2. A laptop usually sells for £1320 (including VAT). A store is advertising a discount of 15%
if it is purchased on a Sunday and a further 10% student discount. What is the price that a
student should pay including VAT) for a Sunday purchase?
(10 Marks)

Answer:

f(x)=-x when x belongs to (-infinity, 3)

f(x)=-2 when x belongs to [3, 6]

f(x)=2x-7 when x belongs to (6, infinity)

Answer:

z=9

Step-by-step explanation:

z-5=4. /+5

z=4+5

z=9

Answer:

z<-1

Step-by-step explanation:

5<z=4

collect like terms

z=<4-5

z<-1

This question is solved by proportions.

Step 1:

A nurse is preparing to administer cefaclor 40 mg/kg/day.

This means that the first step is finding the baby's weight in kg.

The child weighs 48lb. Each lb has 0,453592kg.

So the child weighs 48*0.453592 = 21.7724kg.

Step 2:

Here, we find the daily dose.

For each kg, the baby is administered 40 mg.

Since the baby weighs 21.7724 kg, the daily dose is of 40*21.7724 = 870.896 mg.

Step 3:

Here, we find how many mL in a day.

For 375 mg, 5 mL are administered. How many mL for 870.896 mg?

375 mg - 5 mL

870.896 mg - x mL

Applying cross multiplication:

[tex]375x = 5*870.896[/tex]

[tex]x = \frac{5*870.896}{375}[/tex]

[tex]x = 11.6[/tex]

Step 4:

Here, we find how many mL per dose.

Equal doses every 8 hours, so 24/8 = 3 doses per day.

11.6/3 = 3.9

Thus, the nurse should administer 3.9 mL per dose.

For more on proportional variables, you can check https://brainly.com/question/23536327.

Answer:

x = 3.9 ml  quantity of ml / dose

Step-by-step explanation:

The child weighs 48 lbs.

Then the weigh in kgs is  48 * 0.454 = 21.792 kgs  (since 1000 lbs = 454 kgs)

If the nurse has to prepare doses according to 40 mg/kg/day then for a child of 21.792 kgs it is needed  21.792*40 mg or 871.68 mg/day, and the fact that he or (she) need to take three doses then each dose will be  of

871.68/3 = 290.56 mg

So far we know that each dose should contain 290.56 mg, now we have the cefactor in a suspension wich density is 375 mg/5 ml or 75 mg/ml

Then by rule of three

if              75  mg     ⇒   1 ml

        290.56 mg     ⇒     x (ml)

x = 290.56/75  ( mg*ml)/ mg

x = 3.87 ml round to the nearest tenth

x = 3.9 ml

Answer:

The minimum number of drivers you would need to survey is 601.

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].

The margin of error is:

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

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

What is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04?

The number is n for which M = 0.04.

We don't have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex]. Then

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

[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]

[tex]n = 600.25[/tex]

Rounding up:

The minimum number of drivers you would need to survey is 601.

Answer:

D. 3

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.

Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.

Answer:

euan had lowest score on test 2

The student with lowest score on test 2 is Euan.

Bar graph is used for the graphical representation of data or quantities by using bars or strips.

Here,

The z-score results of four students on two different mathematics tests is represented by the given bar graph.

Calculating the scores of each students for the two tests respectively.

1) Carla

Test 1: 0.75

Test 2: -0.5

2) Dave

Test 1: -0.5

Test 2: 1

3) Euan

Test 1: 0.25

Test 2: -1

4) Felicia

Test 1: 1.25

Test 2: 1.5

Hence,

The student with lowest score on test 2 is Euan.

To learn more about bar graph, click:

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Answer:

ABC

Step-by-step explanation:

= 2^14.2^3 +  2^14

= 2^14. (2^3 +1)

= 2^14 . 9  

Vì 2^14.9 chia hết cho 9 nên 2^17 + 2^14 chia hết cho 9

(. là dấu nhân)

Answer:

đúng

Step-by-step explanation:

Answer:

263

Step-by-step explanation:

with 955 in the account, you subtract all the amount withdrawed from the main money in the account.

955-245-447

=263

The [tex]\pm[/tex] symbol means "plus minus".

Writing [tex]1.5 \pm 0.85[/tex] is the same as saying [tex]1.5 + 0.85\ \text{ or } \ 1.5 - 0.85[/tex]

The lower bound, or left endpoint, is 1.5 - 0.85 = 0.65

The upper bound, or right endpoint, is 1.5 + 0.85 = 2.35

Based on what you have, it looks like you probably followed those steps. However, you have the items in the wrong order. You should have 0.65 listed first and 2.35 listed last. Also, you need to have "or equal to" as part of the inequality sign.

So you should have [tex]0.65 \le x \le 2.35[/tex]

As for your graph, you have the endpoints in the wrong spot.

The left endpoint should be between the 0.6 and 0.7 to indicate 0.65

The right endpoint should be between 2.3 and 2.4 to indicate 2.35

See the diagram below.

Answer:

Hence we do not have enough evidence to conclude that a liquid diet caused more weight loss.

Step-by-step explanation:

Here the answer is given as follows,

Answer:

(4,0)

Step-by-step explanation:

When line intercepts x axis, y must be 0

when y =0

3x-2(0)=12

x=4

hence answer is (4,0)

Answer:

4,0

Step-by-step explanation:

Calculate the area by using 2 rectangles:

13 x 5 = 65 square feet

5 x 4 = 20 square feet

Total area = 65 + 20 = 80 square feet.

Multiply price per square foot by total area:

6.25 x 80 = 500

Cost = $500

Answer:

x = 2 yd

Step-by-step explanation:

Angles of 45 degreees = two congruent legs

for the Pythagorean theorem

2x^2 = 8

x^2 = 4

x = 2

9514 1404 393

Answer:

  152.3°

Step-by-step explanation:

The arcsine function only gives angles in quadrants I and IV. Since this is a quadrant II angle, its value will be ...

  θ = 180° -arcsin(0.4649) = 180° -27.7°

  θ = 152.3°

9514 1404 393

Answer:

  $48.64

Step-by-step explanation:

The monthly payment amount is given by the amortization formula ...

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the loan amount, r is the annual interest rate compounded n times per year for t years.

Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...

  A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))

  A ≈ $48.636 ≈ $48.64

You will need to pay $48.64 each month to pay off the charge in 5 years.

If you're familiar with surface integrals, start by parameterizing the surface by the vector-valued function,

r(u, v) = 3 cos(u) sin(v) i + 3 sin(u) sin(v) j + 3 cos(v) k

with 0 ≤ u ≤ 2π and 0 ≤ v ≤ arccos(1/√8).

Then the area of the surface (I denote it by S) is

[tex]\displaystyle\iint_S\mathrm dA = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}\left\|\dfrac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm dv\,\mathrm du \\\\ = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}9\sin(v)\,\mathrm dv\,\mathrm du \\\\ =18\pi \int_0^{\arccos\left(1/\sqrt8\right)}\sin(v)\,\mathrm dv = \boxed{\frac{9(4-\sqrt2)\pi}2}[/tex]

hopefully this answer can help you to answer the next question. can you choose this answer as the brainliest answer and give five stars

Answer:

6,78

Step-by-step explanat

ion:data size :10

Sample mean:15

Standard sample deviation :6,782

Answer:

6,78

Step-by-step explanation:

Answer:

yes, the volume = 16 ft^3

Answer:

12 days

Step-by-step explanation:

The answer of the problem is the LCM of 3 and 4=12. Hence the answer is 12 days

On 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.

It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.

We have:

Amira starts an exercise program on the 3rd of March.

She will swim every 3 days and cycle every 4 days.

Total days =3 + 4 = 7 days = 1 week

The day she swims and cycles on the same day = LCM of 3 and 4

= 3, 6, 9, 12, 15

= 4, 8, 12, 16

= 12

Thus, on 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.

Learn more about the LCM here:

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Answer:

C

Step-by-step explanation:

Answer:

θ = [tex]\frac{\pi}{4}[/tex]  

θ = [tex]\frac{7\pi}{4}[/tex]

Step-by-step explanation:

2cosθ - √2 = 0

First, add √ 2 to both sides

2cosθ - √2 = 0

          +√2  +√2

2cosθ = √2

Divide both sides by 2

2cosθ/2 = √2 / 2

cosθ = [tex]\frac{2}{\sqrt{2}}[/tex]

Use arccos to find θ

arccos([tex]\frac{2}{\sqrt{2}}[/tex]) = [tex]\frac{\pi}{4}[/tex]  and  [tex]\frac{7\pi}{4}[/tex] = θ

Answer:

A.

Step-by-step explanation:

A. is the answer because they list all of the sandwiches, soups, and beverages with every possible combination.

Step-by-step explanation:

what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?

if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.

so, all possible outcomes are 4²⁰.

that means the probability to guess all 20 right is

1/4²⁰

a tiny, tiny number.

and the probabilty to have all wrong ?

she has 4 choices to pick 1 of 3 wrong answers.

so, the probability is 3/4 to answer the first question wrong.

for that she has again then the same chance to get the second question wrong too.

so, it is 3/4 × 3/4 = 9/16

and so on.

the probability to guess all 20 wrong is then

(3/4)²⁰ ≈ 0.0032

that is still a small number but much, much larger than the probability to get everything right.

still, even the goal to truly get everything wrong is highly unlikely.

Answer:

x=52 Here is y

Step-by-step explanation:

Answer:

Hello,

Answer : 1400 and 1575

Step-by-step explanation:

Let's say a and b the ywo numbers

[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]

Answer:

C. [tex]-2x^3+2\sqrt{x}[/tex]

Step-by-step explanation:

[tex]\sqrt{x} -x-(2x^3-\sqrt{x} -x)[/tex]

Change the signs of g(x)

[tex]\sqrt{x} -x-2x^3+\sqrt{x} +x[/tex]

Simplify

[tex]-2x^3+2\sqrt{x}[/tex]

I hope this helps!

pls ❤ and mark brainliest pls!