Evaluate f(3)

A. 18
B. 12
C. 4
D. 21

Answer:

[tex]\sqrt[6]{2\\}[/tex]

Step-by-step explanation:

Rewriting

2 ^1/2 ÷ 2 ^ 1/3

We know a^ b ÷ a^c = a^ (b-c)

2 ^ (1/2 -1/3)

Getting a common denominator

2^ ( 3/6 - 2/6)

2^ 1/6

[tex]\sqrt[6]{2\\}[/tex]

Answer:

[tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:

[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]

Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:

[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]

We just need to subtract 1/3 from 1/2 to get:

[tex]2^{\frac{1}{6} }[/tex]

This is the same as the 6th root of 2, which is the second option.

Answer:

The fuel efficiency of Lily's car in kilometers per liter is 12.5 km/litre.

Step-by-step explanation:

Answer:

PQ = 46

Step-by-step explanation:

The midsegment ST is half the length of the third side PQ , that is

ST = [tex]\frac{1}{2}[/tex] PQ , so

5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction

10x - 44 = 3x + 19 ( subtract 3x from both sides )

7x - 44 = 19 ( add 44 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

Then

PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46

Answer:

−3x^2+2x /x−2

Step-by-step explanation:

4x−9x^3/ 3x^2−4x−4

=  −9x^3+4x /3x^2−4x−4

=  x(−3x+2)(3x+2) /(3x+2)(x−2)

=  −3x^2+2x /x−2

Answer:

The point you are rotating at (also called the centre of rotation)

The angle of rotation (usually in degrees but I don't know your school)

Direction of the turn

Step-by-step explanation:

Answer:

$425.6 should be budgeted for weekly repairs and maintenance.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean $400 and standard deviation $20.

This means that [tex]\mu = 400, \sigma = 20[/tex]

How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?

This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 400}{20}[/tex]

[tex]X - 400 = 20*1.28[/tex]

[tex]X = 425.6[/tex]

$425.6 should be budgeted for weekly repairs and maintenance.

Answer:

First Option

Step-by-step explanation:

Given:

In the first year, the car will decrease in value by 25%.

The cost of a car is Rs. 200,000.

To find:

The worth of the car after 1 year.

Solution:

The cost of a car is Rs. 200,000 and in the first year the car will decrease in value by 25%. So, the worth of the car after 1 year is:

[tex]Worth=200000-\dfrac{25}{100}\times 200000[/tex]

[tex]Worth=200000-\dfrac{1}{4}\times 200000[/tex]

[tex]Worth=200000-50000[/tex]

[tex]Worth=150000[/tex]

Therefore, the worth of the car after 1 year is Rs. 150,000.

Answer:

$240

Step-by-step explanation:

They spend 5% of their monthly income on transportation, so you want to work out 5% of 4800.

An easy trick with 5% is to divide by 10 (drop the ending 0) and then divide by 2. This would be 4800/10/2, or 480/2, which gives 240.

**This content involves using percentages which you may wish to revise.

We have a linear function y=kx+b and we know that                                                       [tex]\displaystyle\bf \left \{ {{5*1+c=2} \atop {5p+c=-2}} \right.=>\left \{ {{c=-3} \atop {5p+c=-2}} \right. => 5p-3=-2 => p=\frac{1}{5}[/tex]                                       [tex]\displaystyle\bf Answer: \boxed{C) \quad p=\frac{1}{5} }[/tex]                            

Answer:

5/7 or 0.71 is the answer

Answer:

The answer is A

Step-by-step explanation:

C’(4, –2)

The coordinates of C' are (1, 0)

A translation moves a shape up, down or from side to side, but it does not change its appearance in any other way.

Given that, On a coordinate plane, triangle A B C has points (-2, -1), (-2, -3), (-5, -1).

When Triangle ABC is translated 6 units to the right and 1 units up.

We know that rule for translating b unit up and a unit right is

(x, y) → (x+a, y+b)

Hence, the coordinates for C' =

(-5, -1) = (-5+6, -1+1) = (1, 0)

Hence, the coordinates of C' are (1, 0)

For more references on translation, click;

https://brainly.com/question/12463306

#SPJ6

Answer:

The image point is (-1,-2)

Step-by-step explanation:

Firstly, we have to reflect the given point over the line y = -x after which we perform the translation using the coordinate (5,2)

Mathematically;

If we reflect a point (x,y) over the line y = -x

we have the coordinate change to (-y,-x)

so, (4,6) becomes (-6,-4)

Then for the translation, we add 5 to the new x-axis coordinate, then add 2 to the new y-axis coordinate

we have this as;

(-6 + 5, 2-4) = (-1,-2)

Answer:

A ∩ B

Step-by-step explanation:

The shaded part is in common between the two diagrams

We can write this part in this way :

A ∩ B

in a sale, normal prices are reduced by 10%

nathalie bought a pair of shoes in the sale for £54

what was the original price of the shoes

[tex]x = 60[/tex]

Explanation

[tex] \sf based \: on \: the \: given \: conditions \: write : x = \frac{54}{ 1 - 01} [/tex]

[tex] \sf calculate \: the \: sum \: difference: x = \frac{54}{0.9} [/tex]

convert decimal to fraction: x= 54 / 9 / 10

[tex] \sf \: divide \: a \: fraction \: by \: multiplying \: its \: reciprosal : x = 54 \times \frac{10}{9} [/tex]

[tex] \sf \: write \: as \: a \: single \: fraction : x = \frac{54 \times 10}{9} [/tex]

[tex] \sf \: reduce \: fraction \: to \: the \: lowest \: term \: by \: cancelling \: the \: greatest \: [/tex]

[tex] \sf \: common \: factor : x = 6 \times 10[/tex]

[tex] \sf \: calculate \: the \: product \: or \: quotient : x = 60 [/tex]

[tex] \sf{ \boxed{answer : x = 60}}[/tex]

Answer:

(g+5)x(g-3)

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

1/2bh

1/2 (6*4) =12

Considering there are three triangles we will multiply by 3

12*3=36

9514 1404 393

Answer:

  9

Step-by-step explanation:

The triangles are similar, so corresponding sides are proportional.

  AE/AD = EC/DB

  (x+3)/(x -1) = x/(x -3)

  x^2 -9 = x^2 -x . . . . . . . cross multiply

  x = 9 . . . . . . . . . . . add x+9-x^2 to both sides

Answer:

10

Step-by-step explanation:

given :

length WX ≅ (congruent means equal) length XY

therefore ,  WX = 3

WZ = WX + XZ

WZ = 3 + 7

WX = 10

Answer:

d

Step-by-step explanation:

its the correct answer

Hope this helps:)

Answer:

55.1 ft ; 236.7 ft^2

Step-by-step explanation:

radius = 7.5 ft

Perimeter of the semicircles = 2 * radius * pi = 2 * 7.5 * pi = 47,12389 ft

Perimeter of the rectangle = 4 * 2 = 8 ft

Total perimeter = 55,12389 ft

Area of the semicircles = radius^2 * pi = 7.5^2 * pi = 176,714587 ft^2

Area of the rectangle = 4 * 15 = 60 ft^2

Total area = 236,714587 ft^2

Answer:

Volume of cone = 33.49 inch³

Step-by-step explanation:

Missing information;

Height of cone = 8 inch

Diameter of cone = 4 inch

Find:

Volume of cone

Computation:

Radius of cone = Diameter of cone / 2

Radius of cone = 4 / 2

Radius of cone = 2 inch

Volume of cone = [1/3][πr²h]

Volume of cone = [1/3][(3.14)(2)²8]

Volume of cone = [1/3][(3.14)(4)8]

Volume of cone = [1/3][(3.14)(32)]

Volume of cone = [1/3][100.48]

Volume of cone = 33.49 inch³

Answer:

First Term = 6

Common Ratio = 3

Step-by-step explanation:

According to the Question,

Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .

Now, on solving  [tex]\frac{S_{8} }{S_{4} }[/tex]  we get,

[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]  

[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]

[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )

So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .

Answer:

2400

2640

360

Step-by-step explanation:

I am not sure the description is totally clear.

my assumptions are (based on my interpretations of the text) :

the retailer buys from the dealer with 15% discount.

but the retailer has to sell the jacket for the same price as the dealer.

so, both mark the sale price as 2400.

if the customer buys from the retailer, the retailer makes 15% profit (the discount he got from the dealer).

15% = 2400 × 15/100 = 24 × 15 = 360

the retailer makes this profit no matter what other fees or taxes are added.

if the customer buys from the dealer, the dealer makes these 15% and some more (we don't know how much) profit.

now, the final price is to include also 10% VAT

100% = 2400

1% = 2400 / 100 = 24

10% = 24 × 10 = 240

so,

final price = SP + VAT = 2400 + 240 = 2640

Answer:

500ml orange juice is the most cost effective

√9 is rational and √3 irrational number