Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £90 per night, how much will Tara pay for 4 nights?

Answer:

$58.8 million

Step-by-step explanation:

43% of x = 25.3 million

.43x = 25300000

x = 25300000 ÷ .43

x = 58837209.30

x = 58.8 million

Answer:

Pink, shiny cars were preferred by buyers at that time

Step-by-step explanation:

Rewriting the sentence, removing unnecessary words

Hi there!

[tex]\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}[/tex]

[tex]f(x) = x^2 - \frac{2}{x}[/tex]

Recall the power rule:

[tex]\frac{dy}{dx} x^n = nx^{n-1}[/tex]

Rewrite the function for ease of differentiation:

[tex]f(x) =x^2 - 2x^{-1}[/tex]

Use the power rule:

[tex]f'(x) = 2x + 2x^{-2}[/tex]

Take the derivative once more:

[tex]f''(x) = 2 - 4x^{-3}[/tex]

Rewrite:

[tex]f''(x) = 2 - \frac{4}{x^{3}}[/tex]

Answer:

Step-by-step explanation:

As you can see in the venn diagram that is attached below, The individuals that drink milk are in green, those that drink curd are in yellow, and those that drink both are in light blue. Since the sum of those that drink milk with those that drink curd is 110 and a total of 120 students were surveryed. Then this means that 10 of the students neither drink milk nor curd. These students are represented outside of the venn diagram but within the box of surveyed students.

Step-by-step explanation:

V = πr²h

V = 3 × 14² × 28

v = 16464cm³

Answer:

The 2nd one

Step-by-step explanation:

Did the test

Answer:

[tex]2 \times 4 \times 8 \times 50 \times 125 \\ \\ = 400000[/tex]

Answer:

6/7 inches

Step-by-step explanation:

If 7 stamps fit perfectly, we can find the width of each stamp by dividing the width of the frame by 7:

= 6/7

So, the width of each stamp is 6/7 inches

Answer:

80 degrees

Step-by-step explanation:

First find the the angles N and L:

5x=3x+40

2x=40

x=20

m<N= 100 m<L=100

Now we know that the sum os all Interior angles of a parallelogram is 360

and you know that opposite sides are equal

hence,

2y= 360-2(100)   y being angle M (or o)

2y= 160

y=80

Answer:

(b) [tex]x \ge -3[/tex]

Step-by-step explanation:

Given

[tex]g(x) = \sqrt{x + 3}[/tex]

Required

The domain

For [tex]g(x) = \sqrt{x + 3}[/tex] to be defined, the following must be true

[tex]\sqrt{x + 3} \ge 0[/tex]

Square both sides

[tex]x + 3 \ge 0[/tex]

Subtract 3 from both sides

[tex]x \ge -3[/tex]

Hence, the domain is:

(b) [tex]x \ge -3[/tex]

Answer:

y = -4x + 2

Step-by-step explanation:

Given the following data;

Points (x1, y1) = (0, 2)

Perpendicular line = y = ¼x + 5

To find the equation of the straight line passing;

Mathematically, the equation of a straight line is given by the formula: y = mx + c

Where;

From the question, we can deduce that the slope (m) of the perpendicular line is ¼.

y = ¼x + 5 = mx + c

Since the points are perpendicular to the equation of line, it must have a slope that is its negative reciprocal because the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, ¼ = -4

Next, we would write the equation of the straight line using the following formula;

y - y1 = m(x - x1)

Substituting into the formula, we have;

y - 2 = -4(x - 0)

y - 2 = -4x - 0

y - 2 = -4x

y = -4x + 2

Answer:

Step-by-step explanation:

Rule defining the reflection across the line x = -2 has been given as,

[tex]r_{x=-2}[/tex]

Line x = -2 will work as a mirror for the given triangle J, K, L.

That means distance of the vertices J, K and L and image points J', K' and L' will be equidistant from the line x = -2,

Vertices of the image triangle J'K'L' will be,

J' → (-5, 2)

K' → (-3, 2)

L' → (-4, 1)

Answer: 7(n + 4)

Step-by-step explanation:

I'm not sure how to explain this one, but I'll try:

Seven times the sum of a number, n, and four

7 times n + 4   (sum means addition)

Hello!

(1/3)^2x = (1/3)^x+14 <=>

<=> 2x = x + 14 <=>

<=> 2x - x = 14 <=>

<=> x = 14

Good luck! :)

Answer:

Step-by-step explanation:

Answer:

15.24m

Step-by-step explanation:

1-foot=0,304m then 50-foot=0,304*50=15,2 m

(1) False. [tex]\{0\}\in\mathscr{U}[/tex] is saying "the set containing only 0 (that is, {0}) is an element of [tex]\mathscr U[/tex]", but this is not the case. [tex]\mathscr U[/tex] is the set containing only 0 and 1.

(2) True. [tex]\{0\}\subset\mathscr{U}[/tex] means "the set {0} is a subset of [tex]\mathscr{U}[/tex]". 0 itself is an element of [tex]\mathscr U[/tex], so {0} is indeed a subset of [tex]\mathscr U[/tex].

(3) True. 0 is clearly an element of [tex]\mathscr U[/tex].

(4) False. This statement says "0 is a subset of [tex]\mathscr U[/tex]" but 0 itself is not a set, it's a number.

Given:

The x- intercepts of a parabola are (0,-6) and (0,4).

The parabola crosses the y- axis at -120.

Lucas said that an equation for the parabola is [tex]y=5x^2+10x-120[/tex] and that the coordinates of the vertex are (-1, -125).

To find:

Whether Lucas is correct or not.

Solution:

The x- intercepts of a parabola are (0,-6) and (0,4). It means (x+6) and (x-4) are the factors of the equation of the parabola.

[tex]y=a(x+6)(x-4)[/tex]             ...(i)

The parabola crosses the y- axis at -120. It means the equation of the parabola must be true for (0,-120).

[tex]-120=a(0+6)(0-4)[/tex]

[tex]-120=a(6)(-4)[/tex]

[tex]-120=-24a[/tex]

Divide both sides by -24.

[tex]\dfrac{-120}{-24}=a[/tex]

[tex]5=a[/tex]

Substituting [tex]a=5[/tex] in (i), we get

[tex]y=5(x+6)(x-4)[/tex]

[tex]y=5(x^2+6x-4x-24)[/tex]

[tex]y=5(x^2+2x-24)[/tex]

[tex]y=5x^2+10x-120[/tex]

So, the equation of the parabola is [tex]y=5x^2+10x-120[/tex].

The vertex of a parabola [tex]f(x)=ax^2+bx+c[/tex] is:

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the equation of the parabola, [tex]a=5,b=10,c=-120[/tex].

[tex]-\dfrac{b}{2a}=-\dfrac{10}{2(5)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{10}{10}[/tex]

[tex]-\dfrac{b}{2a}=-1[/tex]

Putting [tex]x=-1[/tex] in the equation of the parabola, we get

[tex]y=5(-1)^2+10(-1)-120[/tex]

[tex]y=5-10-120[/tex]

[tex]y=-125[/tex]

So, the vertex of the parabola is at point (-1,-125).

Therefore, Lucas is correct.

Answer:

Option (2)

Step-by-step explanation:

From the table attached.

First column is representing the x-values (input values) and second column is representing the value of the function (output values).

For x = -6,

f(x) = 8

For x = 7,

f(x) = 3

For x = 4,

f(x) = -5

For x = 3,

f(x) = -2

For x = -5,

f(x) = 12

Therefore, f(x) = -2 is one of the output values.

Option (2) will be the correct option.

The value that is an output of the function among the options is -2.

A function relates an input to an output.

A function relates each element of a set with exactly one element of another set.

Therefore, the output are the dependent variable. They are also called range.

Generally, they are regarded as range, output or dependent variables.

Therefore, the output of the table is f(x) values which includes the following:

Hence, the output of the function in the option is -2.

learn more on functions here: https://brainly.com/question/26608835

Answer: John Graunt

Step-by-step explanation:

John Graunt is referred to as the Columbus of statistics because his book made a fundamental contribution by attempting to demonstrate the quantitative characteristics of birth and death data.

He's regarded as the founder of demography which is the statistical study of the population of human beings.

Answer:

then why are you asking?

Step-by-step explanation:

okay

Answer:

-2,456,000

Step-by-step explanation:

-2.456 x  [tex]10^{6}[/tex] = -2,456,000

Hello,

Answer is C

[tex]a_1=0.5=\dfrac{1}{2} \\\\a_2=-0.1=-\dfrac{1}{10} =a_1*(-\dfrac{2}{10} )=a_1*(-\dfrac{1}{5} )\\\\a_3=0.02=\dfrac{2}{10^2} =a_2*(-\dfrac{2}{10} )=a_2*(-\dfrac{1}{5} )=a_1*(-\dfrac{1}{5} )^2\\...\\a_n=a_1*(-\dfrac{1}{5} )^{n-1}\\\\\boxed{a_n=0.5*(-0.2)^{n-1}}\\[/tex]

Answer:

a. you risk losing your job

b. you expose your company to litigation by violating the software agreement.

Step-by-step explanation:

Doing this puts our job at a risk and it also exposes the company that you work for to litigation. Legally, there is an agreement that puts a limit to the total number of licenses that should be in use. When you use more licenses than you should, this could be regarded as theft. Normally the best thing that you should do is to ask purchasing that they make payments for another 10 licenses. It is very likely that this software company would know of this violation. as the users try to register this software, the software company could get knowledge of this. The activations are not to be shared.

Answer:

[tex]g(-2)=20[/tex]

Step-by-step explanation:

Given [tex]g(x)=2x^2-2x+8[/tex], substitute what is in the parentheses for [tex]x[/tex] to find an output.

For [tex]g(-2)[/tex], the term [tex]-2[/tex] is in the parentheses. Thus, substitute [tex]x=-2[/tex] into [tex]2x^2-2x+8[/tex] to find [tex]g(-2)[/tex]:

[tex]g(-2)=2(-2)^2-2(-2)+8,\\g(-2)=2\cdot 4+4+8,\\g(-2)=8+4+8,\\g(-2)=\boxed{20}[/tex]

Answer:

a) 8

b) 20

c) 20

Step-by-step explanation:

a) Insert X=0 from g(0) to the equation: 2(0) power of 2 - 2x0 +8.

b) Insert X=(-2) from g(-2) to the equation: 2(-2) power of 2 - 2x(-2) +8.

c) Insert X=3 from g(3) to the question 2(3) power of 2 - 2x3 +8.

Answer:

Each area is equal to half the area of ABCD

Step-by-step explanation:

AX ≅ CY    

In parallelogram, opposite sides are equal.

AB = CD

AX + XB = CY + YD

 CY + XB = CY + YD

          XB = CY + YD - CY

XB  = CY

Both trapezoids have equal area

Area of AXYD + area of BXYC =  area of ABCD        

Answer:

A. )  Each area to equal to half of the area of ABCD

Step-by-step explanation:

Edge 2021

Answer:

see explanation

Step-by-step explanation:

To verify cos²A + sin²A = 1 with A = 90° , then

cos²90° + sin²90°

= (0)² + (1)²

= 0 + 1

= 1