Evelyn bought 8.4 gallons of gas for $23.94. what equation can be used to determine the price of each gallon of gas?

Answer:

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]

Step-by-step explanation:

Given

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]

Required

Simplify

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]

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Considering the denominator of the first bracket

[tex]1 - cos^2x[/tex]

This can be rewritten using different of two squares as follows:

[tex](1 - cosx)(1 + cosx)[/tex]

So, [tex]1 - cos^2x[/tex] can be replaced with [tex](1 - cosx)(1 + cosx)[/tex] in the given expression.

Also, from trigonometry identity

[tex]tan\frac{x}{2} = \frac{1 - cos x}{sin x}[/tex]

So, [tex]tan\frac{x}{2}[/tex] can be replaced with [tex]\frac{1 - cos x}{sin x}[/tex] in the given expression

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[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex] becomes

[tex](\frac{sinx}{(1-cosx)(1+cosx)}) * \frac{1 - cos x}{sin x}[/tex]

[tex](\frac{sinx * (1 - cos x)}{(1-cosx)(1+cosx) * sin x})[/tex]

Cancel out similar expressions

[tex]\frac{1}{1+cosx}[/tex]

The expression cannot be further simplified.

Hence:

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]

The simplified form of the expression :

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]

We have some trigonometric formula as:

[tex]sin2x=2sinx= cosx\\2cos^{2} x=1+cos2x[/tex]

We have the expression

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} \\=\frac{sinx}{sin^{2} x} .tan\frac{x}{2} \\=\frac{1}{sin x} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .\frac{sin\frac{x}{2}}{cos\frac{x}{2}} \\=\frac{1}{2cos^{2} \frac{x}{2}}\\=\frac{1}{1+cos{x} }[/tex]

Therefore, the simplified form of the expression is:

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]

Learn more:https://brainly.com/question/13126358

Answer:

- 5

Step-by-step explanation:

Step 1:

g ( x ) = - 3x + 1      Function

Step 2:

g ( x ) = - 3 ( 2 ) + 1       Input x

Step 3:

g ( x ) = - 6 + 1      Multiply

Answer:

g ( x ) = - 5      Add

Hope This Helps :)

Answer:

The age of the wood is [tex] t =  17527.5 \  years [/tex]

Step-by-step explanation:

   From the question we are told that 88% of  of the C-14 found in living trees of the same type had decayed , this means that the proportion of C-14 that is remaining is mathematically evaluated as

    [tex]  1 - 0.88 = 0.12[/tex]

Hence

[tex] N = 0.12N_o[/tex]

Here  N represents the remaining C-14 while [tex]N_o[/tex] is the original  amount of  C-14

Generally the half life of C-14 is  [tex]h =  5730 \  years[/tex]

Generally from the formula of radioactive decay

       [tex]N  =  N_o  *  2^{-\frac{t}{h} }[/tex]

=>    [tex]0.12N_o =  N_o  *  2^{-\frac{t}{5730} }[/tex]

=>    [tex]0.12  =    2^{-\frac{t}{5730} }[/tex]

taking the natural log of both sides

=>  [tex] ln [0.12]  =   ln[ 2^{-\frac{t}{5730} }][/tex]

=>  [tex] ln [0.12]  =  -\frac{t}{5730}ln(2) [/tex]

=>   [tex] t =  17527.5 \  years [/tex]

The appropriate age of burned wood will be "17527.5 years".

According to the question,

The proportion of C-14 = 1 - 0.88

                                      = 0.12

then,

N = 0.12 N₀

Now,

The half-life of C-14 will be:

h = 5730 years

By using Radioactive decay formula, we get

→      N = N₀ × [tex](2)^{-\frac{t}{h} }[/tex]

By substituting the values,

0.12N₀ = N₀ × [tex](2)^{-\frac{t}{5730} }[/tex]

   0.12 = [tex]2^{-\frac{t}{5730} }[/tex]

By taking "log" both sides,

ln[0.12] = ln[[tex]2^{-\frac{t}{5730} }[/tex]]

ln[0.12] = -[tex]\frac{t}{5730 \ ln(2)}[/tex]

hence,

The age will be:

         t = 17527.5 years

Thus the above response is correct.

Find out more information about radioactive decay here:

https://brainly.com/question/1236735

Answer:

I haven't seen this question before, but the correct way to write it is 78+78+78=234

Answer:

Complete the statements.

Substitute the given value for the

✔ variable

.

Use the

✔ order of operations

to simplify.

First, complete the  

✔ multiplication

inside the parentheses.

Next, complete the

✔ subtraction

inside the parentheses.

Last, complete the addition.

The value is

✔ 8

.

Step-by-step explanation:

Plz give me brainlest

Answer:

Variable, order of operations, multiplication, subtraction, 8.

Step-by-step explanation:

Got it right Edge2021

Answer:

it is 7.1

Step-by-step explanation:

how i got my answer is because jasmine ran 8.2 minute per mile

and Katie was 1.1 slower than jasmine so we will have to subtract  like this

8.2

- 1.1

  7.1 so katie ran 7.1 minutes per mile

If Katie ran at a rate that was 1.1 minutes per mile slower than Jasmine's.She takes 29.2 minutes to run.

It is defined as the change in values of a dependent variable with respect to the independent variables. the rate of change of distance with respect to time denotes the speed i.e. m/sec.

It is given that, Katie ran 4 miles. She ran at a rate that was 1.1 minutes per mile slower than Jasmine.

Time is taken by Katie for the given rate,

T = 5 miles × 8.4 mins / mile

T = 42 minute

The rate for Jasmine,

r = 8.4 - 1.1

r=7.3

The time for which Katie run,

t = 4 × 7.3

t = 29.2 minute

Thus, if Katie ran at a rate that was 1.1 minutes per mile slower than Jasmine's. She takes 29.2 minutes to run.

The question is incomplete.

The complete question is"Katie ran 4 miles at a rate of 1.1 miles slower than jasmine how many minutes did Katie run if jasmine ran 5 miles at 8.4 minutes per mile"

Learn more about the rate of change here:

brainly.com/question/12786410

#SPJ2

Answer:

1. Vertex-M sides- LM MN

2. Vertex-D sides- ED CD

3. Vertex-R sides- SR RQ

4. Vertex-T sides- ST TU

5. angle 3 angle D angle CDE

6. angle 4 angle F angle GFE

7. angle 1 angle F angle GFE

8. angle 3 angle I angle HIJ

Answer:

n = 484

Step-by-step explanation:

If Confidence Interval  CI = 95 %   then α = 5%  and α/2 = 2,5 %

α/2 = 0,0125

MOE for normal distribution is:

MOE = z * σ/√n

For α/2 = 0,0125    ⇒ z(score) = -2,2

MOE = |-2,2| * 4/√n

0,4*√n = 8,8

√n = 8,8 / 0,4

√n = 22

n = 484

Answer:

Step-by-step explanation:

A...................................

∠MIH and ∠IHS are same side interior angles and sum up to 180° as per property, therefore

B...................................

∠AVM and ∠VAS are same side interior angles

and ∠VAS and ∠LAH are vertical angles, which are equal as per property of vertical angles, so:

C...................................

Obtuse angle at the intersection of AV and HI, if name the intersection point O:

Answer:

176.37 pounds are in 80 kilograms

Step-by-step explanation:

The kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.

A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms.

Answer:

A) 1.75

Step-by-step explanation:

75% = .75

Growth Factor = 1 + Growth Rate (decimal)

Growth Factor = 1 + .75

Growth Factor = 1.75

I hope this helps!

-TheBusinessMan

Answer:

Home Depot

Step-by-step explanation:

Home Depot Has better charges because you have to multiply the question to see which one is lower.

Answer:

x=4

Step-by-step explanation:

it tel you that f(x) = 7 so replace "f(x)" for 7 in the equation. You then get 7 = 4x - 9 so now you solve for x. You have to isolate x so you add 9 to the other side since you do the opposite of -9. Once you add 9 and 7, then divide the answer by 4. You should get 4 = x.

Work:

f(x) = 4x - 9

7 = 4x - 9

7 + 9 = 4x

16 = 4x

16 ÷ 4 = x

4 = x

Complete question :

A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.

Answer : 1/3

Step-by-step explanation:

For a coin :

Sample space = (T, H)

Probability = required outcome / Total possible outcomes

Probability of tail, p(T) = 1 / 2 = 0.5

For a fair die:

Sample space = (1, 2, 3, 4, 5, 6)

Required outcome = number greater than 2 = (3, 4, 5, 6) = 4

P(number greater than 2) = 4/6 = 2/ 3

Hence, probability of a tail, then a number greater than 2 :

(1/2 * 2/3) = 2 /6 = 1/3

Answer:

on what

Step-by-step explanation:

??????

Answer:

What do you need help with?

Step-by-step explanation:

Upload a picture

Answer:

8/15

Step-by-step explanation:

Answer:

yeah fr

Step-by-step explanation:

Answer:

4000 and 7000

Step-by-step explanation:

The image showing the complete question is attached.

Answer:

1) Scale factor = 2

2) Scale factor = 4

3) Scale factor = ½

4) Scale factor = 2

5) Scale factor = 1

6) Scale factor = ¼

7) Scale factor = 1

Step-by-step explanation:

Scale factor is a number by which the dimensions of an object are multiplied in order to create an enlarged or reduced object.

Now, from the image attached;

1) From P to Q, we see that the length of Q seems to be double that of P. Similarly, the width of Q seems to be double that of P. Thus, each dimension of P is said to be multiplied by 2 to achieve the enlarged dimensions of Q.

Thus, scale factor = 2

2) From P to R, we see that the length of R seems to be 4 times that of P. Similarly, the width of R seems to be 4 times that of P. Thus, each dimension of P is said to be multiplied by 4 to achieve the enlarged dimensions of R.

Thus, scale factor = 4

3) From Q to S, we see that the length of S seems to be half of that of Q. Similarly, the width of S seems to be half of Q. Thus, each dimension of Q is said to be multiplied by ½ to achieve the reduced dimensions of S.

Thus, scale factor = ½

4) From Q to R, we see that the length of R seems to be double that of Q. Similarly, the width of R seems to be double that of Q. Thus, each dimension of Q is said to be multiplied by 2 to achieve the enlarged dimensions of R.

Thus, scale factor = 2

5) From S to P, we can see that the dimensions of both rectangles remain the same. Thus, S was multiplied by a factor of 1 to get P. Scale factor = 1

6) From R to P, we see that the length of P seems to be a quarter that of R. Similarly, the width of P seems to be quarter of R. Thus, each dimension of R is said to be multiplied by ¼ to achieve the reduced dimensions of P.

Thus, scale factor = ¼

7) From P to S, we can see that the dimensions of both rectangles remain the same. Thus, P was multiplied by a factor of 1 to get S. Scale factor = 1

Answer:

-7 minus 9 = -16

-3-(-10) =7

8-12=-4

4-(-5)=9

Step-by-step explanation:

im in 7th grade on edginuity got it all right

Answer:

The square root of the variance.

The average distance from the mean expected of the data.

Step-by-step explanation:

Standard deviation is a measure of dispersal. It determines the average distance from the mean expected of the data.

                Standard deviation = [tex]\sqrt{variance}[/tex]

Answer:

A)+17311 represent the value in the statement.

B)-237 represent the value in the statement.

Step-by-step explanation:

A) The highest elevation in a country is Mt. Snowy with an altitude of 17,311 feet.

Elevation is in the positive direction

So, the positive integer will represent the given situation

So, The highest elevation in a country is Mt. Snowy with an altitude of +17311

Thus +17311 represent the value in the statement.

B)The lowest elevation in the country is Green Valley with an altitude of 237 feet below sea level.

Below the sea level means negative direction

So, the negative integer will represent the given situation

So, The lowest elevation in the country is Green Valley with an altitude of - 237 feet below sea level.

Thus -237  represent the value in the statement.

Answer:

39pounds 6oz

Step-by-step explanation:

15x2=30

1x30=30pounds

5x30=150oz

30p+150oz=39.37500

37500p=6oz

39pounds and 6 oz

Answer:   x= -5   hope this helps

Step-by-step explanation:

Answer: The heaviest 19% of fruits weigh more than 753grams.

Step-by-step explanation:

Let X = fruit's weights that are normally distributed.

Given: [tex]\mu=720,\ \ \ \sigma=38[/tex]

To find : x such that P(X>x)=19%

i.e. P(X<x) = 81%  [100%-19%=81%]

i.e. P(X<x) = 0.81

[tex]P(\dfrac{X-\mu}{\sigma}<\dfrac{x-720}{38})=0.81[/tex]

Since, [tex]Z=\dfrac{X-\mu}{\sigma}[/tex] and from z-table the z value for p-value of 0.81 (one -tailed) = 0.8779

[tex]\dfrac{x-720}{38}=0.8779\\\\\Rightarrow\ x-720 =38\times0.8779\\\\\Rightarrow\ x-720 =33.36\\\\\Rightarrow\ x = 33.36+720=753.36\approx753[/tex]

Hence, the heaviest 19% of fruits weigh more than 753grams.

Answer:

Step-by-step explanation:

b .  v vvhc . fhd

Answer:

d = 7

Step-by-step explanation:

1.5d + 9.25 = 4 + 2.25d

Combine the constants and the variables.

5.25 = 0.75d

Divide.

d = 7