbers pretending the decimal isn't there. after you multiply the 2 numbers together... add , then just bring the decimal point back down in a straight line. it should cancel out the zero, which leaves you with 832.

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The third quartile of the given data set is 37.

In order to determine the third quartile or the five-number summary for the data, we would arrange the data set in an ascending order:

15,18,20,21,24,26,29,34,37,40,41

For the first quartile (Q₁), we have:

Q₁ = [(n + 1)/4]th term

Q₁ = (11 + 1)/4

Q₁ = 3rd term

First quartile (Q₁) = 20

For the third quartile (Q₃), we have:

Q₃ = [3(n + 1)/4]th term

Q₃ = 3 × 3

Q₃ = 9th term

Third quartile (Q₃) = 37

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Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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