1) Jack wants to buy a new smart phone for
£495. He has already saved £108.
Each week he earns £60.
He saves 40% of his earnings.
How many more weeks must he save for?
(4 marks)​

Answer:

Step-by-step explanation:

9994ddaefeaf

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

The area under the probability distribution is a measure of the probability of all the possible outcomes. Since the sum of all the probabilities of all the possible outcomes must be 1, the total area under the probability distribution must also be 1. This is because the probability of an event happening is the area under the curve of the probability distribution at that event. Thus, the total area under the probability distribution must always equal 1.

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².

A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.

Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:

Total surface area = 2πr(h + r)

Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:

165π = 2π(5 + h)5 + 2π(5)²

Simplifying this equation, we get:

165π = 10πh + 150π

Dividing both sides by 10π, we get:

h + 15 = 33

Therefore, the height of the cylinder is 18 cm (33 - 15).

Now, let's find the volume of the cylinder. The volume of a cylinder is given by:

Volume = πr²h

Substituting the values of r and h, we get:

Volume = π(5)²(18)

Simplifying this equation, we get:

Volume = 450π

Therefore, the volume of the cylinder is 450π cubic centimeters.

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Complete Question:

The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.

Answer:

$124407.36

Step-by-step explanation:

Simple interest formula: I = P x R x T / 100

22 x 12 months = 264 months (=22 years)

7854 x 6 x 264 / 100 = $124,407.36

Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

Explanation:

First we have to see that there's a first transformation from triangle ABC to triangle A'B'C'. This first transformation is a translation. Since the units are not shown in the graph I can only tell the direction of the translation: it's a translation to the right and down (more units to the right than down).

Then there's a final transformation from triangle A'B'C' to triangle A''B''C'', which is a reflection over the y-axis

Answer:

0. Translation to the right and down

1. Reflection over the y-axis

The expression that can be used to represent Rebekah's age in years given Yvonne's age is 3y - 1.

Mathematical expressions are statements that contain a combination of numbers and variables.

Given that Yvonne's age is y.

Rebekah's age = one less than 3 times y. 'less' means subtraction and 'times' means multiplication.

(3 x y) - 1

3y - 1

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The perimeter first figure that is made of a square and equilateral triangle is 52 cm.

What exactly are squares?

A square is a two-dimensional planar shape with four equal sides and four 90-degree angles. The features of a rectangle are similar to those of a square, but the distinction is that a rectangle has just its opposing sides equal.

A square's most significant qualities are

The diagonal of a square is divided into two isosceles triangles.

Square area=(side)²

Square perimeter=4*side

Now,

For first figure given that

sides of square are 14 cm in length

and length of side of equilateral triangle are=5 cm

but for finding perimeter of the figure only 3 sides of square and 2 sides of triangle are needed.

So, perimeter=3*14+2*5

=42+10

=52 cm

hence,

         The perimeter first figure 52 cm.

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The expression 2⁻³ = 1/8 into logarithmic form is log₂(1/8) = -3

In logarithmic form, the equation 2⁻³ = 1/8 can be written as log base 2 of 1/8 = -3.

Mathematically, we have

log₂(1/8) = -3

This means that the exponent that gives 2⁻³ is -3, and the logarithm base 2 of 1/8 is -3.

Logarithmic form is often used to solve exponential equations where the variable is in the exponent.

In logarithmic form, the variable is moved from the exponent to the logarithm, making it easier to solve for the unknown variable.

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Answer:

1) Translated to left by 2 unit.

2) Translated down by 1 unit.

3) Compressed vertically by 1/2 unit.

Step-by-step explanation:

Given :  Graph of the function \(f(x)=\frac{1}{2}(3)^{x+2\)

To find : How does f(x) relates to its parent function.

Solution : First we figure out its parent function

Parent function is the simplest form of the function.

f(x) parent function is \(g(x)=3^x\)

Now, how f(x) relates to g(x)

1. The parent function has been translated to the left.

Translated to left means

f(x)→f(x+b) , graph of f(x) has been translated by b unit.

In g(x)→g(x+2), graph of g(x) has been translated by 2 unit.

→The graph of g(x) has been translated to the left by 2 unit in the graph of f(x).

2)The parent function has been translated to the down.

Translated to down means

f(x)→f(x)-b , graph of f(x) has been translated left by b unit.

In g(x)→g(x)-1, graph of g(x) has been translated down by 1 unit.

→The graph of g(x) has been translated to the down by 1 unit in the graph of f(x).

3)The parent function has been compressed.

Compressed means

f(x)→a g(x) , graph of f(x) has been compressed by a unit.

In g(x)→(1/2)f(x), graph of g(x) has been compressed vertically by 1/2 unit.

→The graph of g(x) has been compressed vertically by 1/2 unit in the graph of f(x).

Answer:

Multiplication property of the equality

The fully factorized expression is: (3x + y)(9x² - 3xy + y²) + 8 + 9xyz.

To factorize the expression 27x³ + y³ + 2³ + 9xyz, we can use the sum of cubes formula and factor out common terms.

Let's break it down step by step:

Start with the given expression:

27x³ + y³ + 8 + 9xyz.

Notice that the first three terms, 27x³ + y³ + 8, form a sum of cubes expression.

The sum of cubes formula is a³ + b³ = (a + b)(a² - ab + b²).

Apply the sum of cubes formula to the first three terms:

27x³ + y³ + 8 = (3x + y)(9x² - 3xy + y²) + 8.

Now we have (3x + y)(9x² - 3xy + y²) + 8 + 9xyz.

The fourth term, 9xyz, cannot be factored further because there are no common factors.

The expression 27x³ + y³ + 2³ + 9xyz can be factorized as (3x + y)(9x² - 3xy + y²) + 8 + 9xyz.

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Answer (assuming that the shape is a right triangle):

If looking for the hypotenuse: 21.63

If looking for one leg, given other leg is 12, and the hypotenuse is 18: 13.42

Step-by-step explanation:

Given the length of two sides of a right triangle, we can use the pythagorean theorem to find the length of the third side. The pythagorean theorem is \(a^{2} + b^{2} = c^{2}\) or \(c=\sqrt{(a^{2} + b^{2})}\). Given this question, I do not know what side of the triangle the problem is looking for, I would assume the hypotenuse, so let's do that first.

\(c = \sqrt{(12^{2} +18^{2})} \\c = \sqrt{468} \\c = 21.63\)

Or we can manipulate the equation to find different scenarios of possible legs. Such equation that can be used is \(a = \sqrt{c^2 - b^2}\), where c is the hypotenuse.

Only one scenario is possible, with the hypotenuse being 18 because the hypotenuse cannot be less than one of the legs, or that leg basically becomes the hypotenuse because such side is the largest (12 < 18).

So our last scenario is, if we are looking for one leg, given other leg is 12, and the hypotenuse is 18.

\(a = \sqrt{18^2-12^2} \\a = \sqrt{180} \\a = 13.42\)

These are our possible answers.

Using the exterior angles theorem, the measures of the named angles are:

m∠PQR = 51°

m∠PRQ = 96°

Based on the exterior angles theorem, the measure of the exterior angle of a triangle has an angle degree that is equal to sum of the interior angles of the triangle.

Therefore, the following equation would be set to find the value of x:

33 + 10x + 1 = 17x - 1

34 + 10x = 17x - 1

Combine like terms

34 + 1 = 17x - 10x

35 = 7x

35/7 = 7x/7

5 = x

x = 5

m∠PQR = 10x + 1 = 10(5) + 1 = 51°

m∠PRQ = 180 - (17x - 1) = 180 - (17(5) - 1) = 96°

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Answer:

-29

Step-by-step explanation:

replace the variables with the numbers provided. m = -4 so replace the m in the equation with -4:

3 - (-4)n

same thing with the n.  n=-8 so replace the n in the equation with -8:

3 - (-4)(-8)

and then all you have to do after that is solve it using PEMDAS

multiply -4 and -8 first:

3 - 32

then solve 3-32 and you end up with -29.

The braking distance is the distance the car travels before coming to a stop after the brakes are applied

a. The braking distances are as follows;

b. If the car takes 450 feet to brake, it was traveling with a speed of 98.211 ft./s

Reason:

The given function for the braking distance is D = 2.6 + v²/22

a. The braking distance if the car is going 25 mph is therefore;

25 mph = 36.66339 ft./s

\(D = 2.6 + \dfrac{36.66339^2}{22} = 63.7 \ ft.\)

At 25 mph, the braking distance is approximately 63.7 ft.

At 55 mph, the braking distance is given as follows;

55 mph = 80.65945  ft.s

\(D = 2.6 + \dfrac{80.65945^2}{22} \approx 298.35 \ ft.\)

At 55 mph, the braking distance is approximately 298.35 ft.

At 85 mph, the braking distance is given as follows;

85 mph = 124.6555 ft.s

\(D = 2.6 + \dfrac{124.6555^2}{22} \approx 708.92 \ ft.\)

At 85 mph, the braking distance is approximately 708.92 ft.

b. The speed of the car when the braking distance is 450 feet is given as follows;

\(450 = 2.6 + \dfrac{v^2}{22}\)

v² = (450 - 2.6) × 22 = 9842.8

v = √(9842.2) ≈ 98.211 ft./s

The car was moving at v ≈ 98.211 ft./s

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Answer:

20 square yards

Step-by-step explanation:

Area of workshop

= length * width

= 5 * 4

= 20 square yards

Answer:

Step-by-step explanation:

The distance covered for the different routes are northern route = 2,000 miles ,central route is insufficient information , and southern route ≈ 1,500 miles.

Distance covered by the rider completed the whole way represents the Mean distance.

Let us analyze the northern, central, and southern routes in terms of the median distance covered and the mean distance covered,

Northern Route (Maine to Washington),

Number of attempts= 2

Distance covered by both riders = 2,000 miles

Both riders quit in Montana.

Since there have only been 2 attempts on the northern route,

Consider the median distance covered to be the same as the mean distance covered, which is 2,000 miles.

Central Route (Virginia to California),

Number of attempts = 19

Riders who didn't make it out of Virginia = 9

Riders who made it all the way to the Pacific = 10

For the central route, the information provided does not indicate the exact distances covered by the riders who succeeded or failed.

This implies, cannot determine the median or mean distance covered on this route.

Southern Route (Florida to San Diego),

Number of attempts = 32

Rider who completed the whole way = 1

Rider who quit before starting = 1

Riders who quit in Texas (between 1,300 and 1,700 miles) = 30 (evenly distributed)

Since the 30 riders who quit in Texas were evenly distributed between 1,300 and 1,700 miles,

Estimate the median distance covered to be approximately halfway between these values, which is 1,500 miles.

The rider who completed the whole way represents the mean distance covered on this route.

Therefore, distance for the routes,

Northern Route is Median distance covered = Mean distance covered = 2,000 miles.

Central Route is Insufficient information to determine median or mean distance covered.

Southern Route is Median distance covered ≈ 1,500 miles,

Mean distance covered = Distance covered by the rider who completed the whole way.

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The above question is incomplete, the complete question is,

Doug is going to ride his bicycle 3 , 000 miles across the United States, from coast to coast. He wants to choose the route that will give him the greatest chance of success. Here's what he finds in his research: There have been 2 attempts on the northern route from Maine to Washington. Both of those riders made it 2 , 000 miles and quit in Montana. There have been 19 attempts on the central route from Virginia to California; 9 of those riders didn't make it out of Virginia and the other 10 made it all the way to the Pacific. There have been 32 attempts on the southern route from Florida to San Diego. One of those riders made it the whole way. Another realized he was out of shape, and quit before he even started. The other 30 riders quit somewhere in Texas. They were evenly distributed between 1 , 300 and 1 , 700 miles. For the northern route, the median distance covered will be the mean. For the central route, the median distance covered will be the mean. For the southern route, the median distance covered will likely be the mean.

Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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the probability of A or B occurring is 0.64.

Disjoint events refer to events that have no common elements. If two events are disjoint, they cannot occur at the same time. Let A and B be two disjoint events such that P(A) = 0.21 and P(B) = 0.43.

To find the probability of either event occurring, find P(A or B). The probability of either event happening

\(P(A\cup B) = P(A) + P(B) - P(A\cap B)\)

Here, A and B are disjoint events, so P(A and B) is zero. That is,

\(P(A\cup B) = P(A) + P(B) - P(A\cap B)\)

\(= P(A) + P(B)\)

= 0.21 + 0.43

= 0.64

Therefore, the probability of A or B occurring is 0.64.

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Answer:

d= 8 t

Step-by-step explanation:

In 1 hour 30 minutes it ran for 12 miles.

So, time t =1.5 hours(Because 1 hour 30 minutes)

distance d =12

We know distance d= rate 'r' * time 't'.

So, using given information , find the rate

12= r *1.5

Divide both sides by 1.5

8=r

So,  equation would be d =8 t.

Where 't' is in hours.

Answer:

Use a factor tree. For example, 625 = 5 x 125 = 5 x 5 x 25 = 5 x 5 x 5 x 5. Because there are 4 fives, and we are looking for the square root, (5 x 5) (5 x 5) = 625. Therefore the square root of 625 is 25.

The correct answer of cos(θ) is option (b) -40/41.

To find cos(θ) when the terminal side of angle θ in standard position intersects the unit circle at point P(-40/41, -9/41), we can use the coordinates of P.

In a unit circle, the x-coordinate represents the value of cos(θ). Therefore, cos(θ) is given by the x-coordinate of the point P.

In this case, P has coordinates (-40/41, -9/41). The x-coordinate is -40/41.

So, cos(θ) = -40/41.

The correct answer is option (b) -40/41.

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Answer:

Condition:

If a series converges, then the terms of the series approach 0.

Converse:

If the terms of a series approach 0, then the series converges.

K=basketball, S= baseball

10K

5S

3 K & S

26 total

P(K) = 10/26, P(S) = 5/26 P(K^S) = 3/26

P(K v S) = P(K) + P(S) - P(K^S) = 10/26 + 5/26 - 3/26 = 12/26 = 6/13

Probability of randomly getting a student who plays either basketball or baseball = 6/13