A website has a 24-hour sale offering 12% off all purchases.

Dina buys a sweatshirt in the sale.
She pays £24.20 for the sweatshirt.

Calculate the original price of the sweatshirt.

Answer:

The relationship between weeks and the total amount is:

[tex]y=10x[/tex]

Step-by-step explanation:

We have here a linear relationship between weeks and the total amount. The equation of a line is:

[tex]y=mx+b[/tex]

Where:

We need two points to find the slope.

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let's use any pair points from the plot.

[tex]m=\frac{60-40}{6-4}[/tex]

[tex]m=10[/tex]

And we also see that the y-intercept is 0, therefore the equation will be:

[tex]y=10x[/tex]

I hope it helps you!

Answer:

y=10x and Over 4 weeks, Aurora saves $40

Step-by-step explanation:

Answer:

I cant see the question, sorry bro.

Answer:

Step-by-step explanation:

(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.

Let n=3

It is given that Alice always plays first.

Then, for the first move, Alice has a choice of removing 1 or 2 stones.

Case 1:

Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.

Case 2:

Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.

Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)

Now, let us assume that Bob has a winning strategy for n=3p.

We will now check if Bob has a winning strategy for n=3p+3

It is given that Alice plays first.

Case 1:

Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.

Case 2:

Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.

Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)

Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.

(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.

If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.

We will prove the given fact for both the forms simultaneously

Let m=0, i.e., n=1 or n=2

Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)

Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2

Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5

Let n=3k+4

Since Alice plays first, she has a choice to remove 1 or 2 stones.

Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.

Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.

Case 1:

Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.

Case 2:

Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.

Thus, in either case, Alice has a winning strategy.

Let n=3k+5

Since Alice plays first, she has a choice to remove 1 or 2 stones.

Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.

Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.

Case 1:

Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.

Case 2:

Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.

Thus, in either case, Alice has a winning strategy.

Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)

Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.

Answer:

B. f(x) = | x + 61 |

Step-by-step explanation:

An absolute value function is known by single vertical parenthesis demarcating the equation on both sides.

The only option with this indication is option B.

B. f(x) = | x + 61 |

This equation can be solved in two ways;

first; f(x) = - (x + 61)

second; f(x) = x + 61

Answer:

no

explanation:

Side lengths do not adhere to the triangle inequality theorem. Which states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side

Answer:

30%

Step-by-step explanation:

Find the total number of candies in the jar.

8 + 5 + 1 + 6 = 20

The probability of choosing a green candy is 6/20 = 3/10 = .3 = 30%

Answer:

(d) above [tex]74.1^o[/tex]

Step-by-step explanation:

Given

[tex]\tan w = 3.52[/tex]

Required

Determine w, using a calculator

We have:

[tex]\tan w = 3.52[/tex]

Take arctan of both sides

[tex]w = \tan^{-1}(3.52)[/tex]

Using a calculator, we have:

[tex]w \approx 74.1^o[/tex]

From the given options, (d) is true

Answer:

4(x - 4) = 4x - 16

Step-by-step explanation:

4(x - A) = 4x - 16

4x - 4A = 4x - 16

Equating Constant terms (terms without x): -4A = -16

                                                                     A = 4

Therefore , 4(x - 4) = 4x - 16

The answer is 4.

In order to find the answer, divide 4 from the each number on the right side. You pull the 4 out from 4x, and 4 from 16 to arrive at 4(x - 4).

9514 1404 393

Answer:

  m = 18

Step-by-step explanation:

In an arithmetic progression, the middle term of three is half the sum of the terms on either side.

  a1 +a3 = 2(a2)

  (m +9) +(2m +7) = 2(2m -1)

  3m +16 = 4m -2 . . . . . . collect terms

  18 = m . . . . . . . . . . . . . . add 2-3m

Answer:

$315

Step-by-step explanation:

He earns $63 everyday, and then you just have to multiply that by 5 since he works 5 days in a week.

Answer:

7[tex]\sqrt{2}[/tex] or 9.89

Step-by-step explanation:

sin45= [tex]\frac{7}{x}[/tex]

x=[tex]\frac{7}{sin 45}[/tex]

x= 7[tex]\sqrt{2}[/tex] or 9.89

Answer: 405 dollars

Step-by-step explanation:

200 * x = 270

x = 270 * 300/200. x =405 dollars

Answer:

theres no photo :))) btw God bless you

Answer:

Solution given:

perpendicular [P]=15m

base[B]=8m

hypotenuse [H]=17m

rate :4 plants per square metre

no of plants=?

we have

Area of triangular garden: ½(P*B)=½(15*8)=60m²

Now

Total no of plants =rate ×Area =4×60=240

Michael needs 240 plants in the garden

Answer:

The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

In a simple random sample of 352 students at a college, 92 reported that they have at least $1000 of credit card debt.

This means that [tex]n = 352, \pi = \frac{92}{352} = 0.2614[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 - 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.2011[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2614 + 2.575\sqrt{\frac{0.2614*0.7386}{352}} = 0.3217[/tex]

As percent:

0.2011*100% = 20.11%

0.3217*100% = 32.17%.

The 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt is (20.11%, 32.17%).

Answer:

4.right

5. obtuse

6. acute

7. obtuse

8.acute

9. right

10. right

11. acute

12. obtuse

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

complementary angles

Step-by-step explanation:

Complementary angles add to 90 degrees

Supplementary angles add to 180 degrees

A right angle is 90 degrees so they are complementary angles

Answer:

purple and red has same area

Step-by-step explanation:

Area of purple = 4 x 4 = 16 square cm

Area of red = 2 x 8 = 16 square cm

Area of yellow = 3 x 5 = 15 square cm

Answer:

Each classmate received 1/16

Step-by-step explanation:

5/8= 0.625

0.625 ÷ 10 = 0.0625

= 1/16

Answer: It's the absolute maximum, the vertex is (-2, -8).

Step-by-step explanation:

Just go to desmos graphing calculator and input the equation y = -2x^2-8x-16. You'll find the vertex and other things too.

Answer:

no

Step-by-step explanation:

8÷ 1/2

Copy dot flip

8 * 2/1 = 16

Divide 8 things in half you get 16

1/2 of 8 = 1/2 * 8 = 4

Half of 8 things is 4

They are not the same

Answer:

8 ÷ 1/2 = 16

I disagree.

Step-by-step explanation:

8 ÷ 1/2

8 × 2/1

8 × 2

16

Answer:

C

Step-by-step explanation:

Answer:

32x10^4 and 3.2x10^5

Step-by-step explanation:

Mind marking me brainliest? :)

Answer:

first and the 3rd one

Step-by-step explanation:

Answer:

4% per annum

Step-by-step explanation:

Recall :

Simple interest = principal * rate * time

Given that :

Time = 3 ; simple interest = 84 ; principal = 700

84 = 700 * rate * 3

84 = 2100 * rate

Rate = 84 /2100

= 0.04

= 0.04 * 100% = 4% per annum

Answer:

$1,260

Step-by-step explanation:

30% off  

pay 70%

70% = 0.7

1,800 * 0.7 = 1,260

$1,260