A torch and battery cost £2.50 altogether.The torch costs £1.50 more than the battery.

What fraction of the total price is the torch?

Answers

Answer 1

Answer:

4/5

Step-by-step explanation:

t + b = 2.50

t = b+1.50

Substitute

b+1.50+ b = 2.50

Combine like terms

2b + 1.50=2.50

2b =1

b = .5

t = b+ 1.5

t = .5+ 1.5

t = 2

The fraction of the total price

t/2.50

2/2.50

20/25

4/5

Answer 2

Answer:

80% of the total price is torch.

Step-by-step explanation:

Let

t=cost of torch

b=cost of battery

A torch and battery cost £2.50 altogether.

t+b=2.5

The torch costs £1.50 more than the battery.

t-b=1.5

Keep in mind:

When equations of the form

a+b = Sum

a-b = Diff

then the solution is immediately

a=(Sum+Difference)/2

b=(Sum-Difference)/2

and apply the rule,

t=(2.5+1.5)/2 = £2

b=(2.5-1.5)/2 = £1

Torch / total

= 2/2.5

= 80%


Related Questions

What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060

Answers

Answer:

Option (D)

Step-by-step explanation:

Sum of interior angles of a polygon is represented by the expression,

Sum of interior angles = n(n - 1)×180°

Here n is the number of sides of a polygon

If n = 18,

Sum of 18 sided polygon = (18 - 1) × 180°

                                         = 7 × 180°

                                         = 3060°

Therefore, sum of interior angles of a 18 sided polygon will be 3060°.

Option (D) will be the answer.

Answer:

2880

Step-by-step explanation:

SUM=_-2=

18-2=16

16*180 = 2880 OR

18*160 = 2880 degrees

1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)

3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)

7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?

Answers

Step-by-step explanation:

68$53++83(-$(7(3($++$

Answer: 5. -x^2 + 7x + 18

Explanation:

(x+2)(9-x)
= 9x - x^2 + 18 - 2x
= -x^2 + 7x + 18

Help ASAP please .
Which expression represents the volume of the sphere,
in cubic units?
3/4pi(6)^2
4/3pi(6)^3
3/4pi(12)^2
4/3pi(12)^3

Answers

Answer:

second option

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )

Here r = 6 , thus

V = [tex]\frac{4}{3}[/tex]π(6)³

Answer:

Second option

Step-by-step explanation:

Volume of a sphere =  [tex]\frac{4}{3}*\pi *r^{3}[/tex]

→ Substitute in the value of radius

Volume of a sphere =  [tex]\frac{4}{3}*\pi *6^{3}[/tex]

Find the values for a and b that would make the equality true.
-3(2x2 + ax + b) = –6x2 + 12x – 15
a =
b=

Answers

Answer:

a = - 4, b = 5

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms on the right side.

- 3(2x² + ax + b)

= - 6x² - 3ax - 3b

Comparing like terms with - 6x² + 12x - 15

x - term → - 3a = 12 ( divide both sides by - 3 )

                    a = - 4

constant term → - 3b = - 15 ( divide both sides by - 3 )

                               b = 5

The sum of three numbers is 180. If the first number is (2 x minus 11), and the second is (x minus 4) which expression represents the third number? 165 minus 3 x 187 minus x 195 minus x 195 minus 3 x

Answers

Answer:

The third number is 195-3x

Step-by-step explanation:

Given:

sum of three numbers, a, b, c is 180.

a=2x-11

b=x-4

c= ?

Solution:

a+b+c = 180

2x-11 + x-4 + c = 180

c = 180 - (2x-11) - (x-4)

= 180 -2x+11 - x+4

= 180 + 11 + 4 -2x -x

= 195 -3x

Answer:

D

Step-by-step explanation:

pllllllease help me asap

Answers

Answer & Step-by-step explanation:

When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, let's use this equation to solve for the rate of change of each question.

Problem 1:

[tex]Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}[/tex]

The rate of change of this equation is 2/3

Problem 2:

[tex]Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2[/tex]

The rate of change for this equation is 2

Problem 3:

[tex]Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6[/tex]

The rate of change for this equation is 6

Find the value of x in each case:

Answers

Answer:

45

Step-by-step explanation:

From the figure given, TV and RS are parallel.

Therefore, angle VTS and angle RST equal (Alternate angles)

Thus, angle VTS = angle RST = x

Angle T + angle S + angle R = 180° (sum of angles in a triangle)

2x + x + x = 180

4x = 180

Divide both sides by 4 to solve for x

x = 180/4

x = 45

The value of x in each case is 45

If we input 45 as a value of x in the angles in the triangle, the sum of what we have will give us 180°.

Answer:45

Step-by-step explanation:

Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?

Answers

Answer:

[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]

Step-by-step explanation:

In the attached diagram

CA=CO+OA

CO=DB

Therefore:

5=2+OA

OA=3 Units

The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:

OB=12 units

OA=3 units

Using Pythagoras theorem

[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]

El número de lados de un polígono de 4690,44 cm² de área, 38,7 cm de apotema y cuya longitud de su lado es 12,12 cm.

Answers

Answer:

su respuesta sería 21521.3

the base of a triangle is x cm and its height is (x-7) Write down the expression of the triangle

Answers

Step-by-step explanation:

if you mean the area of the triangle then it is S = 1/2*x(x-7)

Answer:

Step-by-step explanation:

b= x cm

h = (x - 7) cm

Area of triangle = [tex]\frac{1}{2}*x*(x-7)\\\\[/tex]

                           [tex]\frac{x*x-x*7}{2}\\\\=\frac{x^{2}-7x}{2}[/tex]   square cm

Predict the number of pancakes that would have 48 chocolate chips

Answers

The answer would be 6 number of pancakes. Hope it helps

A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h

Answers

Answer:

d) 405 = 15 times 4.5 times h

The height of the prism 'h' = 6 inches

Step-by-step explanation:

Explanation:-

Given Volume of prism

                            V = 405 cubic inches

Given length of the prism

                         L = 15 inches

Given width of the prism

                       W = 4.5 inches

The volume of the prism

                        V = l w h

                       405 = 15 ×4.5× h

                       405 = 67.5 h

Dividing '67.5' on both sides , we get

                      h = 6 inches

Final answer:-

The height of the prism 'h' = 6 inches

Answer: V = l w h. 405 = 15 times 4.5 times h

Step-by-step explanation:

Given the following :

Volume of prism = 405 in^3

Length = 15 inches

Height = h

Width = 4.5 inches

Recall :

The volume of a prism is the product of the Base and the height.

That is;

Volume = Base × height

However, Base of prism is given by the area of the base shape of the prism.

From our parameters Base shape of the prism is a rectangle.

Therefore, Area of rectangle = Length × width

= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism

Therefore, Volume of prism equals ;

Volume = 15 × 4.5 × h

Volume = 405in^3

Volume = Base × height

405 = 15 × 4.5 × h

A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?

Answers

Answer:

the slope of the perpendicular bisector is -2/3

Step-by-step explanation:

The slope of the line joining the two points P1(0,3), P2(6,12) is given by

m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5

The slope m2 of a line perpendicular to the previous line is given by

m1*m2 = -1

solving

m2 = -1/m1 = -1/ (3/2) = -2/3

THerefore the slope of the perpendicular bisector is -2/3

A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.

Answers

Answer:

0.5

Step-by-step explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]

The probability of selecting a purple marble given that the marble has dots on it is 0.5.

Pls answer this question.... ​

Answers

Answer:

2310cm³

Step-by-step explanation:

volume= πr²h

22/7× radius of circle × height

circumference= πd

44cm=22/7×d, diameter= 7 cm, radius= 3.5cm

v= 22/7× 3.5× 21 = 2310cm³

The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?

Answers

Answer:

10

Step-by-step explanation:

This is an arithmetic sequence.  The common difference is -6, and the first term is 52.

a = 52 − 6(n − 1)

When n = 8:

a = 52 − 6(8 − 1)

a = 52 − 42

a = 10

(04.03 MC)
Choose a system of equations with the same solution as the following system:
6x + 2y = -6
3x – 4y = -18​

Answers

Answer:

x = -2 and y = 3

{y = -3 x - 3, y = (3 x)/4 + 9/2} = x = -2 and y = 3

Step-by-step explanation:

Solve the following system:

{6 x + 2 y = -6

3 x - 4 y = -18

Express the system in matrix form:

(6 | 2

3 | -4)(x

y) = (-6

-18)

Solve the system with Cramer's rule:

x = -6 | 2

-18 | -4/6 | 2

3 | -4 and y = 6 | -6

3 | -18/6 | 2

3 | -4

Evaluate the determinant 6 | 2

3 | -4 = -30:

x = -6 | 2

-18 | -4/(-30) and y = 6 | -6

3 | -18/(-30)

Simplify -6 | 2

-18 | -4/(-30):

x = -1/30 -6 | 2

-18 | -4 and y = 6 | -6

3 | -18/(-30)

Simplify 6 | -6

3 | -18/(-30):

x = -(-6 | 2

-18 | -4)/30 and y = -1/30 6 | -6

3 | -18

Evaluate the determinant -6 | 2

-18 | -4 = 60:

x = (-1)/30×60 and y = -(6 | -6

3 | -18)/30

(-1)/30×60 = -2:

x = -2 and y = -(6 | -6

3 | -18)/30

Evaluate the determinant 6 | -6

3 | -18 = -90:

x = -2 and y = (-1)/30×-90

(-1)/30 (-90) = 3:

Answer: x = -2 and y = 3

___________________________________________

Solve the following system:

{y = -3 x - 3

y = (3 x)/4 + 9/2

Express the system in standard form:

{3 x + y = -3

-(3 x)/4 + y = 9/2

Express the system in matrix form:

(3 | 1

-3/4 | 1)(x

y) = (-3

9/2)

Write the system in augmented matrix form and use Gaussian elimination:

(3 | 1 | -3

-3/4 | 1 | 9/2)

Add 1/4 × (row 1) to row 2:

(3 | 1 | -3

0 | 5/4 | 15/4)

Multiply row 2 by 4/5:

(3 | 1 | -3

0 | 1 | 3)

Subtract row 2 from row 1:

(3 | 0 | -6

0 | 1 | 3)

Divide row 1 by 3:

(1 | 0 | -2

0 | 1 | 3)

Collect results:

Answer:  {x = -2 , y = 3

Fernando is playing hide-and-seek with Darnel and Joy. Darnel is hiding 5 meters south of Fernando, and Joy is hiding due east of Darnel. If Fernando is 8 meters from Joy, how far apart are Darnel and Joy? If necessary, round to the nearest tenth.

Answers

Answer:

6.2 metres apart

Step-by-step explanation:

Find attached a diagram for proper elucidation of the question. The resulting shape is a right angled triangle with hypotenuse FJ, and the other two sides DF and DJ respectively.

Using Pythagoras theorem to get the side DJ which is the distance between Daniel and Joy. According to the theorem, the square of the hypotenuse of a right angled triangle is equal to the sum of the other two sides.

FJ² = DF² + DJ²

From the diagram, FJ = 8 and DF = 5. Substituting this values into the theorem above to get DJ;

8² = 5²+DJ²

DJ² = 8²-5²

DJ² = 64 -25

DJ² = 39

DJ = √39

DJ = 6.2 (to the nearest tenth)

This shows that Darnel is 6.2 metres away from Joy

Create a list of steps, in order, that will solve the following equation.
3(x + 1)2 = 108

Solution steps:

- Add 1 to both sides

- Divide both sides by 3

- Multiply both sides by 3

- Subtract 1 from both sides

- Square both sides

- Take the square root of both sides

PLSS HELP!!

Answers

Take a to be the first choice and so on
The order is b,f,d
Umm...I could really use up all the steps but hope it helps
Please mark as brainliest

you roll a 6-sided die with faces numbered 1 through 6, and toss a coin what is the probability of rolling a 2 or getting heads

Answers

Answer:

2/3

Step-by-step explanation:

You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.

Add 1/2 and 1/6 to get 2/3

Plz help urgently ❤️Plz

Answers

Answer:

1st fig ans=12x ^2-7x-21.

2nd fig ans

i) ( x-15)(x+2)

ii) 2(x+7)(x-9)

iii) -3x(2x+1)(5x-3)

Hope it will help uh....

Answer:

1C 2 D 3 c

Step-by-step explanation:

1, X^2-13x-30

X^2-15x+2x-30

X(x-15)+2(x-15)

(X+2)(x-15)

2, 2x^+4x-126..... Simplified As

(2x-14)(x+9)

3, -30x^3+3x^2+9x ..... Simplified as

-3x(2x+1)(5x-3)

an elastic band. which is 72cm

Answers

Initial length = 72 cm

Stretched length = 90 cm

Find the increased in length:

increase = 90 - 72 = 18

Find the percentage increase:

Percentage increase = change/original x 100

Percentage increase = 18/72 x 100 = 25%

Answer: The elastic band's length is increased by 25%

A study of an association between which ear is used for cell phone calls and whether the subject is​ left-handed or​ right-handed began with a survey​ e-mailed to 5000 people belonging to an otology online​ group, and 717 surveys were returned.​ (Otology relates to the ear and​ hearing.) What percentage of the 5000 surveys were​ returned? Does that response rate appear to be​ low? In​ general, what is a problem with a very low response​ rate? Of the 5000​ surveys, nothing​% were returned. This response rate ▼ appears does not appear to be low.

Answers

Answer:

Of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

Step-by-step explanation:

Given:

Total sample collected = 5000

Survey returned = 700

i) What percentage of the 5000 surveys were​ returned?

To find percentage returned, we have:

[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]

Percentage returned = 14%

ii) Does that response rate appear to be​ low?

Yes, the response is significantly low as only 14% is returned out of expected 100%

iii) In​ general, what is a problem with a very low response​ rate?

The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.

Therefore, of the 5000​ surveys, 14​% were returned. This response rate APPEARS to be low.

The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___

Answers

Answer:  g(x) = -7x

To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.

1. Who conducted the study described in the article?
A. a
group of
parents
B. Yale University
C. the U.S. government
McDonald's

Answers

where is the article? it is not posted

- 2 = 2+v/4 solve for the variable

Answers

Hey there! :)

Answer:

v = -16.

Step-by-step explanation:

Given:

-2 = 2 + v/4

Subtract 2 from both sides:

-2 -2 = 2 - 2 + v/4

-4 = v/4

Multiply both sides by 4:

-4 · 4 = v/4 · 4

-16 = v

There are 100 sophomores at a school. 85% of them are good students. What would the percent of good students be at school if (round the answer up to the nearest ones) ten “F” students would come to this school?

Answers

Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer

Step-by-step explanation:

Answer:

77% (rounded)

Step-by-step explanation:

1. Find 85% of 100

           100 x 0.85 = 85

     SO 85 students out of 100 students are good students.

2. Add the 10 more students to the total number.

             100 + 10 = 110 total students

3. Find the percent of good students in the total number of current students.

          85/110 = 0.77 * 100 (to convert to percent) = 77%

 

A study is performed involving two remedies for midwest farm crops who experienced the worst drought in years. In the midwest, 450 crop fields were given randomly one of two remedies. Specifically, 220 were given Remedy A and 230 were given Remedy B. A total of 74 of the 450 crop fields were salvageable, 35 from Remedy A group and 39 from Remedy B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.3822: H0: Salvage rates are the same for Remedy A and B Ha: Remedy B has a greater salvage rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points)

Answers

Answer:

Explained below.

Step-by-step explanation:

(A)

The p-value is well defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

The p-value of the test was, p = 0.3822.

That is the probability that Remedy B has a greater salvage rate than A is 0.3822, given that rates are the same for Remedy A and B.

(B)

The significance level of the test is: α = 0.05.

A small p-value (typically ≤ 0.05) specifies strong evidence against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value of the test is very large. The null hypothesis will not be rejected.

Concluding that salvage rates are the same for Remedy A and B.

(C)

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false.

In this case a type II error could have been made as the null hypothesis was not rejected.

The type II error could have been made because of the following reasons:

The sample size selected is too small. Significance level of the test must be small.

As the sample selected is quite large, the only potential consequence of this error is that the significance level of the test must be small.

Which of the following expressions are equivalent to -9/6?

Answers

Answer: a and b

Explanation:

-9/6 = 9/-6 and -9/-6

the correct answer is:

A. 9/-6

Which expression is equivalent to 2 (a + 2 b) minus a minus 2 b?

Answers

Answer:

a -2b

Step-by-step explanation:

2 (a + 2 b) - a - 2 b

Distribute

2a +4b -a-2b

Combine like terms

2a-a +4b-2b

a -2b

Answer:

a

Step-by-step explanation:

Other Questions
which statement best describes how the british government contributed to the industrial revolution beginning in great britain? A. the british government prevented industrial secrets from leaving the country so that only british companies could build on other british innovations.B. the british government refused to allow imported manufactured goods, forcing the british people to buy locally made products of all kinds. C. the british government discouraged agriculture development and progress while subsidizing heavy industry.D. the british government exercised strict control over workers, requiring that a certain percentage of them work for manufacturing companies. Rohit visited a pumpkin patch with his family. The table shows the relationship between the weight and price of a pumpkin.A table titled Pumpkin Patch Sales with two columns and six rows. The first column, Weight in pounds, has the entries, 4, 8, 12, 16, 20. The second column, Price in dollars, has the entries, 6, 12, 18, 24, 30.Which statement describes the slope of a graph of the data?For each additional pound, the price increases $0.50. For each additional pound, the price increases $1.50. For every additional dollar, the pumpkin can increase by 1.5 pounds. For every additional dollar, the pumpkin can increase by 0.5 pounds. if you can save it and solve it there on the paper solution solution solution DNA is an example of a:O A. CompoundB. Elementc. MixtureD. Atom A customer wishes to place a buy order for a security that has not been registered with the SEC. The security may be purchased if the security: How many atoms are in 9.35 moles of lithium? Which is the first step that geological must do to compare rock layers at distant locations.A. Find the absolute age of rocks at both locations B. Compare a layers at one location to layers at other locations C. Identify index fossils in one or more layers at one locations D. Collect fossil from different locations to study the organisms lifestyles What was the purpose of the Eisenhower Doctrine? The American chocolate wafer and cream cookie most of us know (and love?) is made by Nabisco and sold under the nameOreo. But an earlier brand of chocolate wafer cream-filled cookie called HydroxTM was sold from 1908 until around 1999.In 2008 a company called Leaf Brands that specializes in reviving disappeared food items decided to try to bring Hydroxcookies back. The trademark by that time was owned by the cereal maker Kellogg. Someone from Leaf contacted Kellogg'sconsumer affairs office and explained that he was a big fan of Hydrox cookies. He asked if the company had any plans tobring it back. Kellogg's consumer affairs representative said "Sorry- no plans to ever revive the Hydrox brand." Does thismean that Leaf Brands is free to use the Hydrox name? Please explain whether trademark law protects (or doesn't) atrademark that is owned but no longer being used by a company. list out the rhyming words from the poem of the clothes line The Atlantic Ocean is between San Francisco and Sydney. true or false Provide the word or words that correctly fill in the blank. New York Times v. United States (1971) is considered a landmark case in the area of _[blank]_. presidential powers congressional oversight freedom of religion freedom of the press Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. He discovers that $5$ of these coins are worth $12$ dollars in total. Assuming that the value of each coin is the same, how many dollars is his entire collection worth? what is u over 4-4= -20 Triangle $ABC$ has its vertices $A$, $B$, and $C$ on the sides of a rectangle 4 units by 5 units as shown. What is the area of triangle $ABC$ in square units? Earn 9+ points with this question:A circle is centered at O(0,0) and has a radius of sqrt(38). Where does the point K(6,1) lie?a) Inside the circleb) On the circlec) Outside the circle What is the probability of a yellow on this spinner?Be sure to reduce.[?] Please Help Me!!!!! The displacement of a particle d (in km) as a function of time t (in hours) is given by: d(t) = 2t^3 + 5t^2 3. Find the displacement, velocity and acceleration at t = 4 hours. Indicate the correct units for each of these quantities. Determine the inverse of this function. f(x) = 3 cos(2x 3) + 1