Sipho’s Mum wants him to learn to save his money. Sipho’s mum offers to add double the amount of money he saves in his bank account each month.

If x is the amount of money Sipho saves in the month and y is the total amount of money in Sipho’s bank account at the end of the month after his Mum’s deposit, write an equation to show the relationship between x and y. (Do not include any spaces in your answer)

Answer: [tex]4\sqrt{2}+1[/tex]

Step-by-step explanation:

[tex]x=0 \implies y=a+b \implies a+b=9\\\\x=30 \implies \frac{\sqrt{3}}{2}a+b=1+4\sqrt{3}\\\\\implies \frac{\sqrt{3}}{2}a-a=4\sqrt{3}-8\\\\a=\frac{4\sqrt{3}-8}{\frac{\sqrt{3}}{2}-1}=\frac{8\sqrt{3}-16}{\sqrt{3}-2}=8\\\\\implies b=9-8=1\\\\\therefore y=8\cos x^{\circ}+1\\\\x=45 \implies y=8\left(\frac{\sqrt{2}}{2} \right)+1=4\sqrt{2}+1[/tex]

Answer: do it youself

Step-by-step explanation:

10, 24, 26 are the Pythagorean triples. Therefore, option (i), (iii) and (iv) are the correct answers.

Pythagorean triples are a²+b² =c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

i) 10, 24, 26

Here, 26²=10²+24²

676=100+576

676=676

So, the given set of numbers are Pythagorean triples

ii) 2, 3, 5

Here, 5²=2²+3²

25≠13

So, the given set of numbers are not Pythagorean triples

iii) 3a, 4a, 5a; where a is any whole number

Here, (5a)²=(3a)²+(4a)²

25a²=9a²+16a²

25a²=25a²

So, the given set of numbers are Pythagorean triples

iv) 7, 24, 25

Here, 25²=24²+7²

625=576+49

625=625

So, the given set of numbers are Pythagorean triples

v) 12, 13, 15

Here, 15²=12²+13²

225=144+169

225≠313

So, the given set of numbers are not Pythagorean triples

Therefore, option (i), (iii) and (iv) are the correct answers.

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Answer:

8/3

Step-by-step explanation:

The function that fits the points (-1, 21) (3, 45) (4, 81) is 6x²-6x+9.

Quadratic Regression is a method according to which we can make an equation of a quadratic curve from given no. of x and y data points

Quadratic Regression Equation(y) = a + b x + c x^2

The formula for its coefficients is,

c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }

Where,

Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]

Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]

Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]

Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]

Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]

x and y are the Variables.

a, b, and c is the Coefficients of the Quadratic Equation

n = Number of Values or Elements

Σ x= Sum of First Scores

Σ y = Sum of Second Scores

Σ x2 = Sum of the square of the First Scores

Σ x 3 = Sum of Cube of First Scores

Σ x 4 = Sum of Power Four of First Scores

Σ xy= Sum of the Product of First and Second Scores

Σ x2y = Sum of Square of First Scores and Second Scores

when we input the points (-1,21),(3,45),(4,81)

we get the equation 6x²-6x+9

which looks like this (The image has been attached),

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The value of adjacent side x in radical form is obtained as 7/√2.

What is radical form?

Instead of employing exponents to describe the same item, a radical form of an expression uses radical signs like the square root, cube root, etc.

The given triangle is a right-angled triangle with other two angles measuring 45° as given in the diagram.

The value of hypotenuse is 7.

The adjacent side is taken to be x.

Apply the cosine formula -

cos θ = adjacent / hypotenuse

cos 45° = x/7

1/√2 = x/7

x = 7/√2

Therefore, the value of x in radical form is 7/√2.

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The probability that a randomly chosen senior does not plan to attend college right away and majors in math is 12.5%.

Step 1: Calculate the probability of not attending college immediately after high school:

100% - 77%

= 23%

Step 2: Calculate the probability of majoring in math among those who do not attend college right away: 11%

Step 3: Calculate the probability of not attending college right away and majoring in math:

11% / 23%

= 0.125

The probability of a randomly chosen senior not attending college immediately following high school and majoring in math can be calculated by first determining the probability of not attending college right away. This can be done by subtracting the percentage of seniors who plan to attend college immediately from 100%. This yields 23%. Then, the probability of majoring in math among those who do not attend college right away can be determined by taking the percentage of those who plan to major in math among this group, which is 11%. Lastly, the overall probability of not attending college right away and majoring in math can be calculated by taking the probability of majoring in math among those who do not attend college right away and dividing it by the probability of not attending college right away. This yields 11% / 23%, or 0.125.

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Answer:

y-1=3(x-2)

Step-by-step explanation:

This is the equation you have to fill in y-y1=m(x-x1) to fill in this you have to lable the points (2,1)

x,y

Answer:

----------------------------

Translate each wording to mathematical expression and compare with the given 18 = 3 × 6.

A) 18 is 3 times as many as 6:

B) 18 is 2 times as many as 9:

C) 3 is 6 times as many as 18:

D) 6 is 3 times as many as 18:

James should set up the refreshment stand on the incentre of the obtuse triangle.

The incentre of a triangle is defined as the intersection between the angle bisectors of a triangle. The inradius is the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal.

The inradius is defined as the radius of an inscribed circle in the triangle. Therefore, the required shortest equal distance from his stand to each road so that the stand is at the same distance for all three roads is on the incentre.

Hence, the correct option is C.

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The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:

3.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:

N = 3 x 2 x 1

N = 6.

(the first chosen has 3 possible options, the second has two and the third has one).

The six possible outcomes are given as follows, considering the order Red - Green - Blue:

Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.

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Answer: 6.9%

Step-by-step explanation:

Substituting into the percent error formula,

[tex]\frac{|10.9-10.2|}{10.2} \times 100 \approx 6.9\%[/tex]

The estimate of the average pulse rate in beats per minute of an animal that weighs 640 kilograms is given as follows:

29.6 beats per minute.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

(this is because there are multiple types of regression, such as logistic, exponential and quadratic regression).

The points for this problem are given as follows:

(3, 130), (28,75), (56, 75), (192, 95), (362,48), (465, 66), (521, 34).

Inserting these points into a calculator, the regression equation is given as follows:

y = -0.11x + 100.

Hence, for a weight of x = 640 kg, the estimate of the average heart rate is given as follows:

y = -0.11(640) + 100

y = 29.6 beats per minute.

The table is given by the image presented at the end of the answer.

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The second post is 30 feet tall because the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall.

1. ratio of shadows is 2:1, so for every 2 feet of shadow, the post is 1 foot tall

2. 60 feet of shadow divided by 2 is 30 feet tall

3. 24 feet of shadow divided by 2 is 12 feet tall

4. 30 feet tall is the second post

The goal post that casts a 60-foot shadow is 20 feet tall, and the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall. To find the height of the second post, we divide the length of the shadow by 2. The second post casts a 24-foot shadow, so when we divide it by 2, the post is 12 feet tall. Therefore, the second post is 30 feet tall. This is because for every 2 feet of shadow, the post is 1 foot tall, so for the 60-foot shadow, the post was 20 feet tall, and for the 24-foot shadow, the post is 12 feet tall. Therefore, the second post is 30 feet tall.

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Answer: It is not possible to determine whether rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin just by looking at the statement provided.

A dilation is a transformation that changes the size of a shape but not its shape or orientation. In a dilation, the center of dilation is a fixed point and all other points move away from or towards it by a scale factor.

The statement provided does not include any information about the scale factor, the coordinates or measurements of the rectangle's vertices or any other information that would allow to determine if EFGH is the result of a dilation of ABCD. The statement only indicates that the center of dilation is at the origin.

In order to determine if rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin, we would need additional information such as the scale factor, the coordinates or measurements of the rectangle's vertices, and the direction of dilation (enlargement or reduction)

It's worth noting that a dilation with center of dilation at origin can be performed only if the shape is symmetric.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a rectangle can be found by multiplying its length and breadth. In this case, the length is 11/5 cm and the breadth is 13/5 cm. Therefore, the area of the rectangle is (11/5 cm)*(13/5 cm) = 143/25 sq. cm = 5.72 sq. cm.

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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At $63 price point should they sell the pads to have a demand of 14 thousand pads.

p(x) = -5x + 133

Substitute x with 14,

p(14) = -5(14) + 133

       = -70 + 133

       = 63.

The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. [1] This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.

The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.

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Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.  

L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.

A - Attribution: Identifying the source of the assertion and assessing its reliability.

I - Investigation: Research and evidence collecting to support or reject the allegation.

M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.

Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.

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The angle through which the plane turns is B; 90 degrees clockwise

When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).

We are given that  plane is heading in a direction of 045° and changes course in a clockwise direction to 135°.

To Subtract the angles to get the answer

135 - 45 = 90

In terms of compass, 45 degrees is directly pointed at northeast while 135 degrees is pointed directly at southeast. We have zero degrees pointed straight north.

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In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is  

= 4 + (-6) + (8) + (-1)

Rebecca's energy level after Turn 1 = -2

Rebecca's energy level after Turn 2 = 6

Rebecca's energy level after Turn 3 = 7

Following the rule of the video game the expression is written in steps below

Rebecca is currently at energy level 4

= 4

Turn 1: 6 trees cut

= 4 + (-6)

= 4 - 6

= -2

Turn 2: 8 trees planted

= 4 + (-6) + (8)

= -2 + 8

= 6

Turn 3: 1 tree cut

= 4 + (-6) + (8) + (-1)

= 6 - 1

= 7

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Answer: 560

Step-by-step explanation:

240 / 3 = 80 x 7 = 560

Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.

1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.

Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.

Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:

Year 1: Interest earned is P3,000 (P150,000 x 2%).

Year 2: Interest earned is P3,000 ($150,000 x 2%).

Year 3: Interest earned is P3,000 ($150,000 x 2%).

Year 4: Interest earned is P3,000 ($150,000 x 2%).

Year 5: Interest earned is P3,000 ($150,000 x 2%).

Interest earned overall: P15,000

After five years, the total will be P150,000 plus P15,000, or P165,000.

Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:

Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.

Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.

Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.

Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.

Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.

Interest earned in whole was P15,612.12096.

2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.

  Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .

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Answer: The answer to part a is the same if you eat 5 cookies from each batch as you are baking because the number of cookies you have is the product of the number of batches times the number of cookies per batch minus the number of cookies you eat.

In the expression 14(5) + 2 = 3(24)

14(5) represents the total number of cookies you put in 14 bags. (14 x 5) = 70

2 represents the number of cookies left after you have put 5 cookies in each of the 14 bags.

3(24) represents the total number of cookies you made from the 3 batches of cookies. (3 x 24) = 72

So the equation can be read as:

The total number of cookies you put in bags (70) plus the number of cookies left (2) is equal to the total number of cookies made from the 3 batches (72).

Step-by-step explanation:

Answer: The answer is. 2x² - 3x + 6. Step-by-step explanation: f(x) = 2x² + 1. g(x) = 3x - 5. To find f - g(x) subtract g(x) from f(x).

I hope this helps! Have a Wonderful day! <3

One possible solution of the inequality x + y ≤ 18 and 0.1x + 0.05y ≥ 1.20 is 12 dimes and 4 nickels

An equation is a expression that shows the relationship between numbers and variables.

Let y represent the nickels and x represent the dimes

1 nickel = $0.05, 1 dime = $0.1

She has a maximum of 18 coins worth at least $1.20 combined. Hence:

x + y ≤ 18    (1)

Also;

0.1x + 0.05y ≥ 1.20    (2)

One possible solution is 12 dimes and 4 nickels

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The expression for the t1 with the tension in cable 1 that does not depend on t2 is T1sinθ1 + T2sinθ2 = mg

While we looking into the given diagram we have identified that the angle made by strings 1 and 2 are 01 and 02 respectively.

Here we also know that the tension made by strings 1 and 2 are T1 and T2 respectively.

Here let us considering that the diagram shown is the following tension components are available

And the weight of the block mg acting on the body directing the force downwards then the components are written as,

Here the Vertical component of T1 is T1 sinθ1 which acts upwards and the horizontal component of T1 is T1cosθ1 which acts to the left

Where as the another vertical component of T2 is T2sinθ2 which acts upwards then the horizontal component of T2 is T2cosθ2 acting towards right

Here we have to maintain a state of equilibrium, then the upward forces and downwards forces must be equal even as the forces on the right and left hand side must balance

According to this details the balancing the vertical components we obtain

=> T1sinθ1 + T2sinθ2 = mg

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Among the five friends Eric, Mark, Tom, Danny, and Cliff the fourth in line is Danny.

Given the information, we can make the following deductions:

Eric is the first one in line.

Cliff is standing directly behind Danny, so he is the fifth one in line.

Mark is somewhere behind Eric and Tom, but there are two people between Cliff and Mark, so it's Tom is the third one in line.

As we know that Mark is somewhere behind Eric and somewhere in front of Tom, Mark is the second one in line.

The five friends standing sequence will be - Eric, Mark, Tom, Danny, and Cliff.

Hence, the Fourth one in line is Danny.

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The equation of the tangent to the curve x=tan(θ) and y=sec(θ) at the point (1,√2) can be found by both eliminating the parameter and without eliminating the parameter.

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